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

TL;DR

This paper develops a microscopic quantum pseudospin-1/2 model for magnetic pyrochlore oxides, revealing significant quantum fluctuations, phase transitions, and exotic states like quadrupolar and spin ice, relevant to experimental observations.

Contribution

It derives a generic anisotropic superexchange pseudospin-1/2 Hamiltonian for rare-earth pyrochlores from first principles, incorporating quantum effects and symmetry considerations.

Findings

Quantum fluctuations induce phase transitions to quadrupolar states.

Evidence of cooperative quadrupole moments and pseudospin chirality.

Possible realization of singlet quantum spin ice states.

Abstract

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 Pr^{3+} 4f moments in Pr_2TM_2O_7 (TM = Zr, Sn, Hf, and Ir) by starting from the atomic non-Kramers magnetic doublets and performing the strong-coupling perturbation expansion of the virtual electron transfer between the Pr 4f and 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 Nd^{3+}, Sm^{3+}, and Yb^{3+} 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 Pr^{3+} case. The model also shows a formation of 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 the experiments is discussed.