One- and two-magnon excitations in a one-dimensional antiferromagnet in a magnetic field

Abstract

We have carried out a comprehensive experimental and theoretical study of the inelastic scattering in the one-dimensional near-Heisenberg antiferromagnet ${\left(\mathrm{C}{\mathrm{D}}_3\right)}_4$NMn${\mathrm{Cl}}_3$ (TMMC) at low temperatures, $0.3<~T<~2.5$ K, in magnetic fields varying between 0 and 70 kOe; the field is applied perpendicular to the chain axis. In zero field at long wavelengths we observe two sets of excitations, a low-energy acoustic branch corresponding to spin motion within the dipolar-determined easy plane and a high-energy optical branch corresponding to oscillations out of the plane. For magnetic fields greater than 30 kOe and $T\simeq 2$ K we observe as many as four distinct excitations—the two one-magnon modes plus two sharp excitations at higher energies. Our theroretical analysis suggests that the two higher-energy modes correspond to two-magnon processes in the longitudinal response function. The theory, which is done within the harmonic approximation expanding out to fourth order in the magnon operators, gives a good qualitative description of the data but underestimates the two-magnon intensities by a factor of 2 or 3. We also observe a marked anticrossing of the one- and two-magnon branches; this latter result shows that anharmonic effects are quite important in the spin dynamics. Finally at $T=0.3\mathrm{}$ K and zero field we observe a gap of 0.1 meV in the acoustic spin-wave dispersion relation due to a very small in-plane anisotropy field of 71 ± 30 Oe.