Heisenberg Linear Chain Research Articles

Influence of third-nearest-neighbor interactions on the ground state of Heisenberg linear chains.

Antiferromagnetic ground-state energies for infinite Heisenberg linear chains with up to third-nearest-neighbor interactions have been determined by means of numerical extrapolations. On the other hand, new conditions to produce a ferromagnetic ground state have been established for finite chains. These conditions are expressed as lower bounds for the coupling constants. The particular case in which the coupling constant for third-nearest-neighbor interactions is zero is compared in two different ways with previous calculations by other authors, showing good correspondence.

Magnetic exchange interactions in the linear-chain chromium(III) compounds

Abstract : Magnetic susceptibility and magnetization studies on the linear chain chromium(III) compounds catena-fluorophthalocyaninatochromium(III), CrPcF n, and catena-cyanophthalocyaninatochromium (III), CrPcCNn, reveal that the chromium (III) ions in CrPcFn and CrPcCNn are magnetically exchange coupled. The magnetic susceptibility data for CrPcFn may be fit with Heisenberg linear chain theory for antiferromagnetic exchange with J = -12.2/cm and g = 2.00. The magnetic susceptiblity data for CrPcCNn may be fit with Heisenberg linear chain theory for ferromagnetic exchange with J = 0.2/cm and g = 1.98. CrPcCNn provides the first example of ferromagnetic exchange in a linear chain of chromium (III) ions. The difference in the exchange interactions in CrPcFn and CrPcCNn may be understood in terms of the electronegativities of the bridges and in terms of the orbitals which transmit the superexchange interactions. Originator supplied keywords include: Electrical conductivity (phthalocyanine); Low-dimensional conducting materials.

Linear chain antiferromagnetic interactions in Cs2CuCl4

The magnetic susceptibility of polycrystalline samples of Cs2CuCl4 has been measured over the temperature interval 1.1–30 K. A broad maximum in the data, centered around 2.6–2.7 K, is consistent with the existence of lower-dimensional antiferromagnetic interactions in this compound. The model used for fitting the data is the Heisenberg linear chain of Bonner and Fisher, with a small molecular-field correction. The parameters resulting from the data analysis are 〈g〉=2.20±0.02, −J/k=2.0±0.1 K, and −zJ′/k=0.10±0.05 K.

ChemInform Abstract: EPR, MAGNETIC AND STRUCTURAL INVESTIGATIONS ON THE WEAK‐EXCHANGE HEISENBERG LINEAR CHAIN BIS(N‐METHYLPHENAZINIUM) BIS(DICYANOETHENEDITHIOLATO)CUPRATE(II), ((NMP)2)(CU(MNT)2)

Chemischer InformationsdienstVolume 16, Issue 13 Physical Organic Chemistry ChemInform Abstract: EPR, MAGNETIC AND STRUCTURAL INVESTIGATIONS ON THE WEAK-EXCHANGE HEISENBERG LINEAR CHAIN BIS(N-METHYLPHENAZINIUM) BIS(DICYANOETHENEDITHIOLATO)CUPRATE(II), ((NMP)2)(CU(MNT)2) P. KUPPUSAMY, P. KUPPUSAMYSearch for more papers by this authorB. L. RAMAKRISHNA, B. L. RAMAKRISHNASearch for more papers by this authorP. T. MANOHARAN, P. T. MANOHARANSearch for more papers by this author P. KUPPUSAMY, P. KUPPUSAMYSearch for more papers by this authorB. L. RAMAKRISHNA, B. L. RAMAKRISHNASearch for more papers by this authorP. T. MANOHARAN, P. T. MANOHARANSearch for more papers by this author First published: April 2, 1985 https://doi.org/10.1002/chin.198513055AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume16, Issue13April 2, 1985 RelatedInformation

Ground-state spin pairing of general-spin linear-chain Heisenberg models.

Simple products of singlet-coupled spin pairs are identified as exact eigenstates for a certain class of antiferromagnetically signed linear-chain Heisenberg models with both bond-length alternation and next-nearest-neighbor interactions. Where such an eigenstate becomes a ground state, a cusp is noted to arise in the ground-state energy. Differences between the spin-1/2 and higher-spin cases appear.

EPR, magnetic and structural investigations on the weak-exchange Heisenberg linear chain bis(N-methylphenazinium) bis(dicyanoethenedithiolato)cuprate(II), [(NMP)2][Cu(mnt)2

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTEPR, magnetic and structural investigations on the weak-exchange Heisenberg linear chain bis(N-methylphenazinium) bis(dicyanoethenedithiolato)cuprate(II), [(NMP)2][Cu(mnt)2]P. Kuppusamy, B. L. Ramakrishna, and P. T. ManoharanCite this: Inorg. Chem. 1984, 23, 24, 3886–3892Publication Date (Print):November 1, 1984Publication History Published online1 May 2002Published inissue 1 November 1984https://doi.org/10.1021/ic00192a010RIGHTS & PERMISSIONSArticle Views79Altmetric-Citations33LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (779 KB) Get e-AlertsSupporting Info (1)»Supporting Information Supporting Information Get e-Alerts

Magnetic Susceptibility Studies on CsCrCl3and RbCrCl3

Magnetic susceptibility studies are made in 4.2 K≦ T ≦573 K on single crystals of linear chain Heisenberg antiferromagnets CsCrCl 3 and RbCrCl 3 . Anomalies in the temperature variation of the susceptibility are observed at temperatures where crystallographic phase transitions caused by cooperative Jahn-Teller effect take place. The anomaly is a discontinuous jump or a turning point according as the transition is of first or second order, respectively. The data are fitted to Fisher's classical theory, and temperature variations of the intrachain exchange interaction constants of the two magnets are evaluated. The constant changes discontinously at the first order transition temperature, and continuously in a temperature range below the second order transition temperature.

