Full-plane persistent spin textures with cubic order intrinsic and anisotropic band splitting in bulk Lead-free materials

Spin-orbit coupling (SOC) effects occurring in noncentrosymmetric materials are known to be responsible for nontrivial spin configurations and a number of emergent physical phenomena such as electrical control of spin degrees of freedom and spin-to-charge conversion. The materials preserving a uniform spin configuration in the momentum-space, known as persistent spin texture (PST), provide long carrier spin lifetimes through persistent spin helix (PSH) mechanism. However, most of the PST studied till now are attributed to the linear in \textbf{\textit{k}} splitting and cease to exist locally around certain high-symmetry-point of first Brillouin Zone (FBZ). The persistent spin textures with purely cubic spin splittings have drawn attention owing to unique benefits in spin transport. Here, by using the relativistic first-principles calculations supplemented with \textbf{\textit{k.p}} analysis, we report the emergence of purely cubic splitting (PCS) belonging to $D_{3h}$ point group, which is enforced by in-plane mirror and three-fold rotation operations. In addition, the in-plane mirror symmetry operation sustains the PST in larger region (i.e. full planes) of FBZ alongside giant spin splitting. Our results also demonstrate how application of uniaxial strain could be envisaged to tune the magnitude of the PCS, preserving the PST. The observed PSTs provide a route to non-dephasing spin transport with larger spin-Hall conductivity, thus offering a promising platform for future spintronics devices.