Critical behavior of the principal magnetoelectric susceptibilities of GdAl${\mathrm{O}}_3$

The three independent magnetoelectric susceptibilities of GdAl${\mathrm{O}}_3$ have been measured in the critical region $6\times {10}^{-5\mathrm{}}<\frac{\Delta T}{T_N}<1\mathrm{}\times {10}^{-2\mathrm{}}$. For all three elements, we find power-law behavior with the same critical exponent ${\beta }_{\alpha }=0.31\mathrm{}\pm 0.01$. Although ${\mathrm{Gd}}^{3+}$ is an $S$-state ion and the dominant interaction is isotropic Heisenberg exchange, this exponent is Ising-like. This is interpreted as being due to the strong uniaxial character of the magnetic order. Our results are compared with those for other magnetoelectric materials.