Magnetic phase transitions in a random mixture with competing Ising andXYspin anisotropies

Magnetic phase transitions in the randomly mixed antiferromagnet ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{\mathrm{Br}}_2$ with competing Ising and $\mathrm{XY}$ anisotropies have been studied experimentally by ac-susceptibility and magnetization measurements. The concentration—versus—transition-temperature phase diagram of this alloy under zero external magnetic field is constructed. The transition from the paramagnetic to antifer-romagnetic phase was clearly observed in both the Fe- and Co-rich regions. One of the two low-temperature phase boundaries which corresponds to the ordering of the Ising component becomes less sharp. The other one, which represents the ordering of the $\mathrm{XY}$ component, is missing. The absence and the smearing of the transitions are discussed in the random field model. The effect of external magnetic field on the phase transition between the paramagnetic and antiferromagnetic phase has been studied in the Fe-rich region. The external field applied along the $c$ axis of the crystal (the Ising axis) caused the transition to be smeared, and thus the external field produced a random field in this alloy as in the case of diluted antiferromagnets. From these experimental observations, the lower critical dimension of the Ising model is shown to be three.