Strain-Induced Modulation of Spin Splitting and Persistent Spin Textures in Low-Symmetry 2D Hybrid Perovskites: A case study of RP phase

Abstract

We report the observation of a persistent spin texture (PST) in pseudo-2D hybrid perovskite, characterized by significant spin splitting strength on the order of \(3 \, \text{eV} \cdot \textÅ\). Using first-principles density functional theory (DFT) calculations, complemented by a \(\mathbf{k} \cdot \mathbf{p}\) model analysis, we validate the presence of PST and its robustness under various conditions. The material's non-centrosymmetric nature and strong spin-orbit coupling ensure uniform spin orientation in momentum space, enabling long spin lifetimes and promising spintronic applications. Furthermore, we demonstrate the tunability of the spin splitting via the application of external strain and stress, offering a versatile approach to control spin configurations. Our results highlight the potential of this perovskite system for next-generation spintronic devices, where external perturbations can be used to precisely modulate electronic properties.

Figures (5)

• Figure 1: (a) Illustration of a doubly degenerate conduction band at $k = 0$. (b) Spin-split bands along a high-symmetry $k$-path, where $\Delta E$ represents the splitting energy, and $\Delta k$ denotes the momentum shift at the energy minimum. (c), (d), and (e) depict schematics of the spin textures for Rashba, Dresselhaus, and persistent spin splitting mechanisms, respectively. The blue and red arrows indicate the spin orientations in the outer and inner bands, respectively.
• Figure 2: (a) Structure of $(\text{MIPA})_2\text{PbI}_4$ in Aea2 space group. The black, purple, grey, brown, and light pink balls denote the Pb, I, N, C and H, respectively. (b) Brillouin Zone for respective materials including high symmetric $k$-path Y (0,$k_y$,0) - $\Gamma$ (0,0,0) - Z ($k_x$,0,0) is shown.
• Figure 3: The spin-resolved band structures along the high-symmetry path are depicted. The color bars indicate the expectation values of the spin components $S_x$, $S_y$, and $S_z$.
• Figure 4: Spin textures of the valence band for (MIPA)$_2$PbI$_4$ around the $\Gamma$ point obtained using DFT [(a), (b)] and the $k \cdot p$ model [(c), (d)], and spin textures of the conduction band for (MIPA)$_2$PbI$_4$ around the $\Gamma$ point obtained using DFT [(e), (f)] and the $k \cdot p$ model [(g), (h)]. Spin textures are presented using the convention [(a)–(h)] where the energy of the inner branch is less than or equal to that of the outer branch at any $(k_x, k_y)$ point in the given range. The color represents the $y$ component of the spin textures. The $x$ component shows a negligible contribution compared to the $y$ component around the $\Gamma$ line, while the $z$ component is zero in the $k_x$–$k_y$ plane. (i) Band structure of the valence band maximum (VBM) and (j) conduction band minimum (CBm) of (MIPA)$_2$PbI$_4$ around the $\Gamma$–Z line (energy vs. $k_x$), projected onto the $y$ component of the spin direction. The black solid lines and red dashed lines represent results obtained using DFT and model parameterization, respectively.
• Figure 5: (a) and (b) show the variation in the linear spin splitting coefficient as a function of uniaxial strain in the $a$- and $b$-directions, respectively. (c) shows the change in the spin splitting coefficient as a function of stress (GPa).