Uniaxially anisotropic antiferromagnets in a field on a square lattice

Abstract

Classical uniaxially anisotropic Heisenberg and XY antiferromagnets in a field along the easy axis on a square lattice are analysed, applying ground state considerations and Monte Carlo techniques. The models are known to display antiferromagnetic and spin-flop phases. In the Heisenberg case, a singleion anisotropy is added to the XXZ antiferromagnet, enhancing or competing with the uniaxial exchange anisotropy. Its effect on the stability of non-collinear structures of biconical type is studied. In the case of the anisotropic XY antiferromagnet, the transition region between the antiferromagnetic and spin-flop phases is found to be dominated by degenerate bidirectional fluctuations. The phase diagram is observed to resemble closely that of the XXZ antiferromagnet without single-ion anisotropy.PACS. 68.35.Rh Phase transitions and critical phenomena -75.10.Hk Classical spin models -05.10.Ln Monte Carlo method, statistical theory

Classical and quantum anisotropic Heisenberg antiferromagnets

“…Their presence at low temperatures may be conveniently demonstrated by monitoring the probability p 2 (Θ A , Θ B ) to find the two tilt angles at neighboring sites, as illustrated in figure 3. Similar observations hold for the anisotropic XY antiferromagnet on a square lattice [16]. .…”

“…At present, we can locate it, e.g. for the case depicted in figure 7, only with a rather large uncertainty [16,25].…”

“…In that region, the degeneracy is lifted, and the tilt angles Θ A and Θ B , being still uniquely interrelated, change continuously with the field H [16,25]. Above a critical positive value of D, D/J > 2 − 2∆, at the vanishing field, the spins are oriented perpendicular to the easy axis.…”

“…The full Hamiltonian is then H = H XXZ + H D . From a straighforward analysis of the ground states one may obtain the phase diagram at zero temperature [9,16,25]. An example is shown in figure 6.…”

Anisotropic XY antiferromagnets in a field

“…Especially, mean-field approximation [2,4], Monte Carlo simulations [16,17,18,19,20,21,22,23], and renormalization group calculations [3,5,24,25,26] have been applied.…”