Chemical potential of magnon polarons

TL;DR

This work develops a microscopic, rotationally invariant description of spin–lattice coupling to define a conserved angular-momentum chemical potential $μ$ for magnon–polaron quasiparticles in collinear ferromagnets and antiferromagnets. By analyzing high-symmetry crystals with circularly polarized TA phonons, it reveals chiral selectivity: in FM, both magnon–polaron branches share a single $μ$ weighted by their magnon content, while in AFM the four branches split into two chiral sectors each coupled to $μ$ with opposite sign. The authors construct a Boltzmann transport theory, deriving explicit expressions for angular-momentum and heat currents that interpolate to the decoupled limit and reproduce known magnon–polaron transport physics. The framework provides a rigorous basis for angular-momentum transport in strongly hybridized magnon–phonon systems and suggests extensions to lattices with intrinsic phonon angular momentum and to symmetry-engineered materials.

Abstract

Using a rotationally invariant formulation of spin-lattice coupling, we derive a rigorous definition of the chemical potential for magnon-polaron quasiparticles in collinear ferromagnets (FMs) and antiferromagnets (AFMs), valid when magnetoelastic scattering equilibrates magnons and acoustic phonons on timescales much shorter than those associated with quasiparticle-nonconserving relaxation processes. While our microscopic framework applies to generic magnon-phonon interactions, here we focus on high-symmetry crystals where the two transverse acoustic modes form a degenerate doublet. This doublet can combine into circularly polarized phonons, making the chiral selectivity of the coupling manifest: the FM magnon mode hybridizes only with the co-rotating phonon, whereas in collinear AFMs each magnon branch of opposite handedness couples to the phonon of the same chirality. We show that, in both FM and AFM systems, the nonequilibrium magnon-polaron gas is governed by a single chemical potential conjugate to the conserved axial angular momentum. In FMs, the two hybrid branches in the co-rotating sector share this chemical potential, weighted by their magnonic fractions; in AFMs, the four magnon-polaron branches split into two chiral sectors that carry opposite angular momenta and couple with opposite sign to the same chemical potential. Building on this microscopic thermodynamic framework, we formulate a Boltzmann transport theory for magnon-polarons and derive compact expressions for angular-momentum and heat currents that interpolate continuously to the decoupled regime and reproduce the phenomenological magnon-polaron transport framework underlying previous spin Seebeck analyses.

Figures (3)

• Figure 1: Schematic illustration of the magnon eigenmode precession and the rotationally invariant construction used to define the magnetoelastic coupling in a collinear antiferromagnet. (a) Linear spin–wave eigenmodes of the two–sublattice antiferromagnet. The $\alpha$ and $\beta$ modes correspond to counter-rotating collective precessions of the sublattices and carry angular momentum $-\hbar$ and $+\hbar$, respectively, forming the natural chiral basis in which the antiferromagnetic BdG Hamiltonian is diagonal. (b) Equilibrium and displaced positions $\mathbf{R}_i$ and $\mathbf{r}_i$ of a G-type antiferromagnet. The local easy–axis at site $i$ is defined geometrically from the instantaneous positions of the nearest neighbors above and below the site, $\mathbf{r}_{i,\,z\pm}$, thereby ensuring that the anisotropy axis $\hat{\mathbf{e}}^{\pm}_{z}(\mathbf{r}_i)$ simultaneously rotates with lattice distortions and preserves global rotational invariance.
• Figure 2: Ferromagnetic magnon (dashed), transverse acoustic phonon (dotted), and magnon–polaron (red and blue) dispersions for $\mathbf{k} \parallel \hat{\mathbf{z}}$ and $\mathbf{B}_0 \parallel \hat{\mathbf{z}}$ computed using material parameters for YIG, see Table \ref{['tab:my_label']}. For clarity, the magnetoelastic coupling constant $\eta_+$ has been enhanced 30–fold so that the anti-crossing is visible on the scale of the plot. Hybridization between the magnon and the circularly polarized TA phonon with matching handedness produces two magnon–polaron branches with mixed angular–momentum character, determined by their respective magnon weights $s_\mathbf{k}$. For $B_0=3.96 \,\text{T}$, the TA branch becomes locally tangent to the magnon branch, maximizing the phase space for magnon–polaron formation and yielding $s_\mathbf{k}\simeq 1/2$ for both modes over a broad range of wave vectors (see insets).
• Figure 3: Antiferromagnetic magnons (dashed), transverse acoustic phonons (dotted), and magnon–polaron (red and blue) dispersions for $\mathbf{k} \parallel \hat{\mathbf{z}}$ and $\mathbf{B}_0 \parallel \hat{\mathbf{z}}$ computed using material parameters for MnF$_2$, see Table \ref{['tab:my_label']}. For clarity, the magnetoelastic coupling constants $\eta_\pm$ have been enhanced 5–fold so that the anti-crossings are visible on the scale of the plot. Hybridization between the magnons and the circularly polarized TA phonons with matching handedness produces two pairs of magnon–polaron branches, one pair in each chiral channel, with mixed angular–momentum character determined by their respective magnon weights $s_\mathbf{k}$ (see insets). (a) Right–handed channel. (b) Left–handed channel.