  Recent demonstrations on manipulating antiferromagnetic (AF) order have
triggered a growing interest in antiferromagnetic metal (AFM), and potential
high-density spintronic applications demand further improvements in the
anisotropic magnetoresistance (AMR). The antiferromagnetic semimetals (AFS) are
newly discovered materials that possess massless Dirac fermions that are
protected by the crystalline symmetries. In this material, a reorientation of
the AF order may break the underlying symmetries and induce a finite energy
gap. As such, the possible phase transition from the semimetallic to insulating
phase gives us a choice for a wide range of resistance ensuring a large AMR. To
further understand the robustness of the phase transition, we study thermal
fluctuations of the AF order in AFS at a finite temperature. For macroscopic
samples, we find that the thermal fluctuations effectively decrease the
magnitude of the AF order by renormalizing the effective Hamiltonian. Our
finding suggests that the insulating phase exhibits a gap narrowing at elevated
temperatures, which leads to a substantial decrease in AMR. We also examine
spatially correlated thermal fluctuations for microscopic samples by solving
the microscopic Landau-Lifshitz-Gilbert equation finding a qualitative
difference of the gap narrowing in the insulating phase. For both cases, the
semimetallic phase shows a minimal change in its transmission spectrum
illustrating the robustness of the symmetry protected states in AFS. Our
finding may serve as a guideline for estimating and maximizing AMR of the AFS
samples at elevated temperatures.
