Quantum tetrahedral mean-field theory of the pyrochlore lattice

A quantum mean-field theory of the pyrochlore lattice is presented. The starting point is not the individual magnetic ions, as in the usual Curie-Weiss mean-field theory, but a set of interacting corner-sharing tetrahedra. We check the consistency of the model against magnetic susceptibility data and find a good agreement between the theoretical predictions and the experimental data. Implications of the model and future extensions are also discussed.

[1]  D. Ghosh,et al.  Crystal-field studies of magnetic susceptibility, hyperfine, and specific heat properties of a Ho 2 Ti 2 O 7 single crystal , 2000 .

[2]  I. Parkin,et al.  Bulk magnetization of the heavy rare earth titanate pyrochlores - a series of model frustrated magnets , 2000 .

[3]  R. Moessner,et al.  Magnetic Susceptibility of Diluted Pyrochlore and SrCr 9 − 9 x Ga 3 + 9 x O 19 Antiferromagnets , 1999, cond-mat/9906421.

[4]  T. Mason,et al.  Transition to long-range magnetic order in the highly frustrated insulating pyrochlore antiferromagnet Gd 2 Ti 2 O 7 , 1999, cond-mat/9906043.

[5]  I. Swainson,et al.  Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore Antiferromagnet Tb 2 Ti 2 O 7 , 1999 .

[6]  T. Mason,et al.  MAGNETIC AND SPECIFIC HEAT STUDIES OF THE CATION-ORDERED PYROCHLORE NH4COALF6 , 1998 .

[7]  R. Moessner,et al.  LOW-TEMPERATURE PROPERTIES OF CLASSICAL GEOMETRICALLY FRUSTRATED ANTIFERROMAGNETS , 1998, cond-mat/9807384.

[8]  C. Lacroix,et al.  Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid , 1998, cond-mat/9807407.

[9]  R. Moessner.  Relief and generation of frustration in pyrochlore magnets by single-ion anisotropy , 1998 .

[10]  R. Moessner,et al.  Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet , 1997, cond-mat/9712063.

[11]  M. Gingras,et al.  Static Critical Behavior of the Spin-Freezing Transition in the Geometrically Frustrated Pyrochlore Antiferromagnet Y 2 Mo 2 O 7 , 1996, cond-mat/9611121.

[12]  Pedersen,et al.  Frustrated pyrochlore oxides, Y2Mn2O7, Ho2Mn2O7, and Yb2Mn2O7: Bulk magnetism and magnetic microstructure. , 1996, Physical review. B, Condensed matter.

[13]  Arthur P. Ramirez,et al.  Strongly Geometrically Frustrated Magnets , 1994 .

[14]  A. B. Harris,et al.  Ordering by quantum fluctuations in a strongly frustrated Heisenberg antiferromagnet , 1991 .

[15]  J. Greedan,et al.  Spin-glass-like behavior in Y2Mo2O7, a concentrated, crystalline system with negligible apparent disorder , 1986 .

[16]  Jacques Villain,et al.  Insulating spin glasses , 1979 .

[17]  P. W. Anderson,et al.  Ordering and Antiferromagnetism in Ferrites , 1956 .

[18]  J. V. Vleck,et al.  The theory of electric and magnetic susceptibilities , 1934, The Mathematical Gazette.

[19]  C. Lacroix,et al.  Quantum spin liquid: The Heisenberg antiferromagnet on the three-dimensional pyrochlore lattice , 2000 .

[20]  Shi,et al.  Mean-field approach to magnetic ordering in highly frustrated pyrochlores. , 1991, Physical review. B, Condensed matter.

[21]  J. H. Van Vleck,et al.  Effective Field Theories of Magnetism , 1966 .