Mathematics & Physics 2016, 9(4), 454–458 УДК 517.9 Frustrated Heisenberg Antiferromagnets on Cubic Lattices: Magnetic Structures, Exchange Gaps, and Non-Conventional Critical Behaviour Andrey N. Ignatenko∗ Valentin Yu. <...> Irkhin Institute of Metal Physics Kovalevskaya, 18, Ekaterinburg, 620990 Russia Received 10.08.2016, received in revised form 10.10.2016, accepted 11.11.2016 We have studied the Heisenberg antiferromagnets characterized by the magnetic structures with the periods being two times larger than the lattice period. <...> We have considered all the types of the Bravais lattices (simple cubic, bcc and fcc) and divided all these antiferromagnets into 7 classes i.e. 3 plus 4 classes denoted with symbols A and B correspondingly. <...> The order parameter characterizing the degeneracies of the magnetic structures is an ordinary Neel vector for A classes and so-called 4-complex for B classes. <...> We have taken into account the fluctuation corrections for these states within the spin-wave and large-N expansions (N is the number of spin components). <...> Below the Neel temperature TN quantum and thermal fluctuations lift the degeneracy making simple one-wave vector collinear structure preferable for all the classes. <...> A satellite of this effect is the opening of the exchange gaps at certain wave vectors in the spin wave spectrum (there is an analogous effect for the nonuniform static transverse susceptibility). <...> Keywords: frustrated antiferromagnets, order by disorder effect, exchange gaps, spin wave theory, critical indices, large N expansion. <...> Shender [1] studied a garnet antiferromagnet with the magnetic structure consisting of two antiferromagnetic sublattices with Neel vectors which do not interact with each over at the mean-field level. <...> He showed that when fluctuations are taken into account, the interaction between the sublattices appears causing their Neel vectors to order collinearly and opening local exchange gaps in the spin wave spectrum [1]. <...> In this paper we study the classes of antiferromagnets where a similar situation takes place provided that the wave vector of the magnetic structure is not invariant under the lattice symmetry transformations, so that the star of the magnetic wave vector contains several wave vectors. <...> For simplicity we restrict ourselves to the Bravais lattices with cubic symmetry and consider only the magnetic structures with the periods <...>