Highly persistent spin textures with giant tunable spin splitting in the two-dimensional germanium monochalcogenides

Abstract

The ability to control the spin textures in semiconductors is a fundamental step toward novel spintronic devices, while seeking desirable materials exhibiting persistent spin texture (PST) remains a key challenge. The PST is the property of materials preserving a unidirectional spin orientation in the momentum space, which has been predicted to support an extraordinarily long spin lifetime of carriers. Herein, by using first-principles density functional theory calculations, we report the emergence of the PST in the two-dimensional (2D) germanium monochalcogenides (GeMC). By considering two stable formation of the 2D GeMC, namely the pure GeX and Janus Ge 2 XY monolayers (X, Y = S, Se, and Te), we observed the PST around the valence band maximum where the spin orientation is enforced by the lower point group symmetry of the crystal. In the case of the pure GeX monolayers, we found that the PST is characterized by fully out-of-plane spin orientation protected by C 2v point group, while the canted PST in the y-z plane is observed in the case of the Janus Ge 2 XY monolayers due to the lowering symmetry into C s point group. More importantly, we find large spin-orbit coupling (SOC) parameters in which the PST sustains, which could be effectively tuned by in-plane strain. The large SOC parameter observed in the present systems leads to the small wavelength of the spatially periodic mode of the spin polarization, which is promising for realization of the short spin channel in the spin Hall transistor devices.

Full-zone persistent spin textures with giant spin splitting in two-dimensional group IV–V compounds

“…In table 4, we summarize the calculated values of α for all compounds of the A 2 B 2 MLs and compare these results with a few selected PST systems previously reported on several 2D materials. Taking Si 2 Bi 2 ML as an example, we find that that the calculated α is 2.39 eVÅ, which is comparable with that reported on 2D PST materials including GaXY (X = Se, Te; Y = Cl, Br, I) MLs (0.53-2.65 eVÅ) [27] and various 2D group IV monochalcogenide such as GeXY (X, Y = S, Se, Te) MLs (3.10-3.93 eVÅ) [30], and layered SnTe (1.28-2.85 eVÅ) [31][32][33][34]. However, this value is much larger than that predicted on WO 2 Cl 2 ML (0.90 eVÅ) [26] and TMDC MX 2 MLs with line defect such as PtSe 2 (0.20-1.14 eVÅ) [38] and (Mo,W)X 2 (X = S, Se) (0.14-0.26 eVÅ) [37].…”

“…While it remains to be confirmed experimentally, this approach allows us to design the PST without requiring the fine-tuning between the Rashba and Dresselhaus SOCs. This is particularly achieved on the class of materials exhibiting intrinsic spontaneous electric polarization as previously reported on bulk ferroelectric BiInO 3 [23], CsBiNb 2 O 7 [24], layered ferroelectric oxide Bi 2 WO 6 [25], and several two-dimensional (2D) ferroelectric systems including WO 2 Cl 2 [26], GaXY(X = Se, Te; Y = Cl, Br, I) [27,28], hybrid perovskite benzyl ammonium leadhalide [29], and group-IV monochalcogenide [30][31][32][33][34]. More recently, the symmetry-protected PST with purely cubic spin splitting has also been reported in bulk materials crystallizing in the 6m2 and 6 point groups [35].…”

“…The spin textures in the k-space were evaluated by using the spin density matrix of the spinor wave functions obtained from the DFT calculations [50]. As we applied previously on various 2D materials [27,28,30,31,33,38,51,52], we deduced the spin vector component (S x , S y , S z ) of the spin polarization in the reciprocal lattice vector ⃗ k from the spin density matrix, P σσ ′ ( ⃗ k, µ), calculated using the following relation,…”

“…On the other hand, the latter approach may provide an advantage for realizing the PST since the condition of the equal strength of the Rashba and Dresselhaus SOC can be eliminated. However, in addition to producing the local PST in a small part of the FBZ, this approach is limited only for the systems having polar crystallographic axis as previously reported on several bulk ferroelectric materials including BiInO 3 [23], CsBiNb 2 O 7 [24], layered ferroelectric oxide Bi 2 WO 6 [25], and 2D ferroelectric systems such as WO 2 Cl 2 [26], GaXY(X = Se, Te; Y = Cl, Br, I) [27,28], hybrid perovskite benzyl ammonium lead-halide [29], and group-IV monochalcogenide [30][31][32][33][34]. In contrast, for our system, there is no crystallographic polar axis observed in the crystal structure, thus the PST is mainly determined by the WPGS rather than by the CPGS [53].…”

“…In addition, the PST driven by the lower symmetry of the crystal has also been reported on wurtzite ZnO [10 10] surface [36] and several 2D transition metal dichalcogenides (TMDCs) with the line defect [37,38]. Although the symmetry-enforced PSTs have been extensively studied, most of them locally occurred in the small part around the high symmetry ⃗ k points or lines in the first Brillouin zone (FBZ) [23,24,[26][27][28][30][31][32][33][34][35]. This implies that the spin deviation away from the uniaxial SOF appears for the larger region in the FBZ, which has a considerable effect to induce the significant spin scattering and hence limits the stability of the PSH states [23,39].…”