Emergent spin accumulation in non-Hermitian altermagnets

Abstract

The recent interest in non-Hermitian (NH) systems has significantly broadened their application across condensed matter physics, offering a unique framework to explore out-of-equilibrium phenomena. Simultaneously, altermagnets have emerged as a distinct magnetic class, characterized by unconventional spin-split bands protected by crystal symmetries. In this work, we investigate the interplay between non-Hermitian dynamics and spin transport in these materials, focusing on the Edelstein effect. We demonstrate that the introduction of non-Hermiticity in $d$-wave altermagnets and $p$-wave unconventional magnets opens novel susceptibility components that are inaccessible in Hermitian counterparts. Our analysis reveals that these susceptibility channels are highly sensitive to the underlying symmetry of the order parameter. Crucially, our results show that the non-conservative nature of the system leads to the selective gain and loss of specific spin components, a phenomenon that can be tuned by the interplay between dissipation and the altermagnetic order. These components exhibit a distinct gain/loss profile that depends strictly on the Néel vector orientation, providing a new route for manipulating spin degrees of freedom through controlled non-conservative processes in emerging magnetic materials

Figures (6)

• Figure 1: Schematic representation of the in-plane electric field effect at the AM(UM)/FM lead interface. The diagram illustrates the coupling between the external electric field $\vec{E}$ and the interface formed by a ferromagnetic lead (FM) and a unconventional magnet. The respective Fermi surfaces under Rashba SOC are shown, highlighting the $d$-wave symmetry (AM) and the $p$-wave symmetry (UM). The electric field in $\hat{x}$ direction gives the spin accumulation in $i$ direction accordingly with $\delta s_i = \chi_{ix} E_x$.
• Figure 2: Real part of the spin susceptibility tensor for a NH systems with Néel vector along the $z$ direction. Left panel [(a), (c)]: $d$-wave AM and Right panel [(b), (d)] : $p$-wave UM. The transversal component $\chi_{xy}$ [(a) and (b)] decreases for $\gamma \neq 0$ while the diagonal component $\chi_{xx}$ arise for $d_{xy}$ wave (c) and an out-of plane component $\chi_{xz}$ decreases by the action of $\gamma$ (d). For (a) and (c), $\alpha = 0.2$, while for (b) and (d), $t_{x} = 0.2, t_y=0$ and $t_x=0, t_y =0.2$ for $p_x$ and $p_y$ respectively.
• Figure 3: Real part of the spin susceptibility components for a non-Hermitian systems with Neel vector along $x$ direction. Left panel: $d$-wave AM [(a), (c)] and Right panel : $p$- wave UM [(b), (d)]. The transversal component $\chi_{xy}$ [(a) and (b)] decreases for $\gamma \neq 0$, finite out-of plane component $\chi_{xz}$ arise for $d_{xy}$ wave (c) and longitudinal component $\chi_{xx}$ decreases by the action of $\gamma$ (d). For (a) and (c), $\alpha = 0.2$, while for (b) and (d), $t_{x} = 0.2, t_y=0$ and $t_x=0, t_y =0.2$ for $p_x$ and $p_y$ respectively.
• Figure 4: Real part of the spin susceptibility components for a non-Hermitian systems with Neel vector along $y$ direction. Left panel [(a), (c)]: $d$-wave AM and Right panel [(b), (d)] : $p$-wave UM. The transversal component $\chi_{xy}$ [(a) and (b)] decreases for $\gamma \neq 0$, finite out-of plane component $\chi_{xz}$ arise for $d_{x^{2}-y^{2}}$ wave (c) and longitudinal component $\chi_{xx}$ for $p_y$ decrease by the action of $\gamma$ (d). For (a) and (c), $\alpha = 0.2$, while for (b) and (d), $t_{x} = 0.2, t_y=0$ and $t_x=0, t_y =0.2$ for $p_x$ and $p_y$ respectively.
• Figure 5: Momentum-space spin textures for $p_x$-wave and $d_{xy}$-wave magnetic models. The top panel displays the spin textures for the $p_x$-wave UM, while the bottom panel shows the results for the $d_{xy}$-wave AM. From left to right, the columns represent the expectation values of the spin operators $S_{x}$ [(a), (c)], $S_{y}$ [(b), (d)], and $S_z$ [(c), (f)], respectively. In both cases the white line described where the texture is ill-defined. For $p_x$-wave UM, two EP is well pronunced in (b), while for $d_{xy}$- wave AM four EPs arise as can observed in (d) and (e).