The frustrated magnetism of ZnCr 2 O 4

1. The frustrated magnetism of ZnCr2O4 Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research S.-H. Lee NIST W. Ratcliff II Rutgers S.-W. Cheong Rutgers T. H. Kim Rutgers Q. Huang NIST G. Gasparovic JHU

2. Outline • Introduction • History and application of spinels • Exchange interactions for Ti, V, and Cr • Bulk properties of spinels • Composite spin in chromium spinels • Overview of experimental facts • Evidence for composite spin clusters • Evidence for instability near critical point • Conclusions and Outlook

3. Magnetism in spinel oxides • Applications • Ferrite microwave filters • Additive to Portland cement • Active element in NOx sensors • Host of unique forms of magnetism • History of frustration with spinel lattice • 1935 L. Pauling charge ordering to H-ordering in ice • 1956 P. W. Anderson shows that local order can be achieved without long range order • 1990-present resurgence of interest as host for novel magnetic states

4. Exchange Interactions between B-sites eg eg t2g Cr3+ O2- t2g JNNN weak for Ti, V, and Cr JNN(AFM)≈ 5 meV

5. Frustration and short range correlations

6. Outline • Introduction • History and application of spinels • Exchange interactions for Ti, V, and Cr • Bulk properties of spinels • Composite spin in chromium spinels • Overview of experimental facts • Evidence for composite spin clusters • Evidence for instability near critical point • Conclusions and Outlook

7. TN<T<|QCW| : Short range correlations

8. TN<T<|QCW| : Dynamic Short Range Order • Points of interest: • 2p/Qr0=1.4 • ⇒ nn. AFM correlations • No scattering at low Q • ⇒ satisfied tetrahedra S.-H. Lee et al. PRL (2000)

9. T<TN : Resonant mode and spin waves • Points of interest: • 2p/Qr0=1.4 • ⇒ nn. AFM correlations • No scattering at low Q • ⇒ satisfied tetrahedra • Resonance for ħw ≈ J • Low energy spin waves S.-H. Lee et al. PRL (2000)

10. Spin waves: acoustic plus strong resonance Weakly dispersive modes Acoustic spin waves

11. Outline • Introduction • History and application of spinels • Exchange interactions for Ti, V, and Cr • Bulk properties of spinels • Composite spin in chromium spinels • Overview of experimental facts • Evidence for composite spin clusters • Evidence for instability near critical point • Conclusions and Outlook

12. Q-dependence of inelastic scattering

13. Is this evidence for dynamic spin clusters? J-Lab hall A April (2003). r [fm] • Electron scattering from protons • For ZnCr2O4 we might interpret robust Q-dependence as “inter-atomic form factor”. the “parts” would be Cr3+ spin-3/2. R. P. Feynman in Science February (1974)

14. Average form factor for AFM hexagons + ▬ + ▬ ▬ + Tchernyshyov et al. PRL (2001) S.-H. Lee et al. Nature (2002)

15. A possible interpretation of the fit • Physics at the scale of |QCW| order spins antiferromagnetically on hexagons • Staggered magnetization of hexagons is effective low energy degree of freedom • System is transformed from strongly correlated spins to weakly correlated “hexagon directors” • Neutrons scatter from hexagon directors not individual spins

16. Why AFM hexagons? • Low energy manifold has zero spin tetrahedra • Spins on tetrahdra form hinged parallelograms • Spins on hexagons form cart-wheel • Hexagons decouple when Antiferromagnetic • AFM hexagons account for 1/6 of spin entropy

17. Outline • Introduction • History and application of spinels • Exchange interactions for Ti, V, and Cr • Bulk properties of spinels • Composite spin in chromium spinels • Overview of experimental facts • Evidence for composite spin clusters • Evidence for instability near critical point • Conclusions and Outlook

18. Fluctuations in Paramagnetic phase Lorentzian relaxation spectrum: Near Quantum Critical spin system:

19. Instabilities close to QCP T/J 1/S, frustration, H, P, x, … ?

20. Magneto-elastic first order transition

21. Straining to order Edge sharing n-n exchange in ZnCr2O4 depends on Cr-Cr distance,r. The implication is that there are forces between Cr3+ atoms Cr3+ Cr3+ O2- O2- These magneto-elastic interactions destabilize QC spin system on compliant lattice Tchernyshyov et al. PRL (2001) and PRB (2002)

22. Sensitivity to impurities near quantum criticality TN Tf Ratcliff et al. PRB (2002)

23. Low T spectrum sensitive to bond disorder 5% Cd 0 0.5 1.0 1.5 2.0 2.5 Q (Å-1)

24. Inter-atomic form factor is impervious to disorder Ratcliff et al. PRB (2002)

25. ConclusionsOutlook Chromium B-site spinels are ideally frustrated spin systems Robust Q-dependence of scattering indicates hexagon director protectorate Near quantum critical state is sensitive to perturbations: Magneto-elastic coupling produces low T Neel order Bond disorder at % level yields spin freezing Would like to find route to suppress TC/|QCW| for magneto-elastic transition Understand the role of quantum effects for establishing director protectorate Determine detailed magnetic and lattice structure of magneto-elastic low T phase Determine of spin hamiltonian in high T phase for higher level interaction with theory