Quantum fluctuations in the effective pseudospin-1/2 model for magnetic pyrochlore oxides

The effective quantum pseudospin-1/2 model for interacting rare-earth magnetic moments, which are locally described with atomic doublets, is studied theoretically for magnetic pyrochlore oxides. It is derived microscopically for localized Pr3+ 4f moments in Pr2TM2O7 (TM = Zr, Sn, Hf, and Ir) by starting from the atomic non-Kramers magnetic doublets and performing a strong-coupling perturbation expansion of the virtual electron transfer between the Pr 4f and the O 2p electrons. The most generic form of the nearest-neighbor anisotropic superexchange pseudospin-1/2 Hamiltonian is also constructed from the symmetry properties, which is applicable to Kramers ions Nd3+, Sm3+, and Yb3+, potentially showing large quantum effects. The effective model is then studied by means of a classical mean-field theory and the exact diagonalization on a single tetrahedron and on a 16-site cluster. These calculations reveal appreciable quantum fluctuations leading to quantum phase transitions to a quadrupolar state as a melting of spin ice for the Pr3+ case. The model also shows the formation of a cooperative quadrupole moment and pseudospin chirality on tetrahedrons. A sign of a singlet quantum spin ice is also found in a finite region in the space of coupling constants. The relevance to experiments is discussed.