Finite-temperature ordering in two-dimensional magnets

Abstract

We study the two dimensional quantum Heisenberg antiferromagnet on the square lattice with easyaxis exchange anisotropy. By the semiclassical method called pure-quantum self-consistent harmonic approximation we analyse several thermodynamic quantities and investigate the existence of a finite temperature transition, possibly describing the low-temperature critical behaviour experimentally observed in many layered real compounds. We find that an Ising-like transition characterizes the model even when the anisotropy is of the order of 10 −2 J (J being the intra-layer exchange integral), as in most experimental situations. On the other hand, typical features of the isotropic Heisenberg model are observed for both values of anisotropy considered, one in the quasi-isotropic limit and the other in a more markedly easy-axis region. The good agreement found between our theoretical results and the experimental data relative to the real compound Rb2MnF4 shows that the insertion of the easy-axis exchange anisotropy, with quantum effects properly taken into account, provides a quantitative description and explanation of the experimental data, thus allowing to recognize in such anisotropy the main agent for the observed onset of finite temperature long-range order.

Quantum Heisenberg antiferromagnets: a survey of the activity in Florence (Review)

“…In Ref. 85 we have compared our theoretical results also with the neutron scattering experimental data for the staggered magnetization, staggered susceptibility and correlation length of Rb 2 MnF 4 and found an excellent agreement both for the overall temperature behavior and for the value of the critical temperature, that perfectly coincides with the one deriving from the experimental analysis, T c = 38.4 K (i.e., t c = 0.575).…”

“…As a sample of the various results that were obtained, we report in Fig. 15 the comparison 85 with the experimental data 97 for the correlation length of the S = 5/2 magnet Rb 2 MnF 4 , that results quite well described by the anisotropic model with J = 7.42 K and µ = 0.9942. Rb 2 MnF 4 is known to behave as a 2D magnet both above and below the observed transition 76 , so that the critical behavior is not contaminated by the onset of 3D order and a clean characterization of the transition is possible.…”

“…and shows a weaker renormalized exchange j eff (t, µ) < 1 and easy-axis anisotropy µ eff (t, µ) > µ, besides an additional free-energy term that is not reported. By means of H eff a series of thermodynamic quantities were studied 85,88 : internal energy, specific heat, staggered magnetization, staggered correlation function, staggered correlation length, staggered susceptibility. This required extensive classical Monte Carlo simulations, as varying the temperature gives an effective system with different effective anisotropy µ eff (t, µ).…”

“…The quantum phase diagram reported in Fig. 14 could be built up 87,89 in a simpler way starting from the knowledge of the classical one and using a relation that follows from the form of Eq. ( 37),…”

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

“…For example, the experimentally observed transition in K 2 NiF 4 ðS ¼ 1Þ [8], Rb 2 FeF 4 ðS ¼ 2Þ [8], K 2 MnF 4 [9], Rb 2 MnF 4 ðS ¼ 5=2Þ [8], and others, is seen to be possibly due to an easy-axis anisotropy. Usually, from a theoretical point of view, easy-axis anisotropy in Heisenberg magnets can be treated as an easy-axis single ion anisotropy or as an easy-axis exchange anisotropy [10,11].…”