Magnetic "blocking" in very dilute(EuxSr1−x)S: Experiment versus theory

Abstract

Both ac and dc magnetic susceptibilities have been measured for Eu concentrations $x=0.025, 0.05, \mathrm{and} 0.10$ over temperatures in the range from 0.007 K to 4 K. While the dc susceptibility is found to exhibit no peak down to 7 mK, the ac susceptibility shows two distinct maxima around 15 mK and 200 mK. The frequency dependence of the two-peak positions $T_a\left(\nu \right)$ and $T_b\left(\nu \right)$ can be adequately described by an Arrhenius law in the range of our measurements from 10-${10}^6$ Hz. The results for the peak at the higher-temperature $T_b$ are explained quantitatively for $x=0.025\mathrm{}$ and $x=0.05\mathrm{}$, without adjustable parameters, by a model of small random Eu clusters. They consist of Eu atoms coupled by strong exchange forces between nearest-and next-nearest neighbors, and experience energy barriers mainly due to the intracluster dipolar energy. One particular configuration, two nearest-neighbor Eu atoms bonded ferromagnetically, produces the anomaly near $T_b$. Thus $T_b\left(\nu \right)$ arises from ordinary superparamagnetic behavior. In spite of the very low temperatures investigated, quantum-mechanical cluster reorientation is shown to be negligible due to the high-spin quantum number of Eu, even for the smallest clusters. The newly found maximum at the lower-temperature $T_a$ is interpreted as a result of intercluster dipolar energy, giving good agreement for the order of magnitude of $T_a$ and its concentration dependence. Its dependence on frequency remains to be explained.