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Degeneracy Breaking in Some Frustrated Magnets

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Degeneracy Breaking in Some Frustrated Magnets

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    1. Degeneracy Breaking in Some Frustrated Magnets

    2. Outline Motivation: Why study frustrated magnets? Chromium spinels and magnetization plateau Quantum dimer model and its phase diagram Constrained phase transitions and exotic criticality

    3. Degeneracy “breaking” Origin of (most) magnetism: Hund’s rule Splitting of degenerate atomic multiplet Degeneracy “quenches” kinetic energy and makes interactions dominant Degeneracy on a macroscopic scale Macroscopic analog of “Hund’s rule” physics Landau levels ) FQHE Large-U Hubbard model ) High-Tc ? Frustrated magnets ) Spin liquids ?? Complex ordered states Exotic phase transitions ??

    4. Spin Liquids?

    5. Quantum Dimer Models

    6. Chromium Spinels

    7. Pyrochlore Antiferromagnets

    8. Magnetization Process

    9. HgCr2O4 neutrons

    10. Collinear Spins

    11. 3:1 States

    12. Ising Expansion

    13. Effective Hamiltonian

    14. Quantum Dimer Model

    15. R state

    16. Is this the physics of HgCr2O4? Probably not: Quantum ordering scale ť |V| ť 0.02J Actual order observed at T & Tplateau/2 We should reconsider classical degeneracy breaking by Further neighbor couplings Spin-lattice interactions C.f. “spin Jahn-Teller”: Tchernyshyov et al

    17. Einstein Model

    18. Bending Rule States

    19. Constrained Phase Transitions

    20. Dimer model = gauge theory

    21. A simple constrained classical critical point

    22. Numerics (courtesy S. Trebst)

    23. Conclusions Quantum and classical dimer models can be realized in some frustrated magnets This effective model can be systematically derived by degenerate perturbation theory Rather general methods can be applied to numerous problems Spin-lattice coupling probably is dominant in HgCr2O4, and a simple Einstein model predicts a unique and definite state (R state), consistent with experiment Probably spin-lattice coupling plays a key role in numerous other chromium spinels of current interest (multiferroics). Local constraints can lead to exotic critical behavior even at classical thermal phase transitions. Experimental realization needed!

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