Spin correlations in conducting and superconducting materials Collin Broholm Johns Hopkins University

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1 Spin correlations in conducting and superconducting materials Collin Broholm Johns Hopkins University Supported by U.S. DoE Basic Energy Sciences, Materials Sciences & Engineering DE-FG02-08ER46544

2 Overview Neutron scattering from magnetic metals Examples Formalism Magnetism of Kondo insulators Exciton in Kondo insulator SmB 6 Magnetism near Superconductivity Frustration in BaFe 2 Se 3 Relieving frustration in FeSe x Te 1-x Summary

3 2k f Bao et al. (1995) V 2 O 3 Bao et al. V

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5 Excitations in SDW state: No spin waves V 2-y O 3 Bao et al. PRL (1993)

6 Scattering from band electrons Chromium Fermi surface Fukuda et al. (1996) 40 mev 25 mev 16 mev Fishman & Liu (1996) 6 mev Q - Q +

7 Incommensurate at high T at low T 3d formfactor Strongly influenced by % level doping

8 Spin excitations in chromium SDW phase of Chromium PM phase of 5% V in Cr Shirane et al. Perring et al.

9 Spin excitations of itinerant magnets: Neither spin waves nor incoherent electron hole pair excitations. Reflect the underlying band structure (Lindhard susceptibility) Strongly influenced by (exchange) interaction effects which enhance low energy structure Few cases of a detailed theoretical account though see recent DMFT work by Kotliar et al.

10 Overview Neutron scattering from magnetic metals Examples Formalism Magnetism of Kondo insulators Exciton in Kondo insulator SmB 6 Magnetism near Superconductivity Frustration in BaFe 2 Se 3 Relieving frustration in FeSe x Te 1-x Summary

11 Sm B 6

12 Neuprane et al. (2013)

13 Surface conduction in SmB 6 Bi 2 Se 3 Chen et al (2010) The variation of resistance ratio with sample dimensions indicates surface conduction dominates in the low T regime where the bulk insulates The hysteretic effects of a magnetic field on surface conduction is indicative of surface magnetism: We are getting what we asked for!

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15 Mixed valence in SmB6

16 Inter J-multiplet Excitations Alekseev et al. Physica B (1993) Sm 2+ 4f 6 J=0 J=1 Sm 3+ 4f 5 J=5/2 J=7/2

17 Nesting wave vectors for SmB 6 Fuhrman and Leiner et al. PRL (2015) T=5 T=100 K K

18 From scattering to band structure Not a unique procedure Mostly sensitive to locations of band-extrema Simplification: Only body-diagonal hopping Opposite sign of f- and d-electron hopping

19 S(q) & Lindhard susceptibility Data Model A tight binding band structure dominated by body-diagonal hopping through B 6 accounts for the observed scattering. Can we infer the topological index of the band structure from S(q)?

20 A topological band structure With inversion and time reversal symmetry the topological index is determined by the product of parities of occupied Bloch states at 8 symmetry points of 1 BZ: Different parity of occupied state at X and M implies strong topological insulator.

21 From Scattering to Z 2 invariant R X R M X M Band inversion between X and M leads to scattering at the X point and a topological bandstructure.

22 Q=0 magnetism from 4f 6 electrons Nickerson et al. PRB (1971) Bourcherle et al. Physica B (1995) 4f 6 J=0 to J=1 van Vleck 4f 6 form factor

23 Exciton form-factor Bloch s theorem for simple Bravais lattice: The Formfactor F(Q) reflects the spatial extent of spin density: The data is consistent with 5d wave function Surprising given small group velocity

24 Exciton in insulating SmB 6 Total moment sum rule: This is 40% of the total magnetic scattering from Sm 3+ and is not dissimilar to the estimates 50% of Sm in the 3+ state

25 Slave Boson MFT of exciton Risebrough (1990), Nikolic (2015) Slave boson fluctuations yield: Renormalized Hybridization gap Formation of Exciton bound state Exciton dispersion from RPA

