Topological properties and
dynamics of magnetic skyrmions
王明星 王昆 刘华鹏 杨越 张洁 宋化鼎
Introduction
The skyrmion is a hypothetical particle related
originally to baryons. It was described by Tony
Skyrme and consists of a quantum superposition of
baryons and resonance states.
Science, February 13, 2009, Vol 323, Issue 5916
• The existence of skyrmions at room
temperature
• The size is 6nm.
• remain stable against collapse to the atomic
scale
• Lower drive Current.
• high-responsivity
Skyrmions can give a new
approach to electronic memory
mechanisms of skyrmions
• Long-ranged magnetic dipolar interactions.
• The relativistic Dzyaloshinskii–Moriya
(DM) interaction
• Frustrated exchange interactions
• four-spin exchange interactions
Skyrmion crystal (SkX)
Consider a ferromagnet, introduce the DM
interaction
H DM 
 D S
ij
i
Sj
ij
DM interaction destroy centeral inversion
symmetry of the entire spin system , because
Skyrmion configuration also destroy the central
inversion symmetry , so we have reason to believe
that the presence of DM interaction can be
extended Skyrmion phase
external magnetic field B=0
Phys. Rev. Lett. 111, 186805 (2013)
external magnetic field B≠0
In certain magnetic field and temperature
Multi -state wave vector state will be appeared.
For this state corresponds to a bigger entropy which can
reduce the work function Effectively.
Skyrmion crystals can treat as three wave vector with the
same length and the respective angles of 120 °superimpose
together k=0.
Observation of skyrmions in chiral-lattice magnets
Neutron scattering experiments on MnSi and Fe1–xCoxSi
‘A phase’ with a two-dimensional skyrmion crystal (SkX) phase.
the SkX is stabilized by
thermal fluctuations
above the conical state in
a limited region near the
transition temperature,
while the conical state
with the wavevector Q
parallel to the magnetic
field is more stable in the
rest of the phase diagram
the magnetic scattering of neutrons (and
possibly of X-rays)
The reciprocal-space
SANS patterns for the
SkX on the plane
normal to the incident
neutron k-vector shows
up as a hexagon with
the norm of |Q|, that is,
Fourier transform of
the two-dimensional
hexagonal SkX lattice.
LTEM
(001) thin plate of Fe0.5Co0.5Si with B20-type chiral crystal structure
below the magnetic transition
temperature (~40 K)
zero magnetic field
stripy pattern
this corresponds to the proper screw spin structure
propagating along [100] or [010].
A hexagonal lattice is formed by periodic arrays of spin-swirling
structures.
The helicity in each skyrmion reflects the sign of the DM interaction
of this compound, hence indicating the uniformity of the chiral
domain of the crystal structure.
Phase diagrams of thin-film samples
of chiral magnets as a function of
magnetic field and temperature .
The dependence of the SkX phase
diagram for FeGe on the sample
thickness (t).
H, helical state;
FM, ferromagnetic state.
The colour scale indicates the
skyrmion density per square
micrometre.
some examples of the helimagnetic phases
In a thin (~50 nm) c-plane film of
BFSO, in which the magnetic
anisotropy is controlled and
slightly weakened by Sc doping
Ba (Fe 1 x  0.05 Sc x M g 0.05 )12 O19
centrosymmetric magnet
a highly disordered helimagnetic
texture with frequent reversals
of magnetic helicity is observed
at room temperature and in zero
magnetic field
a magnetic field
Emerge SkX phase
each skyrmion shows as either
a black or a white circle-disk in
a random manner
indicate
skyrmion helicity (for example,
clockwise or anticlockwise curl of
the in-plane M) is not correlated
Increase
field strength
skyrmion size tends to decrease
Topological phenomena related to
skyrmions
• “Topological hall effect”
and “Skyrmion hall
effect”
• Both arising from
emergent
electromagnetic field of
Skyrmion crystal
• Difference
Topological phenomena related to
skyrmions
• Take MnSi for example.
• In the phase picture, in SkX
region an anomalous
Hall effect contribution
could be detected. Leading
to topological hall effect.
PRL 102, 186602 (2009)
• Up to now,topological hall effect has been broadly reported in
MnSi 、 MnGe etc.But Skyrmion hall effect is much more
difficult to detected even though theoritical work is already
completed.
• To describe motion of conduction electron in a Skyrmion
crystal,one can have:
• The Boltzmann equation.e and b are emergent electromagnetic
field in Skyrmion crystal,f is the Fermi-Dirac distribution
function.
• Because of the term
,topological hall effect occurs due
to b.
• A modulation occurs in Phase A
region
• ~5nΩ
• The signal contains three parts:
• Normal hall effect, anomalous hall
effect, topological hall effect.
• Topological contribution is the
anomalous modulation.
PRL 102, 186602 (2009)
• Skyrmion hall effect:
motion of Skyrmion itself
• Threshold Jc~~102Acm-2
• When current
density>Jc, driving
Skyrmion crystal to
move
• rotational symmetry in spin space is broken by the external
magnetic field, and hence the spin wave modes are gapped,
that is a phonon of the skyrmion crystal.
• the three k = 0 skyrmion ‘optical’ modes:anticlockwise
(ACW) rotation, clockwise (CW) rotation and breathing
modes of the skyrmion core
a universal current–velocity relation for the skyrmion crystal
almost independent of αG, β and impurity pinning
The reduced critical current density for the skyrmion crystal
was attributed to the deformation of the crystal and of
individual skyrmions to avoid the impurity potential
In summary
A skyrmion is a topologically stable particle observed in
certain magnets, which has peculiar dynamics. Because
skyrmions comprise many spins, thermal and quantum
fluctuations are expected to be small, which is advantageous
for memory
Applications.
From an applications perspective, the nanoscale
fabrication of samples is an important step, along with the
design and demonstration of skyrmion logic circuits enabled
by fundamental understanding of the basic physics of the
skyrmions.