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It is common to observe a notable non-monotonic dependence of thermalconductivity on applied magnetic field in magnetic insulators. This prevalentbehavior prompts the need for an explanation involving components present in awide range of systems. We report the field-dependence of thermal conductivityin the well-characterized effective spin-1/2 paramagnetic insulator CsYbSe$_2$.Along with the data, we propose that the observed non-monotonic fielddependence results from the hybridization of acoustic phonons with spin-flipexcitations across the Zeeman gap, where the magnetoelastic coupling arises viamodulation of the magnetic $g$-tensor by local strain. This hypothesis alignswith a simple theoretical model that qualitatively reproduces key features ofthe data on CsYbSe$_2$. Our results provide a starting point to understand themagnetic field dependence of thermal conductivity in a broad spectrum ofmagnetic insulators.

Generic magnetic field dependence of thermal conductivity in effective  spin-1/2 magnetic insulators via hybridization of acoustic phonons and  spin-flip excitations