Inhomogeneous Level Splitting in Pr x Bi 2-x Ru 2 O 7

1. Inhomogeneous Level Splitting in PrxBi2-xRu2O7 Collin Broholm and Joost van Duijn Department of Physics and Astronomy Johns Hopkins University

2. Collaborators Ruthenium pyrochlores K. H. Kim Rutgers N. Hur Rutgers D. Adroja ISIS Q. Huang NIST S.-W. Cheong Rutgers T. G. Perring ISIS Iridium pyrochlores Satoru Nakatsuji Kyoto Yo Machida Kyoto Yoshiteru Maeno Kyoto Toshiro Sakakibara ISSP Takashi Tayama ISSP PSI seminar

3. Outline • Introduction • Bulk properties of 4dn and 5dn pyrochlores • Spin correlations on TM sites • Crystal field excitations on RE sites • Level splitting in PrxBi2-xRu2O7 • Ground state doublet spin dynamics • Model of inhomogeneous level splitting • Discussion and Conclusions • Possible relevance for other non-Kramers doublet systems PSI seminar

4. A and B sites on vertices of corner-sharing tetrahedra A3+ site is trivalent RE with 8-fold O2- coordination B4+ site is tetravalent TM with 6-fold O2- coordination Can have both A3+ and B4+ magnetism The pyrochlore structure A2B2O7 Nearest neighbor exchange selects a manifold of states characterized by Zero-spin tetrahedra PSI seminar

5. B=Ru site magnetism of Y2Ru2O7 Taira et al. (2000) Taira et al. (1999) • Neutron Diffraction reveals long range magnetic order • ZFC/FC hysteresis suggests some form of disorder that produces glassy canted AFM PSI seminar

6. T=1.5 K “Strong Coupling” Transition in Y2Ru2O7 T=90 K PSI seminar

7. 1.5 K 1.5 K 90 K 90 K PM and AFM Spin Fluctuations • Phase Transition pushes significant spectral weight into “resonance” • The Q-dependence of scattering reflects the form factor for AFM cluster degrees of freedom PSI seminar

8. 2 Magnetic Ions 2 Phase Transitions R2Ru2O7 Er2Ru2O7 Pr3+ M. Ito et al. (2001) Yb3+ N. Taira et al. (2003) PSI seminar

9. Bi-doping increase bandwidth causing Mott Hubbard MIT Magnet order is found only in the insulating state Electronic DOS at EF is enhanced close to the MIT Metal Insulator Transition Yoshii and Sato (1999) PSI seminar

10. A Highly Entropic Metallic State K. H. Kim et al. PSI seminar

11. Praseodymium Crystal Field levels: 116 meV 105 meV 5 K Pr1.2Bi0.8Ru2O7 85 meV 50 meV 200 K 10 meV 0 Five transitions from GS implies it is doublet: PSI seminar

12. Fluctuations in metallic Pr1.2Bi0.8Ru2O7 PSI seminar

13. Inhomogeneous Level Splitting • Broad Spectrum unchanged • Upon heating to • Wave vector dependence • Follows Pr form factor2 Neutron Scattering measures the level splitting spectrum PSI seminar

14. Inhomogeneous two level system • The level distribution function: • Singlet-singlet susceptibility: • Sample averaged susceptibility • Fluctuation-dissipation theorem yields PSI seminar

15. Data Collapse Confirms “quenched broadening” PSI seminar

16. C(T)/T (J/mole-f.u./K2) C(T)/T (J/mole-f.u./K2) Specific heat of r(D)-split doublet PSI seminar

17. Susceptibility of r(D)-split doublet For gapless spectrum low T limiting form is ~lnT PSI seminar

18. Clues to origins of level splitting • T-independent distribution function r(D) • Static not dynamic phenomenon • Continuous not discrete spectrum • Large rare defect or density wave producing distribution of environments • Same distribution describes all x<1.2 • Distribution may not come from Bi doping • Magnetic field enters in quadrature • Electrostatic not magnetostatic inhomogeneity PSI seminar

19. Where else might this occur? • Elements that can have non-Kramers doublet ground states: Pr3+ , Pm3+, Sm2+, Eu3+, Tb3+, Ho3+, Tm3+, Yb2+, and U4+ • Nominally cubic and stoichiometric systems may have clandestine level splitting disorder • Doping effects may be controlled by the induced level splitting PSI seminar

20. Other Materials to Reconsider • Tb2Ti2O7: A non ordering magnet with mysterious low energy mode • Ho2Ti2O7: Long range ordered with unusual thermodynamics • YbBiPt: Ultra heavy fermion system with mysterious low E mode (Robinson et al (1995). • LiHoxY1-xF4 quantum spin glass. Strain induced level splitting adds an effective transverse field • TbxY2-xTi2O7: Dilution has added effect of neutralizing Tb through level splitting PSI seminar

21. Metal insulator transition in R2Ir2O7 Yanagishima and Maeno (2001) Nakatsuji et al. PSI seminar

22. Conclusions • Ir and Ru pyrochlores offer MIT transitions with frustrated magnetism • Y2Ru2O7 : “strong coupling” transition • Spectral weight pushed to finite E resonance • Q-dependence unaffected by ordering • PrxBi2-xRu2O7 : static inhomogeneous distribution of level splittings • Neutrons: “T-independent” broad spectrum • C(T)/T: broadened Schottky anomaly • c(T): possible logarithmic divergence at low T • Watch out for level splitting in non-Kramers ions, which are “not really magnets” PSI seminar