Superparamagnetism and relaxation effects in granular Ni-SiO2and Ni-Al2O3films

Abstract

The susceptibility of an array of fine nickel particles was measured as a function of temperature from 1.5 to 300 \ifmmode^\circ\else\textdegree\fi{}K at a frequency of 5 kHz. The particles were formed by cosputtering nickel with Si${\mathrm{O}}_{2}$ or ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ and varied in diameter between 10 and 100 \AA{}. With increasing temperature, the susceptibility increased from its initial value to a maximum at a temperature ${T}_{B}$ followed by a hyberbolic decrease. A theory based on the relaxation time for single-domain particles $\ensuremath{\tau}={\ensuremath{\tau}}_{0}{e}^{\frac{KV}{kT}}$ ($K$ is the anisotropy energy, $V$ is the particle volume) quantitatively explains the data. At $T=0$ all the particles are blocked by the anisotropy barriers. As the temperature is increased the susceptibility increases because particles for which $\ensuremath{\omega}\ensuremath{\tau}<1$ ($\ensuremath{\omega}$ is the angular frequency) are no longer blocked. Above ${T}_{B}$ all the particles are unblocked and the susceptibility is characteristic of superparamagnetism. Analysis of the data yields information about the particle volume distribution function and a value for the effective anisotropy energy.