Level Splitting in Frustrated non-Kramers doublet systems Collin Broholm and Joost van Duijn Department of Physics and Astronomy Johns Hopkins University Spin Fluctuations in Metallic Pyrochlore Systems

9/13-17/04International Workshop on Frustrated Magnetism 2 Collaborators Ruthenium pyrochlores K. H. Kim Rutgers N. HurRutgers D. AdrojaISIS Q. HuangNIST S.-W. CheongRutgers T. G. PerringISIS Iridium pyrochlores Satoru NakatsujiKyoto Yo MachidaKyoto Yoshiteru Maeno Kyoto Toshiro Sakakibara ISSP Takashi TayamaISSP

9/13-17/04International Workshop on Frustrated Magnetism 3 Outline  Introduction Bulk properties of 4d n and 5d n pyrochlores Spin correlations on TM sites Crystal field excitations on RE sites  Level splitting in Pr x Bi 2-x Ru 2 O 7 Ground state doublet spin dynamics Model of inhomogeneous level splitting  Discussion and Conclusions Possible relevance for other non-Kramers doublet systems

9/13-17/04International Workshop on Frustrated Magnetism 4 The pyrochlore structure A 2 B 2 O 7  A and B sites on vertices of corner- sharing tetrahedra  A 3+ site is trivalent RE with 8-fold O 2- coordination  B 4+ site is tetravalent TM with 6-fold O 2- coordination  Can have both A 3+ and B 4+ magnetism

9/13-17/04International Workshop on Frustrated Magnetism 5 B=Ru site magnetism of Y 2 Ru 2 O 7 □ Neutron Diffraction reveals long range magnetic order □ ZFC/FC hysteresis suggests some form of disorder that produces glassy canted AFM Taira et al. (2000) Taira et al. (1999)

9/13-17/04International Workshop on Frustrated Magnetism 6 “Strong Coupling” Transition in Y 2 Ru 2 O 7 T=90 K T=1.5 K

9/13-17/04International Workshop on Frustrated Magnetism 7 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 1.5 K 90 K 1.5 K 90 K

9/13-17/04International Workshop on Frustrated Magnetism 8 2 Magnetic Ions 2 Phase Transitions N. Taira et al. (2003) Er 2 Ru 2 O 7 M. Ito et al. (2001) Pr 3+ Yb 3+ R 2 Ru 2 O 7

9/13-17/04International Workshop on Frustrated Magnetism 9 Metal Insulator Transition  Bi-doping increase bandwidth causing Mott Hubbard MIT  Magnet order is found only in the insulating state  Electronic DOS at E F is enhanced close to the MIT Yoshii and Sato (1999)

9/13-17/04International Workshop on Frustrated Magnetism 10 A Highly Entropic Metallic State K. H. Kim et al.

9/13-17/04International Workshop on Frustrated Magnetism 11 Praseodymium Crystal Field levels: 10 meV 50 meV 85 meV 105 meV 116 meV K 5 K Pr 1.2 Bi 0.8 Ru 2 O 7 Five transitions from GS implies it is doublet:

9/13-17/04International Workshop on Frustrated Magnetism 12 Fluctuations in metallic Pr 1.2 Bi 0.8 Ru 2 O 7

9/13-17/04International Workshop on Frustrated Magnetism 13 Inhomogeneous Level Splitting  Broad Spectrum unchanged Upon heating to  Wave vector dependence Follows Pr form factor 2 Neutron Scattering measures the level splitting spectrum

9/13-17/04International Workshop on Frustrated Magnetism 14 Inhomogeneous two level system  The level distribution function:  Singlet-singlet susceptibility:  Sample averaged susceptibility  Fluctuation-dissipation theorem yields

9/13-17/04International Workshop on Frustrated Magnetism 15 Data Collapse Confirms “quenched broadening”

9/13-17/04International Workshop on Frustrated Magnetism 16 Specific heat of ()-split doublet C(T)/T (J/mole-f.u./K 2 )

9/13-17/04International Workshop on Frustrated Magnetism 17 Susceptibility of ()-split doublet For gapless spectrum low T limiting form is ~lnT For gapless spectrum low T limiting form is ~lnT

9/13-17/04International Workshop on Frustrated Magnetism 18 Clues to origins of level splitting  T-independent distribution function  ⇒ 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

9/13-17/04International Workshop on Frustrated Magnetism 19 Where else might this occur?  Elements that can have non-Kramers doublet ground states: Pr 3+, Pm 3+, Sm 2+, Eu 3+, Tb 3+, Ho 3+, Tm 3+, Yb 2+, and U 4+  Nominally cubic and stoichiometric systems may have clandestine level splitting disorder  Doping effects may be controlled by the induced level splitting

9/13-17/04International Workshop on Frustrated Magnetism 20 Other Materials to Reconsider  Tb 2 Ti 2 O 7 : A non ordering magnet with mysterious low energy mode  Ho 2 Ti 2 O 7 : Long range ordered with unusual thermodynamics  YbBiPt: Ultra heavy fermion system with mysterious low E mode (Robinson et al (1995).  LiHo x Y 1-x F 4 quantum spin glass. Strain induced level splitting adds an effective transverse field  Tb x Y 2-x Ti 2 O 7 : Dilution has added effect of neutralizing Tb through level splitting

9/13-17/04International Workshop on Frustrated Magnetism 21 Metal insulator transition in R 2 Ir 2 O 7 Yanagishima and Maeno (2001) Nakatsuji et al.

9/13-17/04International Workshop on Frustrated Magnetism 22 Conclusions  Ir and Ru pyrochlores offer MIT transitions with frustrated magnetism  Y 2 Ru 2 O 7 : “strong coupling” transition Spectral weight pushed to finite E resonance Q-dependence unaffected by ordering  Pr x Bi 2-x Ru 2 O 7 : static inhomogeneous distribution of level splittings Neutrons: “T-independent” broad spectrum C(T)/T: broadened Schottky anomaly (T): possible logarithmic divergence at low T  Watch out for level splitting in non-Kramers ions, which are “not really magnets”