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

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

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

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

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

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

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

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

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.

Sm B 6

Neuprane et al. (2013)

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!

Mixed valence in SmB6

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

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

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

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)?

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.

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.

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

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

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

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

Ultra high resolution inelastic scattering [ ] polarisation counts 0.4 80 0.35 70 0.3 60 0.25 50 0.2 40 30 0.15 Fuhrman @ TRISP 0.2 0 0.25 0.5 0.3 0.35 1 0.4 0.45 1.5 0.5 0.55 2 spin-echo I02 time [ps] Use neutron spin echo to probe exciton lifetime on nano-second time scale TRISP @ FRMII

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

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

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

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

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

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.

Low energies: Fe 4 chain-like excitations

High energies: Intra-plaqette modes

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

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

Can critical magnetism induce superconductivity? Z. Mao et al. (2009) Hsu F et al. PNAS 2008;105:14262-14264

Soft Modes Galore! T=25 K ω =1.5 mev 1 1 ( 0 2 2 ) 1 ( 00 2 ) Thampy et al. unpublished

Superconductivity relieves frustration T=1.5 T=25 K 1 1 ( 0 2 2 ) 1 ( 00 2 ) Thampy et al. unpublished

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

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:

Effects of Superconductivity on magnetism J. Leiner

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

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 http://iqm.jhu.edu/publications