Dimensional change of quadrupole orders in pseudospin-$\frac{1}{2}$ pyrochlore magnets under [111] field

TL;DR

This study investigates how electric quadrupole orders in pyrochlore magnets with non-Kramers ions change under [111] magnetic field, revealing a transition from 3D to quasi-2D order through classical Monte-Carlo simulations.

Contribution

It provides the first detailed analysis of quadrupole order dimensional change in pyrochlore magnets under [111] field using Monte-Carlo simulations.

Findings

Zero-field transition from paramagnetic to antiparallel pseudospin order.

Transformation to quasi-2D quadrupole order under [111] field.

Implications for experimental observations in Tb$_{2}$Ti$_{2}$O$_{7}$.

Abstract

We have studied long range orders of electric quadrupole moments described by an effective pseudospin-$\frac{1}{2}$ Hamiltonian representing pyrochlore magnets with non-Kramers ions under [111] magnetic field, in relevance to Tb$_{2}$Ti$_{2}$O$_{7}$. Order parameters and phase transitions of this frustrated system are investigated using classical Monte-Carlo simulations. In zero field, the model undergoes a first-order phase transition from a paramagnetic state to an ordered state with an antiparallel arrangement of pseudospins. This pseudospin order is characterized by the wavevector $\boldsymbol{k}=0$ and is selected by an energetic or an order-by-disorder mechanism from degenerate $\boldsymbol{k}=(h,h,h)$ mean-field orders. Under [111] magnetic field this three-dimensional quadrupole order is transformed to a quasi two-dimensional quadrupole order on each kagom\'{e} lattice separated by field-induced ferromagnetic triangular lattices. We discuss implication of the simulation results with respect to experimental data of Tb$_{2}$Ti$_{2}$O$_{7}$.