1. science
2. physics

The workshop on
"Spin Chirality and Dzyaloshinskii-Moriya Interaction" DMI 2011
St.-Petersburg, 25 - 27 May 2011
Sponsored by
Petersburg Nuclear Physics Institute
Co-Sponsored by
Russian Foundation of Basic Research
Program Committee:
Chairman: Sergey Maleyev (PNPI, Gatchina, Russia)
Alexey Okorokov (PNPI, Gatchina, Russia)
Sergey Grigoriev (PNPI, Gatchina, Russia)
Dmitry Chernyshov (SNBL at ESRF, Grenoble, France)
Vladimir Dmitrienko (Crystallography Institute RAS, Moscow, Russia)
Organizing Committee:
Chairman: Sergey Grigoriev (PNPI, Gatchina, Russia)
Vadim Dyadkin (PNPI, Gatchina, Russia)
Nadya Potapova (PNPI, Gatchina, Russia)
Evgeny Moskvin (PNPI, Gatchina, Russia)
Katy Dyadkina (PNPI, Gatchina, Russia)
Cathie Kobylyanskaya (PNPI, Gatchina, Russia)
Andrey Chumakov (PNPI, Gatchina, Russia)
International workshop
«Spin chirality and Dzyaloshinskii-Moriya Interaction»
Lecture Program
Wednesday, May 25. DM Interaction in cubic ferromagnets without a center of
symmetry
Session 1. MnSi and other B20 systems
Chairman: Kazuhisa Kakurai
8.00 –
10.00
10.00 –
10.50
10.50 –
11.20
Registration
11.20 11.40
11.40 –
12.00
12.00 –
12.30
12.30 –
12.50
12.50 –
13.10
13.10 –
14.30
«Physical properties of the itinerant
magnet
MnSi at ambient and high
pressure»
Sergey М. Stishov
Institute for High Pressure
Physics RAS, Troitsk, Russia
Sergey V. Grigoriev
Petersburg Nuclear Physics
Institute
Gatchina, Russia
«Chiral criticality in Fe-doped MnSi
compounds»
Coffee break
Anatoly Tsvyashchenko
Institute for High Pressure
Physics RAS, Troitsk, Russia
Sergey Demishev
General Physics Institute of
RAS, Moscow, Russia
Theodore Monchesky
Dalhousie University, Halifax,
Canada
«Magnetic structure of cubic MnGe
studies by powder neutron diffraction»
Nicholas Porter
University of Leeds,
England
«Growth by MBE and magnetotransport
of epitaxial CoxFe1-xSi thin films»
Leeds,
«Probing of MnSi and Mn1-xFexSi by
electron spin resonance»
«Magnetic properties of MnSi thin films»
Lunch
3
Session 2. Skyrmion lattice or simple spiral domains in B20 structures
Chairman: Stefan Bluegel
14.30 –
15.20
15.20 –
15.50
15.50 –
16.20
16.20 –
16.40
16.40 –
17.00
17.00 –
17.50
17.50 –
18.40
18.40
Ulrich Roessler
IFW Dresden
Dresden, Germany
Heribert Wilhelm
Oxford Diamond Light Source,
UK
Eugeny Moskvin
Petersburg Nuclear Physics
Institute
Gatchina, Russia
Andriy Leonov
IFW Dresden, Germany
«The skyrmion matters»
«Precursor Phenomena at the magnetic
ordering of the cubic Helimagnet FeGe»
«A-phase in FeGe in light of neutron
scattering»
«Theoretical studies on phase diagrams of
chiral magnets»
Coffee break
Sergey Maleyev
Petersburg Nuclear Physics
«Spin helices in cubic crystals with
Institute
Dzyaloshinskii-Moriya interaction»
Gatchina, Russia
Filipp Rybakov
«Three-dimensional
solitons
in
Institute of Metal Physics, Ural
incommensurate ferromagnets»
div. of RAS, Yekaterinburg
Welcome party
4
Thursday, May 26. DM Interaction in antiferromagnets without center of symmetry
9.00 –
9.50
9.50 –
10.40
Session 3. DM Interaction in antiferromagnets
Chairman: Vladimir Dmitrienko
«Structure and Magnetic Phase Diagram
Sebastian Muehlbauer
of the Dzyaloshinsky-Moriya Spiral
ETH Zürich, Switzerland
Magnet Ba2CuGe2O7»
«Neutron Scattering Activities on
Kazuhisa Kakurai
Multiferroic
Systems
Neutron
JAEA, Tokai, Japan
Diffraction Experiments on Hexaferrites»
10.40 –
11.00
11.00 –
11.50
11.50 –
12.30
12.30 –
14.30
14.30 –
19.00
18.00 –
22.00
22.00
Coffee break
Alexander Ovchinnikov
Ural State University,
Ekaterinburg, Russia
Shuichi Wakimoto
JAEA, Tokai, Japan
«Spin transfer
helimagnet»
torque
in
a
chiral
«Magnetic
chirality
and
electric
polarization in multiferroic YMn2O5»
Lunch
Excursion through the Gulf of Finland to Peterhof (Tsar's summer
residence)
Conference dinner in Peterhof
Buses to Saint-Petersburg
5
Friday, May 27. DM interaction in nanostructures. Crystal handedness and spin
chirality.
9.00 –
9.50
9.50 –
10.40
Session 4. DM interaction in nanostructures
Chairman: Ulrich Roessler
Dieter Lott
«DM at the interfaces of the Rare-Earth
Helmholtz-Zentrum Geesthacht,
multilayer systems»
Germany
«Spin Spiral States in Low-dimensional
Magnets Studied by Low-Temperature
Roland Wiesendanger
Univ. of Hamburg, Germany
Spin-Polarized
Scanning
Tunneling
Spectroscopy»
10.40 –
11.00
11.00 –
11.50
11.50 –
12.40
Coffee break
Stefan Bluegel
Juelich Forschungszentrum,
Germany
«Dzyaloshinskii-Moriya driven spin
structures in ultrathin magnetic films and
chains»
«Spontaneous atomic-scale magnetic
Stefan Heinze
skyrmion lattice in an ultra-thin film: realJuelich
Forschungszentrum,
space observation and theoretical
Germany
foundation»
Session 5. Crystal handedness and spin chirality
Chairman: Sergey Stishov
14.30 –
15.20
15.20 –
15.50
15.50 –
16.10
Vladimir Dmitrienko
A.V.Shubnikov Institute of
Crystallography RAS, Moscow,
Russia
Wojciech Slawinski
University of Warsaw, Warsaw,
Poland
«Dzyaloshinskii–Moriya interaction: How
to measure its sign in weak
ferromagnets?»
«Coupling of the spin and
modulations in CaCuxMn7-xO12»
lattice
Coffee break
6
16.10 –
16.40
16.40 –
17.10
17.10 –
18.00
18.00
Yury Chernenkov
Petersburg Nuclear Physics
Institute
Gatchina, Russia
Vadim Dyadkin
Petersburg Nuclear Physics
Institute
Gatchina, Russia
Sergey Maleyev
Petersburg Nuclear Physics
Institute
Gatchina, Russia
«Antichiral multiferroic YMnO3»
«Structure and spin chirality in B20
structures»
«Can parity non-conserving weak
interaction affect crystal chirality?»
Summary and Closing
7
Physical properties of the itinerant magnet MnSi
at ambient and high pressure.
Sergei M. Stishov
Institute for High Pressure Physics, Troitsk 142190 Russia.
The intermetallic compound MnSi acquired a long period helical magnetic
structure at T≈ 29 K . First experiments on the influence of high pressure on the
phase transition in MnSi showed that the transition temperature decreased with
pressure and tended to zero at about 1.4 GPa . This feature of MnSi promised the
opportunity of observation of quantum critical behavior.
Since then, quite a number of papers has been devoting to high pressure
studies of the phase transition in MnSi. The existence of a tricritical point at the
phase transition line of MnSi was claimed on the basis of the evolution of the AC
magnetic susceptibility of MnSi (χAC) with pressure. Later on a theory was
developed that declared generic nature of first order character of phase transitions
in ferromagnets at low temperatures.
Meanwhile, studies of the AC magnetic susceptibility of MnSi at high
pressure using fluid and solid helium as a pressure medium were carried out. It was
concluded that the radical change of the AC magnetic susceptibility of MnSi with
pressure, observed earlier, could be influenced by non-hydrostatic stresses,
developing in a frozen pressure medium. New studies of thermodynamic and
transport properties of a high quality single crystal of MnSi at ambient pressure
suggested also a first order nature of the corresponding magnetic phase transition
that questioned the early proposed phase diagram.
A review of recent experiments on physics of MnSi at high pressure will be
given as well.
8
Chiral criticality in Fe-doped MnSi compounds
S.V. Grigoriev1, S.V. Maleyev1, V.A. Dyadkin1, E.V. Moskvin1, D. Menzel2, H.
Eckerlebe3
1
Petersburg Nuclear Physics Institute, 188300 Gatchina, St-Petersburg, Russia
2
Techinsche Universitat Braunschweig, 38106 Braunschweig, Germany
3
Helmholtz Zentrum Geesthacht, 21502 Geesthacht, Germany
The cubic B20-type (space group P213) compounds Mn1-yFeySi with y [0 ’
0.15] order in a spin helix structure with a small propagation vector 0.36 ≤ k ≤ 0.70
nm-1. The spin helix structure is well interpreted within the Bak-Jensen (B-J)
hierarchical model. The hierarchy implies that the spin helix appears as a result of
the competition between the ferromagnetic spin exchange and antisymmetric
Dzyaloshinskii-Moriya interaction (DMI) caused by the lack of inverse symmetry
in arrangement of magnetic Mn atoms. The critical temperature of the compounds
TC decreases with the Fe doping and approaches zero, discovering the quantum
phase transition at yC ≈0.15. Additionally, the value of the helix wave vector
increases significantly upon doping. This study is aimed to follow the changes of
the thermal phase transition on its way to the quantum critical point at yC.
The critical spin fluctuations in doped compounds Mn1-yFeySi have been
studied by means of ac-susceptibility measurements, polarized neutron small angle
scattering and spin echo spectroscopy. The temperature dependence of
susceptibility, χ, for the sample Mn0.92Fe0.08Si is shown in Fig.1. Here we also plot
the first derivative of the susceptibility on the temperature dχ/dT to emphasize the
inflection points TC and TDM on the χ(T) dependence. These inflection points
divide the temperature scale into the three regions: (i) from low temperatures to
9
maximum of dχ/dT; (ii) between maximum and minimum of dχ/dT; and (iii) from
minimum of first derivative dχ/dT to the higher temperatures (Fig. 1). Yet another
characteristic temperature, which should be distinguished (denoted as Tk),
corresponds to the minimum of second derivative on the temperature d2χ/dT2
within the range between TC and TDM. To understand what happens in the system at
these temperature points we have added data taken by small angle diffraction of
polarized neutrons. The crossover points can be identified on the basis of combined
analysis of the temperature dependence of ac-susceptibility and polarized SANS
data.
Fig.1. The temperature dependence χ(T) and dχ/dT in the magnetic field H=50 mT; four
different temperature regions Spiral (S – [T<TC]), Highly Chiral Fluctuating (HCF – [TC < T
< Tk]), Partially Chiral Fluctuating (PCF - [Tk < T < TDM]) and Paramagnetic (P – [TDM < T])
are shown for Mn0.92Fe0.08Si compound.
10
From the ac-susceptibility measurements, supported by polarized SANS
data, we have established three specific temperature points (TC, Tk and TDM), which
are plotted in Fig.2. The compounds undergo the transition from the paramagnetic
(P) phase (with Curie-Weiss dependence at T > TDM) to spiral (S) phase (T<TC)
through two intermediate regions of Partially-Chiral Fluctuating (PCF) phase (Tk <
T < TDM) and Highly-Chiral Fluctuating (HCF) phase (TC < T < Tk) (Fig.2). We
have to stress that the transition is only one at T = TC and the other temperature
points correspond to crossovers.
Fig.2. Concentration dependencies of the critical temperature TC and the temperatures of
crossovers to PCF state TDM and to HCF state Tk for Mn1-yFeySi compounds.
The scenario and nature of the phase transition in the Mn1-yFeySi compounds
11
are well described by comparison of the inverse correlation length κ =1/ξ and the
spiral wavevector k. In the high temperature range (T>TDM) the critical fluctuations
are limited by κ > 2k, or ξ < π/k = d/2, where d is the spiral period. For these
fluctuations non-collinearity is not essential and they are close to the fluctuations
of the conventional ferromagnet. In turn, the ac-susceptibility demonstrates CurieWeiss behavior at T>TDM. The transition through the inflection point of
susceptibility at TDM leads to the Partially Chiral Fluctuating state with k < κ< 2k,
or with the correlation length in real space d/2 < ξ< d. The full 2π twist of the helix
is not completed yet inside these fluctuations. This results in rather low degree of
chirality of such fluctuations. Further down on temperature (TC < T < Tk), when the
full 2π twist of the helix is well established within the fluctuations (κ < k), the
Highly Chiral Fluctuating phase appears. The temperature dependencies of κ and
chirality PS demonstrate the crossover at κ ~ k. The crossover is compatible with
the theory [1,2]. The global transition is completed at TC, where the solid spiral
structure arises. It is clear that if one neglects the weak crystal anisotropy, then the
last transition is of the first order. The temperature crossovers first to Partially
Chiral and then to the Highly Chiral fluctuating states are associated with the
enhancing influence of the Dzyaloshinskii-Moria interaction close to TC.
