Unifying Magnons and Triplons in Stripe-Ordered Cuprate Superconductors

Abstract

Based on a two-dimensional model of coupled two-leg spin ladders, we derive a unified picture of recent neutron scattering data of stripe-ordered La 15/8 Ba 1/8 CuO4, namely of the low-energy magnons around the superstructure satellites and of the triplon excitations at higher energies. The resonance peak at the antiferromagnetic wave vector QAF in the stripe-ordered phase corresponds to a saddle point in the dispersion of the magnetic excitations. Quantitative agreement with the neutron data is obtained for J = 130 − 160 meV and Jcyc/J = 0.2 − 0.25.PACS numbers: 74.25. Ha, 75.40.Gb, 75.10.Jm, 75.50.Ee Quantum magnetism in the cuprate superconductors is an intriguing issue. A detailed understanding of the dynamic spin susceptibility as measured by inelastic neutron scattering (INS) experiments should allow to clarify the role of magnetism in the mechanism of high-T c superconductivity. In particular two features have been in the focus of interest: the appearance of the socalled resonance peak [1,2] in the superconducting phase at the antiferromagnetic wave vector Q AF = (1/2, 1/2) (see Fig. 1b) at finite energies (e.g. 41 meV in optimally doped YBa 2 Cu 3 O 7−δ (YBCO)) and the existence of stripe order which manifests itself in superstructure satellites around Q AF (Fig. 1b) [2][3][4]. In general, these superstructure satellites are incommensurate, but they may become commensurate for certain doping concentrations. For many years, these two features have been regarded as separate issues, each of them apparent in only one of the two families of cuprates on which most neutron studies have focused: La 2−x Sr x CuO 4 (LSCO) and YBCO. But recent experimental results show that the resonance peak in YBCO is accompanied at lower energies by incommensurate reflections [5,6], and that stripe order appears also in YBCO [7][8][9]. Very recently, Tranquada et al.[10] observed a resonance peak at Q AF also in stripe-ordered La 15/8 Ba 1/8 CuO 4 (for T > T c ).An S=1 collective mode (the resonance peak) in the superconducting phase is a prominent feature of many different theoretical scenarios. Its interpretation ranges from a particle-hole bound state (see Refs. in [1,2]) to a particle-particle bound state in SO(5) theory [11]. In the stripe-ordered phase the choice of the microscopic model is straightforward. Static stripe order corresponds to a segregation into hole-rich charge stripes and hole-poor spin ladders. Tranquada et al.[10] analyzed their INS data at high energies (including the resonance) in terms of the elementary triplet excitations (triplons [12]) of isolated two-leg ladders (Fig. 1a) which are realized in case of bond-centered stripes [13]. But the incommensurate low-energy excitations were described in a separate model as spin waves (magnons), motivated by the existence of weak long-range order. Based on a model of coupled two-leg S = 1/2 ladders, we derive a unified description of the low-energy superstructure modes, of the resonance peak and of the highenergy excitations observed in Ref. [10]. The super...

Incompatibility of modulated checkerboard patterns with the neutron scattering resonance peak in cuprate superconductors

“…15 The magnetic excitations in these materials have been explained using stripes, a unidirectional modulation of spin and charge. 10,[16][17][18][19][20] In these models, the resonance peak is a saddle point in the dispersion.…”

Detailed magnetic excitation spectra of ordered and disordered spin ladders

“…It has, however, been pointed out that strong quantum fluctuations are important for obtaining the correct high-energy response originating from the quasi-one-dimensional spin excitations of the ladder [2,22,23,24], even though, in certain limits, the magnetic fluctuations can closely resemble the semiclassical results [25]. The importance of the charges in describing the spin response remains controversial, but is expected to affect the details at low energy as mentioned above.…”

“…We discuss effects of interladder coupling, ladder width, and disorder. As opposed to previous microscopic spin-only models, we do not rely on semiclassical linearized spinwave [19,20,21,25], or one-triplon [23] approximations.The spin dynamics is qualitatively different in isolated even and odd leg spin-1/2 ladders [28]; whereas even leg ladders display a spin gap and short-range spin-spin correlations, the odd leg ladders are qualitatively similar to …”

“…We discuss effects of interladder coupling, ladder width, and disorder. As opposed to previous microscopic spin-only models, we do not rely on semiclassical linearized spinwave [19,20,21,25], or one-triplon [23] approximations.…”

Orientational bond and Néel order in the two-dimensional ionic Hubbard model

“…We stress that already the second order calculation in the hopping t yields qualitatively the correct result, i.e., the correct symmetries for the condensate phase, in spite of the very small energy scales t 2 /U (relative to δ) driving the transition 6,7 . Thus we adopt the same strategy in 2D where the CUT has been successfully used before 18,19 , in particular for binding phenomena 20 .We are using the double 1-particle gap ∆ c := 2(E N +1 0 − E N 0 ), the singlet exciton gap ∆ e := E N 1,S=0 −E N 0 , and the spin (triplet) exciton gap ∆ s := E N 1,S=1 − E N 0 where E N 0 stands for the ground state energy and E N 1,S for the first excited state with total spin S for N electrons. At halffilling, the number of electron N equals the number of lattice sites.…”