Persistence of weak ferromagnetism in antiferromagnetic systems on the body-centered octahedral lattice

The possibility of existence of weak ferromagnetism in antiferromagnetic systems on the body-centered octahedral lattice is investigated in the framework of the corresponding spin-1/2J_{1}-J_{2} model in the recursive-lattice approach. The exact solution of the model is found and its phase diagram is determined. The magnetic and thermodynamic properties of all phases are studied, the nature of all phase transitions is established, and an equation that determines the positions of all second-order phase transitions of the model is found. The magnetic and entropy properties of all ground states of the model are also determined. It is shown that the weak ferromagnetism predicted earlier in the pure spin-1/2 antiferromagnetic system on the octahedral lattice remains present even in the case of the model on the body-centered octahedral lattice with antiferromagnetic as well as ferromagnetic interactions between the central site of each elementary octahedron and each of its vertices. However, the presence of the interacting central site suppresses the weak ferromagnetism at very low temperatures, where the standard antiferromagnetic phase emerges. At the same time, the temperature region with the antiferromagnetic phase increases with simultaneous decreasing of the region, where the weak ferromagnetism can be observed, when the strength of the interaction between the central site of each elementary octahedron and each of its vertices increases. Moreover, the phenomenon of weak ferromagnetism disappears completely when this interaction becomes sufficiently stronger than the nearest-neighbor antiferromagnetic interaction between spin variables placed in vertices of each elementary octahedron of the lattice. Moreover, the possibility of the existence of the classical spin-liquid behavior in such magnetic systems is also discussed.