This scenario with two crossovers at TDM, Tk and transformation at TC is
clearly reflected in the nonmagnetic properties of these compounds, such as
resistivity, etc.
References
[1] S.V. Grigoriev, S.V. Maleyev, A.I. Okorokov, Yu. O. Chetverikov, R. Georgii, P. Böni, D.
Lamago, H. Eckerlebe and K. Pranzas, Phys.Rev. B, v.73, (2005) 134420 - Critical fluctuations
in MnSi near TC: A polarized neutron scattering study.
[2] S. V. Grigoriev, S. V. Maleyev, E. V. Moskvin, V. A. Dyadkin, P. Fouquet and H. Eckerlebe,
Phys. Rev. B 81 (2010) 144413 - Crossover behavior of critical helix fluctuations in MnSi.
12
Magnetic structure of cubic MnGe studies by powder neutron diffraction
Anatoly Tsvyashchenko
Institute for High Pressure Physics RAS, Troitsk, Russia
13
Probing of MnSi and Mn1-xFexSi by electron spin resonance
S. V. Demishev, A. V. Semeno, A. V. Bogach, A. L. Chernobrovkin, V. V. Glushkov,
V. Yu. Ivanov, T. V. Ishchenko, N. A. Samarin, and N. E. Sluchanko
A.M.Prokhorov General Physics Institute, Vavilov street, 38, 119991 Moscow, Russia
The aim of the present work is to apply recently developed experimental
technique for studying of the magnetic resonance in strongly correlated metals
[1,2] to the case of MnSi. An additional motivation follows from the fact that up to
now there is only one work [3] dealing with electron spin resonance (ESR) in this
material.
The method suggested in [1,2] includes (i) special experimental layout of cavity
measurements, which excludes effects of macroscopic inhomogeneity of the
magnetic field in the sample due to demagnetization factor; (ii) procedure of
absolute calibration of the ESR line in the units of magnetic permeability R; (iii)
line shape analysis. Finally it is possible to find full set of spectroscopic
parameters, namely oscillating magnetization Mosc, g-factor (hyromagnetic ratio)
and line width W (relaxation parameter). Practical realization of the method [1,2]
requires measurements of the temperature and magnetic field dependences of the
sample resistivity  and static magnetization M0, which should accompany the ESR
data.
Experiments were carried out in the temperature range 1.8-300 K in magnetic
field up to 8 T. SQUID magnetometer (Quantum Design) was used for static
magnetization measurements. The ESR spectra at 60 GHz were measured by
means of original high frequency cavity magneto-optical spectrometer at GPI.
Magnetic resonance in the single crystal of MnSi was detected in the temperature
14
range T60 K. At T >60 K, the amplitude of the ESR line decreases so strongly
that the magnetic resonance becomes unobservable. As long as the resonant field at
60 GHz was about B~2 T, the ESR was probing phase boundary between
paramagnetic (P) phase and spin
polarized (ferromagnetic, FM)
1.5
- LMM model
- Dyson model (T2/TD=5)
1.4
phase [4].
1.3
The result of the ESR line
shape analysis is shown in
Fig. 1. In the whole temperature
1/2
1.2
(R)
absolute calibration and line
4.2K
1.1
10K
1.0
0.9
30K
0.8
50K
0.7
range studied the experimental
R(B ) curve may be adequately
described in the model of
localized
magnetic
1
2
3
4
B (T)
Fig. 1. Magnetic resonance in MnSi.
moments
(solid lines in fig. 1). Moreover the approximation of the R(B ) data within Dyson
model does not meet the experimental case if noticeable spin diffusion (T2/TD>1) is
supposed (see dashed lines in fig. 1). More details of the calculation schema can be
found in [1,2].
15
The comparison of the M0 and Mosc
that
static
and
magnetization coincide in the diapason
T >20 K (fig. 2). At the same time, a
systematic
discrepancy
0.4
dynamic
(although
0.3
M (B/Mn)
shows
0.2
- M0
- Mosc
0.1
comparable with the experimental error)
0
10
20
30
between M0 and Mosc is observed for
T<20 K, where condition M0>Mosc holds.
40
50
60
T (K)
Fig. 2. Static and dynamic magnetization in MnSi.
The possible presence of the low
T (K)
temperature anomaly is supported by
0
temperature dependence of the g-factor
equals
g 2.06
and
is
20
30
40
50
60
a)
g-factor
(fig. 3,a). While for T >15 K the g-factor
10
2.3
2.2
2.1
temperature
independent, it starts to increase below
T=15 K and reaches the value g ~2.2 for
T=4.2 K.
Line width (T)
2.0
b)
0.8
0.6
0.4
width W in MnSi first decreases by ~2
times in the range 30<T<60 K, reaches
minimum at T =30 K and than starts to
increase (fig. 3,b). This non-monotonous
dependence
had
earlier
led
to
the
B )/(0)
With lowering temperature the line
1.0
1
0.9
2
0.8
4
6
8
0.7
c)
0.6
0.5
0
10
20
30
40
50
60
T (K)
hypothesis [4] that spin relaxation in MnSi
Fig. 3. g-factor (a), line width (b) and
may be described by spin fluctuations
magnetoristance (c). In the panel (c)
digits near curves correspond to
magnetic field in Tesla.
magnitude SL2 appearing in the Moriya
16
theory of itinerant magnetism [5]. The computed function SL(T )2 is shown in
fig. 3,b by solid line; it is visible that theoretical dependence reproduces the
amplitude of the W(T ) only in the interval 15<T<60 K. Below T=15 K the line
width increases more rapidly than SL(T )2 and for T=4.2 K the observed value of W
is ~1.6 times higher than expected from the spin fluctuations model [4].
Interesting, that the presence of two characteristic temperatures suggested by
ESR data T~15 K and T~30 K correlates with the results of the magnetotransport
measurements. At T~30 K the minimum of magnetoresistance (B)/(0) occur,
whereas in the vicinity of T~15 K a shoulder on the (B)/(0) temperature
dependence is found (fig. 3,c). The latter feature becomes more pronounced when
magnetic field is increased.
Summarizing results of this part of the work it is possible to conclude that,
firstly, the physical picture of magnetic resonance in MnSi is completely consistent
with the ESR on Heisenberg-type localized magnetic moments. This finding
contradicts to widely accepted understanding of the magnetic properties of MnSi
based on the models of itinerant magnetism and requires new interpretation of the
reduction of the magnetic moment at low temperatures in this material. Secondly,
the phase boundary between paramagnetic and ferromagnetic phases appears to be
complicated and may be described by several characteristic temperatures T~15 K
and T~30 K. This behavior is not foreseen by existing theories of magnetism of
MnSi and requires further clarification.
17
We have carried out measurements of the magnetic resonance in Mn 1-xFexSi
solid solutions. This system demonstrate a quantum phase transition at
concentration xc~0.13-0.15, for which magnetic ordering temperature Tc turns to
zero [6,7]. It is found that
helium temperatures may
be detected up to x~0.23
(fig. 4).
Above
this
concentration
the
absorption line becomes
Cavity absorption (arb. units)
ESR in Mn1-xFexSi at liquid
Mn1-xFexSi
T =4.2K
x=0.05
x=0.15
x=0.23
too broad to be measured
with
the
help
of
our
0
1
2
3
4
5
6
Magnetic field (T)
experimental setup. It is
worth
noting
that
no
Fig. 4. Magnetic resonance in Mn1-xFexSi.
magnetic resonance was
found in the case of FeSi (x =1). Therefore it is possible to conclude that spin
fluctuations in the row MnSi—FeSi should strongly increase, which could be
hardly expected in the Moriya theory [5]. Additionally, the observation of the
magnetic resonance in the range x >xc may require clearing up the quantum phase
transition nature in Mn1-xFexSi.
Authors are grateful to S.M. Stishov and A.E. Petrova for helpful discussions
and for providing single crystals of MnSi. We would like to thank S.V. Grigoriev
for giving us Mn1-xFexSi samples. This work was supported by the Ministry of
Education and Science of the Russian Federation (state program ―Scientific and
18
Pedagogical Personnel of Innovative Russia‖) and by the Russian Academy of
Sciences (program ―Strongly Correlated Electrons‖).
[1] A.V. Semeno et al., Phys. Rev. B, 79, 014423 (2009).
[2] S.V. Demishev et al., Phys. Rev. B, 80, 245106 (2009).
[3] M. Date et al., J. Phys. Soc. Jpn. 42, 1555 (1977).
[4] S.V.Demishev et al., JETP Lett. 93, 213 (2011).
[5] T. Moriya, Spin fluctuations in itinerant electron magnetism, Springer-Verlag, 1985
[6] Y. Nishihara et al., Phys. Rev. B, 30, 32 (1984).
[7] S.V. Grigoriev et al., Phys. Rev. 79, 144417 (2009).
19
Magnetic Properties of MnSi Thin Films
Theodore Monchesky1, Eric Karhu1, Samer Kahwaji1, Michael Robertson2,
Helmut Fritzsche3, Brian Kirby4 and Charles Majkrzak4
1
Department of Physics and Atmospheric Science, Dalhousie University,
Halifax, Nova Scotia, Canada B3H 3J5
2
Department of Physics, Acadia University, Halifax, Nova Scotia,
Canada B4P 2R6
3
National Research Council Canada, Canadian Beam Centre, Chalk River Laboratories, Chalk
River, Ontario, Canada K0J 1J0
4
Center for Neutron Research, NIST, Gaithersburg Maryland 20899, USA
Chiral magnets have recently attracted the interest of the spintronics community
since they present novel opportunities to control electron spin. Heterostructures
consisting of thin layers of helical magnets and traditional ferromagnetics would
enable injection and control of spin-polarized currents into helical magnets. A
spin-polarized current flowing in a helical magnetic system is predicted to induce a
torque that would produce new kinds of magnetic excitations.
We have grown thin crystalline MnSi films on Si(111) by solid epitaxy (SPE)
and molecular beam epitaxy (MBE).
We find that the magnetic structure of the
films is modified by a combination of the epitaxial strain, the demagnetizing field
and inhomogeneities in the crystal chirality. In the rougher SPE samples, the
elastic constants of the film correlate with a reduction in Curie temperature, TC,
below a thickness of 10 nm. Films thicker than 10 nm show an enhanced TC that is
50% larger than bulk.
Smoother films grown by MBE enabled the observation of helical magnetic
order. Polarized neutron reflectometry shows a reduction in the wavelength of the
helix, and the presence of both left and right-handed magnetic chiralities. This is
supported by transmission electron microscopy (TEM) measurements, which
20
demonstrate that the crystal structure of the films consists of left and right-handed
chiral domains that are a few microns in size. Analysis of SQUID measurements
show that the exchange stiffness, A, decreases from 1.1 meV nm2 to 0.80 meV nm2
as the thickness increases from 11 nm to 40 nm, as compared to the bulk value,
A = 0.52 meV nm2. [1] The Dzyaloshinskii-Moriya coefficient therefore drops
from 0.62 meV nm to 0.45 meV nm to give rise to the observed constant 14 nm
helical wavelength over his range of thicknesses.
[1] Y. Ishikawa, G. Shirane, J. A. Tarvin, and M. Kohgi, Phys. Rev. B16, 4956 (1977).
21
Growth by MBE and magnetotransport of epitaxial CoxFe1-xSi thin films.
N. A. Porter1, C. H. Marrows1
1
School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, U. K.
Although a simple compound formed from two of the most common elements
in the Earth's crust, ε-FeSi possesses an unusual insulating, non-magnetic ground
state and temperature induced paramagnetism [1]. In the thermally stable B20
structure ε-FeSi is a narrow gap semiconductor with Kondo-like characteristics [2].
Electron doping of bulk material with cobalt produces the isostructural compound
ε-CoxFe1-xSi that has a ferromagnetic ground state with a Curie temperature, TC,
peaking at x ~ 0.4 with a value of TC ~ 50 K [3]. This state for x < 0.4 is
purportedly highly spin polarised which accounts for the unusual positive linear
magnetoresistance (LMR) found below TC [3, 4]. More recently, as a consequence
of the non-centrosymmetric nature of the B20 phase, the transition metal
monosilicides have demonstrated topologically stable magnetic order comprising a
skyrmion crystal lattice [5, 6]. The influence of the skyrmion lattice on carrier
transport has been reported in MnSi in the form of a topological addition to the
Hall effect [7, 8].
Thus far much of the research on these compounds has been concerned with
bulk material growth [3, 4, 9] with post etching or milling to produce sub micron
material [6]. We have produced phase-pure epitaxial films of ε-CoxFe1-xSi grown
by molecular beam epitaxy for x = 0, 0.3, 0.5 on a reconstructed silicon surface.
The films range from 20 - 200 nm in thickness and have been patterned into Hall
bars with 40 μm width by photolithography and argon ion milling. X-ray
diffraction (XRD) has confirmed the purity of the phase and texture of the films an
22
example of which is shown in figure 1. Vibrating sample magnetometry has
demonstrated the onset of ferromagnetic behaviour below 50 K for x = 0.3, 0.5 and
temperature induced paramagnetism for x = 0.
Magnetotransport down to 2 K of doped films has shown unsaturating LMR
that is characteristic of this material. Measurements of the Hall effect imply a
significant hysteresis in these epilayers that is not observed in bulk but has
previously been reported in polycrystalline films produced by pulsed laser
annealling [10]. Differences in magnetotransport of polycrystalline and textured
films are reported.
Quality thin films of -CoxFe1-xSi are necessary for production of devices such
that one can experimentally determine the spin polarisation of this important
material or manipulate small numbers of skyrmions using spin transfer torque [11].
