A. de Saint-Exupéry (1943)

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1 Christian Pfleiderer (TU Munich) Emergent Electrodynamics of Skyrmions in Chiral Magnets KITP Fragnets12 Conf 11 Oct 2012 A. de Saint-Exupéry (1943)

2 A. de Saint-Exupéry (1943)

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5 BaCuSi 2O 6 40 T c (ρ, χ) T c,l (Larmor) 30 T 0 (ENS) T TE (Larmor) T (K) FL NFL p (kbar) 60 UGe 2 T (K) 40 FM1 20 FM2 T C T x T * 10 s p (kbar) number total number of f-electron SC C. Pfleiderer RMP 81, 1551 (2009) 10 CePd 2 Si T (K) 6 T N 4 AFM 2 2T s p (kbar) year

6 Why we find MnSi interesting... Nature 442, 797 (2006) Science 323, 915 (2009) PRL 102, (2009) Science 330, 1648 (2010) Nature Physics (2012) T c (ρ, χ) T 0 (ENS) T c,l (Larmor) T TE (Larmor) p=0 T (K) 20 p>p c PRB 81, (2010) 10 FL NFL PRB 55, 8330 (1997) p (kbar) Nature 427, 227 (2004) Nature 414, 427 (2001) Nature Physics 3, 29 (2007) PRL 99, (2007) Science 316, 1871 (2007)

7 MnSi = Manganese Silicon X Manganese Silicide X Manganese Suicide

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11 Emergent Electrodynamics of Skyrmions in Chiral Magnets Christian Pfleiderer Physik-Department E21 - Technische Universität München

12 Collaborations S. Mühlbauer F. Jonietz T. Adams A. Bauer A. Neubauer W. Münzer S. Gottlieb P. Niklowitz 3 M. Janoschek 2 F. Bernlochner J. Kindervater M. Tischendorf G. Brandl S. Dunsiger München R. Ritz T. Schulz M. Halder C. Franz M. Wagner A. Chacon M. Hirschberger 1 F. Birkelbach R. Georgii T. Keller (MPI) W. Häußler P. Link B. Pedersen P. Böni R. Hackl (WMI) Köln K. Everschor M. Garst B. Binz A. Rosch Utrecht R. Duine Lausanne H. Berger Berkeley J. Koralek D. Maier J. Orenstein A. Vishwanath Braunschweig P. Lemmens TOPFIT 1 Princeton 2 Los Alamos 3 London

13 Challenges in Spintronics typical current density A/m 2 animation S. Maekawa example for a Landau-Lifshitz Gilbert equation Berry-phase spin torque precession in effective field damping

14 What about Spin Transfer Torques in Helimagnets? A. Rosch, R. Duine et al. (November 2006) typical current density A/m 2 animation S. Maekawa Bloch wall helimagnetism cf. Goto, et al. condmat/ ; Wessely et al., PRL 96, (2006); both consider j Am -2

15 What about Spin Transfer Torques in Helimagnets? A. Rosch, R. Duine et al. (November 2006) typical current density A/m 2 animation S. Maekawa emergent electrodynamics: current density: 10 6 A/m 2!!! animation A. Rosch

16 Outline A Very Short Introduction to B20 Compounds Exploring Spin Torques with Neutrons Rôle of Emergent Magnetic Field Emergent Electric Field Perspectives & Summary

17 A Very Short Introduction to B20 Compounds

18 B20: no inversion center TM Si,Ge Hierarchical Energy Scales in B20 compounds Landau-Lifshitz vol. 8, 52 (1) ferromagnetism (2) Dzyaloshinsky-Moriya (3) crystal field (P2 1 3): TM Si,Ge locked to <111> or <100> B20: no inversion center left-handed right-handed MnGe 170 Mn1-xFexSi Fe1-xCoxSi < 45 FeGe 280 TN (K) (Å) < 28 Cu2OSeO to to 120 >

19 Fluctuation-Induced First Order Transition a helimagnetic Brazovskii transition FM exchange J a = 11meV DM-interaction D a 2 = J Q a 2 = 1.7meV cubic anisotropy J1 a = 0.37meV (a: lattice constant) MIRA, FRM II M. Janoschek, M. Garst et al. arxiv/ cf. claim of a Bak-Jensen 1 st order transition S. Grigoriev et al., PRB 81, (2010)

20 Helimagnon-Bands as Universal Excitations MnSi one parameter (intensity) simultaneously fits all data Janoschek, Bernlochner, Dunsiger, CP, Böni, Roessli, Link, Rosch, PRB 81, (2010) cf. pump-probe measurements in Fe1-xCoxSi: Koralek et al., arxiv/

21 Magnetic Phase Diagram of MnSi and similar B20 TM compounds conical phase (spin-flop phase) A phase previously unknown helical phase Mühlbauer et al, Science 323, 915 (2009)

22 previous work Neutron Scattering Pattern in the A-Phase MnSi cf. Lebech, Bernhoeft (1993) Grigoriev, et al. (2006) new work = angular variation MIRA, FRM II

23 Fluctuation-Stabilized Multi-q Structure triple-q + uniform m Binz, Vishwanath, Aji PRL (2006) perp. single-q: metastable triple-q: metastable thermal Gaussian fluctuations B paramagnet mean field fluct. G B/B c2 conical A crystal Mühlbauer et al, Science 323, 915 (2009) t

