Magnetic ordering in cubic crystals with first and second neighbor exchange

Abstract

The problem of stability of various ferromagnetic and antiferromagnetic spin configurations is considered. Simple cubic, f.c.c. and b.c.c. lattices are analyzed, for all possible ratios of the strengths of the nearest-neighbor and next-nearest-neighbor exchange constants (all other exchange constants are neglected), and for all temperatures. The calculations are carried out by a Green function ‘random phase’ approximation. The results are presented in terms of phase diagrams, and the nature of the instabilities at the phase boundaries is discussed.