Magnetic Phase Diagram of a Lacunar Spinel GaV$_{\mathrm{4}}$Se$_{\mathrm{8}}$

The magnetic field ($H$) - temperature ($T$) phase diagram of a lacunar spinel GaV$_4$Se$_8$ is determined by means of AC magnetic susceptibility and magnetoelectric measurements on single crystals and classical Monte Carlo simulation. GaV$_4$Se$_8$ is pyroelectric below the structural phase transition temperature $T_{\mathrm{S}}=41\,\mathrm{K}$ and magnetically ordered below $T_{\mathrm{C}}=17.5\,\mathrm{K}$. AC magnetic susceptibility measurement has revealed that GaV$_4$Se$_8$ undergoes successive magnetic phase transitions with increasing applied magnetic field. Each phase is assigned to cycloidal, skyrmion lattice and forced ferromagnetic phases. Both cycloidal and skyrmion-lattice magnetic orders induce electric polarization up to around $10\,\mu \mathrm{C/m^2}$ compared with ferromagnetic order, suggesting a spin-driven magnetoelectric nature in GaV$_4$Se$_8$. The skyrmion lattice phase seems to be stable down to $T=2\,\mathrm{K}$ and up to $\mu_0 H=370\,\mathrm{mT}$. This enhanced stability of skyrmion lattice in GaV$_4$Se$_8$ compared with GaV$_4$S$_8$ may provide a key to understand the formation mechanism of the skyrmion lattice.