Thermal Conductivity of CdCr ₂ Se ₄ Ferromagnet at Low Temperatures: Role of Grain Boundaries and Porosity

It is unambiguously demonstrated that the low-temperature magnon specific heat in a ferromagnet varies as <i>T</i>^3/2 and the magnon thermal conductivity, due to the <i>T</i>^1/2-dependent effective velocity of magnons, varies as <i>T</i>². The confirmation of these model behaviors is based on the experimental study of chalcospinel CdCr₂Se₄, which represents a relatively rare example of a ferromagnetic insulator (<i>T</i>_C = 130 K) without undesirable "masking" contributions from itinerant electron excitations and nuclear specific heat, both of which make it 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 <i>D</i> = 33.5 meV Ų and Debye temperature θ_<i>D</i> = 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 the standard model of 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 (∼1 μm) for magnons and longer than the grain size for phonons. The phonon-dominated low-temperature thermal conductivity, moreover, exhibits a ∼<i>T</i>^2.3 temperature dependence instead of the standard predicted model of <i>T</i>³. The relevant scattering mechanisms, both the phonon frequency-independent and frequency-dependent ones, are discussed in detail.