a phenomenological account Wednesday: vortices Friday: skyrmions - PowerPoint PPT Presentation

Topology in Magnetism – a phenomenological account Wednesday: vortices Friday: skyrmions Henrik Moodysson Rønnow Laboratory for Quantum Magnetism (LQM), Institute of Physics, EPFL Switzerland Thanks to Jiadong Zang and Shinichiro Seki for slides, many figures copied from internet Ronnow – ESM Cargese 2017 Slide 1

Skyrmions in Magnetism • Skyrmions – Topological solitons – 3-Q magnetic structure – Models • Skyrmion measurements – SANS, LTEM, STXM, MFM, SPSTM • Skyrmion materials – Bulk materials: Chiral, Polar, Frustrated – Interface systems • Skyrmion fundamentals – Skyrmion types, Lattice effects, dynamics, … • Skyrmion control Ronnow – ESM Cargese 2017 Slide 2

The hairy ball theorem • "you can't comb a hairy ball flat without creating a cowlick“ • Topology concern non-local properties ! Ronnow – ESM Cargese 2017 Slide 3

Stereographic projection Ronnow – ESM Cargese 2017 Slide 4

Topological charge Q=0 Q=1 Q=2 Ronnow – ESM Cargese 2017 Slide 5

Magnetic order - Against all odds • Bohr – van Leeuwen theorem: (cf Kenzelmann yesterday) – No FM from classical electrons • <M>=0 in equilibrium (cf Canals yesterday) • Mermin – Wagner theorem: – No order at T>0 from continuous symmetry in D  2 • No order even at T=0 in 1D Ronnow – ESM Cargese 2017 Slide 6

ǁ Derrick’s Scaling Argument: No stable local texture 𝐹[𝐧] = න 𝛼𝐧 2 + 𝑔 𝐧 𝑒 3 𝑠 ≡ 𝐽 1 + 𝐽 2 𝐧 𝟏 (𝐬) 𝐧 𝟏 (𝜇𝐬) Assume existence of stable Local Texture Scale size of texture 𝐹[𝐧 0 (𝜇𝐬) ] 𝑠 = 𝜇𝑠 𝜇 = 1 is minimized at 2 𝐹[𝐧 0 (𝜇𝐬) ] = ඲ 1 + 1 𝑒 3 ǁ ෨ 𝐽 2 𝜇 3 Τ Τ = 𝐽 1 𝜇 + 𝛼 𝐧 𝜇 3 𝑔 𝐧 𝑠 𝜇 Ways out: 𝑒𝐹 𝑒𝜇 ቚ 𝜇=1 = 0 Dzyaloshinskii-Moriya 𝐽 1 = ∫ 𝛼𝐧 2 < 0 Interaction 𝑒 2 𝐹 𝑒𝜇 2 ቚ 𝜇=1 > 0 Finite Size 7 Ronnow – ESM Cargese 2017 Slide 7

“spin vortices” as local solitonic solution to continuum model Skyrmion lattice of individual skyrmions  3-Q magnetic structure Ronnow – ESM Cargese 2017 Slide 8

Broken Inversion Symmetry Inversion Physical Consequence:     +   S S H J D ( S S ) i j ij i j   ij Dzyaloshinskii-Moriya Interaction (DMI) θ θ ~ D/2J 9 Ronnow – ESM Cargese 2017 Slide 9

Model  • Microscopic       S S D S S H J ( ) i j ij i j   ij Sum over all bonds  • Coarse grained       H J S S D ( S S ) i j ij i j   simple cube ij Sum over neighboring unit cells • Continuum version Ronnow – ESM Cargese 2017 Slide 10

Dzyaloshinskii-Moriya helices H = - Ʃ J ij S i ·S j + D ij ·(S i ×S j ) J favors parallel spins J>0 Ferromagnet J<0 Antiferromagnet D favor perpendicular spins J & D: twist spins by angle tanƟ = D/J Helix with period Q = 2  a J/D Ronnow – ESM Cargese 2017 Slide 11

3Q structure • Superpose 3 helices: Looks like “spin vortices” Ronnow – ESM Cargese 2017 Slide 13

Helical, conical and “A - phase” 1993 Ronnow – ESM Cargese 2017 Slide 14

“for the theoretical prediction, the experimental discovery and the theoretical analysis of a magnetic skyrmion phase in MnSi , a new state of matter.” Ronnow – ESM Cargese 2017 Slide 18

Many networks developing: Interdisciplinary network with 12 project partners from EPFL, University of Basel and Paul Scherrer Institut (PSI) Funded by SNSF via grant CRSII5_171003 Ronnow – ESM Cargese 2017 Slide 19

Skyrmions in Magnetism • Skyrmions – Topological solitons – 3-Q magnetic structure – Models • Skyrmion measurements – SANS, LTEM, STXM, MFM, SPSTM • Skyrmion materials – Bulk materials: Chiral, Polar, Frustrated – Interface systems • Skyrmion fundamentals – Skyrmion types, Lattice effects, dynamics, … • Skyrmion control Ronnow – ESM Cargese 2017 Slide 20

Skyrmion measurements SASXRS Small angle Soft X-ray Resonant Scattering • SANS Small Angle Neutron Scattering Ronnow – ESM Cargese 2017 Slide 21

Skyrmion measurements • Magnetic contrast transmission electron microscopy (LTEM) • Sensitive to in-plane magnetization components • TIE Transfer of intensity: recover phase • Electron holography: towards 3D imaging of magnetic textures Ronnow – ESM Cargese 2017 Slide 22

Skyrmion measurements • Scanning Tunneling X-ray Microscopy • Magnetic Force Microscopy • Spin Polarized STM Ronnow – ESM Cargese 2017 Slide 23

