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Journal of Magnetism and Magnetic Materials

Influence of field on frustrations in low-dimensional magnets

Felix A. Kassan-Ogly, Boris N. Filippov, Akai Kurbanovich Murtazaev, Рамазанов Магомедшейх Курбанович, М. К. Бадиев

Published Feb 25, 2012• 46 citations
Publisher
DOI
10.1016/j.jmmm.2012.02.056

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Abstract. We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic nextnearest-neighbor bonds J2> 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T −2 at J2 < |J1|/4 to χ ∝ T −3/2 at the quantum-critical point J2 = |J1|/4. Another effect of the frustration is the appearance of an extra low-T maximum in the specific heat Cv(T) for J2 � |J1|/8, indicating its strong influence on the low-energy spectrum. Introduction: In low-dimensional frustrated quantum magnets thermal and quantum fluctuations strongly influence the low-temperature physics [1,2]. Special attention has been paid to one-dimensional (1D) J1-J2 quantum Heisenberg magnets, see Ref. [3] and references therein. Recent experimental studies have shown that edge-shared chain cuprates, such as LiVCuO4, Li(Na)Cu2O2, Li2ZrCuO4, and Li2CuO2 [4–13], represent a family of quantum magnets for
Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J 1 and next nearest-neighbor exchange coupling J 2 we investigate the magnetic susceptibility of two-dimensional J 1 - J 2 Heisenberg models with arbitrary spin quantum number s . We use exact diagonalization and high- temperature expansion up to order 10 to analyze the influence of the frustration strength J 2 / J 1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on the ratio J 2 / J 1 by comparing with susceptibility measurements on corresponding magnetic compounds.
Low-temperature magnetization curves of the classical frustrated ferromagnetic chain in the external magnetic field near the transition point between the ferromagnetic and the helical phases is studied. It is shown that the calculation of the partition function in the scaling limit reduces to the solution of the Schr\"odinger equation of the special form for the quantum particle. It is proposed that the magnetization of the classical model in the ferromagnetic part of the phase diagram including the transition point defines the universal scaling function which is valid for the quantum model as well. Explicit analytical formulas for the magnetization are given in the limiting cases of low and high magnetic fields. The influence of the easy-axis anisotropy on the magnetic properties of the model is studied. It is shown that even small anisotropy essentially changes the behavior of the susceptibility in the vicinity of the transition point.