Resonant magnetic mode in superconducting two-leg ladders

Abstract

The spin dynamics of a doped 2-leg spin ladder is investigated by numerical techniques. We show that a hole pair-magnon boundstate evolves at finite hole doping into a sharp magnetic excitation below the two-particle continuum. This is supported by a field theory argument based on a SO(6)-symmetric ladder. Similarities and differences with the resonant mode of the high-Tc cuprates are discussed.PACS numbers: PACS numbers: 75.10.Jm, 75.40.Mg Spin ladders materials are built from weakly coupled ladder units consisting of chain sub-units of spins S=1/2 (so-called "legs") connected via some "rung" couplings and exhibit numerous fascinating and intriguing properties [1]. Among them, the role of the parity of the number of legs is remarkable: only ladders with an even number of legs exhibit a spin gap (ie a finite energy scale for triplet excitations) as seen from different characteristic behaviors of the spin susceptibility observed in SrCu 2 O 3 and SrCu 3 O 5 [2], typical 2-leg and 3-leg compounds respectively.Besides exotic experimental properties, spin ladders are of special interest for theorists as well, especially the simple 2-leg ladder: indeed, it is believed that its ground state (GS) is a close realization of the Resonating Valence Bond (RVB) state proposed by Anderson [3] in the context of high-T C superconductivity. The striking difference between "even" and "odd" ladders mentioned above can naturally be explained in this simple picture since pairing nearest neighbor (NN) spins into spin singlets is more easily realized on rungs with an even number of sites. While the generic two dimensional (2D) Mott insulator (for one electron per site) is antiferromagnetic (AF) and may evolve into an RVB state only at finite doping, the 2-leg spin ladder exhibits a finite spin correlation length. It is therefore an ideal system to investigate doping into the RVB-like spin liquid [4] leading to d x 2 −y 2 -like pairing [5]. As a matter of fact, pressure was shown to induced superconductivity in the intrinsically doped Sr 2 Ca 12 Cu 24 O 41+δ ladder material [6] hence bridging the apparent gap between 2-leg ladder and layerbased cuprates.In this Letter, we investigate the spin dynamics of a 2-leg spin ladder doped with mobile holes. In 2D superconducting cuprates, a resonant mode at an energy around 40 meV was observed by Inelastic Neutron Scattering (INS) [7,8]. This mode was shown to be quite sharp both in energy and in momentum space (centered around the AF wavevector) and its observation seems to be directly linked to the appearance of superconductiv- ity. Anomalous spectral lineshape in photoemission experiments was also interpreted as the effect of a coupling of the quasiparticles to a collective mode [9] related to the pairing interaction. On the other hand, in ladders, the spin dynamics remains largely to be explored. We believe that a closer inspection, both experimentally and theoretically, of the low energy spin excitations in such a basic system will provide insights into the mechanism of pairing mediat...

Combined analytical and numerical approach to study magnetization plateaux in doped quasi-one-dimensional antiferromagnets

“…We have tested the validity of the approach by verifying some of the well-known results for undoped and doped spin-1/2 chains and ladders 3,4,[7][8][9]11,12 . Then, to illustrate the power of the approach, we have studied a doped higher-spin system that would present a problem for a rigorous treatment via traditional bosonization technique.…”

“…This phenomenon can already be observed for a chain doped with a single hole, and it is likely to stem from the existence of a bound state between a hole and a polarized trimer ("magnon"). The same mechanism is at work for instance in lightly doped two-leg ladders 8,33 , where a hole pair-magnon bound state emerges, leading to an irrational magnetization plateau 9 . The formation of such bound states is generic in t − J models due to the Nagaoka effect 10 : holes gain kinetic energy in a ferromagnetic environment.…”

“…This condition restricts the plateau magnetization m to rational values. However, it has been argued that plateaux may also appear at an irrational m, as a result of either quenched disorder 6 or doping with itinerant carriers [7][8][9]11,12 . In the latter case, doping may allow to reduce the m in a controlled way, thus making the plateau more easily accessible to experiments in lower magnetic fields.…”

Contractor-renormalization study of Hubbard plaquette clusters

“…One can improve the approximation by including in the CORE plaquette basis also the two degenerate doublets S z = ±1/2, q = (0, π), (π, 0), comprising the single hole ground state. 10,11 Moreover, the inclusion of these states is mandatory for the purpose of calculating the pair binding energy, which is one of the goals of the present work. Consequently, our CORE scheme consists of keeping the above mentioned M = 9 states.…”

t−Jzladder: Density-matrix renormalization group and series expansion calculations of the phase diagram

“…The t-J z model is a variant in which the rotational symmetry is broken, and the spin interactions are Ising-like. The two-leg t-J ladder has been extensively studied, using exact diagonalization [8,9,10,11,12,13,14,15], quantum Monte Carlo [16], the DMRG technique [17,18,19,20,21,22,23], a combination of different methods [24], or using mean-field or approximate analytic methods [18,25,26,27]. Near half-filling, the model has been explored using dimer series expansions [28,29,30].…”