Heusler compounds: Tunable materials with non trivial topologies. Claudia Felser

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1 Heusler compounds: Tunable materials with non trivial topologies Claudia Felser

2 Tunability of Heusler compounds Tuning the band gap Tuning spin orbit coupling Trivial and topological Heusler Adding spins half metals,magnetic semiconductors Weyl semimetals Localized and delocalized spins Tuning the magnetic sublattices ferro to ferri: Compensated ferrimagnets Centro and non-centro symmetric Weyl Adding anisotropy lattice distortion via van Hove and Jahn Teller In and out of plane magnetization Non collinear spin structures and frustration Dzyaloshinskii-Moriya Berry phase in antiferromagnets Skyrmions

3 Predicting topological insulators ScNiSb LaPtBi LaPtBi S. Chadov et al., Nat. Mater (2010). H. Lin et al., Nat. Mater (2010).

4 REPtBi multifunctional topologic insulators Multifunctional properties RE: La, Er Superconductivity and TI RE: Gd Magnetism and TI RE: Ce Antiferromagnetism with GdPtBi complex behaviour of the Fermi surface RE: Yb Kondo insulator and TI YbPtBi is a super heavy fermion with the highest g value Pt RE Bi (+f n ) + 5 = 18 S. Chadov et al., Nat. Mater. 9, 541 (2010). H. Lin et al., Nat. Mater. 9, 546 (2010).

5 Weyl semimetals

6 Weyl semimetals We need time reversal symmetry breaking (Dirac points are at high symmetry points Weyl points are not at high symmetry points) - Structural distortion - Application of magnetic field or magnetism 3D topological Weyl semimetals - breaking Time reversal symmetry by transport 1. Intrinsic anomalous Hall effect 2. Chiral anomaly S. L. Adler, Phys. Rev. 177, 2426 (1969) J. S. Bell and R. Jackiw, Nuovo Cim. A60, 47 (1969) AA Zyuzin, AA Burkov - Physical Review B (2012) AA Burkov, L Balents, PRL (2012)

7 GdPtBi is magnetic D M (µ B /f.u.) µ 0 H (T) [110] B ll B ll [111] 1.4K 15 K, B ll [111] 100 K, B ll [111] GdPtBi is an Antiferromagnet below 10 K However it is very soft and the spins can be tuned in a magnetic field µ 0 H (T) C. Shekhar et al., arxiv: , (2016).

8 Weyl GdPtBi in a magnetic field C. Shekhar et al., arxiv: , (2016). M. Hirschberger et al.,. Nature Mat. Online arxiv: , (2016).

9 GdPtBi Anomalous Hall Effect In ferromagnets an AHE scales with the magnetic moment Antiferromagnet show no AHE A Hall angle of 0.2 is exceptional 1 would be the Quantum AHE T. Suzuki, & J. G. Checkelsky Nature Physics (2016) doi: /nphys3831 Shekhar et al., arxiv: , (2016)

10 Chiral Anomaly neg. quadratic MR C. Shekhar et al., arxiv: , (2016). M. Hirschberger et al. Nature Mat. online, arxiv: , (2016).

11 Magnetic Heusler compounds with and without inversion L2 1 Co 2 MnAl space group 225 (Fm3"m) Mn 2 CoAl X space group 216 (F4"3m)

12 Weyl Semimetals Breaking symmetry E with Inversion symmetry Breaking time reversal symmetry E without k Magnetic field k

13 Magnetic Heusler compounds with and without inversion 26 Valence electrons Zhijun Wang, et al., arxiv: Guoqing Chang et al., arxiv: Barth et al. PRB 81, Ouardi et al., Phys. Rev. Lett. 110 (2013)

14 Magnetic Weyl semimetals in a magnetic field

15 Kübler, Felser, PRB 85 (2012) AHE in half metallic ferromagnets

16 AHE in half metallic ferromagnets Giant AHE in Co 2 MnAl s s xy xy = 1800 S/cm» 2000 S/cm calc. meas. Kübler, Felser, PRB 85 (2012) Vidal et al. APL. 99 (2011) Kübler, Felser, EPL 114 (2016) Weyl points are the origin for a large Berry phase and a Giant AHE

17 I4/mmm (D0 22 ) Structural distortion Fm3m (L2 1 ) P6 3 /mmc (D0 19 ) tetragonal cubic hexagonal Out of plane M STT-RAM Permanent magnets Compensated ferrimagnets Permament magnets Non-collinear magnetism Topological Hall effect Skyrmions Half metallic ferro/i Spin gapless mag. semiconductors compensated ferrim. Phase transitions Magn. shape memory Magnetocalorics CDW Multiferroics Out of plane M STT-RAM Permanent magnets Antiferromagnets: Mn 3 Ge Ferromagnets: Fe 3 Sn Anomalous Hall effect Spin reorientation transition?

