Presence of the weak ferromagnetism in pure antiferromagnetic systems with octahedral structure: Effective field theory analysis

The recently reported (Jurcisinova E. and Jurcisin M., J. Magn. & Magn. Mater., 513 (2020) 167085) possibility of the existence of the weak ferromagnetism with small but nonzero spontaneous magnetization in pure antiferromagnetic systems with the octahedral structure is confirmed using the six-site effective-field theory cluster approximation of the antiferromagnetic spin-$(1/2)$ Ising model on the octahedral lattice. The sublattice magnetizations, the total spontaneous magnetization, as well as the Neel temperature of the model are found and compared to those obtained in the framework of the recursive lattice approach. The performed analysis allows one to conclude that the existence of the weak ferromagnetism in pure antiferromagnetic systems with the octahedral structure is directly related to their intrinsic geometry. The spontaneous magnetization and the Curie temperature of the ferromagnetic model are also determined and briefly discussed.