Phase transitions in a quasi-two-dimensionalXYrandom magnetic system

The phase transitions of a randomly mixed quasi-two-dimensional antiferromagnet and ferromagnet ${\mathrm{Rb}}_2$ ${\mathrm{Mn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Cr}}_{\mathrm{x}}$ ${\mathrm{Cl}}_4$ have been studied experimentally using ac susceptibility (χ), magnetization, and neutron scattering techniques. A characterization of the single crystals of ${\mathrm{Rb}}_2$ ${\mathrm{Mn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Cr}}_{\mathrm{x}}$ ${\mathrm{Cl}}_4$ grown for this study is made with ac χ and electron-spin-resonance measurements. It turns out that the mixed system is a typical example of an XY magnet in the concentration range 0.1≲x<1.0. The concentration versus transition-temperature (x-T) phase diagram of this alloy under zero external magnetic field is constructed. The transition temperature from the paramagnetic (PM) to the antiferromagnetic phase decreases rapidly with increasing Cr concentration. A transition from the PM phase to the spin-glass (SG) phase is observed in the concentration region 0.34≤x<0.5. The mixed crystals with the concentrations 0.50≤x<1.0 show a reentrant spin-glass (RSG) transition; a sequence of transitions from the PM to ferromagnetic (FM) phase and from the FM phase to SG at a lower temperature. Qualitatively, the x-T phase diagram of ${\mathrm{Rb}}_2$ ${\mathrm{Mn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Cr}}_{\mathrm{x}}$ ${\mathrm{Cl}}_4$ is explained by the theories on competing exchange interactions. The RSG transition is discussed in the context of recent theories on the two-dimensional XY spin glass.