Local magnetic behavior of EuB₆ with Magneto Optic Imaging technique

EuB₆ is a low carrier density ferromagnetic semi-metal which is a convenient system to study nanoscale phase separation between conducting ferromagnetic and insulating paramagnetic domains. EuB₆ undergoes magnetic ordering through stepwise transformation, with two anomalous features in the range of T_c1~15 to 16 K and T_c2 ~ 12 to 14 K and shows a large negative magnetoresistance at T_c1. We perform highly sensitive Magneto-Optic Imaging of a EuB₆ sample which unlike other methods can image local magnetic fields on the surface of a sample. Polaronic magnetic domains in a single crystal of EuB₆ has been successfully imaged through our technique. We identify different regimes related to nucleation of magnetic polarons, the temperature regimes where the polarons completely coalesce and where they finally join up to enter into a state with a long-range magnetic order. These have been identified as T^*, T^*_c1 and T_c2. We investigate the field dependent behavior of T^*, T^*_c1, T_c2 and determine a phase diagram to identify their behavior with field. The above transformation is shown to have features of a critical like phenomena. We also observe an increase in noise as we cross T^*_c1 and T_c2 which is suppressed at T_c2 when an external field is applied.