[1] G. Shirane et al., Phys. Rev. Lett. 59, 351 (1987)
[2] G. Aeppli and Z. Fisk, Comments Condens. Matter Phys. 16, 155 (1992)
[3] N. Manyala et al., Nature 404, 581 (2000)
[4] Y. Onose et al., Phys. Rev. B, 72, 224431 (2005)
[5] S. Mühlbauer et al., Science, 323, 915 (2009)
[6] X. Z. Yu et al., Nature, 465, 901 (2010)
[7] Lee et al., Phys. Rev. Lett., 102, 186601 (2009)
[8] A. Neubauer et al., Phys. Rev. Lett., 102, 186602 (2009)
[9] M. K. Forthaus et al. Phys. Rev. B, 83, 085101 (2011)
[10] N. Manyala et al., Appl. Phys. Lett., 94, 232503 (2009)
[11] F. Jonietz, et al., Science 330, 1648 (2010)
23
Figure 1 – XRD of a 50 nm FeSi film grown by MBE.
Figure 2 – Transport of x = 0.3, 20 nm thick film at 0 and 8 T.
LMR below 100 K suggests a possible high spin polarisation.
24
The skyrmion matters
Ulrich K. Rößler
IFW Dresden, P.O.B. 270116, D-01171 Dresden, Germany.
Existence of chiral skyrmions in magnetism was predicted and investigated
theoretically by Bogdanov, starting in 1989 [1]. At that time, these nonlinear
localized configurations of a magnetic order-parameter field have been called
‗vortices‘, the term ‗skyrmion‘ was introduced in this context only in 2002 [2].
The break-through by Japanese researchers in direct microscopic observations of
such states in nano-layers of magnetic B20 metals (Fe,Co)Si and FeGe [3] leave
little doubt that chiral Skyrmions can exist in magnetic materials [4]. The
elementary mechanism stabilizing these states has been worked out in the earlier
theoretical work of Bogdanov and co-workers [1,5,6]. The mechanism explains
these recent experiments including the reason for their thermodynamic stability [4].
The chiral two-dimensional skyrmion spin-configuration can be realized in noncentro-symmetric magnets with a fixed azimuthal angle that depends on the crystal
symmetry. These magnetic configurations have the distinctive features of
25
topological solitons. The field configuration is both topologically and physically
stable, i.e. chiral Skyrmions have a smooth defect-free core and a definite diameter
fixed by the materials parameters.
In Dzyaloshinskii‘s seminal work on non-centroysmmetric magnets and their
inhomogeneous magnetic states, only one-dimensionally magnetic spiral states had
been identified [7]. Bogdanov‘s major achievement is the recognition that the field
equations of Dzyaloshinskii‘s theory allows true solitonic solutions that destroy the
homogeneity of magnetic states. Helices as one-dimensional modulations in
Dzyaloshinskii‘s theory are also only successions of localized domain-walls, i.e.,
helical kinks. Existence of such localized states, and the mechanism of phase
transformations by their nucleation as fixed (infinite size) mesoscale object are
ruling principles of all continuum systems described by an energy including
Lifshitz invariants [7,8,9]. Therefore, and more impressively, the magnetic state
built up from Skyrmions decomposes into an assembly of molecular units.
Depending on small energy differences owing to additional effects, different
extended textures with variable arrangements of the Skyrmion cores may arise, just
as in a molecular crystal. In three-dimensional magnets (3D), hence, in any
magnetic crystal with Lifshitz invariants in the magnetic free energy, the
skyrmions form tubular string-like solitonic objects with a fixed diameter and a
stable core structure.
Thermodynamic stability of skyrmionic condensed phases relative to helices can
become favourable in cubic chiral helimagnets near the magnetic ordering
transitions [10] where
the magnitude of the order parameter (the local
magnetization) becomes inhomogeneous. Here, spin-structures
twisted into the
localized configuration of the baby-skyrmion have simultaneously strongly varying
26
magnetization density. This picture is now rendered more precisely by a
confinement effect of solitons. Near the magnetic ordering transition, when
directional and longitudinal degrees of freedom start to couple [9 and talk by A.
Leonov], localized chiral modulations begin to interact in an
attractive manner.
This confinement is in contrast to the major part of the H-T-phase diagram in chiral
magnets where kink modulations and Skyrmions have repulsive soliton-soliton
interactions. In this temperature range the condensed phases like helicoids or
Skymion lattices are stable due to the negative formation energy of the chiral
solitonic units overcoming the repulsion. A transformation of these condensed
phases takes place by setting free these units as in a crystal-gas resublimation.
Hence, the radius of the isolated Skyrmion diverges at such nucleation transitions
[8]. This process has been seen in recent direct microscopic observations of
Skyrmions and Skyrmion lattices at low temperatures in nanolayers of B20 metals
[3]. Above a definite temperature which we call confinement temperature, below
the magnetic ordering temperature T_cf < T_N, the soliton-soliton interactions
become oscillatory and attractive for certain separations between solitons.
Magnetic states in that temperature region, therefore, display strong longitudinal
modulations, clustering behavior of localized states, frustration effects, and the
ability to form mesophases [9]. The puzzling magnetic anomalies in chiral
helimagnets, like MnSi and other B20 metals near the magnetic ordering transition,
must be rooted in this mechanism as it is generic to non-centrosymmetric magnets.
In the talk, I will discuss present theoretical understanding of the basic mechanism
that has led to the prediction of Skyrmionic matter in non-centrosymmetric
magnets in connection with the experimental evidence. At low temperatures (i) the
microscopic observations [3] clearly reveal the existence of Skyrmions and
27
condensates of Skyrmions in layers of cubic helimagnets with B20 structure.
Indications of Skyrmionic phases exist also in other magnetic materials. (ii) The
situation in the confinement region, however, is less clear in spite of a wealth of
experimental results. In the temperature region near magnetic ordering, the
solitonic nature of all chiral modulations and the inherent frustration of their
couplings induce a novel and very complex type of magnetic ordering [9,10].
Along the way, I will discuss some controversial points in the debate, such as the
so-called triple-q structure of Skyrmion condensed phases, inconsistence of claims
about existence and the sign of the topological charges of Skyrmion lattices in the
A-phase region of B20 metals, and the distinction between magnetic bubbles
domains and Skyrmions [11].
[1] A. N. Bogdanov, D. A. Yablonsky, Sov. Phys. JETP 68, 101 (1989).
[2] A. N. Bogdanov, U. K. Rößler, M. Wolf, and K.-H. Müller, Phys. Rev. B 66, 214410 (2002).
[3] X. Z. Yu, Y. Onose, N. Kanazawa, J.H. Park, J.H. Han, Y. Matsui, N. Nagaosa, Y. Tokura,
Nature 465, 901 (2010).
[4] U.K. Rößler, A. A. Leonov, A. N. Bogdanov, J. Phys.: Conf. Ser. in press (2011)
[arXiv:1009.4849].
[5] A. Bogdanov and A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994).
[6] A. B. Butenko, A.A. Leonov, U.K. Rößler, A.N. Bogdanov, Phys. Rev. B 83, 052403 (2010).
[7] I. E. Dzyaloshinskii, Sov. Phys. JETP 19, 960 (1964).
[8] P.G. de Gennes, Fluctuations, Instabilities, and Phase transitions, ed. T. Riste, NATO ASI
Ser. B, vol. 2 (Plenum, New York, 1975).
[9] A. A. Leonov, U.K. R, arXiv:1001.1992, unpublished, 2010.
[10] U.K. Rößler, A. N. Bogdanov, C. Pfleiderer, Nature 442, 797 (2006).
[11] N.S. Kiselev, A. N. Bogdanov, R. Schäfer, U.K. Rößler, arXiv:1102.2726.
28
Precursor Phenomena at the Magnetic Ordering of the cubic Helimagnet
FeGe
Heribert Wilhelm1, Michael Baenitz2, Marcus Schmidt2, Sergey Grigoriev3, Evgeny
Moskvin3, Vadim Dyadkin3, Helmut Eckerlebe4, Andrey A.Leonov5, Alex N.
Bogdanov5, and Ulrich K.Rößler5
1
Diamond Light Source Ltd., Chilton, Didcot, OX11 0DE, United Kingdom
2
MPI CPfS, Noethnitzer Str. 40, 01187 Dresden
3
Petersburg Nuclear Physics Institute, Gatchina, Saint-Petersburg, 188300, Russia
4
GKSS Forschungszentrum, 21502 Geesthacht, Germany
5
IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany
Cubic FeGe (B20 structure type) shows helical order below Tc=278.3K. Depending
on temperature and magnetic field a complex sequence of cross-overs and phase
transitions in the vicinity of Tc has been observed in magnetization and acsusceptibility measurements in fields parallel to the [100] direction [1]. In a narrow
temperature range below Tc several magnetic phases have been found before the
field-polarized state occurs. Of particular interest is the so-called A-phase. It splits
in at least two distinct areas, A1 and A2. This has been confirmed by small-angle
neutron scattering data. These data also yield a hexagonal scattering pattern, the
fingerprint of a Skyrmion lattice, within the A1 and A2 regions. Precursor
phenomena found above Tc display a complex succession of temperature-driven
cross-overs and phase transitions before the paramagnetic phase is reached at T 0.
The low-field state for Tc<T<T0 is probably characterized by some kind of
magnetic correlations concluded from nuclear forward scattering data. They
revealed that this phase exists up to about 27GPa, although the helical order is
already suppressed at 19GPa. No signatures of magnetic order have been observed
above 30GPa. Within a phenomenological model for chiral ferromagnets, which
29
includes magnetic anisotropy, Skyrmionic phases and 'confined' chiral modulations
were obtained. The observed precursor phenomena are then a general effect related
to the confinement of localized Skyrmionic excitations.
[1] H. Wilhelm, M. Baenitz, M. Schmidt, U.K.Rößler, A.A.Leonov, and A.N.Bogdanov,
arXiv:1101.0674v1
30
A-phase in FeGe in light of neutron scattering
E. Moskvin,1 S. Grigoriev,1 S. Maleyev,1 V. Dyadkin,1 H. Wilhelm,2 M. Baenitz,3
M. Schmidt,2 and H. Eckerlebe4
1
2
Petersburg Nuclear Physics Institute, Gatchina, Saint-Petersburg, 188300, Russia
Diamond Light Source Ltd, Chilton, Didcot, Oxfordshire, OX11 0DE, United Kingdom
3
Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
4
GKSS Forschungszentrum, 21502 Geesthacht, Germany
Small angle polarized neutron scattering was used to study the magnetic
structure of the single crystal of the cubic polymorph of FeGe in the A-phase – a
small pocket in the (H,T) phase diagram [1]. The magnetic field was applied either
along the scattering vector, H || Q = k'-k – transverse geometry, or along the
neutron beam, H || k – longitudinal geometry. The sample orientation was along
equivalent directions: [100], [110] and [111].
In the transverse geometry, H || Q, a single Bragg peak corresponding to the
spiral with ks = 0.009 Å-1 along [100] appears. When the field increases, at the
H ~ 23 mT, the spiral propagation vector, ks, flips perpendicular to H. At
H ~ 40 mT ks jumps back. On further field increase, at H ~ 60 ’ 80 mT, depending
on temperature, this peak vanishes. Such a behavior occurs only in a small pocket
of the (H,T) phase diagram just below Tc = 278.9 K. This pocket is known as the Aphase. It has been found first for isostructural compound MnSi [2].
For longitudinal geometry, H || k, the scattering picture is rather different.
Instead of one single peak it contains six peaks. Peak positions correspond to the
same ks. Field and temperature values, where this scattering occurs, correspond to
the A-phase. Such a scattering picture has first been observed in MnSi [3] and it
was interpreted as a fingerprint of skyrmionic texture. We think it is more likely a
result of superposition of three spiral modulated structures turned by 120º.
31
This work was performed within the framework of a Federal Special
Scientific and Technical Program (Projects No.02.740.11.0874). E. Moskvin,
S. Grigoriev S. Maleyev, and V. Dyadkin thank for partial support the Russian
Foundation of Basic Research (Grant No 10-02-01205).
[1] H. Wilhelm, M. Baenitz, M. Schmidt, U. K. Rößler, A. A. Leonov, and A. N. Bogdanov.
Precursor phenomena at the magnetic ordering of the cubic helimagnet FeGe.
arXiv:1101.0674v1, (2011).
[2] B. Lebech, P. Harris, J. S. Pedersen, K. Mortensen, C. I. Gregory, N. R. Bernhoeft,
M. Jermy, and S. A. Brown. Magnetic phase diagram of MnSi. J. Magn. Magn. Mater., 140144, 119 (1995).
[3] S. Mühlbauer, B. Binz, F. Jonietz, C. Pfleiderer, A. Rosch, A. Neubauer, R. Georgii, and
P. Böni. Skyrmion lattice in a chiral magnet. Science, 323, 915 (2009)
32
Theoretical studies on phase diagrams of chiral magnets
Andrey A. Leonov, Alexei N. Bogdanov, Ulrich K. Rößler
IFW Dresden, Postfach 270116, D-01171 Dresden, Germany
In non-centrosymmetric magnetic systems, Dzyaloshinskii-Moriya interactions
[1] (DMI) stabilize two-dimensional chiral modulations (Skyrmions) [2,3]. These
solitonic states may exist either as localized countable excitations (Fig. 1 (a), inset)
or condense into multiply modulated phases - Skyrmion lattices [3-5]. Recently,
such Skyrmionic textures have been visualized by Lorentz microscopy in
nanolayers of FeGe and Fe0.5Co0.5Si in a broad temperature range far lower the
Curie point (Tc) [7]. The experimentally observed helical and Skyrmionic states [7]
are in a close agreement with earlier predictions [1,3] and recent theoretical
findings on these "low-temperature" chiral modulations [5,11,12].
