Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
Multi channel topological edgeMulti-channel topological edge states: skyrmion dynamics in
nanostripes of frustrated magnets
Andrey Leonov
1. University of Groningen, Zernike Institute f Ad d M i lfor Advanced Materials
2. IFW Dresden3 Center for Chiral Science Hiroshima University3. Center for Chiral Science, Hiroshima University
Spetses Greece June 29 2016Spetses, Greece, June 29, 2016
Collaborators | 2
School of Physics and Astronomy, University of Glasgow, Glasgow, UK
Zernike Institute for Advanced Materials, University of Groningen, the Netherlands
D. McGrouther, R. J. Lamb, M. Krajnak, S. McFadzean, S. McVitie, R. L. Stamps
M. Mostovoy
IFW Dresden, GermanyA. N. Bogdanov, U. K. Roessler
Dalhousie University, Halifax, CanadaT. Monchesky
Center for Chiral Science, Hiroshima University, JapanY. Togawa, J. Kishine, K. Inoue
Department of Materials Science and Metallurgy, United KingdomJ. Loudon
Department of Physics, University of Hamburg, GermanyGermanyN. Romming, A. Kubetzka, and R. Wiesendanger
Andrey O. Leonov, Spetses, June, 29, 2016
Skyrmion | 3
Possible applicationin spintronics
Multidimensional solitons
Double‐twisted core
Condensationinto the latticeParticle‐like entities
in a continuum
Double twisted core
H
Control and manipulationTopological
in a continuum
manipulation
ChiralityTopologically and
charge
Chirality physically stable
Nanometer scaleThe smallest inhomogeneity
( ) m , – vorticity, - helicity:m
The smallest inhomogeneitysqueezed into the spot
Andrey O. Leonov, Spetses, June, 29, 2016
Why are Skyrmions formed? | 4
1 D aloshinskii Mori a interactions in non centros mmetric cr stals (chiral sk rmions)
Microscopic interactions favoring skyrmions:
1. Dzyaloshinskii-Moriya interactions in non-centrosymmetric crystals (chiral skyrmions)
( ),s sij i jD
1, / 2 / 2m or DJ
2f A D m m m m H H = 0: Helix
D
Andrey O. Leonov, Spetses, June, 29, 2016
“Skyrmionics”
Andrey O. Leonov, Budapest, April, 2015
Why are Skyrmions formed? | 6
Microscopic interactions favoring skyrmions:
JJ SSSS
2. Skyrme mechanism – higher-order derivatives (frustrated achiral skyrmions)
1, [ / 2, / 2]m 2M M2211 nnnn JJ SSSS 1, [ / 2, / 2]m M M
J2>02 21 2
2
( )
. . . u z
f A m A
h o t k m
m m
h m
gradJ2>0
u z
NiGa2S4, a‐NaFeO2, FexNi1xBr2, J1>0NiBr2, FeBr2
Where to look for new skyrmion materials?y
Andrey O. Leonov, Spetses, June, 29, 2016
Outline | 7
Christos Panagopoulos: To balance the scientific program of the meeting, we would appreciate you placing more emphasis on the physics of individual skyrmions.
1. The properties of isolated chiral skyrmions in thin magnetic films
2. Three-dimensional isolated skyrmions with attractive interparticleinteraction
3. Isolated chiral skyrmions with additional surface twists in free-standing layers
4. Isolated frustrated skyrmions, dynamics
Andrey O. Leonov, Spetses, June, 29, 2016
Motivation | 9
- Chiral skyrmions are usually observed in a form of skyrmionic condensates hexagonal lattices and other mesophases (free-standing layers, epitaxial film)g p ( g y , p )
- Isolated skyrmions (not their lattices) are the basic objects in the physics of magnetic skyrmions and are the key elements of all potential applications in spintronics
- SP-STM has been able to identify isolated skyrmions in the saturated state of PdFe/Irfilms and subsequently resolve their internal structure
- We analyze experimental results within the continuum and discrete models and givea consistent description of isolated skyrmions in thin layers
Isolated SkyrmionmesophasesVSskyrmions mesophases
VS
Andrey O. Leonov, Spetses, June, 29, 2016
| 10
New J. of Physics 2016 11
Andrey O. Leonov, Spetses, June, 29, 2016
Bogdanov’s work – Calculus based physics | 11
Spherical coordinates: Cylindrical coordinates:
The equation for isolated skyrmions:
