Magnetic Scattering of Spin Polarized Carriers in $(\mathrm{In},\mathrm{Mn})\mathrm{Sb}$ Dilute Magnetic Semiconductor

Magnetoresistance measurements on the magnetic semiconductor $(\mathrm{In},\mathrm{Mn})\mathrm{Sb}$ suggest that magnetic scattering in this material is dominated by isolated ${\mathrm{Mn}}^{2+}$ ions located outside the ferromagnetically ordered regions when the system is below $T_c$. A model is proposed, based on the $p\mathrm{\text{−}}d$ exchange between spin-polarized charge carriers and localized ${\mathrm{Mn}}^{2+}$ ions, which accounts for the observed behavior both below and above the ferromagnetic phase transition. The suggested picture is further verified by high-pressure experiments, in which the degree of magnetic interaction can be varied in a controlled way.

Figure 1

Magnetization measured by magnetic circular dichroism (a) and reflected in magnetoresistance (b) as a function of the applied field up to 6 T. The Curie temperature is $T_c=7\mathrm{K}$. The solid lines represent the $B_{5/2}$ Brillouin function characterizing the magnetization of isolated ${\mathrm{Mn}}^{2+}$ ions.

Figure 2

(a) Low-field magnetoresistance, showing quadratic field dependence above $T_c$, and linear dependence in the FM phase. Solid lines are fits to the data according to the $B\to 0$ limits of Eqs. (3, 4). (b) Remanent magnetization measured by SQUID as a function of temperature (solid line). The data points show the spin polarization of charge carriers deduced from the initial slope of the magnetoresistance below $T_c$ (the absolute scale was determined by taking $J_{pd}/V=0.17$, see text).

Figure 3

Magnetoresistance measured up to 14 T at selected temperatures below (various blue curves) and above $T_c$ (red and yellow curves). A positive quadratic term attributed to normal magnetoresistance is subtracted at each temperature, as shown in (b). Continuous lines in (a) correspond to Eqs. (3, 4), with $⟨S_z⟩$ given by the Brillouin function for $S=5/2$.

Figure 4

Effect of hydrostatic pressure on magnetoresistance measured below (blue curve) and above $T_c$ (red curve). Open symbols: ambient pressure; solid symbols: $p=2.7\mathrm{GPa}$. Fits for ambient pressure are calculated using Eqs. (3, 4); fits for pressure data are calculated using the same expression, with $J_{pd}$ increased by 5.6%. In the paramagnetic phase we found that $T^{*}$ is also enhanced by pressure (from 7.1 K to 7.6 K), as expected.