Phonon, spin-wave, and defect contributions to the low-temperature specific heat of α-FeOOH

The specific heat of a-FeOOH was measured in the temperature range 0.6 to 30 K by a combination of semi-adiabatic and isothermal techniques. A broad specific-heat anomaly was detected at approximately 1 K. The data above this anomaly were fitted to the equation C = B_asw T³e ^-2/T + ∑ B_n Tⁿ, where ∑ B_nTⁿ represents the harmonic-lattice model for the lattice specific heat, and B_asw T³e ^-2/T represents the magnetic specific heat. The e ^-2/T term that modifies the usual T³ term for an antiferromagnetic spin-wave contribution accounts for a spin-wave gap in the spin-wave spectrum, where △ is the width of the spin-wave gap in Kelvin. As expected, the root-mean-square deviation (RMS) of the fit decreased progressively with inclusion of additional lattice terms, but the Debye temperature, ⊖_D, and the spin-wave gap, △, remained essentially unchanged. The addition of a linear term, yT, decreased the RMS of the fit and eliminated the need for an excessive number of lattice terms. The yT contribution to the specific heat, rather than being electronic in nature, is associated either with a small number of Fe³⁺ vacancies, or with loosely bound particles vibrating in defect sites in the crystallite interfaces. The possibility of the existence of vacancies is implied by the excess water content in the sample (0.083 moles of H₂O per mole of FeOOH) and the presence of the interfaces is indicated by the particle size (determined by BET surface area measurement) being larger than the individual crystallite size (determined by X-ray diffraction).