Abstract-In terms of a semi-phenomenological exchange charge model, we have obtained estimates of parameters of the crystal field and parameters of the electron-deformation interaction in terbium titanate Tb 2 Ti 2 O 7 with a pyrochlore structure. The obtained set of parameters has been refined based on the analysis of spectra of neutron inelastic scattering and Raman light scattering, field dependences of the forced magnetostriction, and temperature dependences of elastic constants.
INTRODUCTIONInterest in investigations of rare-earth (RE) crystals with a pyrochlore structure (rare-earth ions form a three-dimensional network of tetrahedra with connected vertices) is mainly determined by the wide diversity of magnetic behavior that they exhibit at low temperatures [1]. Among titanates RE 2 Ti 2 O 7 , of most interest is terbium titanate Tb 2 Ti 2 O 7 , in which the magnetic long-range order does not manifest itself at least to a temperature of 15 mK [2], whereas, in accordance with calculations, the phase transition from the paramagnetic to an antiferromagnetic state should have occurred at a temperature of 1.8 K [3]. Interestingly, an external pressure induces a long-range magnetic order in Tb 2 Ti 2 O 7 : under a pressure of 8.6 GPa at temperatures below 2.1 K, apart from the spin-liquid phase, an antiferromagnetic order with a complex magnetic structure is observed [4,5].It is known that magnetoelastic interactions can strongly affect the magnetic behavior of rare-earth compounds. In terbium titanate single crystals and powders, an anomalously large parastriction (deformation of the lattice in the paramagnetic phase in an external magnetic field) has been revealed, which achieves values of ~10 -4 in magnetic fields ~1 T at liquid-helium temperatures [6][7][8]. The parastriction of isostructural crystals Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 under the same conditions acquires values that are typical for paramagnets (~10 -6 ) [9]. In addition, in Tb 2 Ti 2 O 7 , an anomalous decrease in the Young modulus and elastic constants upon lowering temperature was revealed [10][11][12][13]. The cooperative Jahn-Teller effect (spontaneous symmetry violation caused by interactions of rare-earth ions via fields of static and dynamic deformations) can suppress the magnetic ordering. In [10], the temperature of a possible structural phase transition was estimated to be c T 0.1 K. Previously, using a semi-phenomenological model of the crystal field, we have calculated parameters that characterize changes in the crystal field caused by macroscopic deformations of the lattice [14]. The change in the elasticity modulus C 44 of Tb 2 Ti 2 O 7 crystals in the temperature range of 100-4.2 K calculated with this set of parameters is consistent with measurement data. However, the change in elasticity modulus 11