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(a) Schematic view of band dispersion showing an anisotropic splitting around k = (0, 0, 0) and (b) the corresponding Fermi line are presented. The red and blue arrows indicate Sz and −Sz spin orientation in the momentum space, respectively. In Fig. (b), the Fermi line has the shifted two pair loops characterized by the shifting wave vector Q along the kx direction where the spins are persisting in the fully outof-plane direction, resulting in the formation of the persistent spin textures (PST). (c) Schematic view of the persistent spin helix (PSH) mode emerge under the PST formation with the wavelength of lP SH = 2π/| Q|. (d) Schematic correlation between the in-plane ferroelectricity and the spin textures is shown. The two stable ferroelectric phases of the 2D materials having opposite in-plane ferroelectric polarization are indicated. The switching spin textures are expected by reversing the in-plane ferroleectric polarization.
Source publication
The coexistence of ferroelectricity and spin-orbit coupling (SOC) in noncentrosymmetric systems may allow for a nonvolatile control of spin degrees of freedom by switching the ferroelectric polarization through the well-known ferroelectric Rashba effect (FRE). Although the FER has been widely observed for bulk ferroelectric systems, its existence i...
Contexts in source publication
Context 1
... dispersion indicates that a strongly anisotropic spin splitting occurs around the k = (0, 0, 0) point, i.e., the energy bands are lifted along k x direction but are degenerated along the k y direction [ Fig. 2(a)]. Importantly, this dispersion is characterized by the shifting ...
Context 2
... Eqs. (10) and (11) implies that a constant-energy cut shows two Fermi loops whose centers are displaced from their original point by ± Q as schematically shown in Fig. ...
Context 3
... shows that the spin configuration in the k-space is locked being oriented in the out-of-plane directions as schematically shown in Fig. 2(b). Such a typical spin configuration forms a persistent spin textures (PST) similar to that observed for [110] Dresselhauss model 55 . Previously, it has been reported that the PST is known to host a long-lived helical spin mode known as a persistent spin helix (PSH) 55-57 , enabling long-range spin transport without dissipation 55-60 , ...
Context 4
... schematic picture of the PSH mode enforced by the unidirectional SOF is displayed in Fig. 2(c), where a spatially periodic mode of the spin polarization with the wavelength l P SH is shown. Such spinwave mode protects the spins of electrons from decoherence through suppressing the Dyakonov-Perel spin relaxation mechanism 61 and renders an extremely long spin lifetime 55-60 . Finally, we study the correlation between spin ...
Context 5
... mechanism 61 and renders an extremely long spin lifetime 55-60 . Finally, we study the correlation between spin textures and ferroelectricity. Here, an important property called reversible spin textures holds, i.e., the direction of the spin textures is locked and switchable by reversing the direction of the spontaneous electric polarization. Fig. 2(d) shows a schematic view of the spin textured ferroelectric in the GaXY ML compounds showing fully reversible out-of-plane spin textures. It is shown that switching the direction of the in-plane ferroelectric polarization from P to − P leads to reversing the direction of the out-of-plane spin textures from z-to ...
Context 6
... doublet remains for the k along the Γ − Y line, which is protected by the ¯ C 2y screw rotation and the ¯ M xy glide mirror reflection. Accordingly, a strongly anisotropic splitting is clearly observed around the Γ point as highlighted by the red line in Fig. 4(a), which is in good agreement with the energy dispersion shown in Eq. (10) as well as Fig. ...
Context 7
... around the Γ point [ Fig. 4(d)]. Here, two circular loops of the Fermi lines with the opposite S z spin components are observed, which are shifted along the Γ − X (k x ) direction. The observed spin textures, as well as Fermi lines, are all consistent well with our k · p Hamiltonian model presented in Eq. (7) and the schematic pictures shown in Figs. 2(a)-(b). Remarkably, the observed unidirectional out-of-plane spin textures in the present system lead to the PST 55,57 , which can host a long-lived helical spin-wave mode through the PSH mechanism 55-60 ...
Context 8
... dispersion indicates that a strongly anisotropic spin splitting occurs around the k = (0, 0, 0) point, i.e., the energy bands are lifted along k x direction but are degenerated along the k y direction [ Fig. 2(a)]. Importantly, this dispersion is characterized by the shifting ...
Context 9
... Eqs. (10) and (11) implies that a constant-energy cut shows two Fermi loops whose centers are displaced from their original point by ± Q as schematically shown in Fig. ...
Context 10
... shows that the spin configuration in the k-space is locked being oriented in the out-of-plane directions as schematically shown in Fig. 2(b). Such a typical spin configuration forms a persistent spin textures (PST) similar to that observed for [110] Dresselhauss model 55 . Previously, it has been reported that the PST is known to host a long-lived helical spin mode known as a persistent spin helix (PSH) 55-57 , enabling long-range spin transport without dissipation 55-60 , ...
Context 11
... schematic picture of the PSH mode enforced by the unidirectional SOF is displayed in Fig. 2(c), where a spatially periodic mode of the spin polarization with the wavelength l P SH is shown. Such spinwave mode protects the spins of electrons from decoherence through suppressing the Dyakonov-Perel spin relaxation mechanism 61 and renders an extremely long spin lifetime 55-60 . Finally, we study the correlation between spin ...
Context 12
... mechanism 61 and renders an extremely long spin lifetime 55-60 . Finally, we study the correlation between spin textures and ferroelectricity. Here, an important property called reversible spin textures holds, i.e., the direction of the spin textures is locked and switchable by reversing the direction of the spontaneous electric polarization. Fig. 2(d) shows a schematic view of the spin textured ferroelectric in the GaXY ML compounds showing fully reversible out-of-plane spin textures. It is shown that switching the direction of the in-plane ferroelectric polarization from P to − P leads to reversing the direction of the out-of-plane spin textures from z-to ...
Context 13
... doublet remains for the k along the Γ − Y line, which is protected by the ¯ C 2y screw rotation and the ¯ M xy glide mirror reflection. Accordingly, a strongly anisotropic splitting is clearly observed around the Γ point as highlighted by the red line in Fig. 4(a), which is in good agreement with the energy dispersion shown in Eq. (10) as well as Fig. ...
Context 14
... around the Γ point [ Fig. 4(d)]. Here, two circular loops of the Fermi lines with the opposite S z spin components are observed, which are shifted along the Γ − X (k x ) direction. The observed spin textures, as well as Fermi lines, are all consistent well with our k · p Hamiltonian model presented in Eq. (7) and the schematic pictures shown in Figs. 2(a)-(b). Remarkably, the observed unidirectional out-of-plane spin textures in the present system lead to the PST 55,57 , which can host a long-lived helical spin-wave mode through the PSH mechanism 55-60 ...
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