Successive single-q and double-q orders in an anisotropic XY model on the diamond structure: a model for quadrupole ordering in PrIr$_2$Zn$_{20}$

TL;DR

This study uses Monte Carlo simulations on an effective quadrupole model to explore complex quadrupole ordering phenomena in PrIr₂Zn₂₀, revealing rich phase behavior influenced by magnetic fields and interactions.

Contribution

It introduces a classical Monte Carlo simulation approach to analyze quadrupole ordering in a diamond-structured model, highlighting the importance of biquadratic interactions for experimental consistency.

Findings

Identification of a phase diagram with single-q and double-q states

Demonstration of the role of biquadratic interactions in weak-field topology

Reproduction of experimental quadrupole ordering features

Abstract

Quadrupole ordering with the ordering wavevector at the L points in PrIr$_2$Zn$_{20}$ under magnetic fields is analyzed using classical Monte Carlo simulations based on an effective $\Gamma_3$ quadrupole model on the diamond structure. We demonstrate that competition between the magnetic field and quadrupole anisotropy leads to a rich phase diagram for magnetic fields applied parallel to [001], which includes switching between a single-q state and a double-q state. We also show that a symmetry-allowed biquadratic intersite interaction, corresponding to a hexadecapole interaction, is crucial for reproducing the weak-field topology observed in experiments.