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Emergence, Stability and Decay of Skyrmions in Chiral Magnets

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Emergence, Stability and Decay of Skyrmions in Chiral Magnets animation C. Schütte Emergence, Stability and Decay of Skyrmions in Chiral Magnets Christian Pfleiderer Physik-Department Technische Universität München Vortices in Daily Life... Kelvin‘s Vortex Model of Atoms Lord Kelvin William Thomson perhaps the first suggestion of (1824-1907) „topological solitons“ Towards a Unified Field Theory key idea: Are bosons non-linear excitations of fermion fields? (Are bosons topological solitons of fermion fields?) Werner Heisenberg (1901-1976) NP 1932 RMP 29 296 (1957) From Tony Hilton Royle Skyrme to Skyrmions key idea: Are fermions non-linear excitations of boson fields? (Are fermions topological solitons of boson fields? winding number → baryon number) Tony Skyrme (1922-1987) Proc. Royal Society London, Series A 260, 130 (1961) Proc. Royal Society London, Series A 262, 237 (1961) Nuclear Physics 31 556 (1962) From Tony Hilton Royle Skyrme to Skyrmions Tony Skyrme (1922-1987) Proc. Royal Society London, Series A 260, 130 (1961) Proc. Royal Society London, Series A 262, 237 (1961) Nuclear Physics 31 556 (1962) from Wikipedia winding number: +2 from Wikipedia On the Winding Number in Spin Systems On the Winding Number in Spin Systems real space OP space On the Winding Number in Spin Systems plot M. Rahn Winding in Two-Dimensional OP-Space skyrmion (trivial) vortex Discovery of the Skyrmion citations per year 250 PRSL - Ser. A 260, 130 (1961) PRSL - Ser. A 262, 237 (1961) Nuclear Physics 31 556 (1962) ISI: >3006 citations (170 before ’83) 0 1962 1983 2011 „Static properties of nucleons in the Skyrme model“ Adkins, Nappi, Witten, Nucl. Phys. B 228 552 (1983) ISI: 1484 citations Ed Witten (ISI 68.800; h=124) 1994 2010 Magnetic Phase Diagram of MnSi (spin-flop phase) Mühlbauer, et al. Science 323, 915 (2009) Neubauer, et al. PRL 102 186602 (2009) Magnetic Phase Diagram of B20 Compounds Fe1-xCoxSi x=20% Fe1-xCoxSi x=20% Manyala et al, Nature Physics(2004) P213 insulators Mühlbauer, et al. Science 323, 915 (2009) Cu2OSeO3 Neubauer, et al. PRL 102 186602 (2009) Münzer, et al. PRB(R) 81 041203 (2010) Seki al., Science 336 198 (2012) Adams, et al. J. Phys. Conf. Series (2010) Adams et al., PRL, 108 237204 (2012) Bauer, et al. PRB(R) 82 064404 (2010) illustration from Bos et al. (2008) Real Space Observation with Lorentz Force Microscopy at room temperature semiconductor insulator FeGe Fe0.5Co0.5Si Cu2OSeO3 Münzer, et al. PRB(R) 81 041203 (2010) Yu et al., Nature 465 901 (2010) Yu et al., Nat. Mater. 