Near the ordering temperature, however, chiral modulations of cubic
helimagnets are characterized by numerous physical anomalies, known as
"precursor" and "A-phase" phenomena (see e.g. [6,9,10,13]). During last years
precursor and A-phase anomalies have become a subject of intensive
investigations [6,11,14] motivated by the expectations to identify Skyrmionic
states [4,5,12].
In the present contribution we give a short overview of the chiral helical and
Skyrmion states near the ordering temperature [4,5,12]. We describe the unique
properties of ‖high-temperature‖ Skyrmions which distinguish them from their
‖low-temperature‖ counterparts.
The equilibrium chiral modulations in cubic helimagnets near the ordering
temperature have been derived by minimization of the phenomenological magnetic
33
energy [1,8] written in the reduced form [11]:
W   d 3 x [ grad m   m  rotm  h (n  m)  am2  m4  f a (m)]
2
(1)
Functional (1) includes three internal variables (components of the rescaled
magnetization vector m  M / M 0 , M 0  k / a2 ) and two control parameters, the
magnetic field h  H / H 0 ( H 0  kM 0 ) with amplitude h and the "effective"
temperature a  a1 / k  J (T  Tc) / k . Here, k  D2 / (2 A) is expressed via
coefficient A of isotropic exchange (first term in (1)) and D – constant of DMI
(second term). a1 and a2 are coefficients of Landau expansion near the ordering
temperatures (third and forth terms). The first five terms in the energy functional
(1) are the necessary (primary) interactions that are essential to stabilize Skyrmions
and helical phases and to describe their properties near magnetic ordering. The last
term fa collects short-range anisotropic contributions that are crucial to determine
the global minimum of the energy functional (1).
Fig. 1. (a) Phase diagram of Skyrmion solutions on the plane (a,h). (b), (c) Solutions for isolated Skyrmions as
profiles
 ( )
and
m(  ) . ac
is Curie ferromagnetic temperature, point B has parameters
(aB , hB )
The structure of isolated Skyrmions near the ordering temperature is characterized
34
by the dependence of the polar angle  (  ) and modulus m(  ) on the radial
coordinate  (we introduce here spherical coordinates for the magnetization
(m, , ) and cylindrical coordinates for the spatial variables (  , , z) ). On the
basis of exponential asymptotics ( Δm   m  m0   exp exp    ,  exp( ) [3], m0
is the magnetization in the homogeneous phase) one can find three distinct regions
in the magnetic phase diagram on the plane (a, h) with different character of
Skyrmion-Skyrmion interactions (Fig.1 (a)): repulsive interactions between
isolated Skyrmions occur in a broad temperature range (area (I)) below the
confinement temperature aL. In this region the interactions are characterized by real
values of the decay of parameter  , the magnetization in such Skyrmions has
always ‖right‖ rotation sense. At higher temperatures, a>aL (area (II)), SkyrmionSkyrmion interaction changes to attractive character and  has complex values
(II); finally, in area (III) near the ordering temperature, aN = 0.25, only strictly
confined Skyrmions exist and  is purely imaginary.
The typical solutions as profiles  (  ) , m(  ) for isolated Skyrmions in each region
are plotted in Fig. 1 (c). Due to the coupling between two order parameters –
modulus m and angle  – the profiles display antiphased oscillations in the region
II (Fig. 1 (c)). The solutions for isolated Skyrmions exist only below a critical line
h0(T) (Fig. 1 (a)). As the applied field approaches this line, the magnetization in the
Skyrmion center gradually shrinks (Fig. 1 (b)), passes through zero, and the
Skyrmion collapses. The coupling of angular and longitudinal order parameters
may be so strong, that oscillations in the asymptotics of isolated Skyrmions are not
damped. This is the region of confinement (III in Fig. 1 (a), −0.5 < a < 0.25) welldefined from the major part of the magnetic phase diagram with regular
modulations by the confinement temperature aL.
35
Fig. 2. (a), (b)
 -Skyrmion lattices with the magnetization in the center of the lattice cell opposite or along the
field; (c) square half-Skyrmion lattice.
In the region of confinement Skyrmions exist only as bound states in the form of
square half-Skyrmion (Fig. 2 (c)) and ±  hexagonal lattices (Fig. 2 (a), (b)). Their
properties differ drastically from the ‖low-temperature‖ Skyrmions of the region I
(Fig. 1 (a)): (i) Due to the ‖softness‖ of the magnetization modulus the field-driven
transformation of the Skyrmion lattices evolves by distortions of the modulus
profiles m( ) both in the hexagonal and square Skyrmion lattices [11], while the
equilibrium periods of the lattices do not change strongly with increasing applied
field. (ii) At zero field with increasing temperature a the modulus m in hexagonal
and square lattices gradually decreases to zero at the ordering temperature aN =
0.25. Nevertheless, the lattices retain their symmetry and the arrangement of
axisymmetric Skyrmions up to the critical point. This is an instability-type
nucleation transition into the paramagnetic phase [11]. (iii) For temperatures aB < a
< aN the clusters of Skyrmions are more stable than the isolated Skyrmions. For
aL<a < aB the isolated Skyrmions condense into the lattice by a first-order phase
transition below the line hc. For higher temperatures a > aB isolated Skyrmions
exist as a distinct branch of solutions and disappear in field h0 which is weaker
than the field hn where the continuous transition occurs between the lattice and
homogeneous state. Therefore, the metastable Skyrmion lattice as the densest
36
infinite cluster is more stable than isolated Skyrmions at high temperatures. The
confinement effects of chiral Skyrmions strongly change the picture of the
formation and evolution of chiral modulated textures and shed new light on the
problem of precursor states observed as blue phases in liquid crystals and in chiral
magnets [4, 5, 6, 11,12].
The relative stability of Skyrmion states over one-dimensional modulations
depends crucially on other additional effects, such as magnetic anisotropy, dipolar
couplings, thermal fluctuations, quenched defects etc. Owing to the formation of
mesophases with attractively coupled Skyrmions in the confinement region of the
phase diagram one cannot expect a clear hierarchy of magnetic couplings to rule a
simple sequence of magnetic phases near magnetic ordering.
[1] I.E. Dzyaloshinskii, Sov. Phys. JETP 19, 960 (1964).
[2] A.N. Bogdanov and D.A. Yablonsky, Sov. Phys. JETP 68, 101 (1989).
[3] A. Bogdanov, A. Hubert, J. Magn. Magn. Mater. 138, 255 (1994).
[4[ U. K. Rößler et al., Nature 442, 797 (2006).
[5] U. K. Rößler et al., arXiv:1009.4849, (2010);
[6] C. Pappas et al., Phys. Rev. Lett. 102, 197202 (2009); C. Pappas et. al. arXiv:1103.0574v1
(2011), Phys. Rev. B, in press.
[7] X.Z.Yu et al., Nature, 465, 901 (2010); Nature Mater. 10, 106 (2011).
[8] P. Bak and M. H. Jensen, J. Phys.C: Solid State Phys. 13, L881 (1980).
[9] B. Lebech et al., J. Magn. Magn. Mater. 140, 119 (1995).
[10] S. Muhlbauer et al., Science, 323, 915 (2009).
[11] A. A. Leonov et al., arXiv: 1001.1992v3 (2010).
[12] A. B. Butenko et al., Phys. Rev. B 82, 052403 (2010).
[13] H. Wilhelm et al. arXiv:1101.0674v1 (2011).
37
Spin helices in magnets with Dzyaloshinskii-Moriya interaction
S.V. Maleyev
Petersburg Nuclear Physics Institute, 188300 Gatchina, St-Petersburg, Russia
The Dzyaloshinskii-Moriya interaction (DMI) is responsible for the spin
helical structure in different types of materials including cubic B20 metals (MnSi
etc), multiferroics (RMn2O3) and two dimensional surface monolayer (Fe on W
etc). In all cases the DMI destroys conventional ferro- or antiferrimagnetic
structure giving rise to incommensurate helix with period d ~ J/D, where J and D
are exchange and DM interactions, respectively. In cases of the multiferroics or
the surface monolayers the DMI gives rise to cycloidal order.
The DMI mixes spin-waves (SW) with momenta q and q  k and gives
rise to the spin-wave gap  , which appears as a result of the spin-wave interaction
in the Hartree-Fock approximation [1]. The magneto-elastic interaction contributes
to the gap too. As a result we have    Int   Me where the second term is
2
2
2
negative one. A competition between these two terms leads to the quantum phase
transition under pressure, which is observed in MnSi and FeGe [2].
The classical energy depends on the field component along k only.
Perpendicular field component leads to the similar SW mixing along with the SW
Bose condensation at q  nk , where n=1, 2,…. In the simplest case of B20
magnets due to abovementioned phenomena the spin-wave energy at q  k is
given by [1,2]:
 q  Ak (q||2  3q4 / 8k 2  2  3H 2 / 8)1/ 2
38
where || and  denote components along and perpendicular to k and A is the spinwave stiffness at q  k. This strong SW anisotropy leads to infra-red divergences
in the 1/S expancion for the energy at H    8 / 3  HC 2 . As a result a
conventional umbrella state in the field becomes unstable at H  HC1  HC 2 and
the helix vector k turns perpendicular to H . This so called A-Phase exists in a
narrow field range HC1  H  HC 2 and then the umbrella state is restored up to the
2
transition to ferromagnetic state at H C  Ak . Really this A-Phase is very narrow
and can be observed near TC only, where it becomes broader due to critical
slowing down. Rough estimations are in qualitative agreement with experimental
data for MnSi [3].
In general case of the helical structure there are tree critical fields H || and
two different perpendicular components given rise rather complex magnetic field
phase diagram.
References
[1] S.V.Maleyev, Phys.Rev.,B73 (2006) 174402..
[2] S.V.Maleyev, J. Phys. Condensed Matter 21 (2009) 141001.
[3] S.V.Maleyev, ArXiv: 1102.3524.
39
Three-dimensional solitons in incommensurate ferromagnets
A B. Borisov, F.N. Rybakov
Institute of Metal Physics, Ural Division,
Russian Academy of Sciences, Yekaterinburg 620990, Russia.
In certain magnetic crystals with significant effect of Dzyaloshinskii-Moriya
(DM) interaction the different long-periodic structures can exist [1]. For such
structures the periods are incommensurate with crystal-chemical ones. In such
materials can also exist planar topological excitations [2,3], including skyrmions
and their lattices [4,5,6]. Three-dimensional solitons in these magnetic materials
have not been studied before now [7]. According to the Hobart-Derrick (HD)
theorem [8,9], stable static 3D solitons do not exists for usual ferromagnets and
only dynamical ones are allowed [10,11,12]. It was shown [13] that the energy
functional with DM energy term does not fall under the prohibition of the HD
theorem. In this work we firstly present three-dimensional static magnetic solitons
with finite energy in magnetic crystals and investigate their features and stability.
Let us consider the energy functional, which is proposed in [14,13]:
E

2
   M  dr   
2
i
2



2
M x  M y  dr 
2

 D  M    M  dr  H 0   M 0  M z  dr
(1)
Energy includes exchange energy term ( Eexch ), uniaxial magnetic anisotropy
energy ( Eanis ), Dzyaloshinsky-Moriya energy ( EDM ) and Zeeman energy in an
external magnetic field ( EH ). Magnetization modulus  M  M 0 is constant at the
low temperature. We parametrize the magnetization vector M in terms of the
angular variables  and  , as
40
M  M 0  m  M 0  (sincos sinsin cos)
(2)
The energy functional is invariant with respect to simultaneous spatial rotations
by an arbitrary angle  the spatial coordinates and the magnetization vector, to
        
(3)
where  is the polar angle of a cylindrical coordinate system (r   z) . Thereby,
we shall study solitons with an axially symmetric distribution of the polar angle of
the magnetization and a vortex structure for the azimuthal angle:
   (r z)      (r z)
(4)
In models with the three-component unit vector field m  (m1 m2  m3 ) , where
m2  1 , for localized structures the field m asymptotically approaches the ground
state value m0  (0 01) as  r   . Such fields map the R3 {} space to the twodimensional sphere S 2 and are classified by the homotopy classes  3 (S 2 )  Z and
characterized by the integer-valued Hopf index
H 
1
(8 )2
 F  A dr
(5)
where Fi   ijk m  ( j m k m) and ( A)  2F . The expression for the Hopf index
H of the fields (4) simplifies [15]:
H
1
4



0
 
sin ( r z   z r )drdz
(6)
41
(a)
Figure 1. A shape of the calculated static toroidal topological soliton with
(b)
 H  1 . (a) - distribution of
magnetization; (b) - contours of the constant values of the polar angle  which parameterize the magnetization
vector.
To determine the structure of three-dimensional solitons, we used advanced
algorithm for minimizing energy functional, previously used in [16]. Fig.1 shows a
calculated configuration of the field M for Hopf soliton (hopfion) with  H  1 .
Toroidal surfaces correspond to the constant values of the polar angle:   const (
Fig.6 ).
The index H , as shown on Fig.2, admits the simple geometric interpretation as
the linking number of two preimage closed curves corresponding to an arbitrary
pair of points on the S 2 sphere.
42
Figure 2. Two preimages of the points on the
perspective. Blue curve correspond to
S 2 sphere for calculated hopfion with  H  1 , different
(11 )  (07  0) , orange curve - to (2 2 )  (01 15 ) .