Quasi-one-dimensional antiferromagnetism in (CH3NH3)MnCl3⋅2H2O

(CH3NH3)MnCl3⋅2H2O, MMC, contains chains of cis-[MnCl4(H2O)2] octahedra corner-linked via single Cl atoms. These chains are very similar to those in CsMnCl3⋅2H2O, CMC, but more widely separated by the larger cations. We have measured the magnetic susceptibilities of MMC between ∼1 and 100 K at 80 Hz and its heat capacity between ∼1 and 20 K. Susceptibilities above ∼10 K are well described by models of the antiferromagnetic linear Heisenberg chain with S=5/2, g=2.00, and J1/k=−3.01 K, very nearly the same intrachain coupling as in CMC. Below TN =4.12 K weak interchain interactions (∼6×10−3‖J1‖) produce long-range AF order in three dimensions with preferred spin alignment along or near the a axis. The linear chains in MMC are more nearly independent than those in CMC.

Classical treatment of a heisenberg linear chain with spin alternation; application to the MnNi(EDTA)-6H 2O complex

The thermodynamic behaviour of an exchange-coupled linear system with two alternating spin sublattices is investigated from a classical point of view. A closed formula is derived for the magnetic susceptibility which is easily adapted to real spin systems, using appropriate scaling transformations. The proposed approach is shown to describe successfully the behaviour of a new bimetallic chain complex MnNi(EDTA)-6H 2O. In particular, a minimum in the xT versus T plot is observed at very low temperature, in agreement with theory.

Magnetic Susceptibility Analyses of Alternating and Ladder-Like Copper (II) Linear Chain Compounds

The new approximation methods are applied to the analyses of the magnetic susceptibilities of the alternatingly spaced Heisenberg chain and the ladder-like systems of spin one-half. The magnetic susceptibility of antiferromagnetic compounds Cu-HTS and Cu-OTS which are recently found good examples of the alternating Heisenberg linear chains has been analyzed by the use of ( q +1)-approximation and the exchange coupling parameters have been estimated. As an example of antiferromagnetic compounds having ladder-like structure, hydrazinium copper (II) chloride has been taken up and the pair-approximation is applied for the analysis of its magnetic susceptibility. Both approximations have proved to be quite effectual and expedient method to analyze the magnetic properties of low-dimensional spin systems.

High-field (40 T) magnetization studies of linear Heisenberg chains with alternating exchange

We present susceptibility vs temperature, and high-field magnetization data on two Cu2+ chain compounds with alternating exchange constants.

EPR investigation of the high-temperature dynamics of the impurity-doped Heisenberg linear chain TMMC:Cu

Frequency-dependent EPR experiments from 1 to 18 GHz were performed on tetra-methyl-ammonium-manganese-chloride (TMMC) doped with 1%, 4%, 7% and 9% Cu2+ to study the influence of magnetic impurities on the high-temperature dynamics. The experimentally observed omega L-1/2 dependence of the magnetic resonance linewidth on the angular Larmor frequency omega L demonstrates directly that the long-wavelength dynamics in the doped samples is diffusive in this case as in the pure undoped system. From the experiment it is possible to extract the exchange interaction constant mod JMnCu/kB mod to be 1.7+or-0.4K. This value obtained is comparable with that found in low-temperature experiments. Observations of half-field transitions are reported in this impure 1d system.

Relation between Exchange Interaction and Crystal Structure of Verdazyl Radicals. As Studied by Means of McConnell’s Spin Density Hamiltonian

Abstract The exchange interactions in four kinds of verdazyl crystals, 2,4,6-triphenylverdazyl (TPV), 2,4,6-triphenyl-3-methylverdazyl (MeTPV), 2,4,6-tri-p-tolylverdazyl (TTV), and 2,6-di-p-tolyl-4-phenylverdazyl (DTPV), have been studied by means of McConnell’s spin density Hamiltonian. The calculated exchange parameters, J, have been compared with the experimental values derived from the magnetic susceptibilities. The observed order of J’s J⁄k=−5.4 (TPV), −9.1 (MeTPV), −11.1 (DTPV), and 0–−0.3 K (TTV), can be qualitatively explained by the following equation: J∝\undersetijΣ (−1⁄rij)ρilρjl+1, where ρil and ρjl+1 are π-spin densities on atoms i and j of the l-th and (l+1)-th molecules in the crystallographic column and rij is the interatomic distance between atoms i and j. The magnetic susceptibility data of MeTPV and TTV between 1.6 and 300 K are presented and interpreted with the Heisenberg linear chain model. The susceptibility of DTPV is re-interpreted in the same framework as above.

