Hybrid dyons, inverted Lorentz force, and magnetic Nernst effect in quantum spin ice

Topological magnets host two sets of gauge fields: that of native Maxwell electromagnetism, owing to the magnetic dipole moment of its constituent microscopic moments, and that of the emergent gauge theory describing the topological phase. Here, we show that in quantum spin ice, the emergent magnetic charges of the latter carry native electric charge of the former. We both provide a general symmetry-based analysis underpinning this result, and discuss a microscopic mechanism which binds a native electric charge to the emergent magnetic one. This has important ramifications. First and foremost, an applied electric field gives rise to an emergent magnetic field. This in turn exerts an “inverted” Lorentz force on moving emergent electric/native magnetic charges. This can be probed via what we term a magnetic Nernst effect: Applying an electric field perpendicular to a temperature gradient yields a magnetization perpendicular to both. Finally, and importantly as a further potential experimental signature, a thermal gas of emergent magnetic charges will make an activated contribution to the optical conductivity at low temperatures.

Figure 1

(a) Emergent magnetic charge (small red sphere) emits a uniform emergent $\vec{b}$ flux. Resonance of the hexagonal plaquette [Eq. (3)] picks up a phase $\varphi$, half the solid angle subtended by the plaquette, as indicated by the cone. This couples linearly to the local native electric polarization, indicated by the outward displacement of an ion (blue sphere). (b) Left: Inverted Lorentz force—a horizontal thermal gradient $\vec{\nabla }T$ sets up a density gradient, and hence net drift current of emergent $e$ charges (green and yellow denoting opposite charges) from the hot to the cold end, where the charges get pair created and pair annihilated, respectively. Switching on a native electric field $\vec{E}$ induces a parallel emergent magnetic field $\vec{b}$ which leads to a Lorentz force deflecting oppositely charged $e$ charges, moving with the same drift velocity $v_d$, in opposite directions, indicated by the green (yellow) arrow. Right: Magnetic Nernst effect in the steady state—a surface $e$-charge distribution, which corresponds to a net magnetization (thin arrows) $\vec{M}\propto \vec{E}\times \vec{\nabla }T$, sets up an emergent electric field that balances the inverted Lorentz force.