Effect of biquadratic exchange on the phase diagram of a spin-1 transverse XY model with single-ion anisotropy

Abstract

The two-time Green function method is employed to explore the effect of the biquadratic exchange interaction on the phase diagram of a d-dimensional spin-1 transverse XY model with single-ion anisotropy close to the magnetic-field-induced quantum critical point. We work at level of the Anderson-Callen-decoupling-like framework for both easy-plane and easy-axis single-ion anisotropy. The structure of the phase diagram is analyzed with analytical estimates and numerical calculations by adopting Tyablikov-like decouplings for the exchange higher order Green functions in the equation of motion. For dominant bilinear short-range exchange interaction the structure of the phase diagram close to the quantum critical point remains qualitatively the same of that in absence of biquadratic interaction including reentrant critical lines. When the biquadratic exchange becomes increasingly dominant its role appears more effective and tends to reduce or destroy the reentrant character of the critical lines.

Devlin-like approach to a spin-1 transverse XY model with biquadratic exchange and single-ion anisotropy

“…The equality in (29) suggests that a QCP exists for any d and D < z(J + I) with coordinates (H c (D) = z(J + I) − D, T = 0). Remarkably, it coincides with that predicted by the ACD framework [16].…”

“…However, this scheme complicates sensibly the mathematical treatment without a substantial change of the qualitative physics arising from the simplest and controllable RPA. In conclusion, since as far as we know no alternative reliable study has been made for exploring the effect of BQE around magnetic-field-induced QCPs in presence or in absence of SIA, we believe that the ACD [16] and the present Devlin-like predictions may stimulate further theoretical and experimental research activity about the presence of reentrances or non-reentrances in the phase diagrams of innovative magnetic materials which exhibit magnetic-field-induced QPTs in the presence of uniaxial crystal-field anisotropy.…”

“…In the last decade there has been a renewed interest in investigating the role played by the interplay between quantum fluctuations, bilinear and biquadratic exchange interactions and crystal lattice geometry which is expected to result in a rich variety of quantum phases and exotic phenomena [1][2][3][4][5][6][7] especially when magnetic field induced quantum phase transitions (QPTs) [8][9][10][11] are present. In this context, the effect of competition between biquadratic exchange (BQE) and single-ion anisotropy (SIA) has been explored for quantum anisotropic magnetic models by using different approximate schemes (see, for instance, [12][13][14][15][16]). In these studies the powerfull two-time Green function (GF) method [17][18][19][20] has played an important role.…”

“…Very recently [16], we have achieved a preliminary study of the relatively simple spin-1 XY ferromagnetic model in a transverse field (or transverse XY (TXY) model) [35] with competing BQE interactions and crystal-field SIA via the two-time GF method by adopting the Anderson-Callen decoupling (ACD) scheme [36] for the SIA-like higher order GFs which enter the appropriate equations motion. Due to the well known limits of the ACD for anisotropic models with finite temperature phase transitions, in the present paper we explore the role played by the BQE on the quantum critical phase diagram of a d-dimensional spin-1 TXY ferromagnetic model with easy-axis SIA via the Devlin two-time GF scheme [37].…”

Spin wave resonance frequency in ferromagnetic thin film with the biquadratic exchange interaction

“…In addition, the existence and importance of higher-order spin coupling have been confirmed by many researchers [32][33][34][35][36]. However, only a few works systematically studied the biquadratic exchange (BQE) interaction dependence of magnetic behavior in a ferromagnetic thin film [37][38][39][40][41][42][43][44]. The BQE interaction is a higher-order interaction between in-plane nearest-neighbor sites, which contributes to the spin wave frequencies as well as to the saturation field.…”