Critical exponents and amplitudes of the ferromagnetic transition in ${\mathrm{La}}_{0.1}{\mathrm{Ba}}_{0.9}\mathrm{V}{\mathrm{S}}_3$

To study the origin of the magnetic transition in $\mathrm{Ba}\mathrm{V}{\mathrm{S}}_3$, we measured the dc magnetization on ${\mathrm{La}}_{0.1}{\mathrm{Ba}}_{0.9}\mathrm{V}{\mathrm{S}}_3$ sintered samples near the ferromagnetic transition. Effective critical exponents and amplitudes are obtained by means of standard modified Arrot plots and the Kouvel-Fisher method, while asymptotic critical exponents and amplitudes are obtained by means of “correction to scaling” analysis. The two methods yield similar results, but the latter is superior with respect to the achieved uncertainty. The obtained results indicate that the universality class of magnetic interactions driving the transition changes from short to long range when cooling through $T_c$.

Figure 1

Magnetization curve of ${\mathrm{La}}_{0.1}{\mathrm{Ba}}_{0.9}\mathrm{V}{\mathrm{S}}_3$ in applied external field $H=1\mathrm{Oe}$. Temperature steps are $\Delta T=0.02\mathrm{K}$ inside the range $15–25\mathrm{K}$, $\Delta T=0.2\mathrm{K}$ outside. Inset: from $1∕\chi$ vs $T$ curve, one has ${\mu }_0=1.46{\mu }_B$ (dashed line).

Figure 2

Modified Arrot plots in the critical region $18.00⩽T⩽19.98\mathrm{K}$, with the ${\beta }_{\mathit{eff}}$ and ${\gamma }_{\mathit{eff}}$ values for which the best linear isotherms are obtained. The isotherm passing through the origin gives $T_C=18.92\mathrm{K}$. Points outside the range $0.1T<H<1.3T$ (not shown) have been excluded from the analysis (see text).

Figure 3

Kouvel-Fisher plots of $M_s$ and ${\chi }_0$. The inverse of slopes give ${\beta }_{\mathit{eff}}=0.501$ and ${\gamma }_{\mathit{eff}}=1.366$, the intercepts on the $T$ axis give $18.91<T_C<18.92\mathrm{K}$. Arrows mark the temperature range used for linear best fits.

Figure 4

Isothermal magnetization curves in the $18.00⩽T⩽20.00\text{−}\mathrm{K}$ interval. Temperature steps are $\Delta T=0.02\mathrm{K}$.

Figure 5

Logarithmic scaling plot of $H∕{ϵ}^{\beta +\gamma }$ vs $M∕{ϵ}^{\beta }$ in the critical region. The experimental points fall on two branches of a universal curve by using the values of the critical exponents and of $T_C$ obtained by means of CTS analysis. The points on the isotherm at $T_C$ have diverging coordinates and are not reported.

Figure 6

Values of ${\chi }^2$ for best fits resulting from Kouvel-Fisher method and CTS analysis plotted as function of reduced temperature. ${\chi }^2=1∕(N-N_p){\sum }_i{[(y_{\mathit{\text{fit}}}-y_{\mathit{exp}})∕y_{\mathit{exp}}]}^2$ where $N$ is the number of data points and $N_p$ is the number of free fitting parameters.