Thermal conductivity of CdCr$_{2}$Se$_{4}$ ferromagnet at low temperatures: role of grain boundaries and porosity

Abstract: It is unambiguously demonstrated that the low temperature magnon specific heat in a ferromagnet varies as T$^{3/2}$ and the magnon thermal conductivity, due to T$^{1/2}$ - dependent effective velocity of magnons, as T$^{2}$. The confirmation of these model comportments is based on the experimental study of chalcospinel CdCr${2}$Se${4}$, which represents relatively rare example of a ferromagnetic insulator (T${C}$ = 130 K) without undesirable masking contributions of the itinerant electron excitations and nuclear specific heat that both make impossible to conclusively unveil the role of magnons. The ratio of the magnon to lattice specific heat is found to reach 87:13 at 2 K and is in accordance with predictions based on the spin-wave stiffness D = 33.5 meVA$^{2}$ and Debye temperature $θ{D}$ = 237 K. On the other hand, the ratio of the magnon to phonon thermal conductivity reaching 27:73 at 2 K is much lower than expected for standard model of the grain boundary limited transport. This suggests that mean free paths for long-wavelength magnon/phonon heat carriers are largely different - shorter than the grain size (of 1$μ$m) for magnons and longer than grain size for phonons. The phonon dominated low temperature thermal conductivity exhibits, moreover, a T$^{2.3}$ temperature dependence instead of the standard predicted model in T$^{3}$. The relevant scattering mechanisms, both the phonon frequency independent and dependent ones, are discussed in detail.