Cyclic four-spin exchange on a two-dimensional square lattice: Possible applications in high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superconductors

Roger, M.; Delrieu, J.M.

doi:10.1103/physrevb.39.2299

Cited by 76 publications

(70 citation statements)

References 21 publications

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“…Raman and neutron diffraction experiments evaluate this coupling to be around J N N =130 meV(128±6 meV [1,2],134±5 meV [3,4,5], respectively). Nevertheless, the corresponding simple Heisenberg Hamiltonian does not reproduce entirely the features of the Raman spectrum [6,7,8,9,10,11] and additional effects such as second-neighbor magnetic coupling J N N N and four-spin cyclic exchange have been invoked [12,13,14,15]. While an upper bond for J N N N (|J N N N | ≤9 meV) has been given from Raman experiments [5], the amplitude of the four-spin operator in this kind of compounds is a matter of discussion.…”

Section: Introductionmentioning

confidence: 99%

Proposal of an extendedt−JHamiltonian for high-Tccuprates fromab initiocalculations on embedded clusters

Calzado

Malrieu

2001

Phys. Rev. B

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A series of accurate ab initio calculations on Cu p O q finite clusters, properly embedded on the Madelung potential of the infinite lattice, have been performed in order to determine the local effective interactions in the CuO 2 planes of La 2−x Sr x CuO 4 compounds. The values of the first-neighbor interactions, magnetic coupling (J N N =125 meV) and hopping integral (t N N =-555 meV), have been confirmed. Important additional effects are evidenced, concerning essentially the second-neighbor hopping integral t N N N =+110meV, the displacement of a singlet toward an adjacent colinear hole, h abc SD =-80 meV, a non-negligible hole-hole repulsion V N N − V N N N =0.8 eV and a strong anisotropic effect of the presence of an adjacent hole on the values of the first-neighbor interactions. The dependence of J N N and t N N on the position of neighbor hole(s) has been rationalized from the two-band model and checked from a series of additional ab initio calculations. An extended t-J model Hamiltonian has been proposed on the basis of these results. It is argued that the here-proposed three-body effects may play a role in the charge/spin separation observed in these compounds, that is, in the formation and dynamic of stripes.

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Section: Introductionmentioning

confidence: 99%

Proposal of an extendedt−JHamiltonian for high-Tccuprates fromab initiocalculations on embedded clusters

Calzado

Malrieu

2001

Phys. Rev. B

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“…At fourth order in a κ = t/U expansion, the J λ 's appear as 4 and J 4 /U = 20κ 4 [11,12]. More intricate expressions are obtained for a more general three-band Hubbard model [13]. The effective interaction between next-nearest neigbour pairsJ (2) 2 becomes negative (i.e.…”

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Spin Correlations in the Paramagnetic Phase and Ring Exchange inLa2CuO4

et al. 2005

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Spin correlations in the paramagnetic phase of La2CuO4 have been studied using polarized neutron scattering, with two important results. First, the temperature dependence of the characteristic energy scale of the fluctuations and the amplitude of the neutron structure factor are shown to be in quantitative agreement with the predictions of the quantum non-linear sigma model. Secondly, comparison of a high-temperature series expansion of the equal-time spin correlations with the diffuse neutron intensity provides definitive experimental evidence for ring exchange.Heisenberg was the first to realize that strong effective spin interactions arise from the principle of the indistinguishability of the particles [1]. Dirac generalized this concept, in the context of Group Theory, to include higher order interactions[2]. Multi-particle exchange dominates the physics of the quantum solid 3 He[3] but, surprisingly, is generally not taken into account for electronic magnetic materials. The most powerful technique for exploring exchange interactions is the study of excitations from the ordered phase using inelastic neutron scattering. However, ambiguities in the interpretation of magnon dispersion curves sometimes mean that higher order terms remain hidden. By employing the independent approach of studying the instantaneous spin correlations in the paramagnetic phase, we obtain complementary information that enables a better understanding of the exchange mechanism. In this letter we describe studies of the diffuse magnetic scattering from La 2 CuO 4 which provide compelling, quantitative evidence for the existence of four-particle cyclic exchange.La 2 CuO 4 is of great intrinsic interest both as the parent compound of a canonical high-temperature superconductor, and as a very good realization of a two-dimensional quantum Heisenberg antiferromagnet (2DQHAF). Magnetic Raman experiments [4], infrared absorption studies [5,6] and inelastic neutron scattering measurements [7] show definitively the inadequacy of the nearest-neighbour Heisenberg model, and suggest the possibility that four-particle exchange may be significant.In an important series of experiments to study the diffuse magnetic scattering from La 2 CuO 4 using unpolarized neutrons[8] the temperature dependence of the magnetic correlation length was found to agree with the predictions of the quantum non-linear sigma model (QNLσM) [9]. However, the observed amplitude shows dramatic deviations from the predictions of this theory [8]. The QNLσM is the simplest possible effective action for a 2DQHAF that is compatible with the long-wavelength spin waves and that does not assume a spontaneously broken symmetry. Moreover, its predictions should hold even in the presence of four-spin exchange, as discussed below. Here we study the dynamical spin correlations above the Néel temperature using polarized neutrons, and find complete agreement of the observed 2D critical fluctuations with the predictions of the QNLσM.Dirac's approach provides the most transparent theoretical fram...

