The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

Klümper, Andreas

doi:10.1007/s100510050491

Cited by 160 publications

(215 citation statements)

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“…The specific heat in the spin-liquid phase for temperatures of 5 T 10 K is a nearly linear function of T at low fields (H H sat /4) and becomes nonlinear at higher fields. The observed evolution is in qualitative agreement with numerical results obtained for a Heisenberg S = 1 2 chain model [22]. The temperature dependence of the specific heat in the ordered helical state can be roughly approximated as a sum of linear and C m ∝ T 3 terms whereas for the SM state the cubic term is replaced by the C m ∝ T 2 contribution.…”

Section: Discussionsupporting

confidence: 87%

Magnetic field driven 2D-3D crossover in theS=12frustrated chain magnetLiCuVO4

et al. 2015

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(2015) Magnetic field driven 2D-3D crossover in the S=12 frustrated chain magnet LiCuVO4. Physical Review B, 91 (17). 174410. Permanent WRAP URL:http://wrap.warwick.ac.uk/87838 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Publisher statement: © 2015 American Physical Society A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP URL' above for details on accessing the published version and note that access may require a subscription.For more information, please contact the WRAP Team at: wrap@warwick.ac.uk PHYSICAL REVIEW B 91, 174410 (2015) Magnetic field driven 2D-3D crossover in the S = We report on a heat-capacity study of high-quality single-crystal samples of LiCuVO 4 -a frustrated spin S = 1 2 chain system-in a magnetic field amounting to 3/4 of the saturation field. A detailed examination of magnetic phase transitions observed in this field range shows that although the low-field helical state clearly has three-dimensional properties, the field-induced spin-modulated phase turns out to be quasi-two-dimensional. The model proposed in this paper allows one to qualitatively understand this crossover, thus eliminating the presently existing contradictions in the interpretations of NMR and neutron-scattering measurements.

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Section: Discussionsupporting

confidence: 87%

Magnetic field driven 2D-3D crossover in theS=12frustrated chain magnetLiCuVO4

et al. 2015

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“…1). Using the same lattice contribution and C mag (T, B) results calculated for the AFHC in finite field [16], this ansatz (broken line in Fig. 1) also captures the main features of the experimental data at B = 4 T.…”

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confidence: 53%

“…At temperatures T < 10 K, considered here for the specific heat, and for J 2 /k B ≫ 10 K (see below), the magnetic degrees of freedom of azurite are dominated by the chain of spin-1/2 Cu 2+ -monomers, which are antiferromagnetically coupled via the rungs of the diamond backbone [1]. Using the magnetic specific heat C mag of the AFM S = 1/2 Heisenberg chain (AFHC) [16], and including a lattice contribution C lat ∝ (T /Θ D ) 3 , the zerofield specific heat C p (T ) is well fitted down to 2.5 K. In this fit, the magnetic coupling J AF HC /k B = 7.0(1) K and a Debye temperature Θ D = 188 K were used (solid line in Fig. 1).…”

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confidence: 99%

Nature of the Spin Dynamics and1/3Magnetization Plateau in Azurite

et al. 2008

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We present a specific heat and inelastic neutron scattering study in magnetic fields up into the 1/3 magnetization plateau phase of the diamond chain compound azurite Cu3(CO3)2(OH)2. We establish that the magnetization plateau is a dimer-monomer state, i.e., consisting of a chain of S = 1/2 monomers, which are separated by S = 0 dimers on the diamond chain backbone. The effective spin couplings Jmono/kB = 10.1(2) K and J dimer /kB = 1.8(1) K are derived from the monomer and dimer dispersions. They are associated to microscopic couplings J1/kB = 1(2) K, J2/kB = 55(5) K and a ferromagnetic J3/kB = −20(5) K, possibly as result of d z 2 orbitals in the Cu-O bonds providing the superexchange pathways.PACS numbers: 75.30. Et, 75.10.Pq, 75.45.+j Great interest has surrounded the observation of a 1/3 magnetization plateau in azurite CuThis material, famous as a painting pigment of deepblue colour, has been proposed as a realisation of the exotic diamond-chain Hamiltonian of coupled spin-1/2 moments, written aŝHere, J 2 is the magnetic coupling of the diamond backbone, while J 1 and J 3 represent the coupling of the monomers along the chain [3, 4, 5] (Fig. 3). Depending on the relative coupling strengths J 1 , J 2 , J 3 , this model affords a host of exotic phases and quantum phase transitions, including possibly M = 1/3 fractionalisation [6] or exotic dimer phases [4]. However, determining the magnetic exchange couplings in azurite has proved difficult, yielding controversial results. While a susceptibility χ study claims, subsequent numerical studies of χ dispute this claim, proposing a ferromagnetic (FM) J 3 , and thus a non-frustrated scenario [2]. The general issue underlying these starkly contrasting interpretations of the same experimental data is that of the nature of magnetic coupling in low-dimensional (low-D) quantum magnets. In azurite Cu 3 (CO 3 ) 2 (OH) 2 , the Cu 2+ ions (S = 1/2) are in a square-planar coordination on two inequivalent sites [7]. The system has a monoclinic crystal structure (space group P2 1 /c, lattice parameters a = 5.

