Heisenberg Linear Chain Research Articles

Magnetic properties of the quasi one-dimensional Heisenberg linear chain antiferromagnet: manganocene

Magnetic susceptibility measurements on the rhombic form of manganocene, Mn(C 5H 5) 2, are reported between 0.94 and 297.5 K. A pronouced minimum in the 1/x corr m versus T curve is located at T min = 141 ± 1 K. The results are well reproduced by the solution of Fisher to the quasi one-dimensional Heisenberg linear chain modified such as to include interchain interaction for J/k = −14 K, g = 2x = −5 K. A less accurate approximation to the experimental results has been achieved in terms of the pair model ( J/k = −22.5 K, g = 2.0). The results are in excellent agreement with the zigzag chain structure of C 5H 5Mn units reported for the compound.

Exchange coupling in the sulfur-bridged quasi-linear-chain compound bis(dimethyldithiocarbamato)copper(II). Observations on exchange in sulfur-bridged copper(II) compounds

Abstract : Magnetic susceptibility data have been collected on a powdered sample of the linear chain compound bis(dimethyldithiocarbamato) copper(II). The data are fitted to a Heisenberg linear chain odel for exchange coupled S=1/2 ions including an interchain correction term. The best fit parameters are J(interchain) = -1.22 /cm, J(interchain) = 0.47 /cm with the EPR average g value of 2.03. Data for Cu(dmtc)2 infinity and three other sulfur-bridged copper(II) compounds exhibit a correlation between the exchange coupling constant and the geometry of the Cu2S2 bridging unit. (Author)

Specific heat of (C 6H 11NH 3) CuCl 3 (CHAC), a system of ferromagnetic chains

The heat capacity of (C 6H 11NH 3) CuCl 3 (CHAC) has been measured for 0.45 < T < 60 K. Three-dimensional ordering is observed at T = 2.214 K. The data in the paramagnetic region can be described by a ferromagnetic S = 1 2 Heisenberg linear chain model system with J/ k = +45 ± 5K.

Proton relaxation in an [formula omitted] antiferromagnetic linear chain system

The low frequency spin dynamics of the S = 12 antiferromagnetic Heisenberg linear chain has been studied at low temperatures. Experimental information has been obtained from proton relaxation data on CuSO4·5H2O. The relevant spin correlation functions have been evaluated theoretically, via the XY-model and the Bulaevskii approximation.

Study of magnetic resonance and specific heat of [(CH3)3NH]MnCl3 · 2H2O

Specific heat and ESR of [(CH3)3NH]MnCl3 · 2H2O at low temperatures are reported. The experimental data are analyzed with the model of the antiferromagnetic Heisenberg linear chain with single ion anisotropy. Below TN, the EPR mode of g = 2.02 persists while three antiferromagnetic lines appear at higher fields.

Experimental examination of exact solutions for low-dimensional magnetic systems by optical birefringence

By measuring optical birefringence Δn, rigorous solutions of the nearest-neighbour correlation function <SjSi > have been examined for linear-chain Heisenberg and two-dimensional Ising prototype antiferromagnets. The temperature behaviour of Δn above critical points gives important information about the growth of spin correlations associated with magnetic phase transitions.

Spectral density method for an anisotropic linear chain

The spectral density method is used to study the thermodynamic properties of an anisotropic antiferromagnetic Heisenberg linear chain in an external magnetic field. Insecond order approximation without the decoupling procedure for the two particle correlation function, we are able to obtain many results in terms of both the temperature and the magnetic field for different values of the anisotropy parameter. The ground state of the model is investigated and the singular behaviour of some thermodynamic quantities near the critical field is determined. In particular, explicit analytical solutions are given for small anisotropy parameters. Our results are compared with the ones obtained by means of other methods and some exact results are reproduced.

Synthesis, magnetic susceptibility, and Moessbauer spectra of iron(III) dimers and iron(II) polymers containing 2,5-dihydroxy-1,4-benzoquinones

Abstract : Several iron complexes of the dianions of 2,5-dihydroxy-1,4-benzoquinone (DHBQ) and 2, 5-dichloro-3,6-dihydroxy-1,4-benzoquinone (CA, chloranilate dianion) have been prepared and studied by magnetic susceptibility and Moessbauer spectroscopic methods. Iron(II) salts react with these dihydroxybenzoquinones to give polymeric Fe(DHBQ)(H2O)2 and Fe(CA)(H2O)2. If the reaction is carried out in the presence of pyrazine, pyr, (Fe(CA)(pyr))(n) and (Fe(DHBQ)(pyr)) are obtained. Infrared spectral results are consistent with the presence of bridging bidentate pyr in these complexes, and thus sheet polymers. Dimeric Fe2(DHBQ)3(H2O)4 and Fe2(CA)3(H2O)4 .4H2O are obtained by reacting FeCl3 with the respective dihydroxybenzoquinones. Magnetic susceptibility vs. temperature data obtained for the polymeric materials are fit to a S=2 Heisenberg linear chain model. The presence of an anisotropy in the recoilless fraction (Goldanskii-Karyagin effect) is observed in the Fe57 Moessbauer spectra of the Fe(III) dimers and is substantiated by measurements on the temperature dependence of the Moessbauer parameters.

