Frequency and field dependent susceptibility of magnetite at low temperature

We report the temperature dependence of in-phase and quadrature susceptibilities, k′ and k″, between 20 K and 300 K for a stoichiometric natural single crystal of magnetite. Measurements were made for amplitudes of the AC driving field ranging from H = 30 A/m to 2 kA/m and frequencies ranging from f = 40 Hz to 4 kHz. In cubic magnetite above the Verwey transition, Tv = 120 K, k′ is limited by self-demagnetization and does not vary greatly with T, H or f. As the crystal cools through T_v and transforms to monoclinic structure, k′ decreases by about a factor 2, with a further more gradual decrease of 10-20% in cooling from 40 to 20 K. Saturation remanence also drops sharply at T_V but shows no further change in cooling below 40 K. Thus it appears that domain walls remain pinned throughout the 20-40 K range but small segments undergo reversible oscillations in an AC field, the amplitude of oscillation decreasing steadily with cooling below 40 K. In this same range, k″ reaches a peak, while the temperature at which k′ decreases most rapidly changes with frequency. Both observations indicate that domain wall oscillations lag appreciably behind the driving field at very low temperature. Both k′ and k″ increase markedly with increasing AC field amplitude below T_V. The field dependence is particularly strong below 40 K. Analysis of the k′(f) data between 20 and 40 K based on an Arrhenius thermal activation equation gives a pre-exponential frequency factor f_o ≈ 2.5 × 10⁸ s^-1 and an activation energy ΔE = 0.035 eV. The ΔE is appropriate for electron hopping but f_o suggests an indirect mechanism for wall mobility related to changes in electron ordering within walls.