Boundaryconditionsconditions
r
Andrey O. Leonov, Spetses, June, 29, 2016
A. N. Bogdanov, D. A. Yablonskii (1989); A. N. Bogdanov, A. Hubert (1994), (1999).
Solutions for localized skyrmions | 12
Linear cores (arrow-like profiles): Exponential tails:
Andrey O. Leonov, Spetses, June, 29, 2016
Experiment: isolated skyrmions in PdFe/Ir(111) bilayers | 13
The first scenario in a decreased magnetic field
- Neel-type modulations- A uniaxial anisotropy of “easy-axis” type
- Cycloid is the ground state- Enhanced coercitivity prevents py y yp
- Experimental reproduction ofthe magnetization profiles
y pthe formation of skyrmion lattices- unique opportunity to investigate ISin a broad range of applied fields
Andrey O. Leonov, Spetses, June, 29, 2016
Isolated skyrmions - from elongation to collapse | 14
Andrey O. Leonov, Spetses, June, 29, 2016
Repulsion between isolated skyrmions | 15
0 inttotE E E >0 >0
Andrey O. Leonov, Spetses, June, 29, 2016
Evolution of isolated skyrmions into spin spirals | 16Effects observed:- The evolution from IS to spin spirals
( ) k i (2) h d l d l d- (c) a skyrmion (2) has developed an elongated shape
- Due to the repulsive interaction skyrmion labeled (1) p y ( )has jumped to a different position
- (e) edge states in the form of a half-skyrmion (4)
- evolution of the half-skyrmion (4) into the fullskyrmion
- (f) more skyrmions have adopted elongated shapes
- elliptical instability has different values fordifferent skyrmions and strongly depends ondifferent skyrmions and strongly depends onskyrmion-skyrmion interaction, interaction withsample edges and defects
Th l f i i d f t- The role of pinning defects
Andrey O. Leonov, Spetses, June, 29, 2016
| 22Evolution of isolated skyrmions into spin spirals | 17
Niklas RommingAndrey O. Leonov, Spetses, June, 29, 2016
Condensation of repulsive skyrmions into the hexagonal lattice | 18
The second scenario in a decreased magnetic field
0 inttotE E E 0
A. Bogdanov, A. Hubert, J. Magn. Magn. Mat. 138, 255 (1994), 195, 182 (1999); phys. stat. sol. (b) 186, 527 (1994).Andrey O. Leonov, Spetses, June, 29, 2016
| 19
J. of. Phys.: Cond. Matter. 2016 22Can skyrmion particles exist in a vacuum
other than the homogeneous state?
Andrey O. Leonov, Spetses, June, 29, 2016
Motivation | 20
( ) ( ) ( )y z x x z y z x y y x z x y z z y x
DMIm m m m m m m m m m m m
m m( ) ( ) ( )y z x x z y z x y y x z x y z z y x
Cone Spiral and Skyrmions
Andrey O. Leonov, Spetses, June, 29, 2016Is it possible to make skyrmions compatible with the encompassing cone phase?
Skyrmions in the cone phase | 21
The problem of compatibility of isolated skyrmions with the conical phase
Andrey O. Leonov, Spetses, June, 29, 2016
Skyrmions in the cone phase | 22
mx(z), my(z), mz (z) Energy density
Asymmetric skyrmions
Andrey O. Leonov, Spetses, June, 29, 2016
y y
Attraction of isolated skyrmions in the cone phase | 23
Shell
r
Shell
Andrey O. Leonov, Spetses, June, 29, 2016
| 24
Phys Rev Lett 2016 3Phys. Rev. Lett. 2016 3
Andrey O. Leonov, Spetses, June, 29, 2016
Motivation | 25
- 2D monolayers – thin films - bulk magnets- 2D monolayers – thin films - bulk magnets
- Why are skyrmions totally suppressed in bulk, but arisein free standing layers?in free-standing layers?
- Specific stabilization mechanism – chiral surface twists
- New surface phases?
Andrey O. Leonov, Spetses, June, 29, 2016
| 26Chiral Surface Twists
Surface
twists
The reasonfor chiral
storted
mions
for chiralbobbers?
Und
isskyr
ce s
L
Surfac
twists
F. N. Rybakov A. B. Borisov, and A. N. Bogdanov, Phys. Rev. B 87, 094424 (2013); F. N. Rybakov, A. B. Borisov, S. Blügel, and N. S. Kiselev, Phys. Rev. Lett. 115, 117201 371 (2015).
Andrey O. Leonov, Spetses, June, 29, 2016
Chiral Surface Twists - Theory | 27
Model:
- confinement ratio
- twisted modulations
Additional energy due to twisted modulations:
Solutions for skyrmions and helicoids in thin layers of cubic helimagnets are inhomogenousalong the film thickness: their strucure can be thought of as a superposition of common in-plane modulations and specific twisted modulations propagating in the perpendicular direction.