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“…In strongly correlated electron systems, such as the high-T c cuprates and related antiferromagnets, ring exchange processes are typically much weaker than the pair exchange J [5] and are often neglected. Four-spin ring exchange has, however, been argued to be responsible for distinct features in the magnetic Raman [6] and optical absorption spectra [7]. Neutron measurements of the magnon dispersion have also become sufficiently accurate to detect deviations from the standard pair exchange Hamiltonian (the Heisenberg model) and such discrepancies have been attributed to ring exchange [8,9].…”

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Striped Phase in a QuantumXYModel with Ring Exchange

et al. 2002

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We present quantum Monte Carlo results for a square-lattice S = 1/2 XY-model with a standard nearest-neighbor coupling J and a four-spin ring exchange term K. Increasing K/J, we find that the ground state spin-stiffness vanishes at a critical point at which a spin gap opens and a striped bondplaquette order emerges. At still higher K/J, this phase becomes unstable and the system develops a staggered magnetization. We discuss the quantum phase transitions between these phases.PACS numbers: 75.10.Jm, 75.40.Mg, Ring exchange interactions have for a long time been known to be present in a variety of quantum many-body systems [1] and have been investigated rather thoroughly in solid 3 He [2]. They are also important for electrons in the Wigner crystal phase [3,4]. In strongly correlated electron systems, such as the high-T c cuprates and related antiferromagnets, ring exchange processes are typically much weaker than the pair exchange J [5] and are often neglected. Four-spin ring exchange has, however, been argued to be responsible for distinct features in the magnetic Raman [6] and optical absorption spectra [7]. Neutron measurements of the magnon dispersion have also become sufficiently accurate to detect deviations from the standard pair exchange Hamiltonian (the Heisenberg model) and such discrepancies have been attributed to ring exchange [8,9]. Recently, ring exchange has attracted interest as a potentially important interaction that could lead to novel quantum states of matter, in particular 2D electronic spin liquids with fractionalized excitations [10,11,12,13,14,15]. Furthermore, for bosons on a square lattice ring exchange has been shown to give rise to a "exciton Bose liquid" phase [16].Here we study the effects of ring exchange in one of the most basic quantum many-body Hamiltonians-the spin-1/2 XY-model on a 2D square lattice. We use a quantum Monte Carlo method (stochastic series expansion, hereafter SSE [17,18,19]) to study the low-temperature behavior of this system including a four-spin ring term. Defining bond and plaquette exchange operatorsthe Hamiltonian iswhere ij denotes a pair of nearest-neighbor sites and ijkl are sites on the corners of a plaquette. For K = 0 this is the standard quantum XY-model, or, equivalently, hard-core bosons at half-filling with no interactions apart from the single-occupancy constraint. This system undergoes a Kosterlitz-Thouless transition at T /J ≈ 0.68 [20,21] and has a T = 0 ferromagnetic moment M x = S x i ≈ 0.44 [22,23]. The K-term corresponds to retaining only the purely x-and y-terms of the full cyclic exchange.In a soft-core version of the pure ring model (J = 0), Paramekanti et al. recently found a compressible but non-superfluid phase (exciton Bose liquid) for weak onsite repulsion U [16]. As the hard-core limit is approached they found a transition to a staggered chargedensity-wave phase. Hence, the ground state of the spin Hamiltonian (3) can be expected to change from an easyplane ferromagnet with a finite spin stiffness ρ s and a magnetization M x at...

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Cyclic four-spin exchange on a two-dimensional square lattice: Possible applications in high-Tcsuperconductors

Cited by 76 publications

References 21 publications

Proposal of an extendedt−JHamiltonian for high-Tccuprates fromab initiocalculations on embedded clusters

Proposal of an extendedt−JHamiltonian for high-Tccuprates fromab initiocalculations on embedded clusters

Spin Correlations in the Paramagnetic Phase and Ring Exchange inLa2CuO4

Striped Phase in a QuantumXYModel with Ring Exchange

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