Skyrmion measurements Transport effects Hall effect  B Anomalous Hall  M Topological Hall  Q Ronnow – ESM Cargese 2017 Slide 24

Skyrmion spectroscopy • Seki et al. Ronnow – ESM Cargese 2017 Slide 25

Skyrmion hosts • Interface or “ABCABC” • Chiral and Polar bulk materials multilayer of FM and high-Z compounds • Pfleiderer • Albert Fert • Tokura, Seki • Stuart S Parkin • Keszmarki • Manny others… • Many others… Ronnow – ESM Cargese 2017 Slide 26

Skyrmions in fabricated interfaces/multilayers Ronnow – ESM Cargese 2017 Slide 27

Skyrmions and magnetic bubbles • In plate-geometry bubbles are stabilized by dipole fields • Hot topic in 1980’s • Reached commercial products, but not competitive MnSi Intel 1Mbit bubble memory Ronnow – ESM Cargese 2017 Slide 28

Current Driven Skyrmions (movies Eric Fullerton) 50 µm -1.2 Oe Ronnow – ESM Cargese 2017 Slide 29

Moving Skyrmions Logic Gates Racetrack Memory Ronnow – ESM Cargese 2017 Slide 30

• Skyrmions move in small currents • Race- track memory… Ronnow – ESM Cargese 2017 Slide 31

Skyrmion materials: Bulk materials Material SG Ordering Helimag. Transport Skyrmion SkL References Temp Period property motion Dimensi on j c ~10 6 A.m -2 S. Mühlbauer et al. , Science 323 , 915 (2009) MnSi P 2 1 3 30 K 18 nm Metallic 2D F. Jonietz et al. , Science 330 , 1648 (2010) M. Mochizuki et al. , Nat. Mater. 13 , 241 D T (2014) j c <10 6 A.m -2 X.Z. Yu et al. , Nat. Mater. 10 , 106 (2010) FeGe P 2 1 3 280 K 70 nm Metallic 2D X.Z. Yu et al. , Nat. Comm. 3 , 988 (2012) 11 – 36 K W. Münzer et al. , PRB 81 , 041203(R) (2010) Fe 1-x Co x Si P 2 1 3 40-230 nm Metal / 2D X.Z. Yu et al. , Nature 465 , 901 (2010) semi- conductor S.V. Grigoriev et al., PRB 79, 144417 (2009) Mn 1-x Fe x Si P 2 1 3 7-16.5 K 10-12 nm Metallic 2D K. Shibata et al., Nature Nano. 8, 723 (2013) Mn 1-x Fe x Ge P 2 1 3 150-220 5 - 220 nm Metallic 2D K Y. Tokunaga et al., Nat. Com. 6, 7638 (2015) Co x Zn y Mn z P4 1 32 140-480K 110-190nm Metallic 2D GaV 4 S 8 C 3v 13 K 22nm Semi- 2D conductor anisotrop D T Cu 2 OSeO 3 P 2 1 3 58 K 50 nm Insulating 2D S. Seki et al. , Science 336, 198 (2012) T. Adams et al ., PRL 108 , 237204 (2012) Magneto- M. Mochizuki et al. , Nat Mat 13 , 241 (2014) E <10 5 V/m electric N. Kanazawa et al ., PRL 106 , 156603 (2011) MnGe P 2 1 3 170 K 3 nm Metallic 3D? N. Kanazawa et al ., PRB 86 , 134425 (2012) Ronnow – ESM Cargese 2017 Slide 32

Bulk systems have more stable skyrmions • Large sample  100000 skyrmions resolved (Cu 2 OSeO 3 ) • Allows quantitative analyses, such as delauney triangulation Ronnow – ESM Cargese 2017 Slide 33

Defects and angles • Defects classifiable – eg a 5-7 or a 5-8-5 defect – “loss” of row along 2 directions or peak in “local Fourrier ” Map SkL angle: – Defects creates far-stretching rotations – Model system for understanding lattice defects Ronnow – ESM Cargese 2017 Slide 34

Skyrmions as arena for real-space imaging of phase transitions c b a Ronnow – ESM Cargese 2017 Slide 35

The 3 rd dimension – how protected? Ronnow – ESM Cargese 2017 Slide 36

White Karube Tokunaga Ronnow – ESM Cargese 2017 Slide 37

Metastability could come from topological protection ? Ronnow – ESM Cargese 2017 Slide 38

Square lattice ? Ronnow – ESM Cargese 2017 Slide 39

Topological protection + D/J(T) => long skyrmions • Consequence: – Relationship helical domains / elongated skyrmions – Edges of helical domains carry half-skyrmions = merons – Crossing phase transition can pump skyrmions Ronnow – ESM Cargese 2017 Slide 40

Skyrmion hosting insulator Cu 2 OSeO 3 Crystal structure, P 2 1 3, no inversion symmetry ‘Generic’ magnetic phase diagram + SkL phase Cubic unit cell contain 16 Cu2+ S=1/2 4 tetrahedral forming “3 -up-1- down” S=1 Combined to single S=4 in skyrmion simulations S. Seki et al. , Science 336, 198 (2012) S. Seki et al. , Phys. Rev. B 86, 060403(R) (2012) Ronnow – ESM Cargese 2017 Slide 41

Can create skyrmions with electric field A. Kruchkov, arxiv 1702.08863 & 1703.06081, to be submitted soon… Ronnow – ESM Cargese 2017 Slide 42

Identification of skyrmions in image data – easy if complete skyrmion phase pre-treatments dynamical box algorithm manual revisions • aligning • scanning by a box • adding and/or • Area • finding local minima removing • Delaunay triangulation selection • overlapping minima with • filtering • interactive programs centers raw data identification triangulation LoG filtered 43 Ronnow – ESM Cargese 2017 Slide 43