For 3D toroidal solitons (4) was founded an asymtotic behavior formula [7]:
Q(r, z ) :
(1 + g r 2 + z 2 ) r
eg
r2 + z2
(| r |® Ґ ),
(7)
H0
D
 h
 l0    
 M0
2 
(8)
(r 2 + z 2 )3/ 2
where
  1  h  (4  2   2 )  l0   
The critical value   0 corresponds to the boundary between homogeneous
magnetization state and conical phase [14]. Points which are plotted in Fig.3
correspond to positive calculations results for hopfions (  H  1 ) and for H  0
solitons.
It turned out that all the solitons which were found are stable with respect to
scaling perturbations [7], but any criteria for the rigorous stability of 3D solitons of
the model (1) has not been found yet.
43
Figure 3. Phase diagram and results of the numerical calculations. Each circle corresponds to a successful
computational cycle, i.e., to establishing the existence of a soliton and determining its structure.
[1] Yu. A. Izyumov, Usp. Fiz. Nauk 144, 439 (1984) [Sov. Phys. Usp. 27, 845 (1984)].
[2] A. B. Borisov, V. V. Kiselev, Physica D. 31, 49 (1988).
[3] A. B. Borisov, V. V. Kiselev, Physica D. 111, 96 (1998).
[4] A. N. Bogdanov, D. A. Yablonsky, Zh. Eksp. Teor. Fiz. 95, 178 (1989) [JETP 68, 101
(1989)].
[5] A. Bogdanov, A. Hubert, Phys. Stat. Sol. (b) 186, 527 (1994).
[6] U.K. Roessler, A.N. Bogdanov, C. Pfleiderer, Nature 442, 797 (2006).
[7] A. B. Borisov, F. N. Rybakov, Low Temp. Phys. 36, 766 (2010).
[8] R. H. Hobart, Proc. Phys. Soc. 82, 201 (1963).
[9] G. M. Derrick, J. Math. Phys 5, 1252 (1964).
[10] A. M. Kosevich, B. A. Ivanov and A. S. Kovalev, Phys. Rep. 194, 117 (1990).
[11] N. R. Cooper, Phys. Rev. Lett. 82, 1554 (1999).
[12] A. B. Borisov, F. N. Rybakov, Pisma v Zh. Eksp. Teor. Fiz. 90, 593 (2009) [JETP Lett. 90,
544 (2009)].
[13] A. Bogdanov, Pisma v Zh. Eksp. Teor. Fiz. 62, 231 (1995) [JETP Lett. 62, 247 (1995)].
[14] V. G. Bar‘yakhtar, E. P. Stefanovsky, Fiz. Tverd. Tela 11, 1946 (1969) [Sov. Phys. Solid
State 11, 1566 (1970)]
[15] A. Kundu and Y. P. Rybakov, J. Phys. A 15, 269 (1982).
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264 (2008)].
44
Structure and Magnetic Phase Diagram of the Dzyaloshinsky-Moriya Spiral
Magnet Ba2CuGe2O7
S. Mühlbauer1, S. Gvasaliya1, E. Pomjakushina2, A. Zheludev1
1
2
Institute for Solid State Physics, ETH Zürich, Zürich, Switzerland
Laboratory for Developments and Methods, Paul Scherrer Institute
PSI, Villigen, Switzerland.
We have used neutron diffraction and measurements of the susceptibility in canted
fields to re-investigate the magnetic phase diagram of the tetragonal
antiferromagnetic (AF) insulator Ba2CuGe2O7. Below a transition temperature of
TN = 3.2 K, non-centrosymmetric Ba2CuGe2O7 exhibits an incommensurate,
almost AF cycloidal magnetic structure, caused by the Dzyaloshinsky-Moriya
interaction. For a magnetic field applied along the tetragonal c-axis the almost
cycloidal spin structure distorts to a soliton lattice [1,2]. For increasing field the
distance between solitons increases until an incommensurate/commensurate phase
transition is observed at Hc = 2.4 T. An extended intermediate phase of prior
unknown origin observed close to the transition field [3,4], has been indentified as
new phase with an AF cone structure. The AF cone is characteristic of a 2k
structure: (i) A large AF commensurate component is aligned perpendicular to the
magnetic field. (ii) A small, incommensurate, rotating component of the spins is
oriented perpendicular to the commensurate component. The AF cone phase was
only found to be stable for the magnetic field applied almost parallel to the c-axis.
For a large misalignment of the magnetic field a smooth crossover to a distorted
soliton phase was observed instead.
[1] A. Zheludev et al., Phys. Rev. B, 56, 14006 (1997)
[2] A. Zheludev et al., Phys. Rev. B, 59, 11432 (1999)
[3] A. Zheludev et al., Phys. Rev. B, 57, 2968 (1998)
[4] A. N. Bogdanov and A. A. Shestakov, Low Temp. Phys., 25, 76, (1999)
45
Neutron Scattering Activities on Multiferroic Systems
- Neutron Diffraction Experiments on Hexaferrites K. Kakurai1, S. Wakimoto1, S. Ishiwata2, D. Okuyama3, M. Nishi4, Y. Tokunaga5,
Y. Kaneko5, T. Arima6, Y. Taguchi3 and Y. Tokura2,3,5
1
Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195,
Japan
2
Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of
Tokyo, Tokyo 113-8656, Japan.
3
Cross-Correlated Materials Research Group (CMRG) and Correlated Electron Research Group
(CERG), RIKEN, Advanced Science Institute,
Wako, 351-0198, Japan
4 Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Chiba, 2778581, Japan
5 Multiferroics Project, ERATO, Japan Science and Technology Agency (JST), Wako, Saitama
351-0198, Japan
6 Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 9808577, Japan
The discovery of magnetoelectric (ME) effects caused by a cycloidal spin order
has initiated an intense research on new class of ME materials [1]. Among them
one interesting class of materials is the hexaferrites such as Y-type (A2Me2Fe12O22:
Me=transition metal) , M-type (AFe12O19: A=Pb, Ca, Sr, Ba, etc.), where types of
elementary blocks and their stacking order are different [2]. These materials show
a variety of complex magnetic ordering.
In this contribution we report recent neutron diffraction experiments on
multiferroic hexaferrites performed at the JRR-3 Neutron Science Facility of Japan
Atomic Energy Agency (JAEA) located in Tokai.
The spins in Ba2Mg2Fe12O22 are known to be ferrimagnetically ordered with
large magnetic moment and the smaller moments in two kinds of alternating block
layers containing Fe ions. Neutron diffraction studies revealed the collinear-spin
ferrimagnetic structure below 553K and proper screw below 195K in zero
46
magnetic field [3]. Recent magnetization measurements have indicated a transition
to a longitudinal conical spin state below about 50K, where the magnetic field
induced ferroelectric polarization is observed up to a field of 4 Tesla. Beyond this
field value the system becomes paraelectric [4].
We report extensive neutron diffraction experiments to clarify the magnetic
structures in the field induced ferroelectric phases. By using the polarized neutron
diffraction technique, we have demonstrated that the ferroelectric phase with the
largest electric polarization P with k0 =(0,0,3/2) has a transverse conical spin
structure. The spin-current model does qualitatively describe the field dependence
of the observed P and the disappearance of P in the collinear ferrimagnetic phase
above 4 T. Thus the foundation of the magnetization-electric polarization coupling
principle in the conical magnet has been firmly established using polarized neutron
scattering experiments [5].
To realize high-Tc multiferroics a search for a hexaferrite system with a conical
magnetic structure at higher temperatures, even at room temperature (RT), was
undertaken. We report magnetization and neutron diffraction measurements on Mtype barium hexaferrites revealing that by tuning the Sc concentration the
longitudinal conical state is stabilized up to above RT. Magnetoelectric
measurements have shown that a transverse magnetic field can induce electric
polarization at lower temperatures and that the spin helicity is non-volatile and
endurable up to near the conical magnetic transition temperature. Thus the M-type
barium hexaferrites with optimized Fe-site substitution is confirmed to be
promising candidates of multiferroic materials for the RT operation [6].
47
Acknowledgments
This work was in part supported by Grant-in-Aid for Scientic Research on
Priority Areas ‖Novel States of Matter Induced by Frustration‖ (Grant Nos.
19052004 and 20046017) from the MEXT, Japan and by Funding Program for
World-Leading Innovative R&D on Science and Technology (FIRST Program)
from JSPS.
References
[1] T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, Y. Tokura, Nature 426, 55 (2003).
[2] J. Smit and H. P. J. Wijn, Ferrites (Philips Technical Library, Eindhoven, 1959), p. 177-190.
[3] N. Momozawa, Y. Yamaguchi, and M. Mita, J. Phys. Soc. Jpn. 55, 1350 (1986).
[4] S. Ishiwata, Y. Taguchi, H. Murakawa, Y. Onose and Y. Tokura, Science 319, 1643 (2008).
[5] S. Ishiwata, D. Okuyama, K. Kakurai, M. Nishi, Y. Taguchi and Y. Tokura, Phys. Rev. B 81,
174418 (2010).
[6] Y. Tokunaga, Y. Kaneko, D. Okuyama, S. Ishiwata, T. Arima, S. Wakimoto, K. Kakurai, Y.
Taguchi, and Y. Tokura, Phys. Rev. Lett. 105, 257201 (2010).
48
Spin transfer torque in a chiral helimagnet
A.S. Ovchinnikov1, J. Kishine2, I.V. Proskurin1
1
2
Ural State University, 620083 Ekaterinburg, Russia
Kyushu Institute of Technology, Kitakyushu 804-8550, Japan.
We derive a current-driven sliding conductivity of the magnetic kink crystal
(MKC) in chiral helimagnet under weak magnetic field applied perpendicular to
the helical axis. For this purpose, we discuss the correlated dynamics of quantummechanical itinerant spins and the MKC which are coupled via the sd exchange
interaction [1,2]. The itinerant spins are treated as fully quantum-mechanical
operators whereas the dynamics of the MKC is considered within classical
Lagrangian formalism. By appropriately treating elementary excitations around the
MKC state, we construct coupled equations of motion for the collective
coordinates (the center-of-mass position and quasi-zero-mode coordinate)
associated with the sliding motion of the MKC. By solving them, we demonstrate
that the correlated dynamics is understood through a hierarchy of two time scales:
Boltzmann relaxation time τel, when a nonadiabatic spin-transfer torque appears,
and Gilbert damping time τMKC, when adiabatic spin-transfer torque comes up.
As a notable consequence, we found that the terminal velocity of the sliding
motion reverses its sign depending on the band-filling ratio of the conduction
electron system.
[1] J. Kishine, A.S. Ovchinnikov, Phys. Rev. B 81, 134405 (2010).
[2] J. Kishine, A.S. Ovchinnikov, I.V. Proskurin, Phys. Rev. B 82, 064407 (2010).
49
Magnetic chirality and electric polarization in multiferroic YMn2O5
S. Wakimoto1, H. Kimura2, M. Fukunaga2, Y. Sakamoto2, K. Kakurai1, Y. Noda2
1
QuBS, Japan Atomic Energy Agency, Tokai, Ibaraki, Japan
2
IMRAM, Tohoku University, Katahira, Sendai, Japan.
1. Introduction
RMn2O5 (R = rare earth, Y, Bi) shows generally magnetic phase transition from
paramagnetic phase to commensurate antiferromagnetic phase (CM phase) at
~40K, and exhibits concomitantly spontaneous electric polarization. Then at lower
temperature (< 20K) system transforms into incommensurate antiferromagnetic
phase (LT-ICM phase) in which the electric polarization is reduced as weak
ferroelectric phase[1].
In addition, in the LT-ICM phase, a wide variety of
magneto-electric (ME) effect has been reported[2,3,4].
As the origin of the magnetic-driven electric polarization in the RMn2O5
system, two models have been proposed; one is the inverse Dzyaloshinskii-Moriya
mechanism[5] expressed by P ∝ Si × Sj, and the other is the exchange striction
model[6] expressed by P ∝ Si ∙Sj. The crystal structure of RMn2O5 contains
chains of Mn4+O6 octahedra, which is connected by Mn3+O5 pyramids. The Mn4+
spins forms cycloid structure[7] which contribute to the inverse DM mechanism.
On the other hand, magnetic exchange along Mn4+-Mn3+ chains contributes to the
exchange striction mechanism. Distinguishing these two mechanisms is important
to understand the ME effects in this system.
2. Experiment
50
As motivated above, we have prepared
YMn4+(Mn1-xGax)3+O5 where non-magnetic
Ga3+ ions dilute Mn3+ spins.
should
weaken
mechanism.
the
This doping
exchange
striction
The T-x phase diagram of
YMn4+(Mn1-xGax)3+O5 is shown in Fig.1.
Note that the YMn2O5 system, as temperature
decreases, transforms firstly into a high
temperature
incommensurate
antiferroFig.1. T-x phase diagram.
magnetic
(HT-ICM)
phase
which
is
paraelectric. For x < 0.12, the system still exhibits phase transitions in the order of
HT-ICM, CM and LT-ICM phases on cooling, whereas for x > 0.12 the system
transforms from HT-ICM to LT-ICM directly.
