Magnetic Polarons in EuB6

We present results of small-angle neutron scattering (SANS) experiments on the rare-earth, magnetic semiconductor $\mathrm{EuB_6}$. This compound exhibits two phase transitions: Upon cooling from an insulating state at high temperature, it first becomes metallic with a drop at a $T_M$ of 14.5 K, after which it orders ferromagnetically with a $T_C$ of 11.8 K. We carried out SANS experiments over a large range of scattering wave vectors $q$ from 0.006 to 0.140 \AA$^{-1}$ and temperatures from 2 to 60 K. The experiments show a Lorentzian dependence on the wave vector in the magnetic scattering intensity for temperatures just above $T_C$, which demonstrates the presence of magnetic polarons. Below $T_C$, the polarons merge together, and most of the observed intensity is, as indicated by a Lorentzian square dependence, from scattering of wall domains. We calculated a correlation length from this Lorentzian fit and obtained a range of $10^2$ to $10^3$ \AA{} for the size of the magnetic polarons.