Magnetization Process in the Shastry-Sutherland System SrCu₂(BO₃)₂: Results of Third-Order Dimer Expansion

Abstract

The magnetization process in the Shastry-Sutherland system is studied by using the thirdorder perturbation expansion. It is shown that the 1/3-plateau is realized by the second-order perturbation, which is not prevented by the off-diagonal part. In each subspace whose magnetization per dimer is less than 1/3, the lowest energy state is determined by a small but finite energy-gain due to the third-order correlated flip terms and there exists no plateau originating from the third-order effect. Our results are compared with those of the exact diagonalization method to discuss the validity of truncation of states in our perturbation theory.In the last couple of years there has been a growing interest in the phenomenon of magnetization plateaus in two-dimensional spin systems. For instance, the existence of plateaus in the magnetization curve is theoretically shown in the multiple-spin exchange model on the triangular lattice 1) and the Heisenberg antiferromagnet on the 1/5-depleted square lattice. 2) As for the experimental investigations of this phenomenon, recently, Kageyama et al. measured the magnetization curve of SrCu 2 (BO 3 ) 2 up to the magnetic field H = 45 T and observed intermediate plateaus at 1/8 (for 27.9 < H < 29.8 T) and 1/4 (for 37.0 < H < 41.0 T) of the full Cu moment. 3) In this compound, magnetic ions Cu 2+ (S = 1/2) are arranged as shown in Fig. 1.As a model for this system, Miyahara and Ueda 4) proposed a Heisenberg antiferromagnet with nearest neighbor (NN) and next nearest neighbor (NNN) couplings:which is equivalent to a model with the exact dimer ground state (for J <∼ 0.7J) proposed by Shastry and Sutherland. 5) It is reported that experimental data of the uniform susceptibility are reproduced by this model with J 100 K and J 68 K, where the exact diagonalization method is employed. 4) Another estimation J 83 K and J 55 K is obtained on the basis of the theoretical calculations of the spin gap and the susceptibility by the dimer expansion, where the disconnected dimer model defined by the first term in eq. (1) is taken as an unperturbed part and the interdimer coupling in the second term is taken as a perturbation. 6, 7)The existence of the exact dimer ground state in the present model stems from a symmetric relation in the interdimer coupling as pointed out in ref. 4. This leads to other interesting properties: an almost dispersionless triplet excitation spectrum 4) and the experimental observation of the second lowest band of triplet excitations. 8) It is natural to expect that the observed magnetization plateaus in SrCu 2 (BO 3 ) 2 originate from the symmetric properties of the interdimer coupling. 4) We now turn to the study of the magnetization process. At first we present the magnetization curves for the clusters composed of 8 ( √ 8 × √ 8), 10 ( √ 10 × √ 10) and 12 ( √ 8 × √ 18) dimers in Fig. 2, where we choose J /J(≡ λ) = 0.35. We find considerable system size dependence in the magnetization curves especially for M ≤ M s /2, where M s represents the saturation value of the magnetiz...

Dynamics and Instabilities of the Shastry-Sutherland Model

“…The Shastry-Sutherland model (SSM) has become a paradigmatic Hamiltonian of frustrated quantum magnetism [1, 2] because it includes an exactly solvable ground state [1], very heavy low-energy excitations [3-8], exotic phases obtained upon varying the ratio J /J between two competing exchange constants [4,7,[9][10][11][12][13][14][15][16], and a series of magnetic field induced magnetization plateaux [3,[17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Its realization in SrCu 2 (BO 3 ) 2 [3,32,33] enabled various experimental studies, including magnetization [32, 34-39], specific heat [40], inelastic neutron scattering (NS) [41-47], far-infrared [48], electron spin resonance (ESR) [49, 50], Raman scattering [51], and nuclear magnetic resonance (NMR) [37,52,53].…”

Magnetic Chern bands and triplon Hall effect in an extended Shastry-Sutherland model

“…In this situation one is interested in the Chern number C p of p as an entity which can be calculated as follows. Let n and m be two bands being part of p. The Berry vector potential is then generalized to [40][41][42] A mn (k) ≡ i u mk | ∇ k |u nk (18) which allows to define the non-Abelian Berry curvature…”

Variational treatment of the Shastry-Sutherland antiferromagnet using projected entangled pair states

“…30 Albrecht and Mila used Schwinger Boson mean field theory to argue in favor of a first order transition Experiments on SrCu 2 (BO 3 ) 2 in strong external fields show the existence of magnetization plateaus 8,9 . While the ground state in absence of an external field is believed to be the dimer-state, the magnetization steps were originally thought to be formed by strongly localized triplets forming a periodic patterns which may spontaneously break the translational symmetry 12,13,14,15,16,17 (for an alternative explanation hypothesis see Ref. 18).…”