Frustrated diamond-chain quantum XXZ Heisenberg antiferromagnet in a magnetic field

Abstract

We consider the antiferromagnetic spin-1/2 XXZ Heisenberg model on a frustrated diamond-chain lattice in a z-or x-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 XY chains which are exactly solvable through the Jordan-Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound.

Influence of the Heisenberg Exchange Interaction Anisotropy on the Magnetization Process of a Frustrated Diamond Chain in a Strong Magnetic Field

“…Formally, the expressions for the effective Hamiltonians (7) and (13) are identical to those obtained earlier in work [15] in the case 0 ≤ Δ < 1. However, they describe a qualitatively different case where the parameter of Heisenberg exchange interaction anisotropy Δ > 1.…”

“…The research of the properties of such spin systems in strong magnetic fields c ○ O.M. KRUPNITSKA, 2015 and at low temperatures is based on the concept of localized magnons [2][3][4][5][6], which allows the problem to be reduced to the consideration of a certain classical lattice gas consisting of hard objects. The characteristic features of spin systems, in which the existence of localized magnons is allowed, are a plateau and a jump in the magnetization curve at the saturation field and = 0 (i.e.…”

“…The issue concerning the magnetization of a frustrated diamond chain with the Heisenberg interaction in an arbitrarily oriented field was formulated in work [15]. However, the analysis was confined to the case where the parameter of exchange interaction anisotropy 0 ≤ Δ < 1.…”

Localized-Magnon Chains and Interchain Interactions

“…In general, the suggested approximation works reasonably well. However, from previous studies for the pure one-dimensional case [7,8] we know that the accuracy of the strong-coupling approach becomes better if the vertical dimer bond J 2 > 0 increases. As to localized-magnon features, the interchain coupling washes out the remarkable ground-state magnetization jump at the saturation field.…”

“…Thus, to provide theoretical predictions for, say, low-temperature high-field magnetization curve one has to extend the localized-magnon description taking into consideration deviations from the ideal flat-band geometry, exchange interaction anisotropy, and interchain interactions. In our previous studies we examined effects of nonideal flat-band geometry [7] and exchange interaction anisotropy [8]. In the present study, we focus on the effect of interchain interactions, unavoidably present in a real compound.…”