Lack of static lattice distortion in Tb2Ti2O7

We investigated the possibility of temperature dependent lattice distortions in the pyrochlore compound Tb2Ti2O7 by measuring the internal magnetic field distribution, using muon spin resonance, and comparing it to the susceptibility. The measurements are done at temperatures as low as 70 mK and external fields up to 6 kG. We find that the evolution of the width of the field distribution can be explained by spin susceptibility only, thus ruling out a temperature dependent hyperfine coupling. We conclude that lattice deformations are absent in Tb2Ti2O7. PACS numbers: 75.50.Lk, 75.10.Nr Lack of static lattice distortion in Tb2Ti2O7 2 Despite its short-range AFM correlations at temperatures lower than 100K, the Tb2Ti2O7 remains in a fluctuating paramagnetic spin-liquid state down to 70mK [1]. This very unusual state of matter has attracted considerable attention of experimentalist and theorist alike. Recently it was demonstrated that, under pressure [2] high magnetic field [3] or both [4], Tb2Ti2O7 does order magnetically. The possibility that this order stems from magneto-elastic coupling was considered in all cases [2, 3, 4]. This type of coupling allows the lattice to distort in order to relieve the magnetic frustration, concomitantly lowering the total system energy. Thus the magneto-elastic coupling, which is a small perturbation to the spin Hamiltonian, can select one ground state out of the macroscopically degenerate ground states [5, 6]. In the most spectacular case the magneto-elastic coupling leads to long range spin order accompanied by a new lattice structure such as in ZnCr2O4 [7] and CdCr2O4[8]. An alternative and less dramatic possibility is a selection of a ground state with short range spin order and short range lattice deformation. In the latter case the original lattice structure is preserved on the average. This might be the situation in Y2Mo2O7 where evidence for lattice deformations were found by several methods [6, 9, 10]. In this work we study the possible existence of magneto-elastic coupling in Tb2Ti2O7 using the muon spin resonance (μSR) technique. The basic idea is to investigate the nature of the changes in the local environment of the muon as the temperature decreases. We determine whether only the spin polarization is changing or whether the lattice is involved as well. Electronic spin polarization contributes to the shift of the muon spin rotation frequency. Lattice distortions are responsible for muon spin polarization relaxation. Comparing these two quantities provides information on the presence or absence of magneto-elastic coupling. Transverse [TF] and longitudinal field [LF] μSR measurements were performed with powder samples on the GPS and LTF spectrometers at Paul Scherrer Institute, Switzerland. The measurements were carried out with the muon spin tilted by 50 relative to the direction of the applied magnetic fields, and positron data were accumulated in both the forward-backward (longitudinal) and the up-down (transverse) directions simultaneously. This allowed us to determine both transverse and longitudinal muon spin relaxations rates. In Fig. 1 we show the LF [panel (a)] and the TF [panel (b)] data at two temperatures and applied field of 2kG. The TF data are shown in a reference frame rotating at a field of 1.5kG. Several aspects can be seen in the raw data: From the time scale it is clear that the transverse relaxation is by far greater than the longitudinal one. The longitudinal relaxation increases as the temperature decreases, as was observed previously [11]. Finally, the transverse relaxation increases and the muon rotation frequency decreases upon cooling. The μSR LF polarization is best described by the root exponential PLF (t) = ALF exp(−(t/T1) 1 2 ) +BLF (1) where the parameter ALF is set by taking into account the tilt of the muon spin relative to the longitudinal magnetic field, T1 is the longitudinal relaxation time, BLF is the Lack of static lattice distortion in Tb2Ti2O7 3 0.25 0.50 0.75 1.00 2 4 6 8 0.0 0.1 0.2 0.3 0.4 0.5 -1.0 -0.5 0.0 0.5 1.0 Time ( sec) Po la riz at io n 60mK 9K LF=2kG