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arXiv:0807.1071 · Physical Review Letters

Effective Theory of Magnetization Plateaux in the Shastry-Sutherland Lattice

A. Abendschein, Sylvain Capponi

Published Nov 26, 2008• 70 citations
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Abstract

We use the nonperturbative Contractor-Renormalization method (CORE) in order to derive an effective model for triplet excitations on the Shastry-Sutherland lattice. For strong enough magnetic fields, various magnetization plateaux are observed, e.g., at 1/8, 1/4, 1/3 of the saturation, as found experimentally in a related compound. Moreover, other stable plateaux are found at 1/9, 1/6, or 2/9. We give a critical review of previous works and try to resolve some apparent inconsistencies between various theoretical approaches.

DOI
10.1103/physrevlett.101.227201

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•Nov 20, 2012•3 citations
We use the nonperturbative Contractor-Renormalization method (CORE) in order to derive an effective model for triplet excitations on the Shastry-Sutherland lattice. For strong enough magnetic fields, various magnetization plateaux are observed, e.g., at 1/8, 1/4, 1/3 of the saturation, as found experimentally in a related compound. Moreover, other stable plateaux are found at 1/9, 1/6, or 2/9. We give a critical review of previous works and try to resolve some apparent inconsistencies between various theoretical approaches.
Spin-1/2 Heisenberg model on the Shastry-Sutherland lattice is considered within the many-body perturbation theory developed from the exactly solved spin-1/2 Ising-Heisenberg model with the Heisenberg intradimer and Ising interdimer interactions. The former model is widely used for a description of magnetic properties of the layered compound SrCu _2 2 (BO _3 3 ) _2 2 , which exhibits a series of fractional magnetization plateaux at sufficiently low temperatures. Using the novel type of many-body perturbation theory we have found the effective model of interacting triplet excitations with the extended hard-core repulsion, which accurately recovers 1/8, 1/6 and 1/4 magnetization plateaux for moderate values of the interdimer coupling. A possible existence of a striking quantum phase of bound triplons is also revealed at low enough magnetic fields.
Motivated by the remarkable properties of SrCu2(BO3) 2 in a magnetic field, we use perturbative continuous unitary transformations to determine the magnetization plateaux of the Shastry-Sutherland model, unveiling an unexpected sequence of plateaux progressively appearing at 2/9, 1/6, 1/9, and 2/15 upon increasing the interdimer coupling. We predict that a 1/6 plateau should be present in SrCu2(BO3)2, even if residual interactions beyond the Shastry-Sutherland are strong enough to modify the other plateaux below 1/3. The method is extended to calculate the magnetization profile within the plateaux, leading to a local structure around triplons that agrees with NMR results on SrCu2(BO3) 2.
Configurations of singlets and triplets on the Shastry-Sutherland lattice (SSL) have been proposed in the literature as variational ground states of the Shastry-Sutherland model at a fixed magnetization M. We prove that isolated triplet excitations on the SSL are unstable if the coupling $\ensuremath{\alpha}$ falls below a critical value ${\ensuremath{\alpha}}_{c}\ensuremath{\approx}2.0.$ The instability should be visible in the compound SrCu2(BO3)2,{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2},SrCu2​(BO3​)2​, where a coupling ${\ensuremath{\alpha}}^{*}=1.48$ is realized.
In this paper, we briefly review our recent studies of the Heisenberg anti-ferromagnet on the Shastry–Sutherland lattice for SrCu2(BO3)2 under magnetic fields. Treating magnetic excitations promoted by the field as Bose particles and using a strong-coupling expansion, we derived an effective Hamiltonian for the magnetic particles. Anisotropic repulsive interactions between particles induce "insulating" states with a stripe spin-density wave structure at magnetization m/msat = 1/3 and with a checkerboard structure at 1/2, and thereby form magnetization plateaux. We also demonstrated how the unique geometry of the Shastry–Sutherland lattice affects dynamical properties and makes a novel type of quintuplet (S = 2) bound states condense for very small magnetization. PACS Nos.: 75.50-y, 75.60Ej, 75.10Jm
Exact ground states of a spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice with Heisenberg intradimer and Ising interdimer couplings are found by two independent rigorous procedures. The first method uses a unitary transformation to establish a mapping correspondence with an effective classical spin model, while the second method relies on the derivation of an effective hard-core boson model by continuous unitary transformations. Both methods lead to equivalent effective Hamiltonians providing a convincing proof that the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice exhibits a zero-temperature magnetization curve with just two intermediate plateaus at one-third and one-half of the saturation magnetization, which correspond to stripe and checkerboard orderings of singlets and polarized triplets, respectively. The nature of the remarkable stripe order relevant to the one-third plateau is thoroughly investigated with the help of the corresponding exact eigenvector. The rigorous results for the spin-1/2 Ising-Heisenberg model on the Shastry-Sutherland lattice are compared with the analogous results for the purely classical Ising and fully quantum Heisenberg models. Finally, we discuss to what extent the critical fields of SrCu2(BO3)2{\mathrm{SrCu}}_{2}{(\mathrm{BO}}_{3}){}_{2}SrCu2​(BO3​)2​ and (CuCl)Ca2Nb3O10{(\mathrm{CuCl})\mathrm{Ca}}_{2}{\mathrm{Nb}}_{3}{\mathrm{O}}_{10}(CuCl)Ca2​Nb3​O10​ can be described within the suggested Ising-Heisenberg model.
Abstract. We study an extended two-dimensional Shastry-Sutherland model in a magnetic field where besides the usual Heisenberg exchanges of the Shastry-Sutherland model two additional SU(2) invariant couplings are included. Perturbative continous unitary transformations are used to determine the leading order effects of the additional couplings on the pure hopping and on the long-range interactions between the triplons which are the most relevant terms for small magnetization. We then compare the energy of various magnetization plateaux in the classical limit and we discuss the implications for the two-dimensional quantum magnet SrCu2(BO3)2. 1.