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arXiv:0902.1456 · Physical Review B

Theory of the Raman spectra of the Shastry-Sutherland antiferromagnet SrCu2(BO3)2 doped with nonmagnetic impurities

Sylvain Capponi, Didier Poilblanc, Frédéric Mila

Published Sep 15, 2009• 4 citations
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Abstract

Controlled doping of ${\text{SrCu}}_{2}{({\text{BO}}_{3})}_{2}$, a faithful realization of the Heisenberg spin-1/2 antiferromagnet on the Shastry-Sutherland lattice, with nonmagnetic impurities generates bound states below the spin gap. These bound states and their symmetry properties are investigated by exact diagonalization of small clusters and within a simple effective model describing a spinon submitted to an attractive extended potential. It is shown that Raman spectroscopy is a unique technique to probe these bound states. Quantitative theoretical Raman spectra are numerically obtained.

DOI
10.1103/physrevb.80.094407

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Canadian Journal of Physics•Jan 1, 2001•0 citations
Controlled doping of SrCu2(BO3)2{\text{SrCu}}_{2}{({\text{BO}}_{3})}_{2}SrCu2​(BO3​)2​, a faithful realization of the Heisenberg spin-1/2 antiferromagnet on the Shastry-Sutherland lattice, with nonmagnetic impurities generates bound states below the spin gap. These bound states and their symmetry properties are investigated by exact diagonalization of small clusters and within a simple effective model describing a spinon submitted to an attractive extended potential. It is shown that Raman spectroscopy is a unique technique to probe these bound states. Quantitative theoretical Raman spectra are numerically obtained.
We study possible paramagnetic phases of antiferromagnets on the Shastry-Sutherland lattice by a gauge-theoretic analysis of fluctuations in a theory with Sp(2N)\mathrm{Sp}(2N)Sp(2N) symmetry. In addition to the familiar dimer phase, we find a confining phase with plaquette order and a topologically ordered phase with deconfined S=1/2S=1/2S=1/2 spinons and helical spin correlations. The deconfined phase is contiguous to the dimer phase and in a regime of couplings close to those found in the insulator SrCu2(BO3)2.{\mathrm{SrCu}}_{2}({\mathrm{BO}}_{3}{)}_{2}.SrCu2​(BO3​)2​. We suggest that a superconductor obtained by doping this insulator with mobile charge carriers will be an attractive candidate for observing the anomalous magnetic flux properties associated with topological order.
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
Using variational algorithm on an infinite Shastry-Sutherland (SS) lattice we show that the introduction of a static nonmagnetic impurity into a dimerized ground state leads to a formation of a small, localized spin polaron surrounding the impurity site. Due to a particular symmetry of the SS lattice, the polaron is extremely anisotropic with a short spatial extent. The presence of nonmagnetic impurities leads to a formation of pronounced in-gap peaks in the dynamical spin structure factor, which we attribute to the spin-doublet excitations of a single unpaired spin S=1∕2S=1∕2S=1∕2 surrounded by triplet fluctuations. Our results are relevant for the description of SrCu2(BO3)2\mathrm{Sr}{\mathrm{Cu}}_{2}{(\mathrm{B}{\mathrm{O}}_{3})}_{2}SrCu2​(BO3​)2​ compound when doped with nonmagnetic atoms at Cu sites.
The magnetic properties of SrCu 2 (BO 3 ) 2 are reviewed from a theoretical point of view. SrCu 2 (BO 3 ) 2 is a new two-dimensional spin gap system and its magnetic properties are well described by a spin-1/2 antiferromagnetic Heisenberg model of the orthogonal dimer lattice. The model has a dimer singlet ground state whose exactness was proven by Shastry and Sutherland for a topologically equivalent model more than 20 years ago. The exactness of the ground state is maintained even if interlayer couplings are introduced for SrCu 2 (BO 3 ) 2 . In the two-dimensional model, quantum phase transitions take place between different ground states for which three phases are expected: a gapped dimer singlet state, a plaquette resonating valence bond state and a gapless magnetic ordered state. Analysis of the experimental data shows that the dimer singlet ground state is realized in SrCu 2 (BO 3 ) 2 . The orthogonality of the dimer bonds, which is the underlying symmetry of the exactness of the ground state, also leads to an unusual property of elementary excitations, namely the almost localized nature of the triplet excitations. Application of an external magnetic field changes the density of the triplet excitations. In general, there is competition between kinetic energies and interaction energies between triplets. The almost localized nature of the triplets makes it easy to form regular lattices. In fact, at certain densities, where the commensurability energy is significant, the triplet excitations form superstructures and plateaux appear at 1/2, 1/3, 1/4 and 1/8 in the magnetization curve. In high-magnetic-field experiments, magnetic plateaux at magnetizations of 1/3, 1/4 and 1/8 have been observed. Translational symmetry of the lattice is spontaneously broken at the plateaux, except for the 1/2 plateau. The 1/3 and 1/4 plateaux are expected to have magnetic superstructures of stripe form while the 1/2 plateau has a square unit cell and the 1/8 plateau a rhomboid cell. Especially at the 1/8 plateau, nuclear magnetic resonance experiments indicate the presence of at least 11 distinct Cu sites with different spin polarizations, which is the first evidence of breaking of the translational symmetry at the plateau phase. The spin texture calculated on the basis of a Heisenberg model with adiabatic spin–phonon coupling is consistent with the experimental results.
The influence of nonmagnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ is studied. A simple extension to Zn-doped Sr Cu2{\mathrm{Cu}}_{2}Cu2​ O3{\mathrm{O}}_{3}O3​ is also discussed. Using exact diagonalization techniques and intuitive arguments we show that Zn doping introduces states in the spin-Peierls gap of CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​. This effect can be understood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn doping according to the numerical data presented here. As recent numerical calculations have shown, similar arguments apply to ladders with nonmagnetic impurities simply replacing the tendency to dimerization in CuGeO3{\mathrm{CuGeO}}_{3}CuGeO3​ by the tendency to form spin singlets along the rungs in SrCu2{\mathrm{SrCu}}_{2}SrCu2​O3{\mathrm{O}}_{3}O3​. \textcopyright{} 1996 The American Physical Society.
We study an extended Shastry-Sutherland model for SrCu2(BO3)2 and analyze the low lying parts of the energy spectrum by means of a perturbative unitary transformation based on flow equations.The derivation of the 1-magnon dispersion (elementary triplets) is discussed.Additionally, we give a quantitative description (symmetries and energies) of bound states made from two elementary triplets.Our high order results allow to fix the model parameters for SrCu2(BO3)2 precisely: J1 = 6.16(10)meV, x := J2/J1 = 0.603(3), J ⊥ = 1.3(2)meV.To our knowledge this is the first quantitative treatment of bound states in a true 2d model.