We have used single crystals of YMn4+(Mn1-xGax)3+O5 with x = 0.047 and 0.12
to measure the relation between the spin chirality and the electric polarization by
polarized neutron diffraction. Polarized neutron experiments were done at the
TAS-1 spectrometer installed at the JRR-3 reactor in JAEA, Tokai. We kept the
incident neutron unpolarized and analyzed the polarization of the diffracted
neutrons by a Heusler analyzer with a spin flipper in front of the analyzer. A guide
field around the sample was kept parallel to the momentum transfer Q by a
Helmholtz coil. With this configuration, the difference in the intensities between
the spin-flip and non-spin-flip channels is a direct measure of the spin chirality Si
× Sj
3. Results and discussion
51
Fig.2. Electric polarization (upper pannels) and spin chiralirty (lower pannels) as a function of temperature.
Solid line and filled symbols are data taken with electric field of +1kV applied on the sequence of field cooling
(FC) shown at the top of each figure, while dashed line and open symbols are taken with -1kV. I, II, and III
corresponds to the HT-ICM, CM, and LT-ICM phases, respectively.
Figure 2 summarizes the electric polarization (P) and spin chirality in various
cooling conditions. For the data of the x = 0.12 sample with field cooling (FC)
indicate that P appears concomitantly with the spin chirality. For the x = 0.047
sample, we performed measurements under two conditions: one is to pole the
sample in the CM phase (Fig. 2 (b)), while the other is to pole the sample in the
LT-ICM phase (Fig. 2 (c)). It is remarkable that in Fig. 2 (b) the sign of P changes
on crossing the CM-LTICM transition, whereas the sign of spin chirality does not.
This implies that the mechanisms of magnetically-driven ferroelectricity in the CM
and LT-ICM phases are different. On the other hand, in Fig. 2 (c), temperature
dependences are rather similar to those of Fig. 2 (a).
These results can be accounted for by assuming that the Si ∙Sj mechanism is
dominant in the CM phase and the Si × Sj mechanism is dominant in the LT-ICM
phase. When poling the x = 0.047 sample at the CM phase, one aligns the Si ∙Sj
poling domains. However, this Si ∙Sj domain has Si × Sj which potentially gives
52
opposite polarization. Since this domain information is preserved on crossing the
CM-LTICM phase transition in zero-field, the sign of P changes as shown in Fig. 2
(b).
The Si × Sj mechanism requires the cycloid structure of spins. In this case, the
polarization direction can be controlled by the direction of cycloid surface, which
should be favorable to the ME effect. Probably this is the reason why a wide
variety of ME effect is observed in the LT-ICM phase of RMn2O5.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
Y. Noda, H. Kimura, M. Fukunaga, S. Kobayashi, I. Kagomiya, and K. Kohn, J. Phys.:
Condes. Matter 20, 434206 (2008).
H. Hur, S. Park, P.A. Sharma, J.S. Ahn, S. Guha, and S-W. Cheong, Nature (London) 426,
55 (2003).
D. Higashiyama, S. Miyasaka, and Y. Tokura, Phys. Rev. B 72, 064421 (2005).
M. Fukunaga, Y. Sakamoto, H. Kimura, Y. Noda, N. Abe, K. Taniguchi, T. Arima, S.
Wakimoto, M. Takeda, K. Kakurai, and K. Kohn, Phys. Rev. Lett. 103, 077204 (2009).
H. Katsura, N. Nagaosa, and A.V. Balatsky, Phys. Rev. Lett. 95, 057205 (2005).
L. C. Chapon, P. G. Radaelli, G. R. Blake, S. Park, and S.-W. Cheong. Phys. Rev. Lett. 96,
097601 (2006).
H. Kimura, S. Kobayashi, Y. Fukuda, T. Osawa, Y. Kamada, Y. Noda, I. Kagomiya, and
K. Kohn, J. Phys. Soc. Jpn. 76, 074706 (2007).
53
Dzyaloshinskii-Moriya Interaction at the interfaces of the Rare-Earth
multilayer System
D. Lott1, S. V. Gigoriev2, Yu. O. Chetverikov2, E. V. Tartakovskaya3, A. T. D.
Grünwald1, R. C. C. Ward4, A. Schreyer1
.
Helmholtz Zentrum Geesthacht, 21502 Geesthacht, Germany.
2
Petersburg Nuclear Physics Institute, 188300 Gatchina, St-Petersburg, Russia
3
Institute for Magnetism of National Ukrainian Academy of Science, 03142 Kiev, Ukraine
4
Clarendon Laboratory, Oxford University, South Parks Rd, Oxford OX1 3PU, United Kingdom
1
The observation of non-collinear magnetic structures in magnetic multilayer
structures (MML) can be the result of the Dzyaloshinskii-Moriya (DM) interaction
induced by the broken symmetry at the interfaces between magnetic and
nonmagnetic layers, as it was theoretically predicted in [1,2]. The DM interaction,
similar to the biquadratic exchange coupling, promotes the non-collinear
arrangement of the spin planes in the MMLs. In favour of the DM interaction, if it
is present in the system, is the fact that the spin arrangement in MML possesses a
certain chirality. In MMLs with ferromagnetic intra-layer coupling, however, it is
in general difficult to detect and study the chirality since the range of interaction
for the DM is usually only present for very few atomic layers from the interfaces
which does not allow to establish a clear spiral structure. MMLs with spiral
arrangements of the spins inside the magnetic layers (Dy, Ho, etc.) on the other
hand are prime candidates to study this effect since the DM interaction causes,
directly or indirectly, an imbalance of the population for either handedness [3].
Our previous measurements [8] with polarized neutrons have demonstrated that
Dy/Y MML structures posses a coherent helical spin structure over many bilayers
with a predominant chirality induced by the in-plane applied magnetic field. It is
therefore suggested that the interplay of the RKKY and the Zeeman interactions
helped to reveal the anti-symmetric Dzyaloshinskii-Moriya interaction since the
54
observed chirality is a fingerprint of the DM interaction resulting from the lack of
the symmetry inversion at the interfaces [1,4].
Furthermore we have studied the conditions when the interplay between RKKY
and Zeemann interactions in the Dy/Y MMLs leads to a considerable change of
their chirality. The variation of the interactions was achieved by either changing
the thicknesses of the Y layers or the Dy layers resulting in a drastic modification
of the strength of the RKKY interaction or the Zeeman interaction, respectively.
We demonstrated by means of polarized neutron scattering that the chirality of the
helix induced by the in-plane applied magnetic field upon cooling depends on the
value of the RKKY versus Zeemann interactions [5]. These results indicate that the
DM interaction play an important role in the magnetic behavior of these Dy/Y
multilayer structures.
[1] A.N. Bogdanov, U.K. Rossler, Phys. Rev. Lett. 87, 037203 (2001).
[2] A. Crepieux, C. Lacroix, J.Magn.Magn.Mat. 182, 341 (1998).
[3] S.V.Grigoriev, Yu.O. Chetverikov, D.Lott, A. Schreyer, Phys. Rev. Lett. 100, 197203 (2008)
[4] I.E. Dzyaloshinskii, Zh. Exp. Teor. Fiz. 46, 1420 (1964) [Sov.Phys. JETP 19, 960 (1964)].
[5] S.V.Grigoriev, D. Lott, Yu. O. Chetverikov, A. T. D. Grünwald, R. C. C. Ward, and A.
Schreyer, Phys. Rev. B 82, 195432 (2010)
55
Spin Spiral States in Low-dimensional Magnets Studied by
Low-Temperature Spin-Polarized Scanning Tunneling Spectroscopy
R. Wiesendanger,
K. von Bergmann, A. Kubetzka, S. Meckler, M. Menzel, and O. Pietzsch
Institute of Applied Physics, University of Hamburg, D-20355 Hamburg, Germany
[email protected], www.nanoscience.de
Magnetism in low-dimensions is a fascinating topic: Even in apparently
simple systems – such as homoatomic monolayers – the nearest neighbor distance,
the symmetry and the hybridization with the substrate can play a crucial role for
the magnetic properties. This may lead to a variety of magnetic structures, from the
ferromagnetic and antiferromagnetic state to much more complex spin structures.
Spin-polarized scanning tunneling microscopy (SP-STM) [1] combines magnetic
sensitivity with high lateral resolution and therefore grants access to such complex
magnetic order with unit cells on the nanometer scale.
Different previously inconceivable magnetic structures are observed in
pseudomorphic homoatomic 3d monolayers on late 5d transition metal substrates.
As shown previously for the Mn monolayer on W(110) [2] the broken inversion
symmetry due to the presence of the surface can induce the formation of spin
spirals where the spin rotates from one atom to the next resulting in a nanometer
sized magnetic period. The driving force for the canting of adjacent magnetic
moments leading to such magnetic states is the Dzyaloshinskii-Moriya (DM)
interaction and a unique rotational sense is found. To investigate whether the DM
interaction is generally to be considered when studying thin film magnetism we
looked at other sample systems. Cr monolayers also grow pseudomorphically on
W(110). The spin-resolved images show stripes very similar to the ones observed
56
in [2] indicating local antiferromagetic order. The stripes observed in large-scale
images show a modulation along the [001] direction. We interpret this observation
as a spin spiral propagating along the [001] direction. Though ab-initio calculations
are lacking for this system this indicates that again we have a cycloidal spin spiral
with unique rotational sense due to the DM interaction. The propagation direction
is perpendicular to that observed for the Mn monolayer which indicates a different
easy magnetization axis for this system [3].
To study the influence of the symmetry of the atomic lattice on spin spiral
states we investigated the pseudomorphic Mn monolayer on W(001) which has a
four-fold symmetry. We again observe a spin spiral in spin-resolved measurements
which has atoms with magnetization components in the surface plane. On larger
sized images one can see a labyrinth pattern due to spin spirals propagating along
the two equivalent [110] directions of the surface. This gives rise to four spots in
the Fourier transform. Note that in addition to the magnetic signal we obtain
atomic resolution for this sample system, which has proven to be very difficult for
other systems studied so far. Ab-initio calculations have confirmed that the spin
spirals have a unique rotational sense due to the DM interaction [4].
The spin spirals of Mn monolayers on W(110) [2] and W(001) [4] are
homogeneous, i.e. the angle between any two neighboring magnetic moments is
constant along the propagation direction. In contrast, the magnetic pattern of the Fe
double layer (DL) on W(110) consists of a regular sequence of out-of-plane
magnetized domains separated by domain walls [5–7]. The average distance
between two walls amounts to about 20 nm. The pattern shows a unique sense of
rotation and can also be described as a spin spiral propagating along the [001]
57
direction. In contrast to the spirals described in Refs. [2, 4] the spin canting does
not occur at a fixed angle in this case, but is smaller in the domains and larger in
the domain walls, the spiral thus being highly inhomogeneous. As for the spin
spirals in the Mn monolayers on W(110) and W(001), the rotational sense of the
spiral in the Fe DL on W(110) could not be measured so far because in the
respective SP-STM experiments the azimuthal component of the tip magnetization
was unknown. For the same reason it remained an open question whether the spiral
is helical or cycloidal, i.e whether the domain walls are of Bloch- or Néel-type.
Starting from phenomenological Dzyaloshinskii-Moriya vectors [8] Monte-Carlo
simulations showed that the unique rotational sense can be explained as a
consequence of DMI [9]. By density functional theory combined with
micromagnetic calculations the DM vector was determined from first principles
[10]. Two domains of opposite magnetization induced in this system by
appropriate boundary conditions were shown to be separated by right-rotating, in
contrast to left-rotating, Néel-type domain walls extending along the [110] axis.
It has been shown that the type of spin spiral and its sense of rotation can be
measured directly by SP-STM experiments performed in a triple axes vector
magnet. The spin spiral in the Fe DL on W(110) is determined to be a rightrotating inhomogeneous cycloid. The non-collinear ground state is a consequence
of interplaying Dzyaloshinskii-Moriya and dipolar energy contributions [11]. In
this case, the SP-STM experiments were performed under ultra-high vacuum
conditions at T = 4.7 K in the magnetic field of a superconducting triple axes
magnet [12]. Using this magnet to align the tip magnetization it is possible to do
SP-STM experiments with the tip magnetization direction being well defined. An
58
external magnetic field was applied along different in-plane directions to align the
tip magnetization accordingly. The magnetic field B = 150 mT was chosen such
that it is weak enough not to affect the magnetic structure of the sample but strong
enough for the alignment of the tip magnetization. The experimental results
obtained allow the conclusion of a right-rotating cycloidal spin spiral propagating
along the [001] axis. In summary, the sense of rotation of a spin spiral, which so
far had to be extracted from theoretical calculations, was for the first time
determined directly from a SP-STM experiment in a triple axes vector magnet.
By reducing the dimensionality of the system from quasi-2D to quasi-1D,
the DM interaction becomes even more important. As an example, we will show
spin spiral states in biatomic Fe chains grown on Ir(001) substrates and discuss the
role of the DM interaction for the observation of complex spin states in atomic
magnetic wires. In particular, we will show the advantage of using SP-STM for
directly revealing non-collinear spin states in atomic magnetic wires which has not
been possible by other competing techniques, such as spin excitation spectroscopy
[13].
59
References
[1]
R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009).
[2]
M. Bode, M. Heide, K. von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer,
A. Kubetzka, O. Pietzsch, S. Blügel and R. Wiesendanger, Nature 447, 190 (2007).
[3]
B. Santos, J. M. Puerta, J. I. Cerda, R. Stumpf, K. von Bergmann,
R. Wiesendanger, M. Bode, K. F. McCarty, and J. de la Figuera,
New J. Phys. 10, 13005 (2008).
[4]
P. Ferriani, K. von Bergmann, E.Y. Vedmedenko, S. Heinze, M. Bode, M. Heide, G.
Bihlmayer, S. Blügel, and R. Wiesendanger,
Phys. Rev. Lett. 101, 027201 (2008).
