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We theoretically study the thermal Hall effect by magnons in skyrmion crystalphases of ferrimagnets in the vicinity of the angular momentum compensationpoint (CP). To this end, we start by deriving the equation of motion formagnons in the background of an arbitrary equilibrium spin texture, which givesrise to the fictitious electromagnetic field for magnons. As the net spindensity varies, the resultant equation of motion interpolates between therelativistic Klein-Gordon equation at CP and the nonrelativisticSchr{\"o}dinger-like equation away from it. In skyrmion crystal phases, theright- and the left-circularly polarized magnons with respect to the orderparameter are shown to form the Landau levels separately within the uniformskyrmion-density approximation. For an experimental proposal, we predict thatthe magnonic thermal Hall conductivity changes its sign when the ferrimagnet istuned across CP, providing a way to control heat flux in spin-caloritronicdevices on the one hand and a feasible way to detect CP of ferrimagnets on theother hand.

Tunable Magnonic Thermal Hall Effect in Skyrmion Crystal Phases of Ferrimagnets