Two-dimensional (2D) magnetic phase transition has been one of the major topics of condensed matter physics. There are many materials in which the magnetic ions are arranged in planes so that there is strong coupling between the spins within a plane, but only a weak coupling between spins in different planes. In materials such as transition metal chlorides (FeCl2, CoCl2, and NiCl2) there is a strong ferromagnetic coupling within the planes and a coupling between planes which is weaker by a factor of 10 or so and antiferromagnetic. In more complicated ferromagnetic layer compounds such as (CH3 NH3)2 CuCl4, the interlayer coupling is down by a factor of more than a thousand. There are also many materials, such as Rb2MnF4, Rb2CoF4, and K2CoF4, in which the coupling within the plane is antiferromagnetic. This can result in a very much reduced coupling between the planes, since one spin may have four spins in the next plane which are at an equal distance, and their effects cancel out. As a result, the coupling between layers in this material is down by a factor of 106. In these layered compounds the magnetic behavior is only 2D-like at a certain distance away from the critical temperature. Close to the critical temperature, there is a long-range correlation of the spins within the layer and such a correlated region will interact between one layer and the next even if the coupling between individual spins is weak, since many spins can contribute coherently. Thus the spin order near the critical temperature is essentially three-dimensional (3D). What condition should be required for the occurrence of a real 2D spin order in layered magnetic systems? We consider a system consisting of only two magnetic layers separated by a distance. The effective interplanar exchange interaction J'eff is given by J'(ξa)2, but not by J', where ξa is the in-plane spin correlation length and J' is the interplanar exchange interaction. If ξa diverges on approaching a critical temperature, the effective interplanar exchange interaction J'eff becomes comparable with the intraplanar exchange interaction J.
Mixed-cation driven magnetic interaction of interstitial electrons for ferrimagnetic two-dimensional electride
