Novel Anisotropy of Upper Critical Fields in Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$

Studying the upper critical field ($\mu_0$$H$$_{\rm{c2}}$) and its anisotropy of superconductors is of great importance because it can provide an unusual insight into the pair-breaking mechanism. Since Fe$_{1+y}$Te$_{1-x}$Se$_x$ exhibits the high $\mu_0$$H$$_{\rm{c2}}$ and small anisotropic superconductivity, it has attracted considerable attention. However, some issues related to $\mu_0$$H$$_{\rm{c2}}$ are still unknown, including the effect of excess Fe content on $\mu_0$$H$$_{\rm{c2}}$ behavior and the origin of the crossover of the $\mu_0H_{\rm{c2}}^c$ -- $T$ and $\mu_0H_{\rm{c2}}^{ab}$ -- $T$ curves. In this work, the value of $\mu_0$$H$$_{\rm{c2}}$ of Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ single crystals with controlled amounts of excess Fe was obtained by resistivity measurements over a wide range of temperatures down to $\sim$ 1.5 K, and magnetic fields up to $\sim$ 60 T. The crossover of the $\mu_0H_{\rm{c2}}^c$ -- $T$ and $\mu_0H_{\rm{c2}}^{ab}$ -- $T$ curves was found to be independent of the excess Fe content. The angle dependence of $\mu_0H_{\rm{c2}}$ was also checked. The $\mu_0H_{\rm{c2}}(\theta)$ symmetry at higher temperature near $T_c$ could be fitted by anisotropic G-L model, and novel fourfold symmetry of $\mu_0H_{\rm{c2}}$ at lower temperature was found. Based on our spin-locking pairing model, the crossover behavior originates from the anisotropic spin-paramagnetic effect, and the novel fourfold symmetry of $\mu_0H_{\rm{c2}}$ could be understood by our extended anisotropic G-L model.