Persistent altermagnetism

Abstract

Persistent spin textures with collinear spin polarization are promising platforms for spintronics applications. However, their typically relativistic spin-orbit origin leads to weak spin splittings and fragile spin coherence. Here, we demonstrate a previously overlooked class of robust collinear spin polarization protected by mirror symmetry in combination with a strong exchange-driven altermagnetic order, which persists even in the presence of spin-orbit coupling. By combining first-principles calculations with a systematic classification of spin and magnetic layer groups, we identify this phenomenon-termed persistent altermagnetic spin polarization (PASP)-to occur in 158 spin layer groups and in representative materials including metallic V$_2$Te$_2$O, insulating La$_2$CuO$_4$, and semiconducting VSI$_2$. Furthermore, we theoretically demonstrate that PASP is ferroelectrically switchable in VSI$_2$. Finally, we show that this PASP switching can lead to large changes in spin-filtering conductance in a model all-altermagnetic junction. Our results open the possibility of employing PASP in all-altermagnetic magnetic memory and spin-transistor devices and establish universal principles of altermagnetism in spin-orbit-coupled monolayers.

Figures (4)

• Figure 1: Persistent spin texture versus persistent altermagnetic spin polarization (PASP). (a) Schematic illustration of the persistent spin texture induced by weak Ising spin-orbit coupling (SOC). (b) Electronic band structures of NbSe$_2$ with (top) and without (bottom) SOC. (c) PASP in a $d$-wave Lieb-lattice altermagnet (AM). (d) Band structure of the Lieb-lattice AM V$_2$Te$_2$O with (top) and without (bottom) SOC. The large altermagnetic splitting of $\sim1.5$ eV is indicated by the blue double arrow in (d). The positive (negative) spin expectation value $\langle S_z \rangle$ is highlighted in magenta (cyan) color.
• Figure 2: Three types of spin polarization in AMs with SOC. (a) Non-collinear relativistic spin texture of the topmost valence band of the non-persistent AM OsF$_4$. (b) Magnetic structure of OsF$_4$. (c) Nonrelativistic spin expectation value for the same band. (d) Strong PASP in the selected band at the Fermi level of the strong persistent AM V$_2$Te$_2$O. (e) Magnetic structure of V$_2$Te$_2$O. (f) Nonrelativistic spin expectation value with large altermagnetic splitting. (g) Weak PASP in the topmost valence band of the weak persistent AM La$_2$CuO$_4$. (h) Magnetic structure of La$_2$CuO$_4$. (i) Nonrelativistic band dispersion with spin degeneracy enforced by the $[C_2||M_z]$ symmetry. The gray plane $\mathcal{M}_z$ in (e,h) denotes the horizontal mirror plane. Transition-metal atoms ($\mathrm{TM} = \mathrm{Os},\mathrm{V},\mathrm{Cu}$) with opposite spin orientations are shown in magenta (TM$\uparrow$) and cyan (TM$\downarrow$). The Te and La atoms in (e) and (h) are omitted for clarity. See SM for the full crystal structures.
• Figure 3: Altermagnetoelectric effect with strong PASP in the ferroelectric AM VSI$_2$. (a,b) Crystal and magnetic structures of VSI$_2$ for opposite directions of the ferroelectric polarization $\boldsymbol{P}_{\rm{E}}$, switchable by an in-plane electric field (black double arrow). V atoms with positive (negative) out-of-plane magnetic moments are shown in magenta (cyan). O (S) atoms are shown in blue (red). Red arrows indicate the direction of $\boldsymbol{P}_{\rm{E}}$. (c) and (d) show the strong PASP of the topmost valence band for the configurations in (a) and (b), respectively. (e) Relativistic band structure corresponding to the configuration in (b,d).
• Figure 4: Spin-filtering junction based on electrically switchable PASP. (a) Schematic of device: the source (S) and drain (D) leads (gray) are composed of identical metallic AMs with fixed PASP aligned along the $\hat{z}$ direction. An altermagnetoelectric (AME) hosting strong PASP forms the central scattering region (blue). (b) and (c) show the energy bands of the model describing the 2D bulk metallic AM leads and the semiconducting AME with switchable ferroelectric polarization $\boldsymbol{P}_{\rm{E}}$, respectively. (d) Calculated zero-temperature linear conductance $G$ for parallel (P, blue line) and antiparallel (AP, black line) mutual orientation of the leads and AME region. (e) Computed tunneling magnetoresistance ratio.