Magnetic Susceptibility and Low-field ESR of an Organic Ion-radical Salt, Tri-p-tolylaminiumyl Chloroantimonate

Abstract The static magnetic susceptibility and the low-field ESR spectra (33.6 and 135 MHz) of powder samples of tri-p-tolylaminiumyl chloroantimonate were measured above 1.7 K. A broad maximum in the susceptibility, which indicates an antiferromagnetic interaction, was observed at 6.0 K; this is consistent with the results of the proton NMR measurements. In the low-field ESR spectra, broadening of the g=2 absorption line and distinct appearance of the g=4 absorption line were observed in the temperature region below Tm, the temperature at which the susceptibility is maximum. The results are interpreted by assuming that the magnetic behavior is due to antiferromagnetic Heisenberg linear chains. An abrupt decrease in the g=2 absorption intensity and a rapid increase in the g=2 absorption linewidth were also found in the temperature range from 3.5 to 2.5 K, while a slight rise in the susceptibility was observed below 2.5 K. These anomalies may imply a magnetic-phase transition in the vicinity of 2.5 K.

Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains

Ground-state instability to bond alternation in long linear chains is considered from the point of view of valence-bond (VB) theory. This instability is viewed as the consequence of a long-range order (LRO) which is expected if the ground state is reasonably described in terms of the Kekul\'e states (with nearest-neighbor singlet pairing). It is argued that the bond alternation and associated LRO predicted by this simple, VB picture is retained for certain linear Heisenberg models; many-body VB calculations on spin $s=\frac{1}{2}$ and $s=1$ chains are carried out in a test of this argument.

Crystal structures of the pseudo-one-dimensional magnetic systems, pyridinium manganese (II) chloride monohydrate and quinolinium manganese (II) chloride monohydrate, and the magnetic behavior of the quinolinium salt

The crystal structures of pyridinium manganese(II) chloride monohydrate (PMC) and quinolinium manganese(II) chloride monohydrate (QMC) both contain bi-bridged linear chains. These chains are hydrogen bonded together to form a two-dimensional network. The magnetic susceptibility of QMC is characteristic of a weak antiferromagnet with a maximum in the susceptibility at 2.0 °K. Analysis of the data in terms of a 1-d Heisenberg linear chain gives an intrachain exchange constant of J/k=−0.36 °K. However, the best model includes significant interchain interactions. Thus, both the structural features and magnetic susceptibility indicate that QMC is a perturbed one-diminsional system. This conclusion is supported by previously reported magnetic susceptibility and ESR data for PMC.

On the spectral-density approach to the correlation functions of a linear magnetic model

We show that, when one uses the spectral-density method (SDM) to study the spin-spin correlation functions for a Heisenberg linear chain, a difficulty appears in a simple procedure usually utilized to avoid the decoupling in the higher spectral density. Such a difficulty does not exist at the first and second order in the SDM with the decoupling procedure. In these approximations the correlation functions are obtained for arbitrary values of the temperature, the magnetic field and the anisotropy parameter.

Spin dynamics of Heisenberg chains: a comparison between theoretical and computer simulation studies

Methods are explored by which computer simulation can be used as a test of the extensive theoretical literature on the linear Heisenberg chain. The computed relaxation function is compared directly with theory where possible. For theories describing the spin-wave frequency and damping a new method is described allowing these to be deduced even when the frequency distribution contains a central diffusive peak and the lineshapes are asymmetric. The computed frequency distribution shows significant discrepancies with all published theories beyond the low-temperature regime.

Sidebands on EPR Lines in the Impure Heisenberg Linear Chain (CH3)4NMnCl3: Cu

The intensity and linewidth of the sidebands on EPR lines have been measured in the impure Heisenberg linear chain (CH 3 ) 4 NMn 1- x Cu x Cl 3 ( x <0.092). The intensity, compared with the pure chain ( x =0), is related to { Δ H p p m [ x ]/ Δ H p p m [0]} 3/2 , where Δ H p p m [ x ] is the peak-to-peak linewidth of the main Zeeman-resonance at concentration x for the applied field along the chain axis. This result is consistent with predictions of one-dimensional spin dynamics.

