Classical Monte Carlo study for antiferro quadrupole orders in a diamond lattice

TL;DR

This study uses Monte Carlo simulations to explore antiferro quadrupole orders in a diamond lattice, revealing complex phase transitions, multicritical points, and unique critical exponents relevant to orbital orders in certain compounds.

Contribution

It introduces classical effective models for quadrupole orders, confirms universality classes, and uncovers novel multicritical phenomena and critical exponents in the context of antiferro quadrupole systems.

Findings

Zero-field transition belongs to 3D XY universality class.

Magnetic field induces competition between collinear and canted orders.

Distinct critical exponents for parasitic ferro quadrupole order.

Abstract

We investigate antiferro quadrupole orders in a diamond lattice under magnetic fields by Monte Carlo simulations for two types of classical effective models. One is an XY model with Z_3 anisotropy, and the other is a two-component phi^4 model with a third-order anisotropy. We confirm that the universality class of the zero-field transition is that for the three-dimensional XY model. Magnetic field corresponds to a Z_3 field in the effective model, and under this field, we find that collinear and canted antiferro-quadrupole orders compete. Each phase is characterized by symmetry breaking in the sector of (sublattice Z_2)x(reflection Z_2 for the order parameter). When Z_3 anisotropy and magnetic field vary, it turns out that this system is a good playground for various multicritical points; bicritical and tetracritical points emerge in a finite field. Another important finding is about the scaling of parasitic ferro quadrupole order at the zero-field critical point. This is the secondary order parameter induced by the primary antiferro order, and its critical exponent beta'=0.815 clearly differs from the expected value that is twice the value for the primary order parameter. The corresponding correlation length exponent is also different, nu'=0.597(12). We also discuss relation of the present effective quadrupole models with the 3-state Potts model as well as implication to undertanding of orbital orders in Pr-based 1-2-20 compounds.