1. Jung Hoon Han (SKKU, Korea)
응집물리학의 스커미온
Jung Hoon Han (SKKU, Korea)
성균관대 한정훈

2. “Topological Numbers”
(Almost) All important numbers in condensed matter physics are topological in nature

3. Examples of Topological Numbers
Quantized circulation in superfluid helium
Quantized flux in superconductor
Chern Number for quantized Hall conductance
Z2 number for quantum spin Hall and
3D topological insulators
(11월 6일 연세대)
Skyrmion numbers

4. Is electric charge a topological number?
Common view: The charge of an elementary particle is just a constant of nature
Tony Skyrme’s view: No, even the charge can be derived from the underlying theory
In Skyrme’s theory, charge is a
topological number of a particular field configuration

5. 2007 Nobel Prize

6. r=R/2
r=R/4
r=R/10
3D Skyrmion
r=R
r=2R
r=10R

7. 2D (Baby)
Skyrmion
2차원 스커미온 위상숫자
3차원 스커미온 위상숫자
Skyrme 왈: 위상수=전하
(양자홀 계에서 최초로 검증)

8. Study of Magnets in Physics
Study of magnetism has taught us about
Electromagnetism and gauge theory (B=xA)
Molecular field (Curie-Weiss) theory
Ginzburg-Landau theory
Renormalization group idea
Spontaneous symmetry breaking in phase transition
Goldstone theorem, Mermin-Wagner theorem
High-Tc puzzle, spin liquids
Quantum Criticality
Magnetic Storage (GMR, CMR, TMR)
Spintronics, QSHE

9. Excitations of Magnets
Topological:
Vortices (p1(S1) homotopy,
circle->circle)
Skyrmions (p2(S2) homotopy,
sphere->sphere)
Non-topological:
At low temperature, magnetic moments ORDER into e.g. a ferromagnet (a phenomenon of SSB). By virtue of Goldstone’s theorem, gapless excitations must exist – spin waves

10. 2D XY Magnet: Vortex Vortices are natural defects in XY magnets
T/J=0.05
T/J=0.90
Vortices proliferate at TKT, disorder the spin system
T/J = 1.1

11. Vortices in Condensed Matter
Superfluid 4He in 2D
Josephson Junction Array
2D Superconductor

12. 2D Heisenberg Magnet: Skyrmion
2D XY Magnet: Vortex
2D Heisenberg Magnet: Skyrmion
Nontrivial homotopy map: p1(S1) = Z -> p2(S2) = Z

13. Unimportance of Skyrmions in Heisenberg Magnet
Unlike vortices in 2D XY magnet,
Skyrmions in 2D Heisenberg magnets are irrelevant excitations
Polyakov’s work:
spin-wave excitations already disorder the phase

14. Exception to the Rule: Quantum Hall FM
Electrons confined to 2D under strong (~10T) magnetic field
All electrons sit within a single LL K lB B
Klaus von Klitzing
(NP ’85)

15. lB Completely spin polarized due to Coulomb exchange
Quantum Hall Ferromagnet (QHFM) K B lB B

16. Skyrmions as Quasiparticles
“usual” quasiparticle
Q=1, S=1/2, Energy=D
“Skyrmionic” quasiparticle
Q=1, S=many, Energy=(1/2)D
Sondhi et al. PRB 47, (1993)

17. Skyrmions are cheapest charge excitations of QHFM
NMR Knight shift data showed charge excitation accompanied by a large spin flip (S~4)
Each Skyrmion carries electric charge
Barrett et al. PRL 74, (1995)

18. Search for Skyrmion Crystal
Skyrmion lattice as a model for nuclear matter
Claims of Skyrme crystal by MacDonalds et al.
Experimental evidence still indirect

19. Analogy to Vortex Matter
NbSe2
Hess et al,
PRL (89) Nb
Tonomura group
Nature (92)
MgB2
Vinnikov et al
PRB (03)
Array of quantized magnetic fluxes (F=h/2e)
Predicted to exist by Abrikosov based on analysis of GL
Possible to find a matter consisting of Skyrmions?

20. “Sightings” of Skyrmion Crystal in Chiral Magnet
Nearly ferromagnetic metal
Spiral spins with a long modulation period l~180A
Dzyaloshinskii-Moriya (DM) interaction
Nakanishi et al. SSC 35, (1980)

21. Recent Breakthroughs in Chiral Magnet (3D)
A new phase with triple-Q Bragg spots in MnSi, Fe1-xCoxSi (3D)
Muhlbauer et al. Science 323, (2009)
For cFM relevant objects are twisting spins called Skyrmions

22. Recent Breakthroughs in Chiral Magnet (2D)
A new phase with triple-Q Bragg spots
in Fe1-xCoxSi (2D)
Perpendicular magnetic field drives
Stripe->Skyrmion Lattice -> FM
via two 1st order phase transitions
Yu et al Nature (2010)

23. Skyrmion Lattice Recipe
Take a helical spin state propagating along Q1-vector Q1

24. Take two helical spin states propagating along Q1 and Q2-vectors

25. Take three helical spin states propagating along Q1, Q2, Q3-vectors
You get a Skyrmion lattice! Q1 Q2 Q3

27. Skyrmion Lattice as a Hidden Abrikosov Lattice
Vortex: Quantum mechanical, U(1)
Skyrmion: classical, O(3)

28. Han,Zang,Yang,Park,Nagaosa, PRB (2010)
Abrikosov’s solution for Abrikosov lattice
CP1 solution for Skyrmion lattice
Han,Zang,Yang,Park,Nagaosa, PRB (2010)

29. 스커미온의 쓸모 지적호기심 (예) 소자응용가능성 (?) 단위 소자 전자(electron) 잘하면
전자소자(electronics)
스핀(spin)
스핀소자(spintronics)
스커미온(skyrmion)
스커미온소자(skyrmionics)?

30. Magnetic Nanodot (포항공대이현우교수)
Vortex in FM nanodisk
[ Waeyenberge et al.,
Nature 444, 461 (2006) ]
Shinjo et al.,
Science 289, 930 (2000)

31. Controlled motion of Skyrmionic object possible

32. Vortex Magnetic Nanodot (포항공대이현우교수)
Vortex polarity as memory
Magnetic-field-induced vortex switching
Waeyenberge et al., Nature 444, 461 (2006)

33. Current-induced Vortex Reversal (포항공대이현우교수)
Theory
Experiment
Sang-Koog Kim et al., APL 91, (2007)
Yamada et al., Nature Materials 6, 269 (2007)

34. Vortex as Microwave Source (포항공대이현우교수)
GMR and microwave data
Line narrower than 300 kHz at ~1.1 GHz
Magnetic dynamics of thick layer
Pribag et al., Nature Physics 3, 498 (2007)

35. Uses of Magnetic Vortex
Magnetic memory
Source of microwave generation
Current control of vortices and Skyrmions possible through spin transfer torque (STT)
Chiral FM
Ordinary FM
Competition
Short-range FM
Short-range DM
Long-range Dipolar
Skyrmion size
10nm<R<100nm
R>100nm
Natural state
Lattice
Single
Magnetic field
Required
Not required
Disk size
Large/small
small
Chirality
Yes No
Can we replace conventional magnetic vortex by Skyrmion?

36. Collaboration Park Jin-Hong, Yang Zhihua (SKKU)
Naoto Nagaosa (U. Tokyo)
Tokura group (U. Tokyo)
Jiadong Zang (Fudan U)