26 Ultra high resolution inelastic scattering [ ] polarisation counts TRISP spin-echo I02 time [ps] Use neutron spin echo to probe exciton lifetime on nano-second time scale FRMII

27 Exciton spectral width Physical HWHM: Sample inhomogeneity Finite relaxation rate. Possible origins:

28 Bulk C(T): Sommerfeld constant in insulator? SmB 6 LaB 6 Insulator Metal

29 Overview Neutron scattering from magnetic metals Examples Formalism Magnetism of Kondo insulators Exciton in Kondo insulator SmB 6 Magnetism near Superconductivity Frustration in BaFe 2 Se 3 Relieving frustration in FeSe x Te 1-x Summary

30 Jahn-Teller Theorem Any molecule or complex ion in an electronically degenerate state will be unstable relative to a configuration of lower symmetry in which the degeneracy is absent

31 Spin-Peierls-like transitions +Jij is controlled by higher energy physics that we like to consider irrelevant at low energies atomic spacing Orbital overlap Orbital occupancy localized or itinerant electronic states + These degrees of freedom can become relevant if produces degenerate state + The result can be intricate interplay between spin charge and lattice sectors

32 Spin Peierls Transition Quantum Critical spin-1/2 chain: Unstable to dimerization Structural dimerization costs lattice energy but reduces magnetic interaction energy Spin-Peierls transition when spin order is absent due to weak inter-chain interactions

33 Spin-ladders and superconductivity [Fe 2 X 2 ] layers Ba 1-x K x Fe 2 Se 3 La 0.8 Sr 0.2 CuO 2.5 Iron spin-ladders analogous to the cuprate spin-ladders Low dimensionality facilitates analysis and offers a means of determining relevant interactions.

34 Low energies: Fe 4 chain-like excitations

35 High energies: Intra-plaqette modes

36 A Frustrated Mott Insulator Magnetic Interactions in iron ladder are frustrated: A weakened form of magnetism possibility of a different ground state Small adjustments of interactions alters ground state energy Material may spontaneously break symmetries to relieve frustration

37 Overview Magnetism near metal-insulator transition Strange Paramagnet in V 2 O 3 Exciton in Kondo insulator SmB 6 Magnetism near Superconductivity Frustration in BaFe 2 Se 3 Relieving frustration in FeSe x Te 1-x? Summary

38 Can critical magnetism induce superconductivity? Z. Mao et al. (2009) Hsu F et al. PNAS 2008;105:

39 Soft Modes Galore! T=25 K ω =1.5 mev 1 1 ( ) 1 ( 00 2 ) Thampy et al. unpublished

40 Superconductivity relieves frustration T=1.5 T=25 K 1 1 ( ) 1 ( 00 2 ) Thampy et al. unpublished

41 From Critical Fluctuations to Resonance Transverse Slice Along Q x +Q y =1 Thampy et al. unpublished T=1.5 T=25 K

42 For simplicity describe low energy magnetism through Heisenberg exchange Define the Q-dependent first moment of the dynamic correlation function : The thermal average of the magnetic exchange energy is Fourier-transforming you can even obtain the individual inter-site terms:

43 Effects of Superconductivity on magnetism J. Leiner

44 Spatially resolved magnetic condensation energy Magnetic Potential Energy: Increased Kinetic Energy Net condensation energy [C(T)]

45 Summary Spin fluctuations in metallic magnets Direct link to strongly correlated physics of correlated electrons Sensitive to nesting conditions Potentially a tool to probe Weyl and Dirac electrons Exciton in topological Kondo insulator Topological band structure apparent in S(Q) Exciton has 5d electron character Finite exciton width: lifetime or heterogeneity? Exciton: Soft mode of surface magnetism? Superconductivity at the edge of magnetism Quantitative evidence: magnetic interactions favor superconductivity in Fe 1.02 Se 0.4 Te 0.6 Magnetism modified within the superconducting coherence volume V 2 O 3 SmB 6 FeSe x Te 1-x