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“…Below T c1 , χ is dominated by the van Vleck term and by contributions of impurities and of remnants of organic solvents [3]. Above T c2 , χ can be described by a 1D S=1/2 Heisenberg chain [17] with exchange constant J ≈ 676 K in TiOCl [2,3]. For TiOBr the position T max ≈240 K of the maximum of χ allows to estimate J ≈ 375 K from T max /J ≈ 0.64 [17], but χ(T ) deviates from the theoretical curve [11,18].…”

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confidence: 99%

Zero-Field Incommensurate Spin-Peierls Phase with Interchain Frustration in TiOCl

et al. 2005

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We report on the magnetic, thermodynamic and optical properties of the quasi-one-dimensional quantum antiferromagnets TiOCl and TiOBr, which have been discussed as spin-Peierls compounds. The observed deviations from canonical spin-Peierls behavior, e.g. the existence of two distinct phase transitions, have been attributed previously to strong orbital fluctuations. This can be ruled out by our optical data of the orbital excitations. We show that the frustration of the interchain interactions in the bilayer structure gives rise to incommensurate order with a subsequent lock-in transition to a commensurate dimerized state. In this way, a single driving force, the spin-Peierls mechanism, induces two separate transitions.PACS numbers: 75.10. Jm, 75.40.Cx, 71.70.Ch Low-dimensional quantum spin systems exhibit a multitude of interesting phenomena. For instance a onedimensional (1D) S=1/2 chain coupled to the lattice may show a spin-Peierls transition to a non-magnetic, dimerized ground state. In recent years, detailed studies of the first inorganic spin-Peierls compound CuGeO 3 have deepened the understanding of spin-Peierls systems substantially [1]. Even richer physics is expected if the spins are coupled additionally to orbital or charge degrees of freedom. A prominent example is the complex behavior of NaV 2 O 5 , which arises from the interplay of spin dimerization, orbital order and charge order [1]. Recently, TiOCl and TiOBr have been discussed as spinPeierls compounds with strong orbital fluctuations [2-9], assuming a near degeneracy of the t 2g orbitals in these 3d 1 systems. Different quantities such as the magnetic susceptibility [2], the specific heat [9], ESR data [3] and NMR spectra [4] point towards the existence of two successive phase transitions, which clearly goes beyond a canonical spin-Peierls scenario in which a single secondorder phase transition is expected. The high transition temperatures of T c1 =67 K and T c2 =91 K found in TiOCl are fascinating in a spin-Peierls context.The structure of TiOX consists of 2D Ti-O bilayers within the ab plane which are well separated by X=Cl/Br ions [10]. Quasi-1D S=1/2 chains are formed due to the occupation of the d y 2 −z 2 orbital in the ground state (see below), giving rise to strong direct exchange between neighboring Ti sites along the b axis (y direction) and negligible coupling in the other directions. Accordingly, the magnetic susceptibility of TiOCl is well described at high temperatures by the 1D S=1/2 Heisenberg model with an exchange constant of J ≈ 676 K [2,3]. In the non-magnetic low-temperature phase, a doubling of the unit cell along the chain direction has been observed by x-ray measurements for both TiOCl [10] and TiOBr [11], supporting a spin-Peierls scenario. However, the following experimental facts are not expected in a canonical spin-Peierls system: (i) the existence of two successive phase transitions [2-4,9], (ii) the first-order character of the low-temperature phase transition [9][10][11], (iii) the observation of inequivalen...

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The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

Cited by 160 publications

References 40 publications

Magnetic field driven 2D-3D crossover in theS=12frustrated chain magnetLiCuVO4

Magnetic field driven 2D-3D crossover in theS=12frustrated chain magnetLiCuVO4

Nature of the Spin Dynamics and1/3Magnetization Plateau in Azurite

Zero-Field Incommensurate Spin-Peierls Phase with Interchain Frustration in TiOCl

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