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 J. Sib. Fed. Univ. Math. Phys., 2016, Volume 9, Issue 4, Pages 454–458 (Mi jsfu505)

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

Abstract: 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 $T_{N}$ 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). However, as the temperature approaches $T_{N}$, the exchange gaps are closing. We have calculated the critical indices $\eta$ and $\nu$ to order of  $1/N$ and found that they differ for A and B classes.

Keywords: frustrated antiferromagnets, order by disorder effect, exchange gaps, spin wave theory, critical indices, large N expansion.

 Funding Agency Grant Number Russian Academy of Sciences - Federal Agency for Scientific Organizations 01201463332 Russian Foundation for Basic Research 16-32-00482_ìîë_à The research was carried out within the state assignment of FASO of Russia (theme “Quant” no. 01201463332), supported in part by RFBR (project no. 16-32-00482).

DOI: https://doi.org/10.17516/1997-1397-2016-9-4-454-458

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UDC: 517.9
Received in revised form: 10.10.2016
Accepted: 11.11.2016
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Citation: Andrey N. Ignatenko, Valentin Yu. Irkhin, “Frustrated Heisenberg antiferromagnets on cubic lattices: magnetic structures, exchange gaps, and non-conventional critical behaviour”, J. Sib. Fed. Univ. Math. Phys., 9:4 (2016), 454–458

Citation in format AMSBIB
\Bibitem{IgnIrk16}
\by Andrey~N.~Ignatenko, Valentin~Yu.~Irkhin
\paper Frustrated Heisenberg antiferromagnets on cubic lattices: magnetic structures, exchange gaps, and non-conventional critical behaviour
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2016
\vol 9
\issue 4
\pages 454--458
\mathnet{http://mi.mathnet.ru/jsfu505}
\crossref{https://doi.org/10.17516/1997-1397-2016-9-4-454-458}

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