We theoretically study the conductivity of a disordered 2D metal when it is coupled to ferromagnetic magnons with a quadratic spectrum and a gap $\mathrm{\Delta }$. In the diffusive limit, a combination of disorder and magnon-mediated electron interaction leads to a sharp metallic correction to the Drude conductivity as the magnons approach criticality, i.e., $\mathrm{\Delta }\to 0$. The correction is nonsingular and is distinctively weaker than, for example, the log-squared correction obtained when disordered electrons couple to diffusive spin fluctuations near a Hertz-Millis transition. The possibility of verifying this prediction in an $S=1/2$ easy-plane ferromagnetic insulator ${\mathrm{K}}_2{\mathrm{CuF}}_4$ under an external magnetic field is proposed. Our results show that the onset of a magnon Bose-Einstein condensation in an insulator can be detected via electrical transport measurements on the proximate metal.

• Received 30 December 2021
• Revised 18 August 2022
• Accepted 20 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.086702