Bicritical and Tetracritical Behavior of GdAl${\mathrm{O}}_3$

We have experimentally investigated the phase diagram of antiferromagnetic GdAl${\mathrm{O}}_3$ near its spin-flop multicritical point ($T_M, H_M$) in the three-dimensional space spanned by the uniform fields $H_{\parallel }$ and $H_{\perp }$ and the temperature $T$. In the $H_{\parallel }-T$ plane, ($T_M, H_M$) appears as a bicritical point, but as a tetracritical point in the $H_{\perp }-T$ plane. The approach of all six boundaries to ($T_M, H_M$) is described by a single exponent $\psi =1.17\mathrm{}\pm 0.02$. This implies crossover exponents $\varphi =1.17\mathrm{}\pm 0.02$ and ${\varphi }_v=\pm 0.03$ in excellent agreement with renormalization group theory.