Spin-glass properties of a crystalline transition-metal oxide: ${\left({\mathrm{Ti}}_{1-x}{\mathrm{V}}_x\right)}_2{\mathrm{O}}_3$

The magnetic properties of ${\left({\mathrm{Ti}}_{1-x}{\mathrm{V}}_x\right)}_2{\mathrm{O}}_3$ single crystals have been studied between 0.05 and 300 K for $0<x<\mathrm{}7.5\%$. The magnetic susceptibility measured between 4.2 and 300 K shows Curie-Weiss laws with effective magnetic moments per V decreasing from 3.8${\mathrm{\mu }}_{\mathrm{B}}$ for $x=0.2\%$ to 2.1${\mathrm{\mu }}_{\mathrm{B}}$ for $x=7.5\%$. These results are attributed to the formation of ${\mathrm{V}}^{2+}$($3d^3$) states at small $x$ and to ${\mathrm{V}}^{3+}$ with one band electron and one electron responsible for the magnetic properties at larger $x$. At low temperatures ($0.05<T<\mathrm{}4.2\mathrm{}$ K), the initial reversible susceptibility ${\chi }_{\mathrm{rev}}\mathrm{}\left(T\right)\mathrm{}$ shows a peak at a temperature $T_G$ proportional to $x$ and is strongly anisotropic. For $T<\mathrm{}{T}_G$, thermoremanent (TRM) and isothermal remanent (IRM) magnetizations are found. The saturated TRM extrapolated to 0 K varies as $\alpha x+\beta x^2$. ${\chi }_{\mathrm{rev}}\mathrm{}\left(0\right)\mathrm{}$ increases with $x$ and the irreversible susceptibility is anisotropic and proportional to $x$. The magnetization has been measured at $T=1.4\mathrm{} \mathrm{and} 4.2$ K in fields up to 150 kG; the magnetic moments obtained from extrapolation of the curves $M\left(\frac{1}{H}\right)$ are in good agreement with the values deduced from the Curie constant. It is shown that the low-temperature specific-heat anomaly, previously found, is due to the spin-glass properties. The spin-glass parameters of ${\left({\mathrm{Ti}}_{1-x}{\mathrm{V}}_x\right)}_2{\mathrm{O}}_3$ are compared to those of some dilute alloys and found to be similar. The origin of the magnetic interactions is discussed; at intermediate V concentration, the usual Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction should take place, with a rather small $k_F$ and predominantly ferromagnetic couplings; for the small-V concentration range, as the crystals are semiconducting, dipolar and magnetoelastic couplings are examined; at large $x$, direct antiferromagnetic exchange between V nearest neighbors should become important. Different sources of magnetic anisotropy are considered and the dipolar coupling is...