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We report studies of thermal conductivity as functions of magnetic field andtemperature in the helimagnetic insulator Cu$_2$OSeO$_3$ that reveal novelfeatures of the spin-phase transitions as probed by magnon heat conduction. Thetilted conical spiral and low-temperature skyrmion phases, recently identifiedin small-angle neutron scattering studies, are clearly identified by sharpsignatures in the magnon thermal conductivity. Magnon scattering associatedwith the presence of domain boundaries in the tilted conical phase and regionsof skyrmion and conical-phase coexistence are identified.

Spin phases of the helimagnetic insulator Cu$_2$OSeO$_3$ probed by magnon heat conduction