Superparamagnetism and relaxation effects in granular Ni-Si${\mathrm{O}}_2$ and Ni-${\mathrm{Al}}_2$${\mathrm{O}}_3$ films

The susceptibility of an array of fine nickel particles was measured as a function of temperature from 1.5 to 300 °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 Å. 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 $\tau ={\tau }_0{e}^{\frac{KV}{kT}}$ ($K$ is the anisotropy energy, $V$ is the particle volume) quantitatively explains the data. At $T=0\mathrm{}$ all the particles are blocked by the anisotropy barriers. As the temperature is increased the susceptibility increases because particles for which $\omega \tau <1\mathrm{}$ ($\omega$ 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.