24 Topological Properties of the Rigorous Solution phase btw fundamental modes projection from above φ center: M antiparallel B winding number per unit cell: lattice of topological knots skyrmions Adams et al., PRL 107, (2011)

25 From Hairy Balls to Skyrmion Lattices Werner Heisenberg RMP (1957) Tony Skyrme Nucl. Phys (1962)

26 Exploring Spin Torques with Neutrons

27 for neutron scattering use special trick: temperature temperature

28 Experimental Setup heat sink thermometers Al window temperature

29 temperature current B

30 temperature current B

31 Current Dependence of the Rotation Angle antisymmetric rotation threshold: 10 6 Am -2 temperature at surface kept constant Jonietz et al, Science 330, 1648 (2010)

32 Summary of Experimental Observations rotation for current perpendicular to field no effect for current parallel to applied field no effect in helical state no effect in conical state sense of rotation changes under: inversion of current direction inversion of field direction inversion small T gradient low threshold for rotation: 10 6 Am -2 same behavior for different sample shapes and orientations

33 Rôle of Emergent Magnetic Field

34 Emergent Magnetic Field of Skyrmions Pfleiderer, Rosch Nature (N&V) (2010) conduction electron tracks spin structure: collect Berry phase express as Aharonov-Bohm phase represents effective field trivial topology: Φ =0 non-trivial topology: B eff 2.5T BUT: complex band structure! Binz, Vishwanath Physica B (2008) Neubauer, et al. PRL (2009)

35 Rôle of the Temperature Gradient Pfleiderer, Rosch Nature (N&V) (2010) counter-force to effective Lorentz force T gradient gradient of spin current resulting torque on skyrmion lattice (assumes rigid skyrmion lattice) Jonietz et al, Science 330, 1648 (2010)

36 Proposal of Rotating Skyrmion Lattices in Temperature or Field Gradients restoring force: higher-order spin-orbit cplg. Everschor et al., PRB (2012)

37 Why ultra-low current densities? very efficent gyro-coupling via Berry phase + coupling over entire magnetic domains very weak pinning forces + low defect concentration (RRR>100) + very smooth magnetic texture (200Å) + very stiff magnetic order cf. collective pinning in superconductors

38 consider Landau-Lifshitz-Gilbert equation Berry-phase spin torque precession in effective field damping two types spin currents: (1) difference of spin polarisation of charge currents cf Zhang & Lee PRL (2004) addt l damping, cf Zang et al PRL (2010) (2) gradients in spin orientation: here super-spin current cf charge supercurrents due to phase gradients

39 consider Landau-Lifshitz-Gilbert equation Berry-phase spin torque precession in effective field damping two types spin currents: (1) difference of spin polarisation of charge currents cf Zhang & Lee PRL (2004) addt l damping, cf Zang et al PRL (2010) (2) gradients in spin orientation: here super-spin current cf charge supercurrents due to phase gradients spin current Magnus force

40 consider Landau-Lifshitz-Gilbert equation generalized Thiele approach (project LLG on zero modes) topological winding number gyrocoupling vector dissipative tensor

41 consider Landau-Lifshitz-Gilbert equation generalized Thiele approach (project LLG on zero modes) topological winding number gyrocoupling vector dissipative tensor for Fpin 0 drift and spin-magnus force ~F Magnus / ~ B (~v s ~v d ) ~F Magnus + ~ F fric = 0 no friction: with friction: ~v d = ~v s ~F fric ~v d ~v d 1 ~ B ~vs

42 Emergent Electric Field

43 Emergent Electric Field due to Skyrmion Motion standard 6-terminal,no T-gradient! Schulz et al. Nature Physics (2012)

44 Emergent Electric Field due to Skyrmion Motion Schulz et al. Nature Physics (2012)

45 Emergent Electric Field due to Skyrmion Motion Schulz et al. Nature Physics (2012)

46 Perspectives & Summary

47 Manyala et al, Nature Physics (2004) Magnetic Phase Diagram of B20 Compounds Fe1-xCoxSi x=20% Fe1-xCoxSi x=20% Mühlbauer, et al. Science 323, 915 (2009) Neubauer, et al. PRL (2009) Janoschek, et al. J. Phys. Conf. Series (2010) Münzer, et al. PRB(R) (2010) Adams, et al. J. Phys. Conf. Series (2010) Bauer, et al. PRB(R) (2010) P213 insulators Cu2OSeO3 Seki al., Science (2012) Adams et al., PRL, (2012) illustration from Bos et al. (2008)

48 Real Space Observation with Lorentz Force Microscopy individual skyrmions near room temperature in multiferroics Fe0.5Co0.5Si FeGe Cu2OSeO3 Münzer, et al. PRB(R) (2010) Yu et al., Nature (2010) CP & Rosch, Nature (N&V) (2010) Yu et al., Nat. Mater (2010) Seki al., Science (2012)

49 Summary Skyrmion Lattices in Chiral Magnets» basic phenomonology in MnSi» theoretical account» proof of topology Emergent Electrodynamics» spin torque effects (SANS)» emergent magnetic field» topological Hall effect» emergent electric field