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Supported by: US National Science Foundation, Research Corporation, NHMFL, & University of Florida

The effect of anisotropy on the Bose-Einstein condensation of magnons in BaCuSi2O6. Stephen Hill, Sung Su Kim and Anthony Wilson Department of Physics, University of Florida, Gainesville, FL 32611, USA. Collaborators:. Stanford - Ian Fisher Cambridge - Suchitra Sebastian

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Supported by: US National Science Foundation, Research Corporation, NHMFL, & University of Florida

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  1. The effect of anisotropy on the Bose-Einstein condensation of magnons in BaCuSi2O6 Stephen Hill, Sung Su Kim and Anthony Wilson Department of Physics, University of Florida, Gainesville, FL 32611, USA Collaborators: • Stanford - Ian Fisher • Cambridge - Suchitra Sebastian • LANL - Cristian Batista, Marcello Jaime, Neil Harrison, Paul Goddard, Vivian Zapf and Ross McDonald • Sao Paolo, Brazil - Armando Paduan-Filho • NHMFL, Tallahassee - Stan Tozer Supported by: US National Science Foundation, Research Corporation, NHMFL, & University of Florida

  2. Introduction to giant spin approximation – why use it? • Mn12 SMM as an example. • A model system: a tetranuclear nickel complex • Evaluation of giant spin Hamiltonian parameters • Excellent application of high-field EPR • Evaluation of single-ion zero-field splitting tensors • Origin of fourth- and higher-order zfs interactions • Assessment of the giant spin approximation • Some consequences • Summary and conclusions

  3. The BaCuSi2O6 structure c Ba Cu Si2O6 Sparta & Roth, Acta Cryst. B60, 491 (2004). ab • T > 610 K: I4/mmm (No. 139), a = 7.1104 Å, c = 11.175 Å • T < 610 K: I41/acd (No. 142), a = 10.0091 Å, c = 22.467 Å • i.e. quasi-2D square lattice of weakly-connected, vertical, symmetric dimers

  4. All Js are antiferromagnetic • Intra-dimer J = 4.45 meV (36 cm-1) • J' = 0.51 meV (4 cm-1) • Jf < J' is frustrating interaction c b a • To lowest order, treat as independent spin-½ dimers • [Cu2+]2 Hamiltonian has perfect cylindrical [U(1)] symmetry Body-centered tetragonal magnetic lattice  J' [Cu2+]2 dimer J J' Each Cu2+ provides a spin-½ Jf • Intra-dimer separation: 2.74 Å • NN inter-dimer distance: 7 Å • NNN inter-dimer distance: ~10 Å

  5. Properties of the isolated dimer Heisenberg: Zeeman: J T+ Energy Triplet (T ) T0 Singlet (S) S T- Magnetic field

  6. Properties of the isolated dimer  Effective two-level system: pseudospin T- S T+ J = 33 K, g = 2.00 Triplet T0 1/T J T- exp S Singlet Low energy degrees of freedom J = 4.45 meV B = 0 B > 20 T At low fields:

  7. Low-field properties of BaCuSi2O6: evidence for a spin gap • J = 4.45 meV ≡51 K • ga = 2.01, gc ~ 2.31 Y. Sasago et al., Phys. Rev. B 55, 8357 (1997). S. Sebastian et al., cond-mat/0606244. Question: what happens for weakly interacting spin dimers?

  8. Insight from the two leg ladder F. Mila, Euro Phys. J. B. 6, 201 (1998). T. Giamarchi & A. M. Tsvelik, PRB 59, 11398 (1999). • For J > J', treat perturbatively; basis of |S and | T  states • Exchanges triplets and singlets on adjacent sites • Describes delocalized band of bosonic excitations (triplons) • This term represents kinetic energy of the triplons J' J i = 1 2 3 4 5.....

  9. Insight from the two leg ladder J' J i = 1 2 3 4 5..... K.E. P.E. C.P. F. Mila, Euro Phys. J. B. 6, 201 (1998). T. Giamarchi & A. M. Tsvelik, PRB 59, 11398 (1999).

  10. Insight from the two leg ladder In 2D J' J i = 1 2 3 4 5..... In 1D T J J - J' -p p Energy S Momentum

  11. Effect of a magnetic field Msat ? Bc2 Paramagnet Ferro- magnet Bc1 T- S Magnetization Magnetic field

  12. Effect of a magnetic field T- S Bc2 Msat Magnetization Finite temperature (smooth evolution) Maxwell-Boltzmann Magnetic field

  13. Effect of a magnetic field • Nothing exotic yet – all explainable in classical terms • Continuous evolution of magnetization from high to low T Sebastian et al., cond-mat/0606244 9 Jun 2006

  14. Clear phase transition for Bc1 > B > Bc2 Heat capacity and magnetocaloric effect: (Marcelo Jaime, NHMFL) l-anomaly • Implies magnetic ordering • Could this be a Bose-Einstein condensation? M. Jaime et al., Phys. Rev. Lett. 93, 087203 (2004).

  15. T > Tc T > Tc T > Tc T- Maxwell-Boltzmann Energy A paramagnet S • Thermal population of singlet (S) and triplet (T ) states • Corresponds to an incoherent mixture of Sand T (p,±p) Momentum

  16. T < Tc ldB > dTT A canted XY antiferromagnet • Macroscopic occupation at (p,±p) points • All spins condense forming a coherent superposition of S and T states T- Bose-Einstein Energy S (p,±p) Momentum

  17. Coherence and broken symmetry a Canted XY antiferromagnet b • XY antiferromagnetic order does break the U(1) symmetry • BEC universality for d≥ 2 c b a • Development of Mz does not break U(1) symmetry

  18. T = 20 K, f = 92.5 GHz

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