Neutron scattering from Skyrmions in helimagnets. Jonas Kindervater

Transcription

1 Neutron scattering from Skyrmions in helimagnets Jonas Kindervater

2 Collaborations TU München - E21 A. Bauer F. Rucker S. Säubert F. Haslbeck G. Benka P. Schmakat G. Brandl A. Chacon P. Böni C. Pfleiderer TU München - FRM II W. Häußler S. Mühlbauer C. Franz T. Schröder C. Fuchs R. Georgii T. Reimann M. Schulz Los Alamos M. Janoschek TU München - E10 I. Stasinopoulos S. Weichselbaumer D. Grundler EPFL Universität zu Köln A. Rosch M. Garst J. Waizner L. Köhler

3 Skyrmions stereographic projection from sphere to plane: topologically stable object with quantized winding number one flux quantum per skyrmion H S. Mühlbauer et al., Science 323, 915 (2009) P. Milde et al., Science 340, 1076 (2013)

4 Skyrmions: Spin Transfer Torque Current driven domain wall motion figure by S. Maekawa Current Density: ~10 12 A/m 2 Current driven motion of Skyrmions figure by A. Rosch Current Density: ~10 6 A/m 2 F. Jomitz et al., Science 330, 1648 (2010) T. Schulz et al., Nat. Phys. 8, 301 (2012)

5 Experimental Evidence for Skyrmions Small Angle Neutron Scattering (SANS) on bulk samples reciprocal space image MnSi Fe 0.8 Co 0.2 Si S. Mühlbauer et al., Science 323, 915 (2009) T. Adams et al., Phys. Rev. Lett. 107, (2011) W. Münzer et al., Phys. Rev. B 81, (2010)

6 Experimental Evidence for Skyrmions Fe 0.5 Co 0.5 Si FeGe Cu 2 OSeO 3 MFM LF-TEM LF-TEM P. Milde et al., Science 340, 1076 (2013) X. Z. Yu et al., Nature Materials 10, 106 (2011) X. Z. Yu et al., Nature 465, 901 (2010)

7 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding into helical/conical phase Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

8 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding into helical/conical phase Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

9 allows to determine where atoms are Neutron Scattering and what they do! B. N. Brockhouse C. G. Shull Nobel Prize 1994

10 Elastic Vs. Inelastic Scattering Elastic scattering Inelastic scattering Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

11 Neutron Sources Fission Spallation FRM II, Germany SNS, USA ILL, France ESS, Sweden

12 Properties of neutrons no charge no measurable dipole moment spin-1/2 particle -> magnetic moment wavelength ~ interatomic distances energy ~ energy of excitations in solids 0.5Å < λ < 30Å 300meV < λ < 0.1meV Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

13 Interaction with matter Electrons electrostatic interaction with e - strong interaction small penetration depth X-rays electromagnetic interaction with e - strong interaction small penetration depth Neutrons interaction with nuclei short range magnetic dipole-dipole interaction between neutron and unpaired e - not short range large penetration depth Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

14 Interaction with matter Electrons electrostatic interaction with e - strong interaction small penetration depth X-rays electromagnetic interaction with e - strong interaction small penetration depth Neutrons interaction with nuclei short range magnetic dipole-dipole interaction between neutron and unpaired e - not short range large penetration depth electrons X-rays neutrons Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

15 Neutrons: Pros / Cons Advantages: penetrating: bulk properties penetrating: extreme sample environments isotope sensitive Disadvantages: kinematic restrictions (can t access all energy & momentum transfers) weak scattering only weak sources magnetic interaction unique magnetic interaction very powerful in magnetism signal limited technique

16 Nuclear Interaction short range (~fm) Fermi pseudopotential isotope dependent (random in Z) depends on spin state of nucleus scattering length: b j σ = 4πb 2 b j NIST Annual report 2003, Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

17 Nuclear Scattering Coherent scattering elastic coherent scattering: positions of atoms inelastic coherent scattering: collective excitations, i.e. phonons, magnons Incoherent scattering elastic incoherent scattering: background inelastic incoherent scattering: self-correlation, i.e. diffusion processes Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

18 Magnetic Interaction with unpaired electrons dipole-dipole interaction weak Formfactor spin dependent Dipole interaction V m r = γμ N σ M(r) γμ N : strenght of neutron s magnetic moment σ: direction of neutron s spin M(r): magnetic moment of the sample

19 Magnetic Scattering form factor selection rule FT of van Hove s spin pair correlation function Magnetic diffraction measures the Fourier transform of magnetization density

20 source Neutron Scattering neutron initial state Neutron final state interaction sample detector

21 Neutron Scattering source Initial state: neutron initial state Neutron final state interaction sample detector speed direction spin state

22 source Initial state: speed direction spin state Neutron Scattering neutron initial state Neutron final state interaction sample Sample state: cryostat magnetic field orientation detector

23 source Initial state: speed direction spin state Neutron Scattering neutron initial state Neutron final state interaction sample Sample state: cryostat magnetic field orientation detector final state: speed: direction Spin state detection

24 Elastic Scattering on Skyrmions How to investigate the structue of Skyrmions? magnetic lattice d ~ 200Å Stabalized in magnetic field Elastic scattering Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

25 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding into helical/conical phase Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

