Frustration effect on magnetic excitations in a two-leg spin-ladder system

TL;DR

This study uses theoretical methods to analyze how frustration influences magnetic excitations in a two-leg spin-ladder system, revealing distinct spectral features for different magnetic phases and effects of frustration on excitation modes.

Contribution

It provides a detailed theoretical analysis of magnetic excitations in a frustrated two-leg spin-ladder, distinguishing phases via spectral weight differences and examining frustration effects on excitation modes.

Findings

Columnar-dimer phase exhibits multi-spinon excitations with a spin gap.

Rung-singlet phase is dominated by triplet excitations in the rung direction.

Frustration shifts the minimum excitation energy from commensurate to incommensurate wavenumbers.

Abstract

We theoretically study the magnetic excitations in a frustrated two-leg spin-ladder system, in which antiferromagnetic exchange interactions act on the nearest-neighbor and next-nearestneighbor bonds in the leg direction, and on the nearest-neighbor bonds in the rung direction. A dynamical spin correlation function at zero temperature is calculated by using the dynamical density-matrix renormalization-group method for possible magnetic phases, i.e., columnar-dimer and rung-singlet phases. The columnar-dimer phase is characterized by multi-spinon excitations with spin gap, while the rung-singlet phase is dominated by the triplet excitation in the rung direction. It is found that a major difference between these two phases appears in the spectral weight of magnetic excitations, in particular, of the bonding and anti-bonding modes in the rung direction. Therefore, we can distinguish one phase from the other by the difference of the spectral weight. Furthermore, we examine frustration effect on both modes in the rung-singlet phase with a perturbation theory from the strong coupling limit. It is shown that the anti-bonding mode is stable against the frustration, and a wavenumber with minimum excitation energy is shifted from the commensurate to incommensurate ones. On the other hand, the bonding mode is merged into the continuum excitation of multiple triplet excitations by increasing the frustration. By comparing our results with inelastic neutron scattering experiments for BiCu$_2$PO$_6$, the magnitude of the magnetic exchange interactions and the ground state will be determined.