Statistical mechanics of classical one-dimensional Heisenberg ferromagnets with single-site anisotropy

Abstract

The exact analytical forms of the low-temperature thermodynamic quantities and correlation functions are obtained for classical one-dimensional Heisenberg ferromagnets with single-site anisotropy including both the systems with an easy axis and with an easy plane. The problem has been managed on the basis of the functional integral method. The calculated results have a few leading terms in series-expansion with respect to the reduced temperature, exhibiting the characteristic points borne out in the recent numerical studies. In particular, the longitudinal correlation function and susceptibility of the system with an easy axis show Ising-like behaviours and the transverse counterparts of the system with an easy plane show isotropic XY- or Heisenberg-like behaviours. Physical implications of the calculated results are also discussed.

Magnetism in Heterobimetallic and Heterotrimetallic Chains Based on the Use of [WV(bipy)(CN)6]– as a Metalloligand

“…However, no out‐of‐phase signals were observed both in absence and under an external magnetic field. Aiming at analyzing the one‐dimensional behavior of this chain and given that the χ M T product for an Ising‐like chain under zero external field increases exponentially with decreasing temperature according to χ M T ≈ C exp(Δ ξ/kT ) ( C being an effective Curie constant and Δ ξ the energy to create a domain wall in the chain), we have plotted ln ( χ M ′ T ) against 1/ T in Figure S8. χ M ′ is the in‐phase ac susceptibility at the lowest frequency studied (1 Hz and H ac = 1 G) in absence of any external applied magnetic field ( H dc = 0).…”

Single‐Chain Magnet Behavior in an Alternated One‐Dimensional Assembly of a MnIII Schiff‐Base Complex and a TCNQ Radical

“…In a ferro‐ or ferrimagnetic one‐dimensional system described in the frame of an anisotropic Heisenberg model, this correlation length exponentially increases on decreasing the temperature, and χT = C eff exp (Δ ξ / T ) 24. 25 According to K. Nakamura and co‐workers, the corresponding gap, Δ ξ , is the energy necessary to create a domain wall in the chain 25. 26 In the Ising limit (| D |≫4| J |/3),27 this energy can be simply expressed as Δ ξ =4 JS T 2 , but its expression becomes nonanalytical in more complicated situations such as ferrimagnetic arrangements, quantum spins, mixed classical‐quantum spins, | D |≤4| J |/3…︁ Figure 5 shows the plot of ln ( χ ′ T ) versus 1/ T , where χ ′ is zero‐field susceptibility deduced from complementary dc and ac measurements.…”

Classical Solitons in Spin-Chains: Susceptibility as Function of Temperature and Frequency

“…Some models (see for example the Nakamura-Sasada spin chain model [6]) show that the parallel susceptibility and the correlation length have the specific "critical" relation, i.e., χ dc ∝ ξ , that results in the temperature dependence χ dc ∝ ξ ∝ exp( /T ) [6]. This behaviour radically differs from a two-or three-dimensional one.…”

“…Recently, the SCM was reported, in which chains are anisotropic Heisenberg systems [5]. It is supposed that at low temperatures, the magnetic behavior of one-dimensional system is better described by such Heisenberg model, which, in the limit of zero field H , predicts Ising-like temperature dependence of the parallel susceptibility [6] …”