# Multiple phase transitions and high-field quadrupolar order in a model for $\beta$-TeVO$_4$

## TL;DR

This study models the complex magnetic phases of $eta$-TeVO$_4$ using an anisotropic Heisenberg model, revealing multiple phase transitions, quadrupolar order, and metamagnetic behavior consistent with experimental observations.

## Contribution

It introduces a cluster mean field approach to analyze the magnetic phases and quadrupolar order in a model for $eta$-TeVO$_4$, incorporating ab-initio exchange parameters.

## Key findings

- Identification of multiple magnetic phases including spiral and collinear states.
- Discovery of finite quadrupolar order in the metamagnetic regime.
- Comparison of theoretical results with experimental data on $eta$-TeVO$_4$.

## Abstract

Motivated by the complex behavior of the frustrated magnet $\beta$-TeVO$_4$, we study an anisotropic Heisenberg model for coupled spin-$1/2$ zigzag chains. Using cluster mean field approach to capture quantum correlations we find, upon reducing temperature in the absence of applied field, (i) a partially ordered state, (ii) a collinear antiferromagnetic phase, and (iii) an elliptical spiral state characterized by finite vector chirality. For finite fields, we find metamagnetic response close to saturation magnetization. We show via explicit calculations that the quadrupolar order parameter is finite in the metamagnetic regime. The exchange parameters reported in the ab-initio study of $\beta$-TeVO$_4$ are used in our study. We compare our results with those reported in recent experiments on $\beta$-TeVO$_4$ and highlight similarities as well as differences between experimental results and our cluster mean field calculations.