Bound magnetic polarons in p -type Cu 2 Mn 0.9 Zn 0.1 SnS 4

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 N\'eel temperature of the matrix ${T}_{N}=8$ 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 ${m}_{s}=143$ Bohr magnetons/BMP at the lowest temperatures is consistent with the expected radius of the hole orbit, of order 10 \AA{}. 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 $2\ifmmode\times\else\texttimes\fi{}{10}^{19}$ 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.