Thermodynamics of spinS=1/2antiferromagnetic uniform and alternating-exchange Heisenberg chains

Abstract

The magnetic susceptibility *(t) and specific heat C(t) versus temperature t of the spin Sϭ1/2 antiferromagnetic ͑AF͒ alternating-exchange (J 1 and J 2 ) Heisenberg chain are studied for the entire range 0р␣р1 of the alternation parameter ␣ϵJ ). For the uniform chain (␣ϭ1), the high-accuracy *(t) and C(t) Bethe ansatz data of Klümper and Johnston ͑unpublished͒ are shown to agree very well at low t with the respective exact theoretical low-t logarithmic correction predictions of Lukyanov ͓Nucl. Phys. B 522, 533 ͑1998͔͒. Accurate (ϳ10 Ϫ7 ) independent empirical fits to the respective data are obtained over t ranges spanning 25 orders of magnitude, 5ϫ10 Ϫ25 рtр5, which contain extrapolations to the respective exact tϭ0 limits. The infinite temperature entropy calculated using our C(t) fit function is within 8 parts in 10 8 of the exact value ln 2. Quantum Monte Carlo ͑QMC͒ simulations and transfer-matrix density-matrix renormalization group ͑TMRG͒ calculations of *(␣,t) are presented for 0.002рtр10 and 0.05р␣р1, and an accurate (2ϫ10 Ϫ4 ) two-dimensional (␣,t) fit to the combined data is obtained for 0.01 рtр10 and 0р␣р1. From the low-t TMRG data, the spin gap ⌬(␣) is extracted for 0.8р␣р0.995 and compared with previous results, and a fit function is formulated for 0р␣р1 by combining these data with literature data. We infer from our data that the asymptotic critical regime near the uniform chain limit is only entered for ␣տ0.99. We examine in detail the theoretical predictions of Bulaevskii ͓Sov. Phys. Solid State 11, 921 ͑1969͔͒, for *(␣,t) and compare them with our results. To illustrate the application and utility of our theoretical results, we model our experimental (T) and specific heat C p (T) data for NaV 2 O 5 single crystals in detail. The (T) data above the spin dimerization temperature T c Ϸ34 K are not in quantitative agreement with the prediction for the Sϭ1/2 uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. Fitting the (T) data using our *(␣,t) fit function, we obtain the sample-dependent spin gap and range ⌬(Tϭ0)/k B ϭ103(2) K, alternation parameter ␦(0)ϵ(1Ϫ␣)/(1ϩ␣)ϭ0.034(6) and average exchange constant J(0)/k B ϭ640(80) K. The ␦(T) and ⌬(T) are derived from the data. A spin pseudogap with magnitude Ϸ0.4⌬(0) is consistently found just above T c , which decreases with increasing temperature. From our C p (T) measurements on two crystals, we infer that the magnetic specific heat at low temperatures TՇ15 K is too small to be resolved experimentally, and that the spin entropy at T c is too small to account for the entropy of the transition. A quantitative analysis indicates that at T c , at least 77% of the entropy change due to the transition at T c and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates ACuMoO4(OH) (A = Na, K)

“…Both the magnitude and the peak temperature of the data in the wide temperature range of 80-300 K are well reproduced by a spin-1/2 1D antiferromagnetic chain model, 21 in which the g factor and the nearest-neighbor interaction J1 are used as variables together with a temperature-independent contribution χ0. The fitting shown by the dashed curve in Fig.…”

“…The inset shows a blowup around the broad maximum. The dashed curve represents a fit to a 1D antiferromagnetic chain model 21 .…”

Microstructural Investigation, Raman and Magnetic Studies on Chemically Synthesized Nanocrystalline Ni-Doped Gadolinium Oxide (Gd1.90Ni0.10O3−δ)

“…To find the dominating magnetic phase and to explain the onset of nonlinearity in the low field region ($ 4000 Oe) even at RT of GNO, we have proposed a combined formula generated from 3D spin wave model and Johnston formula, which includes the term for paramagnetic, ferromagnetic and antiferromagnetic to fit the M-T curve in the ZFC condition. According to this, combined formula [17][18][19]31 becomes…”

Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic Quantum Spin Chains

“…The dominant feature, governing the magnetic and thermodynamic properties at elevated temperatures, is connected with J 1 . In the magnetic susceptibility χ, for example, the maximum due to short-range order is located at k B T max χ = 0.64J 1 , practically independent of α [6]. However as will be shown below, the small energy scale introduces a second distinct anomaly [7], which can be extraordinarily large in the coefficient of thermal expansion.…”

“…(23a) in ref. [6], is used here for numerical computations of F m , the magnetic entropy Figure 3 compares the so-derived C m with results from T-DMRG calculations. A representation C/T is chosen to make the low-temperature anomaly clearer.…”