Altermagnetic Spin Precession and Spin Transistor

Abstract

Altermagnets hold great potential for spintronic applications, yet their intrinsic spin dynamics and associated transport properties remain largely unexplored. Here, we investigate spin-resolved quantum transport in a multi-terminal setup based on a $d$-wave altermagnet. It is found that the altermagnetic spin splitting in momentum space induces an interesting spin precession in real space, giving rise to characteristic spin patterns. This altermagnetic spin precession manifests as a spatial modulation of the Hall voltage, whose oscillation period provides a direct measure of the spin-splitting strength. When the altermagnetism is electrically tunable, the proposed setup functions as a prototype for a highly efficient spin transistor. The key physical effects are shown to be robust against dephasing and crystalline warping. Our work not only identifies a fingerprint signature of altermagnets, offering a direct probe of the altermagnetic spin splitting, but also represents an important step toward bridging their fundamental physics with practical spintronic applications.

Figures (3)

• Figure 1: (a) Schematic of the proposed setup, consisting of a central altermagnetic region connected to two longitudinal leads (1 and 2) and multiple transverse voltage probes. Top and bottom gates ($V_{tg}$ and $V_{bg}$) control the altermagnetic splitting, which is essential for the spin transistor. The $d$-wave altermagnetic Fermi surfaces are illustrated in the inset. (b) Altermagnetic spin precession in real space, with arrows indicating the local spin orientations. (c,d) Spatial distribution of spin component $S_y$ for nonequilibrium propagating electrons under (c) point injection and (d) line injection, with the injected spins polarized along the $x$ direction. The solid and dashed arrows highlight the corresponding spin modulation along the $x$ direction in (c) and (d). A square-root scale is applied to the colorbar to enhance the contrast around zero.
• Figure 2: (a) Transmission probabilities from lead 1 to the upper (blue dashed line) and lower (blue solid line) probes as a function of $x$. The red solid line represents the Hall voltage. (b) Hall voltage as a function of $x$ for different altermagnetic splitting strengths $\alpha_{A}$, with its zeros marked by green points. The gray dashed lines correspond to $\tilde{x}_n(\alpha_A)$. (c,d) Same plots including the dephasing effect with $\Gamma_{v}=0.03$. The relevant parameters are $B=2$, $\mu=1$, $\alpha_{A}=0.8$, and $a=0.5$. The altermagnetic region has a size of $50\times 50$, and the hopping between the leads and the scattering region is $0.1t$.
• Figure 3: Transmission probabilities and Hall voltage as a function of $\alpha_{A}$ at $x=12.5$. All other parameters are the same as in Fig. \ref{['fig2']}.