# GdRh$_2$Si$_2$: An exemplary tetragonal system for antiferromagnetic order with weak in-plane anisotropy

## TL;DR

This study presents GdRh$_2$Si$_2$ as an ideal model for weak in-plane antiferromagnetic anisotropy, demonstrating continuous spin-flop transitions and domain effects, supported by experimental and theoretical analysis.

## Contribution

The paper provides the first detailed experimental and theoretical investigation of weak in-plane anisotropy in GdRh$_2$Si$_2$, highlighting its suitability as a model system for such magnetic behavior.

## Key findings

- GdRh$_2$Si$_2$ exhibits weak in-plane antiferromagnetic anisotropy.
- Experimental data show continuous spin-flop transition and domain effects.
- Theoretical models accurately reproduce the observed magnetic behavior.

## Abstract

The anisotropy of magnetic properties commonly is introduced in textbooks using the case of an antiferromagnetic system with Ising type anisotropy. This model presents huge anisotropic magnetization and a pronounced metamagnetic transition and is well-known and well-documented both, in experiments and theory. In contrast, the case of an antiferromagnetic $X$-$Y$ system with weak in-plane anisotropy is only poorly documented. We studied the anisotropic magnetization of the compound GdRh$_2$Si$_2$ and found that it is a perfect model system for such a weak-anisotropy setting because the Gd$^{3+}$ ions in GdRh$_2$Si$_2$ have a pure spin moment of S=7/2 which orders in a simple AFM structure with ${\bf Q} = (001)$. We observed experimentally in $M(B)$ a continuous spin-flop transition and domain effects for field applied along the $[100]$- and the $[110]$-direction, respectively. We applied a mean field model for the free energy to describe our data and combine it with an Ising chain model to account for domain effects. Our calculations reproduce the experimental data very well. In addition, we performed magnetic X-ray scattering and X-ray magnetic circular dichroism measurements, which confirm the AFM propagation vector to be ${\bf Q} = (001)$ and indicate the absence of polarization on the rhodium atoms.