Coupled cluster treatment of the Shastry-Sutherland antiferromagnet

Darradi, R.; Richter, Johannes; Farnell, Damian J. J.

doi:10.1103/physrevb.72.104425

Cited by 94 publications

(179 citation statements)

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“…Under this assumption, a linear dependence Δα = k Δy with k = 36:6 ± 0:8°Å −1 = 0:64 ± 0:01 Å −1 (Fig. S1) can be deduced from temperature-dependent neutron diffraction experiments (15) to obtain Δα = 2 ffiffi ffi 2 p ky 2ðx + yÞ − kðx 2 + y 2 Þ Δa: [9] Similar functions of x, y, and k can be obtained for Δx, Δy, and Δd the Cu-O distance (SI Text). Finally, replacing x, y, and a by their experimental values (15), we obtain…”

Section: Discussionmentioning

confidence: 99%

“…It has been first shown that this S = 0 wavefunction is the ground state for J′=J K 0:7, separated from the first excited state by a spin gap (4,6,7). More recently, the critical value has been refined to be ' 0:675 (8)(9)(10). The spin gap can be closed [the spin gap never strictly closes, as DzyaloshinskyMoriya terms cause mixing of spin-triplet and spin-singlet states (11)], and cascading magnetic states can be induced, by magnetic fields exceeding '20 T (12).…”

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confidence: 99%

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Magnetic nanopantograph in the SrCu ₂ (BO ₃ ) ₂ Shastry–Sutherland lattice

Radtke

Saúl

Dąbkowska

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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Magnetic materials having competing, i.e., frustrated, interactions can display magnetism prolific in intricate structures, discrete jumps, plateaus, and exotic spin states with increasing applied magnetic fields. When the associated elastic energy cost is not too expensive, this high potential can be enhanced by the existence of an omnipresent magnetoelastic coupling. Here we report experimental and theoretical evidence of a nonnegligible magnetoelastic coupling in one of these fascinating materials, SrCu 2 (BO 3 ) 2 (SCBO). First, using pulsed-field transversal and longitudinal magnetostriction measurements we show that its physical dimensions, indeed, mimic closely its unusually rich field-induced magnetism. Second, using density functional-based calculations we find that the driving force behind the magnetoelastic coupling is the CuOCu b superexchange angle that, due to the orthogonal Cu 2+ dimers acting as pantographs, can shrink significantly (0.44%) with minute (0.01%) variations in the lattice parameters.With this original approach we also find a reduction of ∼10% in the intradimer exchange integral J, enough to make predictions for the highly magnetized states and the effects of applied pressure on SCBO.magnetostriction | high magnetic fields | spin-lattice coupling | density functional theory | Shastry-Sutherland I t has long been understood that magnetoelastic coupling can move magnetic materials phase boundaries in temperature and field and even change the order and/or universality class of magnetic transitions (1). Model Hamiltonians with effective exchange interactions are the common theoretical tool to tackle the complex behaviors of quantum magnet systems (2) and, indeed, these effective exchange interactions depend on subtleties of the electronic structure that, in turn, are naturally linked to the structural degrees of freedom of the system. When magnetoelastic effects are present, structural changes can also modify the macroscopic magnetic state via changes in the effective parameters of the model Hamiltonian. Simply posed, it is challenging to interpret experimental results at a point of high interest in a predicted (H,T) phase diagram of a magnetic material under consideration for fundamental studies or applications without knowing the effects that unavoidable lattice changes have in the exchange interactions as we drive our system toward such a point. Hence, it is highly desirable to be able to quantify such lattice effects.SrCu 2 (BO 3 ) 2 (SCBO) is an especially fascinating example of a low-dimension, frustrated quantum antiferromagnetic system. It crystallizes in a tetragonal structure (3) in which layers of [CuBO 3 ] − (Fig. 1A) are stacked along the c axis and separated by planes of Sr 2+ ions (Fig. 1B). The magnetically active Cu 2+ ions form a 2D arrangement of mutually orthogonal dimers (Fig. 1A). The magnetic properties of this compound can be closely described through a 2D Heisenberg Hamiltonian (4):where J and J′ are respectively the nearest-neighbor (intradimer) and next-nearest...

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Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Magnetic nanopantograph in the SrCu ₂ (BO ₃ ) ₂ Shastry–Sutherland lattice

Radtke

Saúl

Dąbkowska

et al. 2015

Proc. Natl. Acad. Sci. U.S.A.