10 106 (2010) Seki al., Science 336 198 (2012) CP & Rosch, Nature (N&V) 465 880 (2010) Adams et al., PRL, 108 237204 (2012) Outline ● Introductory Remarks on Skyrmions ● Emergence of Skyrmions in Chiral Magnets ➢ Fluctuation-Induced First Order Transition ➢ Magnetic Phase Diagram ➢ Nature of the A-Phase ➢ Poor Man‘s Probe of Topology ● Topological Unwinding of Skyrmions ● Formation of a Topological Non-Fermi Liquid (?) ➢ Non-Fermi Liquid Puzze in MnSi ➢ Hall Effect under Pressure ● List of Untold Stories Challenges in NotSpintronics in this talk typical current density 1012 A/m2 animation S. Maekawa Emergent Electrodynamics of Skyrmions current density: 106 A/m2 !!! Jonietz et al, Science 330, 1648 (2010) Schulz et al. Nature Physics 8 301 (2012) Everschor et al., PRB 86 054432 (2012) animation A. Rosch Collaborations samples bulk properties neutron scattering A. Bauer R. Ritz T. Adams S. Mühlbauer A. Neubauer C. Schnarr A. Chacon R. Georgii W. Münzer M. Halder J. Kindervater W. Häußler S. Gottlieb C. Franz G. Brandl P. Link M. Wagner B. Pedersen F. Rucker S. Dunsiger T. Keller (MPI) M. Janoschek2 P. Böni M. Hirschberger1 F. Jonietz P. Niklowitz3 F. Bernlochner T. Schulz4 A. Tischendorf M. Rahn5 F. Birkelbach 1Princeton 3London TOPFIT 2Los Alamos 4Mainz 5Oxford Collaborations Köln Berkeley Dresden R. Bamler J. Koralek P. Milde S. Buhrandt D. Maier D. Köhler J. Waizner J. Orenstein J. Seidel C. Schütte A. Vishwanath L. Eng K. Everschor M. Garst Lausanne München B. Binz H. Berger T. Schwarze A. Rosch D. Grundler Braunschweig Utrecht R. Hackl (WMI) P. Lemmens R. Duine TOPFIT Hierarchical Energy Scales in B20 Compounds and the Fluctuation-Induced First Order Transition Hierarchical Energy Scales in B20 compounds Landau-Lifshitz vol. 8, §52 (1) ferromagnetism (2) Dzyaloshinsky-Moriya (3) crystal field (P213): Si,Ge Si,Ge locked to <111> or <100> TM TM B20: no inversion center center inversion no B20: TN (K) (Å) MnGe 170 30 to 60 Mn1-xFexSi < 28 180 to 120 Fe1-xCoxSi < 45 > 300 FeGe 280 700 left-handed right-handed Cu2OSeO3 54 620 Breakthrough for „Itinerant Spin Fluctuations“ @RESEDA (FRM II) @RESEDA MnSi Ishikawa et al PRB (1985) Lonzarich JMMM 45 43 (1984) Lonzarich, Taileffer. J. Phys. Cond. Matter 18 4339 (1985) Prediction of a Spontaneous Skyrmion Phase claim of a skyrmion liquid Pappas et al., PRL 102, 197202 (2009) Rößler, Bogdanov, CP, Nature 442, 797 (2006) cf Hamann et al., PRL 107, 037207 (2011) Fluctuation-Induced First Order Transition a helimagnetic Brazovskii transition FM exchange J a = 11meV DM-interaction D a2 = J Q a2 = 1.7meV cubic anisotropy J1 a = 0.37meV (a: lattice constant) experiments @ MIRA, FRM II cf. claim of a Bak-Jensen M. Janoschek, M. Garst et al. 1st order transition arXiv/1205.4780 S. Grigoriev et al., PRB 81, 144413 (2010) Fluctuation-Induced First Order Transition a helimagnetic Brazovskii transition M. Janoschek, M. Garst et al. arXiv/1205.4780 Magnetic Phase Diagram of B20 Compounds Magnetic Phase Diagram of B20 Compounds mostly a spin-flop phase (spin-flop phase) B Ishikawa & Arai JPSJ 53, 2726 (1984) spin-flop T Magnetic Phase Diagram of B20 Compounds (spin-flop phase) Ishikawa & Arai