18 Out and in plan magnetisation Wollmann et al. Phys. Rev. B 92 (2015) arxiv:

19 Cubic Compensated ferrimagnet Mn 2 VGa + Fe 2 MnGa = compensated Wurmehl, et al., J. Phys. Cond. Mat. 18 (2006) 6171 Stinshoff, et al., PRL submitted

20 Compensated tetragonal ferrimagnet Mn Mn Mn Pt Mn Mn Nayak, et al., Phys. Rev. Lett (2013) Nayak, et al., Nature Materials (2015)

21 Giant coercitive field and exchange bias µ 0 H EB (T) µ 0 H EB (T) 3 2 Mn 2.4 Pt 0.6 Ga µ 0 H CF (T) Mn 2.5 Pt 0.5 Ga Mn 2.4 Pt 0.6 Ga µ 0 H CF =5 T µ 0 H EB (T) Mn 1.5 Fe 1.5 Ga Mn 1.8 FeGa H CF =5 T T (K) T (K) Nayak, et al., Phys. Rev. Lett (2013) Nayak, et al., Nature Materials (2015)

22 Thin film of compensated ferrimagnets (a) (b) Ga MnI MnII Pt (c) S(001) F(002) Intensity [arb. unit] S(002) F(004) Mn 2.2 Pt 0.7 Ga 1.1 Mn 2.25 Pt 0.65 Ga 1.1 Mn 2.3 Pt 0.6 Ga 1.1 Mn 2.4 Pt 0.5 Ga 1.1 Mn 2.7 Pt 0.2 Ga 1.1 Mn 2.9 Ga Q [deg.] Roshnee Sahoo, et al. Advanced Materials (2016) DOI: /adma (2016)

23 Exchange bias M [µ B /f.u.] 0.8 (a) K Mn 2.9 Ga x=0.2 x=0.5 x=0.6 x=0.65 x= µ 0 H [T] (b) 300 K M [ µ B /f.u.] (a) Mn 2.2 Pt 0.7 Ga 1.1 (b) Mn 2.25 Pt 0.65 Ga r xy [µw cm] (c) 2 K 50 K 150 K 300 K Mn 2.7 Pt 0.2 Ga 1.1 (d) Mn 2.9 Ga r xy [µw cm] µ 0 H [T] Roshnee Sahoo, et al. Advanced Materials (2016) DOI: /adma (2016)

24 Hexagonal Antiferromagnet Chen, Niu, and MacDonald, Phys. Rev. Lett., 112 (2014) Kübler and Felser EPL 108 (2014) 67001

25 Non-collinear AFM in metallic Mn 3 Ge The anomalous Hall conductivities are normally assumed to be proportional to magnetization Kübler and Felser EPL 108 (2014) 67001

26 Non-collinear AFM Mn 3 Ge/Mn 3 Sn Nayak et al. Science Advances 2 (2016) e Kiyohara, Nakatsuji, preprint: arxiv: , Nakatsuji, Kiyohara, & Higo, Nature, doi: /nature15723

27 Hao Yang, et al., preprint: arxiv: Fermiarcs in the Weyl AFM

28 Anomalous Hall effect

29 Application Spin Hall Effect

30 Stuart S. P. Parkin, et al.: Magnetic Domain-Wall Racetrack Memory, Science 320 (2008)

31 Mn-Pt-Sn non collinear Nayak, et al., to be submitted (2016)

32 Skyrmions The in-focus Lorentz TEM image shows the structural microstructure (martensitic like plates). The stripes in the out of focus images correspond to the helical magnetic structure. They disappear completely for fields > 0.3 T. Skyrmions

33 New Fermions Fermions in condensed-matter systems are not constrained by Poincare symmetry. Instead, they must only respect the crystal symmetry of one of the 230 space groups. Hence, there is the potential to find and classify free fermionic excitations in solid-state systems that have no high-energy counterparts. What comes next? Magnetic Space groups Ag 3 Se 2 Au, Ba 4 Bi 3 Science, 353, 6299, (2016)

34 Summary Heusler compounds offer a tool box for topological phenomena Topological insulators Majorana Dirac Weyl Skyrmions New Fermions?

35 More semiconductors 26 Mn2CoAl CoMn2Al CoFeCrAl CoMnCrSi CoFeVSi 21 FeVTiSi CoVScSi FeCrScSi FeVTiSi FeMnScAl FeMnCrSb 18 V 3 Al 28 CoFeMnSi 10 d 6 p 2 s 18

36 More semiconductors 26 CoMn2Al CoFeCrAl CoMnCrSi CoFeVSi FeMnCrSb 18 V 3 Al 21 FeVTiSi CoVScSi FeCrScSi FeVTiSi FeMnScAl 28 CoFeMnSi

37 Anomalous Hall effect Intrinisic Hall Berry phase Magnetisation? Extrinsic Hall Skew scattering Side jumps

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