Excitation Spectra of Triangular Antiferromagnet Hexagonal RMnO3: Spontaneous Decays of Magneto-Elastic Excitation

Abstract

Frustrated magnets have been a fruitful playground for exploring new states of matter. Contrary to ordinary magnets which have collinear ground states, competing interactions in frustrated magnets cannot be satisfied simultaneously, and it leads to accidental ground state degeneracies of classical ground states. Such competing ground states result in sensitivity to additional perturbations, which might induce peculiar effects on the ground states and excitations.

Arguably, the simplest model magnetic system with geometrical frustration is a two dimensional triangular Heisenberg antiferromagnet (2D THA). In 2D THA, nonlinear spinwave theories predicted that the excitation spectra shows strong anomalies: significant energy shifts and linewidth broadening of magnon. Direct comparison of such theoretical predictions with experiments are rare, however, due to additional complications such as lattice distortions or spin phonon coupling present in real materials. One such candidate material for 2D THA having distorted triangular Mn spins with moderate spin phonon coupling is hexagonal rare-earth manganites (h-RMnO$_3$).

The magnon spectra have been measured by inelastic neutron scattering on single crystal, and reproduced by anharmonic spinwave calculation with an explicit magnon-phonon coupling. The magnetic excitation spectra of Y$_{1-x}$Lu$_x$MnO$_3$ has been measured using MAPS beamline at ISIS, UK and C5 spin polarized spectrometer at Chalk River laboratory, Canada. The overall spectra are quite well reproduced by linear spinwave theory with simple spin Hamiltonian, yet we observed weak additional peaks at high energy which cannot be explained by conventional magnon excitation. Such anomalies motivate us to consider a spin lattice coupling, which affects elastic properties of h-RMnO$_3$, revealed by many previous works. Indeed, a noncollinear spin structure of h-RMnO$_3$ allows a direct magnon-phonon coupling, which can produce additional modes in magnetic excitation spectra. In order to verify this, we measured phonon spectra of YMnO$_3$ above and below T$_N$, using an inelastic x-ray scattering technique. Below T$_N$, we observed an additional phonon mode having the same momentum and energy transfer as magnon, clearly indicating the presence of strong magnon-phonon coupling. Similarly, the additional magnon peaks in inelastic neutron scattering experiment have the same momentum and energy transfer as phonons. Such a strong coupling in the wide momentum space is distinct from previous studies of magnon-phonon coupling confined in narrow regions in reciprocal space. Therefore we call these new hybrid modes magneto-elastic excitation.

In addition to the magnon-phonon coupling, the noncollinear spin structure is also expected to induce the magnon decay of 2D THA h-RMnO$_3$. By analyzing the inelastic neutron scattering data, we observed the evidence of such decays: linewidth broadening of magneto-elastic excitation. In order to reproduce the observed linewidth, we developed a theoretical method to calculate the decay rate of the magneto-elastic modes. The calculation result qualitatively explained the observed momentum dependence of linewidth.