Elastic and inelastic X-ray scattering studies of the low dimensional spin-1/2 quantum magnet TiOCl

Abstract

The ground state for a one dimensional spin 1/2 Heisenberg chain coupled to phonons is a dimerized singlet state known as a "spin-Peierls" state. Currently, the spin-Peierls state is realized in only a handful of known compounds. Even after decades of scientific scrutiny, there is an absence of direct measurements of the lattice dynamics associated with the transition. In this work we present an extensive study of a new one dimensional spin-Peierls compound, TiOC1. The magnetic susceptibility strongly indicates a singlet ground state, with two apparent anomalies observed at T, ,=65 K and Tc2=92 K. Specific heat measurements have been performed and the associated entropy changes quantified. The 65 K transition exhibits a thermal hysteresis, indicative of a first order phase transition. A detailed synchrotron x-ray study of the structure reveals the appearance of superlattice peaks at ( ... ) below 65 K. The intensity of the peaks drop very sharply above T, and a thermal hysteresis is observed which is consistent with a first order phase transition at 65 K. We find that the temperature region between 65 K and 92 K is characterized by a novel incommensurate state. The incommensurate reflections appear at ( ... ). The temperature dependence of the intensity of the incommensurate peaks shows a more gradual onset, with no thermal hysteresis. The incommensurate wavevectors change continuously as a function of temperature and can be analyzed in terms of a mean field theory of phase shifted discommensurations. The observation of the third harmonics enabled a careful characterization of the underlying real space superstructure. We find that all of the observed scattering can be reproduced by a one dimensional long-wavelength modulation of a locally dimerized structure.

(cont.) The lattice dynamics above T 2were characterized by inelastic x-ray scattering measurements. By analyzing the data in terms of a damped harmonic oscillator response function, we are able to extract the phonon frequency and damping for all observed modes. We find a longitudinal acoustic phonon branch whose damping increases for q-vectors close to the zone boundary, which is also associated with an apparent softening of the frequency. Both of these anharmonic effects increase as T2 is approached, and are consistent with a soft phonon description of the dimerization. The anomalous phonon damping and softening are then analyzed using the Cross & Fisher theory of spin-phonon interaction leading to a spin-Peierls transition. We find that the theory succeeds in describing the data for a narrow temperature range about Tc2, for q near the zone boundary. It does not account for the anharmonic effects observed at high temperatures. Our experimental analysis represents one of the most in-depth quantitative tests of the Cross & Fisher theory to date. In addition our results suggest that TiOCl is a particularly ideal realization of a spin-Peierls system.