[5]
M. Bode, O. Pietzsch, A. Kubetzka, S. Heinze, and R. Wiesendanger,
Phys. Rev. Lett. 86, 2142 (2001).
[6]
A. Kubetzka, M. Bode, O. Pietzsch, and R. Wiesendanger,
Phys. Rev. Lett. 88, 057201 (2002).
[7]
A. Kubetzka, O. Pietzsch, M. Bode, and R. Wiesendanger,
Phys. Rev. B 67, 020401(R) (2003).
[8]
I. E. Dzyaloshinskii, Sov. Phys. JETP 5, 1259 (1957); T. Moriya, Phys. Rev. 120, 91
(1960).
[9]
E. Y. Vedmedenko, L. Udvardi, P. Weinberger, and R. Wiesendanger,
Phys. Rev. B 75, 104431 (2007).
[10] M. Heide, G. Bihlmayer, and S. Blügel, Phys. Rev. B 78, 140403 (2008).
[11] S. Meckler, N. Mikuszeit, A. Preßler, E. Y. Vedmedenko, O. Pietzsch, and
R. Wiesendanger, Phys. Rev. Lett. 103, 157201 (2009).
[12] S. Meckler, M. Gyamfi, O. Pietzsch, and R. Wiesendanger,
Rev. Sci. Instrum. 80, 023708 (2008).
[13] C. F. Hirjibehedin, C. P. Lutz, and A. J. Heinrich, Science 312, 1021 (2006).
60
Dzyaloshinskii-Moriya driven spinstructures in ultrathin magnetic films and
chains
Stefan Blügel
Peter Grünberg Institut (PGI) and Institute for Advanced Simulation (IAS), Forschungszentrum
Jülich GmbH and JARA, D-52425 Jülich, Germany.
The surface and interface is distinguished from ordinary bulk physics by the
presence of spin-orbit interaction in a structure inversion asymmetric environment,
which gives rise to the well-known Rashba effect [1,2], or an unconventional
scattering at magnetic and non-magnetic impurities [3] that leads to chiral spin
textures and homochiral magnetic structures [4-6], which had been overlooked in
the past. These magnetic structures bear similarities with cycloidal spirals found in
multiferroic materials and exhibit a very rich magnetic phase diagram [7]. I focus
in my talk on the Dzyaloshinskii-Moriya interaction caused by spin-polarized
electrons in the structure inversion asymmetric environment of Cr, Mn, Fe metal
films on W substrates. We found that due to the large spin-orbit interaction of the
W substrate the Dzyaloshinskii interaction exceeds a critical strength and competes
with the exchange interaction and causes homochiral magnetic structures. Even if
the Dzyaloshinskii-Moriya interaction is not strong enough to create new ground
states, we show that it can be still visible in the formation of domain walls [6] or
dynamical quantities such as magnons. The investigation is extended to one
dimensional systems such as magnetic metallic chains at step edges. The work
calculations have been carried out with the FLEUR code [8] extended to treat
noncollinear magnetic structures in the presence of spin-orbit interaction [9].
61
Homochiral magnetic order in a one-atomic layer thick film of Mn atoms on a W(110) surface. The local
magnetic moments at Mn atoms shown as red and green arrows are aligned antiferromagnetically between nearestneighbor atoms. Superimposed is a spiral pattern of unirotational direction. The top picture shows a left-rotating
cycloidal spiral, which was found in nature. The bottom picture shows the mirror image, a right rotating spiral,
which does exist [4].
Acknowledgement:
In part, this work was carried out in collaboration with Gustav Bihlmayer, Paolo
Ferriani, Marcus Heide, Stefan Heinze, Samir Lounis, Benedikt Schweflinghaus,
Bernd Zimmermann from the theory side and Matthias Bode, Andre Kubetzka,
Kirsten von Bergmann, Matthias Menzel of the Wiesendanger group from the
experimental side.
62
[1] Yu. M. Koroteev, G. Bihlmayer, J. E. Gayone, E. V. Chulkov, S. Blügel, P. M. Echenique,
and Ph. Hofmann, Phys. Rev. Lett. 93, 046403 (2004).
[2] T. Hirahara, T. Nagao, I. Matsuda G. Bihlmayer, E.V. Chulkov, Yu.M. Koroteev, P.M.
Echenique, M. Saito, and S. Hasegawa, Phys. Rev. Lett. 97, 146803 (2006).
[3] J.I. Pascual, G. Bihlmayer, Yu. M. Koroteev, H.-P. Rust, G. Ceballos, M. Hansmann, K.
Horn, E. V. Chulkov, S. Blügel, P. M. Echenique, and Ph. Hofmann, Phys. Rev. Lett. 93,
196802 (2004).
[4] M. Bode, M. Heide, K. von Bergmann, S. Heinze, G. Bihlmayer, A. Kubetzka,
O. Pietzsch, S. Blügel, R. Wiesendanger, Nature 447, 190 (2007).
[5] P. Ferriani, K. von Bergmann, E.Y. Vedmedenko, S. Heinze, M. Bode, M. Heide, G.
Bihlmayer, A. Kubetzka, S. Blügel, R. Wiesendanger, Phys. Rev. Lett. 101, 027201 (2008).
[6] M. Heide, G. Bihlmayer, and S. Blügel, Phys. Rev. B 78, 140403 (R) (2008).
[7] M. Heide, G. Bihlmayer, and S. Blügel, Physica B 404, 2678 (2009).
[8] For the description of the code see www.flapw.de
[9] M. Heide, G. Bihlmayer, and S. Blügel, J. Nanosci. Nanotechnol. 11, 1 (2011).
63
Spontaneous atomic-scale magnetic skyrmion lattice in an ultra-thin film:
real-space observation and theoretical foundation
Stefan Heinze
Institute of Theoretical Physics and Astrophysics
Christian-Albrechts-Universität zu Kiel, Germany
Skyrmions are topologically protected field configurations with particle-like
properties that play an important role in various fields of science. They have been
predicted to exist also in bulk magnets and in recent experiments it was shown that
they can be induced by a magnetic field. A key ingredient for their occurrence is
the Dzyaloshinskii-Moriya interaction (DMI) which was found to be strong also in
ultrathin magnetic films on substrates with large spin-orbit coupling [1]. In these
systems the DMI stabilizes spin-spirals with a unique rotational sense propagating
along one direction of the surface [1,2]. Here, we go a step beyond and present an
atomic-scale skyrmion lattice as the magnetic ground state of a hexagonal Fe
monolayer on Ir(111). We develop a spin-model based on density functional theory
that explains the interplay of Heisenberg exchange, DMI and the four-spin
exchange as the microscopic origin of this intriguing magnetic state. Experiments
using spin-polarized scanning tunneling microscopy confirm the skyrmion lattice
which is incommensurate with the underlying atomic lattice.
[1] M. Bode et al., Nature 447, 190 (2007).
[2] P. Ferriani et al., Phys. Rev. Lett. 101, 027201 (2008).
64
Dzyaloshinskii–Moriya Interaction:
How to Measure Its Sign in Weak Ferromagnets?
Vladimir E. Dmitrienko1, Elena N. Ovchinnikova2, Jun Kokubun3, Kohtaro Ishida3
1
2
A.V. Shubnikov Institute of Crystallography, Moscow, 119333 Russia
Faculty of Physics, Moscow State University, Moscow, 119991 Russia
3
Tokyo University of Science, Noda, Chiba 278-8510, Japan.
It is shown that diffraction on antiferromagnetic crystals with weak
ferromagnetism can be used for experimental determination of the sign of the
Dzyaloshinskii-Moriya interaction (DMI) and its relation with the sign of the local
chirality of crystal structure. In this type of crystals, the canting of atomic moments
can be considered as a result of alternating right-hand and left-hand rotations of
moments in accordance with alternating local chirality inside the crystal unit cell.
Three different experimental techniques sensitive to the DMI sign are
discussed: neutron diffraction, Mössbauer γ-ray diffraction, and magnetic (resonant
or non-resonant) x-ray scattering.
In particular, it is demonstrated that the DMI sign can be directly extracted from
interference between magnetic X-ray scattering, sensitive to the phase of
antiferromagnetic order, and charge scattering, sensitive to the crystal structure.
Classical examples of hematite (α-Fe2O3) and FeBO3 crystals are considered in
detail (see [1] for preliminary consideration). This interference distorts strongly the
azimuthal dependence of forbidden reflections and was recently observed in
hematite [2]. However, the results of [2] cannot be directly used for the sign
determination because the orientation of the weak ferromagnetic moment was
indefinite in that work. The application of external magnetic field, fixing the
orientation of the weak ferromagnetic moment and (owing to the DMI) fixing the
phase of antiferromagnetic order relative to crystal structure, is crucial for these
65
experiments.
The expected details of azimuthal dependence were simulated using FDMNES
codes [3] for x-ray scattering amplitude the near absorption edges of magnetic
atoms. We hope that the DMI sign of FeBO3 will be measured in July at XMAS
beamline in Grenoble. Results for a more complicated case of the DMI in crystals
of La2CuO4 type will be also presented.
Two other possible techniques, neutron diffraction and Mössbauer γ-ray
diffraction, sensitive to the DMI sign, are discussed in comparison with magnetic
x-ray scattering.
This work was supported by the Russian Foundation for Basic Research
(project 10-02-00768) and by the Program of Fundamental Studies of Prezidium of
Russian Academy of Sciences (project 21).
[1] V.E. Dmitrienko, E.N. Ovtchinnikova, J. Kokubun, K. Ishida, JETP Lett. 92, 383 (2010).
[2] J. Kokubun, A. Watanabe, M. Uehara, Y. Ninomiya, H. Sawai, N. Momozawa, K. Ishida,
V.E. Dmitrienko, Phys. Rev. B 78 115112 (2008).
[3] Y. Joly, Phys. Rev. B 63 125120 (2001); FDMNES codes can be found at
www.neel.cnrs.fr/fdmnes
66
Coupling of the spin and lattice modulations in CaCuxMn7-xO12
W. Sławiński 1, R. Przeniosło 1, I. Sosnowska 1, and M. Bieringer 2
1
Institute of Experimental Physics, University of Warsaw, 69 Hoża Str, 00-681 Warsaw, Poland
2
Department of Chemistry, University of Manitoba, Winnipeg, R3T 2N2, Canada
The mixed manganese oxide CaMn7O12 is a multiferroic material [1] with a
distorted perovskite structure [2]. The crystal structure [3] and the magnetic
ordering [4] of CaMn7O12 have been studied by using high resolution SR
diffraction and high resolution neutron diffraction. These diffraction studies show a
modulation of the atomic positions in CaMn7O12 at temperatures below 250K and
magnetic structure modulation below TN = 90K [5,6].
The modulation of atomic positions has been described by using a quantitative
model with a propagation vector (0,0,qp) [5,6]. The modulation of the magnetic
structure is described with a propagation vector (0,0,qm).
The present neutron diffraction studies of CaCuxMn7−xO12 (x = 0.0 and 0.1)
confirm the quantitative model describing the atomic position modulations in as
derived from [5]. Neutron diffraction studies confirm the relation between the
atomic position modulation length Lp and the magnetic modulation length Lm =
2Lp between 50 K and the Neel temperature TN. CaCuxMn7−xO12 (x = 0.1 and 0.23)
shows a magnetic phase transition near 50 K associated with considerable changes
of the magnetic modulation length and the magnetic coherence length, similar to
that observed in the parent CaMn7O12. The temperature dependence of the
modulation vectors qp and qm is shown in Fig. 1.
67
Fig. 1 Temperature dependence of the magnetic modulation vector length q m for CaCuxMn7−xO12 (x = 0.0 (open
circles), 0.1 (gray circles) and 0.23 (black circles)) measured on neutron diffractometer D20 (ILL). Two additional
points show qm values obtained on neutron diffractometer D2B for CaMn7O12 (crosses). The temperature
dependence of atomic position modulation vector qp for CaCuxMn7−xO12 (x = 0.0 (open triangles) and 0.1 (gray
triangles)) measured by synchrotron radiation diffractometer ID31 (ESRF) and for x = 0.0 (asterisk) measured with
neutron diffractometer D2B.
References
[1] M. Sánchez-Andújar, S. Yáñez-Vilar, N. Biskup, S. Castro-García, J. Mira, J. Rivas, M.
Señarís-Rodríguez, ―Magnetoelectric behaviour in the complex CaMn7O12 perovskite‖, J.
Magn. Magn. Mater. 321 (2009) 1739-1742.
[2] B. Bochu, J. L. Buevoz, ―Bond lengths in [CaMn3][Mn4]O12 ―A new Jahn-Teller distortion of
Mn3+ octahedral‖, Solid State Communications 36(2) (1980) 133–138.
[3] W. Sławinski, R. Przeniosło, I. Sosnowska, M. Bieringer, I. Margiolaki, A. N. Fitch, E.
Suard, „Phase coexistence in CaCuxMn7−xO12 solid solutions‖ Journal of Solid State
Chemistry 179(8) (2006) 2443–2451.
[4] R. Przeniosło, I. Sosnowska, D. Hohlwein, T. Hauß, I. O. Troyanchuk, „Magnetic ordering in
the manganese perovskite CaMn7O12‖, Solid State Communications 111(12) (1999) 687–692.
[5] W. Sławiński, R. Przeniosło, I. Sosnowska, M. Bieringer, I. Margiolaki, E. Suard,
―Modulation of atomic positions in CaCuxMn7-xO12 (x ≤ 0.1)‖ Acta Crystallogr. B65 (2009)
535-542.