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“…The order parameter M is given by the expectation value of s z i . For the considered quantum many-body model it is necessary to use approximations in order to truncate the expansion of S. We use the well elaborated LSUBn scheme 20,21,23 in which in the correlation operator S all multi-spin correlations over all distinct locales on the lattice defined by n or fewer contiguous sites are taken into account. For example, within the LSUB4 scheme one includes multi-spin creation operators of one, two, three or four spins distributed on arbitrary clusters of four contiguous lattice sites.…”

Section: 14mentioning

confidence: 99%

“…2-4, is not appropriate for the 3d problem under consideration. Therefore, we use the coupled-cluster method (CCM) 6,[20][21][22][23][24] and the rotationinvariant Green's function method (RGM). 5,17,26,[28][29][30] Both methods have been successfully applied to quantum spin systems in arbitrary dimension and are able to deal with frustration.…”

Section: 14mentioning

confidence: 99%

QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

et al. 2006

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Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling J ⊥ on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (J ⊥ = 0) we find that the phases with magnetic long-range order at small J2 < Jc 1 and large J2 > Jc 2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling J ⊥ > 0 the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small J ⊥ ∼ 0.2 − 0.3J1.The properties of the frustrated spin-1/2 Heisenberg antiferromagnet (HAFM) with nearest-neighbor J 1 and competing next-nearest-neighbor J 2 coupling (J 1 -J 2 model) on the square lattice have attracted a great deal of interest during the last fifteen years (see, e.g., Refs. 1-12 and references therein). The recent synthesis of layered magnetic materials 13,14 which can be described by the J 1 -J 2 model has stimulated a renewed interest in this model. It is well-accepted that the model exhibits two magnetically long-range ordered phases at small and at large J 2 separated by an intermediate quantum paramagnetic phase without magnetic long-range order (LRO) in the parameter region J c1 < J 2 < J c2 , where J c1 ≈ 0.4 and J c2 ≈ 0.6. The ground state (GS) at low J 2 < J c1 exhibits semi-classical Néel magnetic LRO with the magnetic wave vector Q 0 = (π, π). The GS at large J 2 > J c2 shows so-called collinear magnetic LRO with the magnetic wave vectors Q 1 = (π, 0) or Q 2 = (0, π). These two collinear states are characterized by a parallel spin orientation of nearest neighbors in vertical (horizontal) direction and an antiparallel spin orientation of nearest neighbors in horizontal (vertical) direction. The properties of the intermediate quantum paramagnetic phase are still under discussion, however, a valence-bond crystal phase seems to be most favorable. 2-4,8,9The properties of quantum magnets strongly depend on the dimensionality.15 Though the tendency to order is more pronounced in three-dimensional (3d) systems than in low-dimensional ones, a magnetically disordered phase can also be observed in frustrated 3d systems such as the HAFM on the pyrochlore lattice 16 or on the stacked kagomé lattice.17 On the other hand, recently it has been found that the 3d J 1 -J 2 model on the body-centered cubic lattice does not have an intermediate quantum paramagnetic phase.18,19 Moreover, in experimental realizations of the J 1 -J 2 model the magnetic couplings are expected to be not strictly 2d, but a finite interlayer coupling J ⊥ is present. For example, recently Rosner et al.14 have found J ⊥ /J 1 ∼ 0.07 for Li 2 VOSiO 4 , a material which can be described by a square lattice J 1 -J 2 model with large J 2 . 13,14This motivates us to consider an extension of the...

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“…Heisenberg antiferromagnet on a square lattice with competing nearest-neighbor (NN) and next-nearest-neighbor (NNN) antiferromagnetic exchange interactions (known as J 1 − J 2 model) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] .…”

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The quantum J1−J′1−J2 spin-1/2 Heisenberg antiferromagnet: A variational method study

Mabelini

Salmon

Sousa

2013

Solid State Communications

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The phase transition of the quantum spin-1/2 frustrated Heisenberg antiferroferromagnet on an anisotropic square lattice is studied by using a variational treatment. The boundaries between these ordered phases merge at the quantum critical endpoint (QCE). Below this QCE there is again a direct first-order transition between the AF and CAF phases, with a behavior approximately described by the classical line α c λ/2.

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Coupled cluster treatment of the Shastry-Sutherland antiferromagnet

Cited by 94 publications

References 43 publications

Magnetic nanopantograph in the SrCu ₂ (BO ₃ ) ₂ Shastry–Sutherland lattice

Magnetic nanopantograph in the SrCu ₂ (BO ₃ ) ₂ Shastry–Sutherland lattice

QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

The quantum J1−J′1−J2 spin-1/2 Heisenberg antiferromagnet: A variational method study

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Coupled cluster treatment of the Shastry-Sutherland antiferromagnet

Cited by 94 publications

References 43 publications

Magnetic nanopantograph in the SrCu 2 (BO 3 ) 2 Shastry–Sutherland lattice

Magnetic nanopantograph in the SrCu 2 (BO 3 ) 2 Shastry–Sutherland lattice

QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

The quantum J1−J′1−J2 spin-1/2 Heisenberg antiferromagnet: A variational method study

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Magnetic nanopantograph in the SrCu ₂ (BO ₃ ) ₂ Shastry–Sutherland lattice

Magnetic nanopantograph in the SrCu ₂ (BO ₃ ) ₂ Shastry–Sutherland lattice