Antiferromagnetic next-nearest neighbour interactions

Figure 4.6 (a) Schematic view of the two degenerate helical arrangements of the spins of a ID frustrated structure with antiferromagnetic next-nearest-neighbour (NNN) interactions. The angle is the one formed between the projections of two adjacent spins, drawn with different colours to... 

In simple cubic compounds like NiO, MnO and CoO the metal ions lie on a face-centred cubic. As pointed out by Ziman (1952), for this structure and for spherical orbitals, antiferromagnetism with a finite Neel temperature must be due to interaction between next-nearest neighbours, because in any antiferromagnetic structure each moment will have as many parallel as antiparallel neighbours. In NiO and CoO the orbitals are not spherical, but in MnO the 3d5 ion is spherical In this compound the Neel temperature is therefore anomalously low, and there remains abnormally strong short-range order above the Neel temperature (Battles 1971). 

Fig. 6.18 Two-dimensional lattice of magnetic centers with antiferromagnetic nearest neighbour interactions. Next nearest neighbour antiferromagnetic interactions cannot be sustained. Note that the representation of alternating up and down spins is a simphflcation that is only valid for the Ising Hamiltonian...

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