Bound magnetic polarons (BMP’s) in $p$-type ${\mathrm{Cu}}_2{\mathrm{Mn}}_{0.9}{\mathrm{Zn}}_{0.1}{\mathrm{SnS}}_4$ were investigated using magnetization measurements. The magnetization $M$ was studied from 2 to 60 K in magnetic fields up to 55 kOe. The data show the characteristic features of BMP’s in the collective regime. In addition, the onset of antiferromagnetic order in the “matrix” surrounding the BMP’s leads to anomalies in the BMP susceptibility at the Néel temperature of the matrix $T_N=8\mathrm{}$ K. Below 15 K the low-field magnetization of the BMP’s is quite anisotropic. A detailed analysis of the isothermal magnetization curves, based on Wolff’s work but with some additional assumptions, separates the BMP contributions to $M$ from the contribution of the matrix. The analysis gives the spontaneous moment $m_s$ of a single BMP as a function of temperature $T$, and the concentration $N$ of BMP’s. The value $m_s=143\mathrm{}$ Bohr magnetons/BMP at the lowest temperatures is consistent with the expected radius of the hole orbit, of order 10 Å. The observed $T$ dependence of $m_s$ is compared with theoretical calculations based on a model that assumes that the wave function in the absence of the $p$-$d$ interaction is hydrogenic. The calculated decrease of $m_s$ with increasing $T$ is somewhat slower than that deduced from the experimental data. The BMP concentration $N$, from an analysis of the magnetization data, is about $2\times {10}^{19}$ BMP/cm${}^3$ in all the samples. This $N$ is consistent with the observed hopping conductivity at low temperatures. High-field magnetization data, up to 300 kOe, show the canted-to-paramagnetic phase transition of the matrix. At 1.4 K the transition is near 225 kOe.

• Received 7 April 1997

DOI:https://doi.org/10.1103/PhysRevB.56.6673