multi-channeltopologicaledgechannel topological edge...

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


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


“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


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


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


| 10

New J. of Physics 2016 11


Bogdanov’s work – Calculus based physics | 11

Spherical coordinates: Cylindrical coordinates:

The equation for isolated skyrmions:

Boundaryconditionsconditions

r


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:


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


Isolated skyrmions - from elongation to collapse | 14


Repulsion between isolated skyrmions | 15

0 inttotE E E >0 >0


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


| 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?


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


Skyrmions in the cone phase | 22

mx(z), my(z), mz (z) Energy density

Asymmetric skyrmions


y y

Attraction of isolated skyrmions in the cone phase | 23

Shell

r

Shell


| 24

Phys Rev Lett 2016 3Phys. Rev. Lett. 2016 3


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?


| 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).


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.


| 28Chiral Surface Twists - Experiment

- Wedge-shape single crystalFeGe (110)

- Lorentz microscopypy- Observation of phase transitions

between different phases


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).


p g pp g

Domain walls between modulated phases | 30


| 31

Nat. Commun. 2015

44


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


| 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).


Attraction | 35

2tot skE E U 0


Inter-skyrmion potential | 36


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.


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


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


Current-driven frustrated skyrmions | 40


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


Skyrmion exchange between the edge states | 42


Skyrmion exchange between the edge states | 43


| 44Skyrmion filtering


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

multi-channeltopologicaledgechannel topological edge...

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