JPSJ 53, 2726 (1984) ???? helical phase Kadowaki JPSJ 51, 2433 (1982) Magnetic Phase Diagram of B20 Compounds (spin-flop phase) Ishikawa & Arai JPSJ 53, 2726 (1984) Wilhelm et al., PRL 107, 127203 (2011) purly based on ac susceptibility @ 1 kHz ill-defined sample shape Magnetic Phase Diagram of B20 Compounds (spin-flop phase) Ishikawa & Arai JPSJ 53, 2726 (1984) ???? helical phase Kadowaki JPSJ 51, 2433 (1982) Magnetic Phase Diagram of B20 Compounds (spin-flop phase) Ishikawa & Arai JPSJ 53, 2726 (1984) Kadowaki JPSJ 51, 2433 (1982) Magnetic Phase Diagram of MnSi Revisited Brazovskii regime Bauer, CP, PRB 85, 214418 (2013) Specific Heat of MnSi T B (mT) 3.5 MnSi c B || <110> 0 ) 1 - +10 K 1 - 3.0 l 120 o T A1 +5 m J 2.5 ( 250 C T +10 2.0 2 700 26 27 28 29 30 31 32 T (K) Bauer, Garst, CP, PRL 110, 177207 (2013) Specific Heat of MnSi first order transition ) 100 T 2 (a) 0 mT (b) 50 mT (c) 100 mT (d) T 120 mT (e) 140 mT (f) 145 mT - T c c T c T c K T c c 1 - l o m J 80 m ( T / l e 60 C ) 100 2 (g) 155 mT (h) 165 mT (i) 180 mT (j) 210 mT (k) 220 mT (l) 230 mT - T T A2 T K T T T A2 c 1 - A2 A2 A2 l o T A1 m T A1 J 80 T m A1 ( T T A1 A1 T / l e 60 C ) 100 ) 2 (m) 280 mT (n) 340 mT (o) 370 mT (p) 390 mT (q) 410 mT (r) 430 mT 2 (s) - - 70 410 mT K K 1 1 - T - l c l o T o m m c T J 80 c J 60 T m c m ( T ( c T T / T / l c l e 60 e 50 570 mT C C 28 29 30 28 29 30 28 29 30 28 29 30 28 29 30 28 29 30 26 28 30 T (K) T (K) T (K) T (K) T (K) T (K) T ( K) second order transition Bauer, Garst, CP, PRL 110, 177207 (2013) Magnetic Phase Diagram of MnSi Revisited MnSi, B || <110> (a) B (a) C(T) Re Im c1 χac χac ) ΔS 0.5 1 tot - 6 0.4 K TCP 1 - ΔS FM l A2 0.4 ) o ) 0.3 TCP C T S m Δ ( T 4 A1 0.3 ( t J n i B m 0.2 B ( 0.2 S B S 2 A1 VI Δ 0.1 B 0.1 A2 H FD PM 0 0 0 0 0.1 0.2 0.3 0.4 0.5 27 28 29 30 31 32 B (T) T ( K) (b) (b) TCP ) ΔS 0.4 1 tot - 5 K C 0.3 1 - ΔS l 4 A2 0.3 ) o ) T S ( m Δ T A1 0.2 ( 3 t J n 0.2 S i B m B B ( A1 2 S 0.1 0.1 Δ 1 B A2 H FD 0 0 0 0.12 0.16 0.20 0.24 28.0 28.5 29.0 B (T) T (K) Bauer, Garst, CP, PRL 110, 177207 (2013) Nature of the A-Phase Neutron Scattering Pattern in the A-Phase previous work cf. Lebech, Bernhoeft (1993) Grigoriev, et al. (2006) new work Mühlbauer et al, Science 323, 915 (2009) Very Weak Pinning to Crystal Lattice: Neutrons all measurements at MIRA (FRM II) (110) (111) (110) (100) dependence on orientation Stabilization through anisotropy? = Bogdanov & Yablonskii JETP 68 101 (1989) spin order not sensitive to orientation! MnSi measurements @ MIRA, FRM II Fluctuation-Stabilized Multi-q Structure triple-q + uniform M Binz, Vishwanath, Aji PRL (2006) perp. single-q: metastable triple-q: metastable Mühlbauer, et al. Science 323, 915 (2009) Monte-Carlo (includes fluctuations) B=0 Buhrandt & Fritz, arXiv/1304.6580 Fluctuation-Stabilized Multi-q Structure triple-q + uniform M Binz, Vishwanath, Aji PRL (2006) perp.
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