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Register a new userHeat capacity of anisotropic Heisenberg antiferromagnet within the spin Hartree-Fock approach in quasi-1D Regime
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Added by
Oleksandr Tsyplyatyev
Publication date
2019
fields
Physics
and research's language is
English
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We study the anisotropic quantum Heisenberg antiferromagnet for spin-1/2 that interpolates smoothly between the one-dimensional (1D) and the two-dimensional (2D) limits. Using the spin Hartree-Fock approach we construct a quantitative theory of heat capacity in the quasi-1D regime with a finite coupling between spin chains. This theory reproduces closely the exact result of Bethe Ansatz in the 1D limit and does not produces any spurious phase transitions for any anisotropy in the quasi-1D regime at finite temperatures in agreement with the Mermin-Wagner theorem. We study the static spin-spin correlation function in order to analyse the interplay of lattice geometry and anisotropy in these systems. We compare the square and triangular lattice. For the latter we find that there is a quantum transition point at an intermediate anisotropy of $sim0.6$. This quantum phase transition establishes that the quasi-1D regime extends upto a particular point in this geometry. For the square lattice the change from the 1D to 2D occurs smoothly as a function of anisotropy, i.e. it is of the crossover type. Comparing the newly developed theory to the available experimental data on the heat capacity of $rm{Cs}_2rm{CuBr}_4$ and $rm{Cs}_2rm{CuCl}_4$ we extract the microscopic constants of the exchange interaction that previously could only be measured using inelastic neutron scattering in high magnetic fields.
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We report on magnetic resonance studies within the magnetically ordered phase of the quasi-1D antiferromagnet LiCuVO_4. Our studies reveal a spin reorientational transition at a magnetic field H_c1 ~ 25 kOe applied within the crystallographical (ab)-plane in addition to the recently observed one at H_c2 ~75 kOe [ M.G. Banks et al., cond-mat/0608554 (2006)]. Spectra of the antiferromagnetic resonance (AFMR) along low-frequency branches can be described in the frame of a macroscopic theory of exchange-rigid planar magnetic structures. These data allow to obtain the anisotropy of the exchange interaction together with a constant of the uniaxial anisotropy. Spectra of 7Li nuclear magnetic resonance (NMR) show that, within the magnetically ordered phase of LiCuVO_4 in the low-field range H < H_c1, a planar spiral spin structure is realized with the spins lying in the (ab)-plane in agreement with neutron scattering studies of B.J. Gibson et al. [Physica B Vol. 350, 253 (2004)]. Based on NMR spectra simulations, the transition at H_c1 can well be described as a spin-flop transition, where the spin plane of the magnetically ordered structure rotates to be perpendicular to the direction of the applied magnetic field. For H > H_c2 ~ 75 kOe, our NMR spectra simulations show that the magnetically ordered structure exhibits a modulation of the spin projections along the direction of the applied magnetic field H.
We apply Projected Hartree-Fock theory (PHF) for approximating ground states of Heisenberg spin clusters. Spin-rotational, point-group and complex-conjugation symmetry are variationally restored from a broken-symmetry mean-field reference, where the latter corresponds to a product of local spin states. A fermionic formulation of the Heisenberg model furnishes a conceptual connection to PHF applications in quantum chemistry and detailed equations for a self-consistent field optimization of the reference state are provided. Different PHF variants are benchmarked for ground-state energies and spin-pair correlation functions of antiferromagnetic spin rings and three different polyhedra, with various values of the local spin-quantum number s. The low computational cost and the compact wave-function representation make PHF a promising complement to existing approaches for ground states of molecular spin clusters, particularly for large s and moderately large N. The present work may also motivate future explorations of more accurate post-PHF methods for Heisenberg spin clusters.
We construct a new mean-field theory for quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition in accord with Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order $1/T$ expansions.
We study the effects of longitudinal magnetic field and temperature on the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the honeycomb lattice in the presence of anisotropic Dzyaloshinskii-Moriya interaction and next nearest neighbor coupling exchange constant. In particular, the temperature dependence of specific heat have been investigated for various physical parameters in the model Hamiltonian. Using a hard core bosonic representation, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. The effect of Dzyaloshinskii-Moriya interaction term on thermodynamic properties has also been studied via the bosonic model by Greens function approach. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various anisotropy parameters. At low temperatures, the specific heat is found to be monotonically increasing with temperature for magnetic fields in the gapped field induced phase region. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum. Also we have studied the dependence of magnetization on Dzyaloshinskii-Moriya interaction strength for different next nearest neighbor coupling constant.
In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies [Hiroi et al.,2001]. It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the Sp(N) symmetric generalisation of this model in the large N limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long range order and a decoupled chain phase emerges.
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