Orientation dependent anomalous Hall and spin Hall currents at junctions of altermagnets with $p$-wave magnets

TL;DR

This work analyzes charge and spin transport across a continuum AM–PM junction with full rotational freedom of crystallographic axes. By enforcing transverse momentum matching and spin-structured boundary conditions, it demonstrates finite longitudinal and transverse spin and charge currents despite zero net magnetization in each material. Key findings show that transverse conductivities can persist or even dominate when longitudinal ones vanish, and that these effects are tunable via orientation angles $\phi_a$, $\phi_p$ and relative spin axis $\beta$. The results establish AM–PM junctions as viable platforms for orientation-controlled, SOC-free anomalous and spin Hall phenomena with potential experimental realizations in specific AM and PM materials.

Abstract

We study charge and spin transport across a junction between an altermagnet (AM) and a $p$-wave magnet (PM) using a continuum model with boundary conditions tailored to the spin-split band structures of the two materials. Remarkably, although neither AM nor PM is spin-polarized, we find that the junction supports finite spin currents both longitudinally and transversely. We compute the longitudinal and transverse charge and spin conductivities as functions of the crystallographic orientations and the relative angle between the Néel vectors of AM and PM. Our results reveal that transverse charge and spin conductivities can be finite even when the longitudinal charge conductivity vanishes. For suitable parameter choices and orientation angles, the transverse conductivities are more prominent than the longitudinal ones. The origin of these effects lies in the matching and mismatching of transverse momentum modes ($k_y$) across the junction combined with the spin-dependent band splitting in AM and PM. Furthermore, while the transverse charge conductivity may be zero for certain orientations, the transverse spin conductivity remains finite due to unequal contributions of opposite $k_y$ channels. These findings highlight AM-PM junctions as a promising platform for tunable generation and control of transverse charge and spin currents driven purely by crystallographic orientation and spin structure.

Figures (8)

• Figure 1: Schematic of the AM–PM junction: light blue rectangle on the left shows AM whereas orange rectangle on the right shows PM. AM is rotated by angle $\phi_a$ and PM rotated by angle $\phi_p$. Fermi surfaces (FS): blue solid loops are for up-spin and red dashed loops are for down-spin. Elliptical loops on the left represent FS's of AM and circular loops on the right represent FS's of PM.
• Figure 2: (a) Longitudinal charge conductivity in units of $e^2/ha$ and (b) longitudinal spin conductivity in units of $e/a$ on the PM versus $\phi_a$ and $\phi_p$, (c,d) Fermi surfaces on the two sides of the junction for (c) $\phi_a=\pi/4$ and $\phi_p=\pi/2$ and (d) $\phi_a=0$ and $\phi_p=0$ at zero bias for the parameters $t_0=0.1t,~t_J=0.75t_0,~c=1,~\beta=0~,V_0=0,~\alpha=0.125t,~\mu_a=5\times 10^{-4}t_0$ and $\mu_p=-3\times 10^{-3}t$.
• Figure 3: (a) Transverse charge conductivity in the units of $e^2/ha$, (b) Transverse spin conductivity in units of $e/a$ on the PM at zero bias. Fermi surface at (c) $\phi_a=\pi/2$ and $\phi_p=\pi/2$ and (d) $\phi_a=0$ and $\phi_p=\pi/2$ for the same set of parameters as in Fig. \ref{['fig:G']}.
• Figure 4: (a) Longitudinal charge conductivity in units of $e^2/ha$, (b) longitudinal spin conductivity in units of $e/a$, (c) Transverse charge conductivity in units of $e^2/ha$ in the PM, versus $\beta$ and (d) Fermi surfaces for the same set of parameters as in Fig. \ref{['fig:G']} except for $\phi_a=0~{\rm and}~\phi_p=\pi/2$.
• Figure 5: (a), (c) Longitudinal and transverse charge conductivity in units of $e^2/ha$, (b), (d) longitudinal and transverse spin conductivity in units of $e/a$ versus $V_0$, for the same set of parameters as in Fig. \ref{['fig:G']} except for $\phi_a=0~{\rm and}~\phi_p=\pi/2$.