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

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