26 Small angle neutron scattering Large scales in real space Å Low Q, small scattering angles 0.54 Å Å -1 collimation detector tube Typical Applications: Soft matter: structure of proteins, polymers, viruses Magnetism: superconducting vortices, Skyrmions Material science: Mg hydrides for hydrogen storage,

27 MLZ neutron guide MLZ, Garching Germany

28 MLZ Sample position Minimize flight path in air allow multiple sample environments Velocity selector rpm max. Detector tube: Vacuum vessel to reduce background Sample detector distance 1-40m He-3 position sensitive detector 1m 2 interior covered with Cadmium

29 Fluctuations of the Skyrmion lattice How to investigate fluctuations of the Skyrmion lattice? magnetic lattice d ~ 200Å Stabalized in magnetic field High energy resolution! Inelastic scattering Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

30 Fluctuations of the Skyrmion lattice How to investigate fluctuations of the Skyrmion lattice? magnetic lattice d ~ 200Å Stabalized in magnetic field High energy resolution! Inelastic scattering Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

31 Fluctuations of the Skyrmion lattice How to investigate fluctuations of the Skyrmion lattice? magnetic lattice d ~ 200Å Stabalized in magnetic field High energy resolution! Inelastic scattering Roger Pynn, Neutron scattering: a primer Los Alamos Science (1990)

32 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

33 Larmor precession Magnetic moment of neutron precesses with the Larmor frequency

34 Neutron Spin Echo invented by F. Mezei in 1972 highest energy resolution among all neutron spectroscopic techniques

35 Neutron Spin Echo invented by F. Mezei in 1972 highest energy resolution among all neutron spectroscopic techniques

36 Neutron Resonance Spin Echo invented by R. Golub & R. Gähler in 1992 Exchange contant field by constant + rf-field allows adjust the resolution according to Dispersion in inelastic measurements

37 MIEZE invented by R. Gähler independent from Neutron beam polarization at sample position allows measurements under depolarizing conditions at the sample

38 MIEZE in strong magnetic fields 5 T Magnet (SANS-1) 17 T Magnet (B ham, UK) J. Kindervater et al. EPJ Web of Conf. 83, (2015)

39 RESEDA REsonance Spin Echo for Diverse Applications NSE/NRSE MIEZE Dynamic range τ = ns E = 2meV 0.02μeV Q max = 2.5 Å -1 (at λ = 3 Å)

40 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

41 Skyrmions in cubic chiral magnets

42 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

43 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

44 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

45 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

46 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

47 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

48 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

49 Skyrmions in cubic chiral magnets Hierarchy of energy scales: ferromagnetic exchange Dzyaloshinskii-Moriya cubic anisotropies

50 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding into helical/conical phase Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

51 Magnetic phase diagram of Fe 1-x Co x Si P. Milde et al., Science 340, 1076 (2013)

52 Topological unwinding in Fe 1-x Co x Si Skyrmion lattice state non-trivial topology emergent magnetic flux 1 flux quantum 1 flux quantum Decreasing field sources/sinks of emergent B-field quantized magnetic charge magnetic (anti-) monopole 1 flux quantum hedgehog defect Helical state trivial topology no emergent magnetic flux 1 flux quantum P. Milde et al., Science 340, 1076 (2013)

53 Topological unwinding in Fe 1-x Co x Si Skyrmion lattice state non-trivial topology emergent magnetic flux 1 flux quantum 1 flux quantum sources/sinks of emergent B-field quantized magnetic charge magnetic (anti-) monopole 1 flux quantum hedgehog defect Helical state trivial topology no emergent magnetic flux 1 flux quantum P. Milde et al., Science 340, 1076 (2013)

54 Outline (1) Introduction to Neutron Scattering Neutron scattering Small angle neutron scattering Neutron Spin Echo (2) Skyrmions in cubic chiral magnets Introduction Topological unwinding into helical/conical phase Field induced tricritical point in MnSi Skyrmionic textures in the paramagnetic phase (3) Conclusion

55 Brazovskii scenario in MnSi Unpolarized SANS: M. Janoschek et al. Phys. Rev. B 87, (2013) A. Bauer et al., Phys. Rev. Lett. 110, (2013)

56 Brazovskii scenario in MnSi Polarized SANS: J. Kindervater et al., Phys. Rev. B 89, (R) (2014) M. Janoschek et al. Phys. Rev. B 87, (2013) A. Bauer et al., Phys. Rev. Lett. 110, (2013)

57 1 st -order Field-induced tricritical point

58 Field-induced tricritical point helical paramagnetic B = 0): 1 st -order Brazovskii transition 1 st -order 1 st -order

59 Field-induced tricritical point 2 nd -order helical paramagnetic (@ B = 0): 1 st -order Brazovskii transition conical field polarized (@ T = 0): 2 nd -order transition 1 st -order 1 st -order

60 Field-induced tricritical point 2 nd -order TCP helical paramagnetic (@ B = 0): 1 st -order Brazovskii transition conical field polarized (@ T = 0): 2 nd -order transition 1 st -order 1 st -order character of the phase transition has to change field-induced tricritical point

61 Field-induced tricritical point small fields: symmetric δ-spike (1 st order) intermediate fields: two peaks (1 st order, skyrmion lattice) higher fields: asymmetric λ-anomaly (2 nd order) A. Bauer et al., Phys. Rev. Lett. 110, (2013)

62 Thank you for your attention.