Electric-Polarization Probe of the Magnon Orbital Moment Current in Altermagnet

Abstract

Efficient transport of spin and orbital moments, and their electrical detection, are among the main challenges in spintronics and orbitronics. In magnetic insulators, these currents are mediated by magnons. In addition to carrying spin and orbital moment, the orbital motion of a magnon combined with its magnetic moment, generates an effective electric dipole moment. Here, we develop a theoretical framework for Seebeck- and Nernst-type transport of the magnon orbital moment (MOM) and its associated electric dipole moment (EDM). We identify a Drude-like scattering contribution and an intrinsic component governed by the generalized Berry curvatures of magnon bands. We show that a measurable transverse voltage generated by the EDM current provides a direct electrical detection scheme for magnon orbital transport. Applying our theory to an hexagonal altermagnet, we obtain an experimentally accessible voltage of approximately $0.4~μ$V. Our results establish a concrete electrical probe of magnon orbital transport and highlight magnons as potential low-dissipation information carriers for orbitronics.

Figures (5)

• Figure 1: MOM and EDM Nernst responses in an hexagonal altermagnet. (a) MOM Nernst effect: oppositely oriented orbital moments flow in opposite transverse directions under a thermal gradient and accumulate at the sample edges. (b) The associated EDM Nernst effect: the transverse flow of EDMs leads to electric polarization and edge accumulation. This enables electrical detection of magnon orbital transport.
• Figure 2: Altermagnetic model and band-geometric properties of magnon bands.(a) Honeycomb lattice of the two-sublattice altermagnetic model. Red (spin-up) and blue (spin-down) arrows denote sublattices A and B, respectively. The NN isotropic exchange interaction is $J$, while anisotropic NNN exchange couplings are $J_1$, $J_1+\delta J$, and $J_1-\delta J$. The DMI vector for the NNN bonds indicated by pink arrows is $\bm D_{A(B)} = +D^z \hat{z}$. The real-space lattice vectors are $\bm a_1 = (\sqrt{3},0)a$ and $\bm a_2 = (\sqrt{3}/2,3/2)a$. (b) Dispersion of the $\alpha$ magnon band, with the hexagonal Brillouin zone boundary shown by the dotted line. (c) and (d) Momentum-space distributions of the MOM and the corresponding OBC of the $\alpha$ mode. (e) and (f) Momentum-space distributions of the EDM and the corresponding DBC of the $\alpha$ mode. The parameters used are $\{J, J_1, \delta J, K, D^z\} = \{12.4, -5.48, 0.8, -0.3, 0.3\}\,\mathrm{meV}$ with spin $S=1$.
• Figure 3: Variation of the response tensors in the $(\delta J, T)$ parameter space for a thermal field $\bm E_T = -(\nabla_y T/T)\hat{y}$. (a) Fermi-sea contribution to the MOM Nernst effect of the MOM polarized along $\hat{z}$. (b) and (c) Fermi-sea and Fermi-surface contributions, respectively, to the EDM Nernst effect of the EDM oriented along $\hat{x}$-axis. (d) Fermi-surface contribution to the EDM Seebeck effect of the EDM with the same orientation. All parameters are identical to those used in Fig. \ref{['fig:model_BGQs']}.
• Figure 4: DMI and temperature dependence of transport coefficients for thermal field $\bm E_T = - (\nabla_y T/T)\hat{y}$. (a) Fermi-sea contribution to the MOM Nernst effect with moment oriented along $\hat{z}$. (b,c) Fermi-sea and Fermi-surface contributions to the EDM Nernst response for dipole oriented along $\hat{x}$. (d) Fermi-surface contribution to the corresponding EDM Seebeck response. All other parameters are the same as in Fig. \ref{['fig:model_BGQs']}.
• Figure 5: Equilibrium polarization and induced transverse voltage.(a,b) Equilibrium polarization $P_0^x$ as functions of $(\delta J, T)$ and $(D^z, T)$, respectively. (c) Spatial profile of electric polarization $P^x(x)$ for a transverse temperature gradient. (d) Transverse electric voltage as a function of sample width $W$. Parameter values: $D^z = 0.3$ meV for (a,c,d), $\delta J = 1.0$ meV for (b,c,d), $T = 100$ K, $\tilde{\tau} = 1$ ns, $a = 1~\text{\AA}$, and $\chi = 1$ for (c,d). All remaining parameters are the same as in Fig. \ref{['fig:model_BGQs']}.