Andrey O. Leonov, Spetses, June, 29, 2016
| 28Chiral Surface Twists - Experiment
- Wedge-shape single crystalFeGe (110)
- Lorentz microscopypy- Observation of phase transitions
between different phases
Andrey O. Leonov, Spetses, June, 29, 2016
Theory VS Experiment | 29
Wedge geometry – FeGe
T=110K
T=250K
The twisted distortions drastically change the energetics of skyrmions and helicoids phases and stabilize them in a broad range of applied magnetic fields
F. N. Rybakov, A. B. Borisov, S. Blügel, and N. S. Kiselev, Phys. Rev. Lett. 115, 117201 371 (2015).
Andrey O. Leonov, Spetses, June, 29, 2016
p g pp g
Domain walls between modulated phases | 30
Andrey O. Leonov, Spetses, June, 29, 2016
| 31
Nat. Commun. 2015
44
Andrey O. Leonov, Spetses, June, 29, 2016
Frustrated triangular magnet | 32
21 2 , ,S S S Si J i J i z u i z
i j i j i iE J J H S K S
, ,i j i j i i
Frustratedskyrmions
Chiralskyrmions
Magnetic bubbles
J2>0y y
sizeJ2 vs J1 J vs D J vs Hd
~ 1nm 5‐100 nm 0.1 ‐1 μm
J1>0 NiGa2S4 ,NiBr2, -NaFeO2
Chiral skyrmions Frustrated skyrmions
vorticity +1 ±1
helicity ±π/2 arbitrary
Task: comprehensive theoretical analysis of the functional in the plane (Ku,H)
T. Okubo et al. Phys. Rev. Lett. 108, 017206 (2012); A. O. Leonov, M. Mostovoy, Nat. Commun. 2015
Andrey O. Leonov, Spetses, June, 29, 2016
| 14Bloch skyrmions
Neel skyrmions
Anti‐skyrmions
Andrey O. Leonov, Budapest, April, 2015Skyrmions with doubled charge
Isolated Skyrmions | 34
A. O. Leonov, M. Mostovoy, Nat. Commun 2015, A. B. Butenko, A. A. Leonov, A. N. Bogdanov, U. K. Roessler, Phys. Rev. B (2010).
Andrey O. Leonov, Spetses, June, 29, 2016
Attraction | 35
2tot skE E U 0
Andrey O. Leonov, Spetses, June, 29, 2016
Inter-skyrmion potential | 36
Andrey O. Leonov, Spetses, June, 29, 2016
Types of edge states | 37
1. the state with parallel in-plane spin components
2. conical spiral state with the in-plane magnetization vector
t ti l th b d
3. fan-like oscillations arounda fixed direction in the xy-
lrotating along the boundary plane.
Andrey O. Leonov, Spetses, June, 29, 2016
Oscillations | 38
- edge states with complex spin structures
- markedly different from those in chiralmagnetsg
- oscillations along the y-coordinate, i.e. in the direction normal to boundarythe direction normal to boundary.
- similar oscillations must bepresent around all magnetic defects inpresent around all magnetic defects in frustrated magnets
Andrey O. Leonov, Spetses, June, 29, 2016
Channeling of frustrated skyrmions | 39
U
The energy of the interaction between skyrmions and edge state in nanostructures‐ The energy of the interaction between skyrmions and edge state in nanostructuresoscillates with y a sequence of edge channels, which run continuously along thesample boundaries strong effect on the skyrmion dynamics in nanostructures
Andrey O. Leonov, Spetses, June, 29, 2016
Current-driven frustrated skyrmions | 40
Andrey O. Leonov, Spetses, June, 29, 2016
Current-driven frustrated skyrmions | 41
- Skyrmions are initially located in the third channel of the edge state 3.
- In general at low applied currents skyrmionsIn general at low applied currents, skyrmionsare confined to an edge channel and move with the "edge state speed“
- At larger currents, skyrmions jump between the channels, shifting closer towards an edge.
-It takes skyrmion a longer time to jumpIt takes skyrmion a longer time to jump between the channels for smaller values of jx
-The velocity peaks correspond to the transitions from one channel to another
Andrey O. Leonov, Spetses, June, 29, 2016
Skyrmion exchange between the edge states | 42
Andrey O. Leonov, Spetses, June, 29, 2016
Skyrmion exchange between the edge states | 43
Andrey O. Leonov, Spetses, June, 29, 2016
| 44Skyrmion filtering
Andrey O. Leonov, Spetses, June, 29, 2016
Conclusions | 45
1. Repulsive isolated skyrmions in bilayers – condensation into the lattice or elliptical instabilityinto the lattice or elliptical instability
A. O. Leonov, T. Monchesky, N. Romming, A. Kubetzka, A. Bogdanov, R. Wiesendanger, New J. of Phys. 2016
2. Attracting isolated skyrmions surrounded by the conical phase
3 Isolated skyrmions with chiral surface twists in thin films
A. O. Leonov, T. Monchesky, J. Loudon, A. Bogdanov, J. of Phys.: Cond. Matt. 2016
3. Isolated skyrmions with chiral surface twists in thin films
A. O. Leonov, Y. Togawa, T. Monchesky, A. Bogdanov et. al., Phys. Rev. Lett. 2016
4. Frustrated skyrmion
A. O. Leonov and M. Mostovoy, Nat. Commun. 2015
Thank you for you attentionAndrey O. Leonov, Spetses, June, 29, 2016
A. O. Leonov and M. Mostovoy, Nat. Commun. 2015