A branching path approach to the large-N limit Heisenberg chain: the S=1/2case

For a Heisenberg linear chain of N one-half spins, a class of solutions is built and explicit expressions for the energy given in the large-N continuum limit using a branching path approach. With such a technique connections with the classical Heisenberg chain appear clearly, and 'quantum' corrections to this classical description can be derived explicitly.

ChemInform Abstract: MAGNETIC PROPERTIES OF α‐LITHIUM EUROPIUM OXIDE AND β‐LITHIUM EUROPIUM OXIDE (LI2EU5O8). EVIDENCE FOR LINEAR‐CHAIN HEISENBERG FERROMAGNETIC BEHAVIOR

Chemischer InformationsdienstVolume 13, Issue 15 Physical Inorganic Chemistry ChemInform Abstract: MAGNETIC PROPERTIES OF α-LITHIUM EUROPIUM OXIDE AND β-LITHIUM EUROPIUM OXIDE (LI2EU5O8). EVIDENCE FOR LINEAR-CHAIN HEISENBERG FERROMAGNETIC BEHAVIOR T. NYOKONG, T. NYOKONGSearch for more papers by this authorJ. E. GREEDAN, J. E. GREEDANSearch for more papers by this author T. NYOKONG, T. NYOKONGSearch for more papers by this authorJ. E. GREEDAN, J. E. GREEDANSearch for more papers by this author First published: April 13, 1982 https://doi.org/10.1002/chin.198215022AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume13, Issue15April 13, 1982 RelatedInformation

Magnetic behavior of the ferromagnetic quantum chain systems (C6H11NH3)CuCl3(CHAC) and (C6H11NH3)CuBr3(CHAB)

Heat-capacity measurements on (C6H11NH3)CuBr3 (CHAB) in the region 0.45 < T<55 K are presented. Three-dimensional ordering is observed at Tc=1.50 K. The data are analyzed together with previously reported measurements on (C6H11NH3)CuCl3 (CHAC). Both compounds appear to be very good approximations of a ferromagnetic S=12 Heisenberg linearchain system with Jk50 K. From the data it is inferred that the intrachain interaction of CHAC contains about 2% uniaxial anisotropy, whereas CHAB contains about 5% easy-plane anisotropy. The results are corroborated by magnetization measurements on CHAB below Tc, which also reveal a metamagnetic transition for Hb (Hc=210Oe). From the value of Hc and the location of the tricitical point the interchain interactions in CHAB were found as zAFJAFk=-0.03 K, zFJFk0.08 K.

Ferromagnetic exchange coupling in sodium biscarbonatocuprate(II) trihydrate

The magnetic properties of sodium biscarbonatocuprate(II) trihydrate, Na2Cu(CO2)2,3H2O, have been measured in the temperature range 1.8-42 K. Magnetic susceptibility and magnetization measurements provide evidence for ferromagnetic interactions in this linear-chain compound. The magnetic susceptibility data are compatible with a Heisenberg linear chain; the best-fit parameters for the complete data set are: J 1.22 �0.04cm-1, g 2.18 � 0.01, and zJ'-0.28 � 0.02cm-l. Data in the temperature range 7-42K yield the best-fit parameters J1.37 � 0.08 cm-1, g 2.12 � 0.01, and zJ' 0.0 cm-1. The g value from this fit agrees with the g value of 2.10 obtained from a fit of the data in the temperature range 10-42 K to the Curie-Weiss law.

Magnetic Susceptibility and Crystal Structure of 1,5-Diphenyl-3-(4-chlorophenyl)verdazyl Radical

Abstract The magnetic susceptibility of 1,5-diphenyl-3-(4-chlorophenyl)verdazyl (Cl-TPV) has been measured on a powder sample in the temperature region between 1.8 and 80 K. It exhibited a round maximum at 21.0 K; this temperature is the highest among those observed for verdazyl monoradicals. The susceptibility can be well described by the Heisenberg linear chain model; the estimated exchange interaction parameter is J⁄k=−16.4 K. The crystal structure of Cl-TPV has been determined by means of X-ray diffraction. The crystal is orthorhombic, with the space group of Pbca and with a=22.041(5), b=7.166(4), c=21.379(5) Å, and Z=8. The molecules are arranged in a column along the b axis. The exchange interaction has been discussed based on the crystal structure and the spin density distribution.

Failure of renormalisation group method in semiclassical limit

The authors compute the ground state energy of a Heisenberg linear chain antiferromagnet for spins s=1/2, 1 . . . infinity by a block renormalisation method. Although this method yields reasonably accurate results in the quantum limit s=1/2, in the semiclassical limit (where the significant parameter in the asymptotic expansion e0=-Js2(1+ gamma /2s+O(1/s)2) is known to be gamma approximately=0.7) the RG procedure yields gamma =0, a highly unsatisfactory result.

ChemInform Abstract: 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)