Magnetization of Zn1−xCoxO nanoparticles: single-ion anisotropy and spin clustering

Abstract

The magnetization of Zn1−xCoxO (0.0055 ≤ x ≤ 0.073) nanoparticles has been measured as a function of temperature T (1.7 K ≤ T ≤ 10 K) and for magnetic field up to 65 kOe using a SQUID magnetometer. Samples were synthesized by three different growth methods: microwave-assisted hydrothermal, combustion reaction and sol-gel. For all studied samples, the magnetic properties derive from the antiferromagnetic (AF) spin clustering due to the Co2+ nearest-neighbors. The magnetization curves have been fitted to the Brillouin function (BF). We have used the normalized root mean square error (NRMSE) between the experimental and calculated BF curves as goodness of fit indicator. For all samples, the magnetization of the Co2+ ions has a BF behavior at T ≥ 6 K with NRMSE≈ 0.004 typically, but below 6 K, it shows a notable deviation. The magnitude of the deviation is found to increase with decreasing temperature and reaches its maximum value at T = 1.7 K with NRMSE ≈ 0.026. The observed deviation as well as the magnetization curve shape have been successfully explained by a model based on single-ion anisotropy (SIA) with uniaxial symmetry for the Co2+ ions and the assumption of randomly oriented nanoparticles. Fits of the magnetization curves have been performed by using this model. The axial-SIA parameter D and the effective Co concentration x¯ corresponding to the technical saturation value of the magnetization were used as adjustable parameters. The quality of the fit using this model is clearly improved with NRMSE around 0.007 at T = 1.7 K. The obtained value of the axial-SIA parameter D (typically D = 4.4 K) is slightly larger that the bulk value D = 3.97 K. No significant change of D has been observed as a function of the Co concentration or the growth process. Comparison of the concentration dependence of the obtained values of x¯ with predictions based on the nearest-neighbors cluster model has been made. The result shows an enhancement of the AF spin clustering independent of the growth method which can be ascribed to a clamped non-random distribution of the cobalt ions in the nanoparticles. The approach of the local concentration (xL) has been used to quantify the observed deviation from randomicity. We obtained xL = 1.4 x. Assuming the picture of a ZnO core / Zn1−xCoxO shell nanoparticle, the thickness of the shell has been estimated from the ratio xL∕x to be one fourth of the diameter of the core.