Abstract
In this paper, we study the doping effects on the magnetic states of $\mathrm{CuCr}{\mathrm{O}}_{2}$ based on the classical frustrated spin model [Lin et al., Phys. Rev. B 89, 220405(R) (2014)]. Several experimental observations can be well reproduced by the Monte Carlo simulations of the modified spin models. Our paper suggests that the disorder induced by V/Al doping cooperating with the frustration in the system may contribute to the emergence of the spin glass state. Furthermore, the hole doping by $\mathrm{M}{\mathrm{g}}^{2+}$ substituting $\mathrm{C}{\mathrm{r}}^{3+}$ enhances the quantum fluctuations and bond disorder which modulate the biquadratic exchanges and in turn results in the promotion of the spiral phase, consistent with the experimental report.
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