Near field infrared spectroscopy of the ferromagnetic semiconductor Ga$_{1-x}$Mn$_x$As at the nanoscale.

We report on the nanoscale infrared response of a prototypical ferromagnetic semiconductor Ga$_{1-x}$Mn$_x$As at Mn doping fractions in the range of x=1.8-7.75 {\%}. These studies have been carried out using an apertureless scattering Scanning Near field Infrared Microscope (s-SNIM) with a pseudoheterodyne detection scheme operating at the wavelength near 10 $\mu $m.. For samples with doping fractions below 7{\%} we observe a contrast-free near field infrared signal, suggesting a homogenous electronic state on the length scale down to 10-20 nm determined by the spatial resolution of s-SNIM.. At doping fractions of 7.66{\%} and 7.74{\%} we find significant contrast in the form of surface clusters ranging in diameter from 15 to 30nm in both topographical and near field images. These clusters occupy approximately 15{\%} of the total image area. We will discuss possible origins of the observed contrast within the framework of the effective polarizability dipolar model of the tip-sample interaction.