Evaluation of Exchange Stiffness From Temperature-Dependent Magnetization in ZnFe 2 O 4 Thin Films

Nano-crystalline magnetic ZnFe 2 O 4 thin films were deposited in oxygen atmosphere at different substrate temperatures (T S ) on amorphous quartz substrate by pulsed laser deposition technique. The T S = 350 °C film was also annealed at different temperatures in air. X-ray diffraction patterns confirmed that all the samples were cubic spinel and the average grain size of the films increased with increasing T S and annealing temperatures (T A ). Spontaneous magnetization at different temperature was obtained from the $M$ – $H$ loops. The temperature dependence of magnetization data was fit using Bloch’s law. The value of exchange stiffness constant (D) was calculated using the fit values of Bloch’s constant. The obtained D values were found to gradually decrease with the increase of average grain size.