Hall effect in the antiferromagnetic state of Ho$_{0.8}$Lu$_{0.2}$B$_{12}$

Detailed measurements of the Hall effect in the Ho$_{0.8}$Lu$_{0.2}$B$_{12}$ antiferromagnetic compound (Néel temperature $T_N = 5.75$ K) in magnetic fields up to $80$ kOe oriented in the (110) plane at temperatures of $1.9$–$6.6$ K are performed. It is established with the contribution separation procedure that the anisotropic positive contribution, which is responsible for the double inversion of the sign of the Hall resistance, dominates in the antiferromagnetic state of Ho$_{0.8}$Lu$_{0.2}$B$_{12}$ in fields of $30$–$50$ kOe. A sharp decrease in the amplitude of the isotropic negative contribution at the transition to the antiferromagnetic phase is found. The nature of the detected anomalies in the antiferromagnetic metal with dynamic charge stripes and spin-wave component of the magnetic structure is discussed.