Field-induced tricritical behavior in the Néel-type skyrmion host ${\mathrm{GaV}}_4{\mathrm{S}}_8$

The lacunar spinel compound ${\mathrm{GaV}}_4{\mathrm{S}}_8$ exhibits a Néel-type skyrmion, which holds great promise for future spintronics and ultrahigh-density magnetic memory devices. To gain more insight into the magnetic interactions, the critical behavior of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ is studied by dc magnetization measurement around the Curie temperature $\left(T_{\mathrm{C}}\right)$. A set of reliable critical exponents ($\beta =0.220\pm 0.024$, $\gamma =0.909\pm 0.005$, and $\delta =5.161\pm 0.003$) is obtained by the modified Arrott plot technique, the Kouvel-Fisher method, and critical isothermal analysis. The generated critical exponents fulfill the universality class of tricritical mean-field theory, which suggests a field-induced tricritical phenomenon. Based on the scaling equations, boundaries between the skyrmion and ferromagnetic phases can be distinguished. A tricritical point is revealed at the temperature of $T_{\mathrm{Tr}}=12\mathrm{K}$ and field of $H_{\mathrm{Tr}}=60\mathrm{mT}$, which is located at the intersection point among the skyrmion, ferromagnetic, and paramagnetic phases. It is suggested that the origin of the tricritical behavior in ${\mathrm{GaV}}_4{\mathrm{S}}_8$ is related to the skyrmion state near the magnetic transition temperature $T_{\mathrm{C}}$.

Figure 1

(a) Temperature dependence of zero-field-cooling magnetization $\left[M\left(T\right)\right]$ under $H=1000\mathrm{Oe}$ for ${\mathrm{GaV}}_4{\mathrm{S}}_8$ (inset plots $dM/dT$ vs $T$); (b) isothermal magnetization $\left[M\left(H\right)\right]$ at $T=2\mathrm{K}$ [inset shows the $M\left(H\right)$ in the low-field region].

Figure 2

(a) Isothermal magnetization curves in the vicinity of $T_{\mathrm{C}}$ [inset shows the enlarged view of $M\left(H\right)$ in the high-field region]; (b) Arrott plot (isotherms of $M^2$ vs $H/M$) for ${\mathrm{GaV}}_4{\mathrm{S}}_8$.

Figure 3

Modified Arrott plot [isotherms of $M^{1/\beta }$ vs ${\left(H/M\right)}^{1/\gamma }$ with (a) 3D Heisenberg model $(\beta =0.365,\gamma =1.386)$; (b) 3D $XY$ model $(\beta =0.345,\gamma =1.316)$; (c) 3D Ising model $(\beta =0.325,\gamma =1.24)$; and (d) tricritical mean-field model $(\beta =0.25,\gamma =1.0)$. Each curve was processed by a proper vertical translation for clear presentation.

Figure 4

Normalized slopes $\left[\mathrm{NS}=S\left(T\right)/S\left(T_{\mathrm{C}}\right)\right]$ of theoretical critical models as a function of temperature.

Figure 5

(a) Temperature dependence of spontaneous magnetization $M_{\mathrm{S}}$ (left axis) and inverse initial susceptibility ${\chi }_0^{-1}$ (right axis) [the solid curves are fitted by Eqs. (1) and (2)]; (b) Kouvel-Fisher plot of $M_{\mathrm{S}}$ (left axis) and ${\chi }_0^{-1}$ (right axis) for ${\mathrm{GaV}}_4{\mathrm{S}}_8$ (straight lines are the linear fitting to the data).

Figure 6

Isothermal magnetization $\left[M\left(H\right)\right]$ at $T=12\mathrm{K}$ for ${\mathrm{GaV}}_4{\mathrm{S}}_8$. The inset represents the same plot on a log-log scale with the fitted straight line following Eq. (3).

Figure 7

(a) Scaling plots of renormalized magnetization $m$ vs renormalized field $h$; (b) $m^2$ vs $h/m$ around the critical temperature for ${\mathrm{GaV}}_4{\mathrm{S}}_8$. The insets are those on the log-log scale.

Figure 8

(a) Magnified $m$ vs $h$ below $T_{\mathrm{C}}$ in the low-field region on a log-log scale with the fitted red solid lines; (b) the magnetic phase diagram of ${\mathrm{GaV}}_4{\mathrm{S}}_8$ derived from the $\left[M\left(T\right)\right]$ and critical analysis (SKL = skyrmion lattice). The cycloidal state is marked; refer to Ref. [4].