Emergent Ising degrees of freedom in frustrated two-leg ladder and bilayers=12Heisenberg antiferromagnets

Abstract

Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of the considered frustrated bilayer is a phase transition which occurs at low temperatures for a wide range of magnetic fields below the saturation magnetic field and belongs to the two-dimensional Ising model universality class. 1 2 J (a) J 1 2 J J (b) FIG. 1: (Color online) Lattices considered in this paper: (a) the frustrated two-leg ladder and (b) the frustrated bilayer. The vertical bonds have the strength J2 > 0 whereas all other bonds have the strength J1 > 0.

Thermodynamic properties of Ba2CoSi2O6Cl2 in a strong magnetic field: Realization of flat-band physics in a highly frustrated quantum magnet

“…[24,25]. The crucial difference to the previous studies [24,25] is the anisotropy of the exchange interaction controlled by the parameter 0 ≤ ∆ ij ≤ 1 (∆ 2 = 0.149 and ∆ 1 = 0.56 are the values relevant for Ba 2 CoSi 2 O 6 Cl 2 , see Ref. [33]).…”

“…The most spectacular experimental results are the magnetization curves m(h) measured at 1.3 K for two field orientations until about 70 T, that exceeds noticeably the saturation field. The magnetization curve m(h) exhibits a stepwise shape with a plateau at half of the saturation magnetization, irrespective of the field direction which is typical for the fully frustrated bilayer AFM [24,25]. Although, the reported magnetic properties of Ba 2 CoSi 2 O 6 Cl 2 strongly resemble the theoretical predictions of [24,25] obtained for the fully frustrated isotropic Heisenberg bilayer AFM, there are several important differences in the appropriate spin model for Ba 2 CoSi 2 O 6 Cl 2 .…”

Quantum phase diagram of a frustrated antiferromagnet on the bilayer honeycomb lattice

“…27, based on methods in Ref. 28, and have been reconsidered in many subsequent studies [29][30][31][32][33][34][35] . In particular the bilayer square lattice model have been investigated previously 33,34 .…”

“…28, and have been reconsidered in many subsequent studies [29][30][31][32][33][34][35] . In particular the bilayer square lattice model have been investigated previously 33,34 . However, the relevant point in our work is that we find a bilayer model with the same geometry proposed for the material Bi 3 Mn 4 O 12 (NO 3 ) wich presents an exact dimer product ground state in the region of the parameter space where ab-initio calculations suggest the material may exist.…”

Low-Temperature Properties of the Quantum Heisenberg Antiferromagnet on Some One-Dimensional Lattices Containing Equilateral Triangles

“…[7,8]. Second, for the antiferromagnetic Heisenberg frustrated three-leg ladder it is also possible to take into account a substantial part of low-lying excited states [9]. Third, one may add to spin Hamiltonian (1) small extra terms which remove the degeneracy due to the chirality.…”