Ferromagnetism of the semi-simple cubic lattice

Abstract

Heisenberg ferromagnet on a lattice with a low coordination number, $$Z=3$$ , has been studied by means of high-temperature series and harmonic spin-wave expansion. The lattice is constructed by removing every second bond from the simple cubic lattice and therefore called ’semi-simple cubic’; it is topologically similar to the Laves graph, alias $$K_4$$ crystal. The openness of the lattice does not prevent ferromagnetic ordering and the thermal dependence of spontaneous magnetization differs little from that of other common lattices with higher Z. The study extends naturally toward a more general model where the bonds previously removed are now reinstated but endowed with a distinct exchange integral, $$J_2$$ . We concentrate on the more interesting frustrated case, $$J_2<0<J_1$$ , and a first prediction in this direction is that ferromagnetism disappears at $$J_2/J_1=2\surd 2-3=-0.172$$ , giving way to a long-wavelength spiral structure propagating along [111].