Dynamical thermal conductivity of the spin Lieb lattice

• Theoretical calculation of frequency dependence of thermal conductivity of the spin Lieb lattice.
• The investigation of the effect of external magnetic field on the dynamical thermal conductivity.
• The investigation of the effect of NNN coupling, temperature and the strength of DMI on the dynamical thermal conductivity.

In the ferromagnetic insulator with the Dzyaloshinskii–Moriya interaction (DMI), we have theoretically investigated the dynamical thermal conductivity (DTC). In other words, we have investigated the frequency dependence of thermal conductivity, κ, of the Lieb lattice, a face-centered square lattice, subjected to a time dependence temperature gradient. Using linear response theory and Green׳s function approach, DTC has been obtained in the context of Heisenberg Hamiltonian. At low frequencies, DTC is found to be monotonically increasing with DMI strength (DMIS), temperature and next-nearest-neighbor (NNN) coupling. Also we have found that DTC includes a peak for different values of temperature, DMIS and NNN coupling. Furthermore we study the temperature dependence of thermal conductivity of Lieb lattice for different values of DMIS, NNN coupling and external magnetic filed. We witness a decrease in DTC with temperature due to the quantum effects in the system.