An approximate quantum theory of the antiferromagnetic ground state

•Proposed is the suppression model of the exchange mixing of the sublattices.•Exchange mixing is suppressed by increasing the magnetic anisotropy energy.•Magnetic anisotropy is mush less then exchange energy but removes spectrum degeneracy.•Mechanism was justified for model operators and for nearest neighbors approximation. The new mechanism is proposed ensuring the sustainability of spin sublattices system to the effect of mutual switching of the spins of different sublattices.Such switching destroys the ferromagnetic order in the sublattices—the effect of exchange intermixing of the sublattices—that should increase the entropy of the antiferromagnetic state.The total destruction of the ferromagnetic order in sublattices determined from the principle of maximum entropy cannot occur being accompanied by a rather rapid increase in energy.At present, the model of the suppression of entropic destruction of sublattices by the growth of the exchange energy is generally accepted.This model was independently proposed by Anderson and Ziman.The mechanism proposed in this paper for suppressing the exchange mixing by increasing the magnetic anisotropy energy turned out to be more effective than the growth of the exchange energy in the Anderson-Ziman model.Surprising here is that this result was obtained under the condition that the magnetic interactions VA determining the energy of the magnetic anisotropy are small enough compared with the Coulomb exchange interaction Vex.It turned out that the reason for such an anomalously strong influence of VA is related to the symmetry difference between the operators Vex and VA.The Vex operator is spatially isotropic, therefore it determines only the mutual orientation of the interacting spins and doesn’t affect their orientation relative to the crystal axes.The VA operator removes this degeneracy.The removal of degeneracy shifts weakly the levels of the exchange energy due to VA≪Vex condition, but it strongly changes the forms of the wave functions.It is established that such a change in the wave functions can ensure the formation of spin sublattices, which are absent in the degenerate state.This mechanism of sublattice formation was justified mathematically for the model operators Vexmod and VAmod.Such choice of the Vexmod and VAmod operators ensured the possibility of obtaining the exact solutions of the equationsVexmodΦ0mod=E0modΦ0mod and (Vexmod+VAmod)Φmod=EmodΦmod. This excludes the dependence of the obtained results with