Hybridization of magnetic excitations between quasi-one-dimensional spin chains and spin dimers in Cu3Mo2O9observed using inelastic neutron scattering

Abstract

We have studied the exchange interactions and the hybridization effects of two kinds of magnetic excitations in Cu${}_{3}$Mo${}_{2}$O${}_{9}$ by using inelastic neutron scattering. This compound has two magnetic subsystems, i.e., the quasi-one-dimensional (q1D) antiferromagnetic (AF) spin system and the quantum spin dimers. We observe two branches in the magnetic excitations and obtain the magnetic parameters as follows. We evaluate the intrachain interaction ${J}_{4}=4.0$ meV in the q1D AF spin system and the intradimer interaction ${J}_{3}=5.8$ meV in the spin dimers. Applying the interchain mean-field theory (CMF) with the random-phase approximation (RPA), we estimate the mass gap of the q1D AF spin system as 1.2 meV. Using the CMF-RPA theory, the ferromagnetic interchain interaction between the magnetic chain along the $a$ axis and the AF one between the magnetic chains at the center and the corner of the unit cell are estimated to be $\ensuremath{-}{J}_{a}={J}_{\ensuremath{\alpha}\ensuremath{\beta}}=0.19$ meV, respectively. The hybridization parameter, which represents the intersubsystem interaction, has the wave-vector dependence as ${E}_{\mathrm{int}}\mathrm{sin}(\ensuremath{\pi}k)$, where ${E}_{\mathrm{int}}=1.6$ meV and ${\mathit{kb}}^{*}$ denotes the wave vector of magnetic excitation along the ${b}^{*}$ direction. The modulation of the molecular field generated by the magnetic excitation of the q1D AF spin system plays an important role in this hybridization.