Taking an electron-magnon duality shortcut from electron to magnon transport

The quasiparticles in insulating magnets are the charge-neutral magnons, whose magnetic moments couple to electromagnetic fields. For collinear easy-axis magnets, this coupling can be mapped elegantly onto the scenario of charged particles in electromagnetic fields. From this mapping we obtain equations of motion for magnon wave packets equal to those of electron wave packets in metals. Thus, well-established electronic transport phenomena can be carried over to magnons: this duality shortcut facilitates the discussion of magnon transport. We identify the magnon versions of normal and anomalous Hall, Nernst, Ettingshausen, and Righi-Leduc effects. They are discussed for selected types of easy-axis magnets: ferromagnets, antiferromagnets, and ferrimagnets. Besides a magnon Wiedemann-Franz law and the magnon counterpart of the negative magnetoresistance of electrons in Weyl semimetals, we predict that certain low-symmetry ferrimagnets exhibit a nonlinear version of the anomalous magnon Hall-effect family.

Figure 1

Magnon transport phenomena termed according to the respective electronic counterparts. Top row, (a)–(d): longitudinal transport. Center row, (e)–(h): normal transverse transport. Bottom row, (i)–(l): anomalous transverse transport. In each panel the left (right) arrows represent the applied fields (the currents).

Figure 2

(a)–(d) Electron-magnon duality interpretation of magnon transport in collinear EA antiferromagnets for selected combinations of forces. The different magnon species (spin up vs spin down) are identified by their dual charge $\pm q$. They “feel” a dynamical Lorentz force due to the dual electromagnetic fields $\mathcal{E}$ and $\mathcal{B}$ and a statistical force due to a temperature gradient $\mathbf{\nabla }T$. The response (not in the dual picture) is indicated (spin or a particle/heat current). (e)–(g) ${\mathbb{Z}}_2$ topological magnon insulator. (e) Square-octagon lattice with eight basis sites and magnetic Néel order. Positive DMI is assumed within octagons for counterclockwise direction (the dashed lines). (f) Spin-degenerate magnon bulk bands with a band gap; $DS=0.05\mathrm{meV},JS=-1\mathrm{meV}$. (g) Slab magnon dispersion with helical edge magnons (red and blue).

Figure 3

Nonlinear anomalous magnon Hall effect in ferrimagnets. Berry curvature dipole vector $\mathit{D}$ vs angle $\varphi$; only $D_x$ is nonzero. For $\varphi =0,\pi /6,\pi /2$, a brick (the left inset), a honeycomb (the right inset), and a chain lattice are formed, respectively. Parameters read $S_{\mathrm{A}}=1,S_{\mathrm{B}}=3/2,k_{\mathrm{B}}T=J,K=0.05J$.