An experimental study on the magnetic properties of the singlet ground-state system in Cu(NO 3) 2.2 [formula omitted]H 2O : II. The long-range ordered state

From the angular dependence of the proton resonance lines measured in the 3d-ordered state in Cu(NO 3) 2.2 1 2 H 2O it is concluded that the magnetic moments ( S= 1 2 ) are coupled into antiferromagnetic (A.F.) alternating Heisenberg linear chains. Weak interchain interactions are responsible for the phase transition to a 3d-ordered state below T ≈0.2 K. The A.F. state is only present in the field region 28 kOe < H < 48 kOe. A very peculiar dependence of the sublattice magnetization >μ ±> on the temperature as well as on both the magnitude and direction of the external field H is found. The strong dependence of the transition temperature on the direction of H is found to be due to the influence of the dipolar contributions on the weak interchain interactions ( J″). Using Tachiki's description, the alternating chains of spins S= 1 2 are described as regular chains of effective spins S' = 1 2 in an effective field (see also paper I). The sublattice magnetization in terms of this effective spin model shows the characteristics of the sublattice magnetization in the ordered state of a system of weakly coupled regular S = 1 2 A.F. chains. The analysis of the data leads to a good understanding of the properties of the 3d-ordered state of the system of weakly coupled S = 1 2 alternating A.F. chains in Cu(NO 3) 2.2 1 2 H 2O.

Study of Magnetic Energy in One-Dimensional S=1/2 Heisenberg Antiferromagnet KCuF3 by Optical Birefringence

Measurements of optical birefringence have been made on single crystals of the a-type KCuF 3 between 6 and 600 K. The observed temperature dependence of birefringence was found to be in good agreement over a wider temperature range above T N with Bonner-Fisher's theoretical results for the magnetic energy of S =1/2 Heisenberg linear chain systems.

EPR in the Impure Heisenberg Linear Chain CsMn1-xCoxCl3·2H2O

The room-temperature EPR linewidth is reported in the impure Heisenberg linear chain CsMn 1- x Co x Cl 3 ·2H 2 O ( x <0.023). A small concentration of Co 2+ has two significant effects on the linewidth. One is an additional broadening due to the Co–Mn exchange interaction combined with the Co 2+ spin-lattice relaxation. The other is a line-narrowing resulting from the inhibitation of the spin diffusion in chains. The former is isotropic and increases linearly with the Co concentration. The latter is anisotropic and refers dominantly to the interchain dipolar contribution to the linewidth, in consistence with a picture in which the intrachain four-spin correlation functions decay faster than the interchain ones.

Magnetic susceptibility of CuCl2⋅TMSO, a ferromagnetic spin 1/2 linear chain

The crystal structure of the title compound (TMSO≡C4H8SO) consists of linear chains of Cu ions with three bridging ligands (2 Cl, 1 O) between each pair of Cu ions. The susceptibility of the salt has been measured between 2.0 and 120 K on a PAR vibrating sample magnetometer and from 80 to 300 on a Faraday balance. The high temperature data shows positive deviation from Curie behavior, with a Curie-Weiss constant of 18.7 K. However, considerable interactions between chains exist and the χT vs T plot shows a maximum at T=7.5 K. The data has been analyzed with several one-dimensional models. At present, the best fit is obtained with an Heisenberg linear chain (J=24.6 cm−1) with a mean field correction for interchain interactions (ZJ′=−1.3 cm−1).

Quasi-one-dimensional behavior of(CH3)2NH2MnCl3(DMMC)

The heat capacity of dimethyl ammonium manganese trichloride has been investigated for $1.6&lt;T&lt;50$ K. A transition to a three-dimensional antiferromagnetically ordered state has been observed at 3.60 K, which is supported by nuclear-magnetic-resonance and susceptibility measurements. The critical entropy did amount to 3.4%. The magnetic heat capacity in the paramagnetic region could be described very well by a $S=\frac{5}{2}$ Heisenberg linear chain system with $\frac{J}{k}=\ensuremath{-}5.8\ifmmode\pm\else\textpm\fi{}0.7$ K. The data for $\frac{\mathrm{kT}}{|J|}&lt;1.5$, together with the earlier data on ${(\mathrm{C}{\mathrm{H}}_{3})}_{4}$NMn${\mathrm{Cl}}_{3}$, corroborate the suggested low-temperature behavior of such a system.

Application of the HLISP program for the irreducible representation matrix of the permutation groups and the partition function of the dilute linear Heisenberg chain

For the irreducible representation matrix of permutation groups the recurrence relations are regarded as a recursive definition, and an HLISP program to calculate it is presented. The partition function of the dilute linear Heisenberg model is calculated by using the reduction of the matrix of the permutation groups.