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Physical review. B, Condensed matter

Ferrimagnetic Heisenberg chains [(1/2-S] (S=1to (5/2): Thermal and magnetic properties

Marc Drillon, Eugenio Coronado, Roland Georges, Jean Claude Gianduzzo, Jacques Curély

Published Dec 1, 1989• 101 citations
Publisher

Abstract

Energy spectra and thermodynamic quantities (partition function, entropy, specific heat, susceptibility) of ferrimagnetic Heisenberg chains, made up of two spin sublattices [(1/2-S], are discussed from the exact results computed for finite rings. Extrapolation of the theoretical data versus the length of finite rings N is discussed for S ranging from 1 to (5/2 and compared with previous reported findings for the [(1/2-\ensuremath{\infty}] spin chain. In the low-temperature region, similarities between the ferrimagnetic chains [(1/2-S] and the regular ferromagnetic ones (with spin S-(1/2) are used for the determination of the limiting curves.

DOI
10.1103/physrevb.40.10992

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Journal of Applied Physics•Jul 15, 1985•36 citations
Energy spectra and thermodynamic quantities (partition function, entropy, specific heat, susceptibility) of ferrimagnetic Heisenberg chains, made up of two spin sublattices [(1/2-S], are discussed from the exact results computed for finite rings. Extrapolation of the theoretical data versus the length of finite rings N is discussed for S ranging from 1 to (5/2 and compared with previous reported findings for the [(1/2-\ensuremath{\infty}] spin chain. In the low-temperature region, similarities between the ferrimagnetic chains [(1/2-S] and the regular ferromagnetic ones (with spin S-(1/2) are used for the determination of the limiting curves.
The low-energy structures of the quantum ferrimagnetic Heisenberg chain consisting of (5/2, 1/2, 1/2) trimers are investigated theoretically. The results of the linear spin-wave theory are compared with those from the numerical exact diagonalization calculation and the matrix product method for the lowest optical mode. The temperature behaviour of thermodynamical properties such as magnetic susceptibility, specific heat and entropy are analysed in the framework of the modified spin-wave theory. The results of the calculations are used to explain the experimental data obtained for the molecule-based heterospin magnets [Mn(hfac) 2 BNO R ] (R = H, F, Cl, Br) with one-dimensional chain structure.
Thermodynamic properties of the quantum Heisenberg spin chains with S=1/2,S=1/2,S=1/2, 1, and 3/23/23/2 are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.
Linear chains (and rings) of S=12S=\frac{1}{2}S=21​ spins with the anisotropic (Ising-Heisenberg) Hamiltonian $\mathcal{H}=\ensuremath{-}2J\ensuremath{\Sigma}\stackrel{N}{i=1}{{{S}_{i}}^{z}{{S}_{i+1}}^{z}+\ensuremath{\gamma}({{S}_{i}}^{x}{{S}_{i+1}}^{x}+{{S}_{i}}^{y}{{S}_{i+1}}^{y})}\ensuremath{-}g\ensuremath{\beta}\ensuremath{\Sigma}\stackrel{N}{i=1}\mathrm{H}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{S}}_{i}$ have been studied by exact machine calculations for N=2to11N=2 \mathrm{to} 11N=2to11, $\ensuremath{\gamma}=0 \mathrm{to} 1$ and for ferro- and antiferro-magnetic coupling. The results reveal the dependence on finite size and anisotropy of the spectrum and dispersion laws, of the energy, entropy, and specific heat, of the magnetization and susceptibilities, and of the pair correlations. The limiting $N\ensuremath{\rightarrow}\ensuremath{\infty}$ behavior is accurately indicated, for all $\ensuremath{\gamma}$, in the region kT∣J∣> 0.5\frac{\mathrm{kT}}{|J|}>~0.5∣J∣kT​> 0.5 which includes the maxima in the specific heat and susceptibility. The behavior of thermal and magnetic properties of infinite chains at lower temperatures is estimated by extrapolation. For infinite antiferromagnetic chains the ground-state degeneracy, the anisotropy gap, and the magnetization, perpendicular susceptibility, and pair correlations at T=0T=0T=0 are similarly studied. Estimates of the long-range order suggest that it vanishes only at the Heisenberg limit $\ensuremath{\gamma}=1$ and confirm the accuracy of Walker's perturbation series in $\ensuremath{\gamma}$.
Quantum phase transitions in alternating spin-(12\frac{1}{2}21​, 52\frac{5}{2}25​) Heisenberg chains
The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim of describing the available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature versus magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger liquid phase, the ferrimagnetic plateau and the fully polarized phase, and the respective quantum critical points and crossover lines.
The magnetic and thermodynamic properties of a ferrimagnetic decorated spin-(12,1)(\frac{1}{2},1)(21​,1) Heisenberg chain with spin-1 pendant spins are investigated for three cases: (A) J1,J2>0{J}_{1},{J}_{2}>0J1​,J2​>0; (B) J1>0{J}_{1}>0J1​>0 and J2<0{J}_{2}<0J2​<0; and (C) J1<0{J}_{1}<0J1​<0 and J2>0{J}_{2}>0J2​>0, where J1{J}_{1}J1​ and J2{J}_{2}J2​ are the exchange couplings between spins in the chain and along the rung, respectively. The low-lying and magnetic properties are explored jointly by the real-space renormalization group, spin wave, and density-matrix renormalization-group methods, while the transfer-matrix renormalization-group method is invoked to study the thermodynamics. It is found that the magnon spectra consist of a gapless and two gapped branches. Two branches in case (C) have intersections. The coupling dependence of low-energy gaps are analyzed. In a magnetic field, a m=32m=\frac{3}{2}m=23​ (mmm is the magnetization per unit cell) plateau is observed for case (A), while two plateaux at m=12m=\frac{1}{2}m=21​ and 32\frac{3}{2}23​ are observed for cases (B) and (C). Between the two plateaux in cases (B) and (C), the sublattice magnetizations for the spins coupled by ferromagnetic interactions have decreasing regions with increasing the magnetic field. At finite temperature, the zero-field susceptibility temperature product $\ensuremath{\chi}T$ and specific heat exhibit distinct exotic features with varying the couplings and temperature for different cases. $\ensuremath{\chi}T$ is found to converge as $T\ensuremath{\rightarrow}0$, which is different from the divergent behavior in the spin-(12,1)(\frac{1}{2},1)(21​,1) mixed-spin chain without pendants. The observed thermodynamic behaviors are also discussed with the help of their low-lying excitations.
The exact solutions of the so-called ferrimagnetic Ising chain made up of two sublattices (S0,S1) are derived from a transfer matrix method. The short-range ferrimagnetic order occurs when considering different spins and/or different Landé factors on both sublattices. Most of the physical features of interest are shown to be involved in the S0=S1=1 system including an alternation of Landé factors (g0,g1) and local anisotropies (K0,K1). Thus, in the limit K0→∞ stabilizing a Kramers doublet, Sz=±1, on even sites, the system behaves like the ferrimagnetic chain (S0=1/2, S1=1). The susceptibility and magnetization curves are discussed in various situations as a function of the significant parameters.