Altermagnetic Spin Precession and Spin Transistor

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 two-dimensional real space, giving rise to characteristic spin patterns. This altermagnetic spin precession manifests as a spatial modulation of the transverse Hall-like 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.