Antialtermagnetic Magnons and Nonrelativistic Thermal Edelstein Effect

Abstract

Odd-parity magnets are noncollinear compensated magnets with spin-split band structure in the absence of spin-orbit coupling and dipolar interactions. In contrast to altermagnets, their spin-polarized band structure breaks inversion symmetry, but preserves time-reversal symmetry rendering their spin texture odd in momentum space. Here, we study the spin dynamics of the magnetic texture and compute the band structure and spin polarization of magnons. We present minimal spin models of noncoplanar odd-parity magnets free of relativistic interactions that host p- and f-wave spin textures for the magnetic excitations. We demonstrate that two of these models exhibit collinear spin textures, i.e., the magnon spin polarization is restricted to a global (quantization) axis independent of the momentum giving rise to antialtermagnetism, previously associated primarily with coplanar ground states. Finally, the nonrelativistic magnonic thermal Edelstein effect -- a nonequilibrium magnetization induced by a temperature gradient -- is shown to exist for p-wave magnets in linear response and inherits its anisotropic angular dependence from the partial-wave character of the spin-polarized band structure. Our findings suggest that insulating antialtermagnets are promising candidates for magnon spintronics applications.

Figures (5)

• Figure 1: Magnons in unconventional magnets. (a) Altermagnets possess collinear magnetic ground states giving rise to two linear Goldstone magnons with quantized spins and even-parity splitting. The spin is confined to a global quantization axis producing a collinear spin texture. (b), (c) Noncoplanar odd-parity magnets generally possess $\mathcal{T} \bm{{\tau}}$ symmetry and exhibit three linear Goldstone magnons with nonquantized spins. (b) Vector odd-parity magnets lack additional symmetries to constrain the magnon spin to a global axis. The magnon spin must be treated as a vector that lives in two- or three-dimensional space. (c) Antialtermagnets are odd-parity magnets with additional symmetries that constrain the magnon spin to a global axis. Although not quantized, the magnon spin forms a collinear spin texture and can be treated as a scalar. Originally proposed in coplanar systems hellenes_unconventional_2024, here we uncover antialtermagnets in noncoplanar systems, which exhibit a $n$-fold spin rotation $C_{n}^{\mathrm{s}}$ and a translation $\bm{{\tau}}'$ with $n \geq 2$.
• Figure 2: Vector $p$-wave kagome model. (a) Lattice structure, magnetic ground state configuration, and magnetic interactions $F$, $J_3$, $J_6$. The gray transparent quadrangle indicates the magnetic unit cell and the red and blue triangles distinguish the opposite local spin configurations related by time reversal. (b) Magnon band structure along a high-symmetry path in the first Brillouin zone [high-symmetry points indicated in (c)]. (c), (d) Isoenergy lines for (c) $\varepsilon = 5 F S$ and (d) $\varepsilon = 10 F S$. In panels (b)--(d), the color represents the spin angle within the $xy$ plane [see inset of (d)], while the line thickness corresponds to the magnitude of the spin. Note that the $k_x$ and $k_y$ axes are rotated by 30° with respect to the $x$ and $y$ axes [see panel (a)]. The parameters are $J_3 = 2 J_6 = F$.
• Figure 3: Antialtermagnetic $p$-wave kagome model. (a) Lattice structure and magnetic ground state configuration. The gray transparent quadrangle indicates the magnetic unit cell and the colored triangles distinguish the 4 different local spin configurations related by (the combination of) time reversal and 2-fold spin rotation. (b) Magnon band structure along a high-symmetry path in the first Brillouin zone [high-symmetry points indicated in (c)]. (c) Isoenergy lines for $\varepsilon = 5 F S$ in the first Brillouin zone (hexagon). In panels (b) and (c), the color represents the $z$ component of the spin (see color bars), while the line thickness corresponds to its magnitude. The parameters are $J_3 = 2 J_6 = F$.
• Figure 4: Three-dimensional $f$-wave model consisting of stacked triangular lattices. (a) Real-space lattice, magnetic ground state configuration, and magnetic interactions $F$, $J_2$, $J_\perp$. Collinear magnetic sites are colored alike. The two layers in the magnetic unit cell are related by time reversal. (b) Band structure along a high-symmetry path in the first Brillouin zone (see inset). (c)--(h) Isoenergy surfaces for $\varepsilon = 2 F S$ [dashed line in panel (b)]. Panels (c), (d) show band 1, (e), (f) show band 2, and (g), (h) show band 3 starting from the lowest energy in panel (b). The color in panels (b)--(h) represents the [111] component of the spin (see color bar). The parameters are $J_2 = -J_\perp = -F$.
• Figure 5: Temperature-dependent linear thermal Edelstein effect of the $p$-wave antialtermagnet with parameters $J_3 = 2 J_6 = F$. Here, $\tau$ is the relaxation time and $a$ is the nearest-neighbor distance. Inset: Nonequilibrium $z$ spin polarization as a function of the direction of $-\grad T$. The angle of 0° corresponds to $-\grad T \parallel \hat{\bm{{x}}}$. Different colors correspond to different temperatures (see legend). For better visibility, the data for $T = 0.01$ (red curve) and $0.11\,F S / k_\text{B}$ (purple curve) have been rescaled by a constant factor (see annotations). Solid and dashed lines indicate positive and negative sign, respectively.