[6] W. Sławiński, R. Przeniosło, I. Sosnowska, M. Bieringer, „Structural and magnetic
modulations in CaCuxMn7−xO12‖ J. Phys.: Condens. Matter 22 (2010) 186001-6.
68
Antichiral multiferroic YMnO3
V. Plakhty1, Yu. Chernenkov1, J. Kulda2, S. Gvasaliya3, B. Roessli4, M. Janoschek5
1
Petersburg Nuclear Physics Institute, Gatchina, St-Petersburg, Russia
2
Institut Laue-Langevin, Grenoble, France
3
Eidgenössische Technische Hochschule, Zurich, Switzerland
4
Paul Scherrer Institute, Villigen, Switzerland
5
Technische Universitat Munchen, Garching, Germany
The ferroelectric YMnO3 (TC = 913 K) has the P63cm symmetry, and its
spontaneous polarization is along z axis. A triangular ordering of the Mn3+ spins in
the (001) planes occurs at TN = 72.3 K. YMnO3 differs from the other triangular
antiferromagnets by the opposite chirality (C) of the spins in the planes at z = 0 and
at z = 1/2. Therefore, the chirality of the unit cell is equal to zero as has been found
in our experiment performed on IN20 at ILL. In this sense one may consider
YMnO3 as a member of the new class of antichiral magnets. The chiral fluctuations
should exist, since the exchange interaction between the layers is very weak.
However, its behavior has been never studied either theoretically or experimentally
before our experiments at PSI on the three axis neutron spectrometer TASP. A
chiral scattering given by the difference of the intensity of scattered neutrons with
opposite polarization, along +z and –z, that coincides with the chirality vector C,
has been definitely observed above the Néel temperature at the energy transfer ~
0.1 meV. However, materials, like YMnO3, order magnetically while being in the
ferroelectric state. It is known that a coupling between the ferroelectric and
antiferromagnetic order takes place in YMnO3 near the Néel temperature, i.e.
YMnO3 behaves as a two-order-parameter compound. Our experiment proves that
YMnO3 is antichiral multiferroic.
69
Structure and spin chirality in B20 structures
V.A. Dyadkin1, S.V. Grigoriev1, E.V. Moskvin1, S.V. Maleyev1, D. Menzel2, D.
Chernyshov3, V. Dmitriev3, H. Eckerlebe4
1
Petersburg Nuclear Physics Institute, Gatchina, Russia, [email protected]
2
Institut fuer Physik der Kondensierten Materie, TU Braunschweig, Germany
3
Swiss-Norwegian Beamlines at the ESRF, Grenoble, France
4
Helmholtz Zentrum Geesthacht, Geesthacht, Germany
The crystallographic and magnetic chirality of the B20 (space group P2 13) solid
solutions Fe1-xCoxSi and pure MnSi grown by the Czochralski method has been
studied. To measure the spin chirality γ we use small angle scattering of polarized
neutrons and determine it as
P0γ = (I+–I-)/(I+ + I-),
(1)
where I+ and I- are the intensities of scattered neutrons with the incident
polarization P0 along and opposite to the guiding magnetic field measured at the
same point of Fourier space [1]. We show that the magnetic chirality is
unequivocally connected with the crystallographic handedness which is by-turn
defined as the chirality of the silicon sublattice [2].
To define the crystallographic chirality we measure the absolute structure by the
single crystal diffraction of the synchrotron radiation taking into account the Flack
parameter x [3]. The possibility to determine presence of inversion twins of the
chiral system is based on the breaking of the Friedel's law: having the wave length
close to the absorption border the chiral system produces the difference of
intensities of opposite Bragg peaks
0 ≠ I(h k l) – I(-h -k -l) = (1-2x)[|F(h k l)|2 – |F(-h -k -l)|2]
(2)
Here F is the scattering amplitude. The responsible term for the intensity difference
is the imaginary contribution into the scattering amplitude:
70
F(Q) = Σ(fj + ifj'') exp(iQr)
(3)
The measured x close to zero shows that the structure is chiral and it is correctly
determined. If x is in-between 0.3 and 0.7 than the system with an inversion centre
in the system or it is a racemic mixture of chiral objects. If x is close to 1 then the
structure must be inverted. In our experiments x was equal 0.00(6) which together
with low R factors (R1 = 1.8%, wR = 4.3%) confirm that the absolute structure has
been defined correctly.
Having samples of Fe1-xCoxSi with well defined chirality, we use them as left
handed and right handed seeds to grow three series of Fe1-xCoxSi compounds of
different concentration and two series of pure MnSi samples. In 90% cases the
grown sample has been found to be enantiopure and to inherit the crystallographic
chirality of its seed crystal. In 10% cases undefined circumstances flip the chirality
over for the next progeny or produce a racemic sample. The spin chirality of these
systems has been found to be congruent to the crystallographic handedness for
MnSi and flipped for Fe1-xCoxSi that implies different signs of the DzyaloshinskiiMoriya interaction constituting the helix structure in these two systems [2].
[1] S.V. Maleyev, Phys. Rev. Lett. 75 (1995) 4682.
[2] S.V. Grigoriev, D. Chernyshov, V.A. Dyadkin et al, Phys. Rev. Lett. 102 (2009) 037204.
[3] H.D. Flack, Acta Cryst. 39 (1983) 876.
71
Can parity non-conserving weak Interaction affects crystal chirality?
Maleyev S.V
Petersburg Nuclear Physics Institute, 188300 Gatchina, St-Petersburg, Russia
It is generally accepted that two enantiomers have exactly equal energy density.
Hence they should have equal population in nature. It is a result of the parity
conservation of the nuclear and electro-magnetic interactions. However, the weak
Interaction breaks this conservation law and leads to very weak energy splitting of
the two enantiomers. This effect gives rise heavy atoms optical activity and
chiral contribution to the Van der Waals Interaction of order of 1013 1014 eV [1].
It may be shown that this energy splitting holds for the Ion pairs with different
symmetry axes only, for example for MnSi and CsCuCl3.
This very small quantity may be important just below the first order transition
temperature Tf where volume of the critical seed is proportional to τ3 = (1 - T/Tf)3.
For sufficiently small τ the chiral part of the seed energy may be of order of T and
the transition would occur into single chiral state.
[1] O.L. Zizimov and I.B.Khriplovich, Sov.Phys.JETP 82, 1026 (1982)
72
Chirality of polycrystalline MnSi: polarized SANS study
N.M. Potapova,1 S. V. Grigoriev, 1 V. A. Dyadkin,1 D. Menzel,2 E. V. Moskvin,1
H. Eckerlebe,3 S. V. Maleyev 1
1
Petersburg Nuclear Physics Institute, Gatchina, 188300 St-Petersburg, Russia.
2
Technische Universitat Braunschweig, 38106 Braunschweig, Germany.
3
Helmholtz-Zentrum Geesthacht, 21502 Geesthacht, Germany.
E-mail: [email protected].
The X-ray and polarized neutron diffraction are used to determine the crystal
handedness and magnetic chirality of the series of high-purity MnSi single crystals
and mixed compounds crystals of Mn1-xFexSi and Fe1-xCoxSi grown by Czochralski
methods [1,2]. We demonstrate that (i) the magnetic chirality of all Mn1-xFexSi
crystals follows its crystallographic counterpart [1], (ii) the opposite coupling
between the crystal handedness and the spin chirality has been found for Fe 1-xCoxSi
compounds [2].
Knowing the rigid coupling between the structural handedness and magnetic
chirality we used the polarized neutron diffraction to indirectly determine the
average handedness of six different polycrystalline samples of MnSi with large
number of crystallites (100 crystals per cm3). These six large MnSi polycrystalline
samples were left over after the Czochralski single crystal growth process. The
samples were prepared as the stoichiometric mixture of Mn and Si which was
molten in the argon atmosphere (pressure was about 2.5 bars) by the tri-arc
method. The seed crystal with the defined chirality (see Table Ошибка!
Источник ссылки не найден.) was submerged into the melt and a new single
crystal was pulled out by the Czochralski technique. After the new single crystal
was taken out from the liquid, the temperature was abruptly decreased and the
73
liquid has crystallized. Such obtained MnSi polycrystal, which was a rest round
lump with the diameter about 10 mm within the crucible, had been used for the
measurements.
The average chirality of these polycrystals deviates unexpectedly high from
zero. This high deviation of the chirality can be explained under the assumption
that these polycrystals consist of rather large monocrystalline domains. The surface
photograph of the MnSi, shown in Fig. 1, has confirmed that the polycrystals
contain grains with the size of about 2×2×2 mm. We have summed up the average
values of the chirality for all samples and have obtained the value of overall = -0.09
 0.02. We note that this error bars are based on the neutron statistics. This indeed
allows one to measure the chirality of all six samples with acceptable accuracy.
The estimated number of crystallites inside all six samples is roughly 6×100=600
and the statistical error is of the order of 0.04. Thus, this net chirality is maybe
related to the yet poor statistics in the numbers of the left or right crystallites inside
the polycrystals.
Fig. 1. Photograph of the surface of the
MnSi polycrystal.
74
[1] S. V. Grigoriev, D. Chernyshov, V. A. Dyadkin, V. Dmitriev, S. V. Maleyev, E. V. Moskvin,
D. Lamago, Th. Wolf, D. Menzel, J. Schoenes, and H. Eckerlebe, Phys. Rev. B, 2010 81,
012408.
[2] S. V. Grigoriev, D. Chernyshov, V. A. Dyadkin, V. Dmitriev, S. V. Maleyev, E. V. Moskvin,
D. Menzel, J. Schoenes, and H. Eckerlebe, Phys. Rev. Lett. 2009, 102, 037204.
75
Name
Organization
Email
Stishov Sergei
Institute for High Pressure
Physics
Moscow, Russia
Petersburg Nuclear Physics
Institute
Gatchina, Saint-Petersburg,
Russia
HPPI RAN,
Troitsk, Russia
A.M.Prokhorov General
Physics Institute of RAS
Moscow, Russia
Dalhousie University
Physics and Atmospheric
Science
Halifax, Canada
University of Leeds
Condensed Matter, School
of Physics and Astronomy
Leeds, England
IFW Dressden Institute for
Theoretical Solid State
Physics
Dresden, Germany
Diamond Light Source Ltd.
Chilton, OX11 0DE, United
Kingdom
PNPI RAS NRD
Gatchina, Russian
Federation
IFW Dresden
Dresden, Germany
PNPI Theoretical dep
Gatchina, Saint-Petersburg
Russian Federation
Institute of Metal Physics,
RAS Laboratory of Theory
of Nonlinear Phenomena
Yekaterinburg, Russia
ETH Zürich Institute for
Solid State Physics
Zürich, Switzerland
[email protected]
Grigoriev Sergey
Tsvyashchenko Anatoly
Demishev Sergey
Monchesky Theodore
Porter Nicholas
Rößler Ulrich K.
Wilhelm Heribert
Moskvin Evgeny
Leonov Andriy
Maleyev Sergey
RYBAKOV PHILIPP
Mühlbauer Sebastian
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
i
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
76
Kakurai Kazuhisa
Ovchinnikov Alexander
Wakimoto Shuichi
Lott Dieter
Wiesendanger Roland
Blügel Stefan
Heinze Stefan
Dmitrienko Vladimir E.
Slawinski Wojciech
Chernenkov Yury
Dyadkin Vadim
Chetverikov Yury
Potapova Nadezhda
Grigoryeva Natalia
Kobylyanskaya Ekaterina
Chumakov Andrey
Japan Atomic Energy
Agency Quantum Beam
Science Directorate
Tokai, Ibaraki, Japan
Ural State University
Ekaterinburg, Russia
Japan Atomic Energy
Agency Quantum Beam
Science Directorate
Tokai Japan
Helmholtz Zentrum
Geesthacht WPN
Geesthacht, Germany
University of Hamburg
Dept. of Physics
Hamburg, Germany
Forschungszentrum Jülich
GmbH
Jülich, Germany
University of Kiel
Kiel, Germany
Institute of crystallography
Theoretical Department
Moscow, Russia
University of Warsaw
Faculty of Physics
Warsaw, Poland
PNPI NRD
Gatchina, Russia
PNPI
Gatchina, Russia
PNPI DCMI
Gatchina, Russia
PNPI
Gatchina, Russia
Saint-Petersburg State
University Faculty of
Physics
Saint-Petersburg, Russia
PNPI
Gatchina, Russia
PNPI RAS OIKS ONI
Gatchina, Russia
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
77
Dyadkina Ekaterina
Chernyshov Dmitry
Moskvin Alexander
Popova Svetlana
Sizanov Alexey
Syromyatnikov Arseny
Tarnavich Vladislav
Ivashevskaya Svetlana
CAMPO Javier
Przenioslo Radoslaw
Bogdanov Alexei
Piyadov Vasya
Petersburg Nuclear Physics
Institute Neutron Research
Department
Gatchina, Russia
SNBL at ESRF
Grenoble, Franse
Ural State University
Department of Theoretical
Physics
Ekaterinburg, Russia
The Ufa State
Technological University
chair The Technological
Machines and equipment
Ufa, Russia
PNPI Theory Division
Saint-Petersburg, Russia
PNPI
Gatchina, Russia
Voronezh state technical
university
Voronezh, Russia
Karelian Research Centre
RAS Institute of Geology
Petrozavodsk, Russia
Spanish Research Council
Phys Condens Matter
Zaragoza, Spain
University of Warsaw
Faculty of Physics
Warsaw, Poland
IFW-Dresden
Dresden Germany
PNPI RAS
Gatchina Russia
[email protected]
[email protected]
[email protected]
[email protected]
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