# Phase diagram of multiferroic KCu$_3$As$_2$O$_7$(OD)$_3$

## TL;DR

This study maps the magnetic field-temperature phase diagram of the multiferroic KCu$_3$As$_2$O$_7$(OD)$_3$, revealing metamagnetic transitions, polarization reversibility, and the underlying symmetry-driven polarization behavior.

## Contribution

It extends previous zero-field studies by determining the full H-T phase diagram and analyzing the magnetic and ferroelectric coupling under high magnetic fields.

## Key findings

- Metamagnetic transitions at ~3.7 T in both phases.
- Reversible ferroelectric polarization under magnetic field.
- Helical magnetic structure rotation with field.

## Abstract

The layered compound KCu$_3$As$_2$O$_7$(OD)$_3$, comprising distorted kagome planes of $S=1/2$ Cu$^{2+}$ ions, is a recent addition to the family of type-II multiferroics. Previous zero field neutron diffraction work has found two helically ordered regimes in \kns, each showing a distinct coupling between the magnetic and ferroelectric order parameters. Here, we extend this work to magnetic fields up to $20$~T using neutron powder diffraction, capacitance, polarization, and high-field magnetization measurements, hence determining the $H-T$ phase diagram. We find metamagnetic transitions in both low temperatures phases around $\mu_0 H_c \sim 3.7$~T, which neutron powder diffraction reveals to correspond to a rotation of the helix plane away from the easy plane, as well as a small change in the propagation vector. Furthermore, we show that the sign of the ferroelectric polarization is reversible in a magnetic field, although no change is observed (or expected on the basis of the magnetic structure) due to the transition at $3.7$~T. We finally justify the temperature dependence of the polarization in both zero-field ordered phases by a symmetry analysis of the free energy expansion.