Crystal field and magnetoelastic interactions in Tb2Ti2O7

Abstract

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

Crystal field states ofTb3+in the pyrochlore spin liquidTb2Ti2O7<

“…4,7,[14][15][16][17][18][19][20] Unfortunately, there are significant discrepancies between the published sets of crystal field parameters. These are partly caused by the fact that some of the models employ a truncated basis containing only the 13 states of the ground state 7 F 6 manifold, whereas others include all the states in the f 8 configuration of Tb 3+ .…”

Structural and magnetic investigations of single-crystalline neodymium zirconate pyrochloreNd2Zr2O7

“…The local magnetic field affecting the Nd 3+ ions, H loc = H + H exch + H dip − H D , involves the external field H, the exchange and dipolar fields H exch and H dip , respectively, corresponding to anisotropic exchange and magnetic dipolar interactions between the Nd 3+ ions that are considered within the self-consistent field approximation, and the demagnetizing field H D = 4πN M/3, where N is the demagnetizing factor, M = n m n /ν is the magnetization, and ν = a 3 /4 is the unit cell volume. There [52,53] with the parameters of the crystal lattice determined in the present work, are given in column A. The final values of the CF parameters used to simulate the dc susceptibility and the magnetization data are given in column B (see text for details).…”

“…[51]. The initial values of the CF parameters were calculated in the framework of the exchange charge model [52,53] by making use of the parameters of the crystal lattice determined in the present work (see column A in Table IV). The effective ionic charges were taken from Ref.…”

Incipient Ferromagnetism inTb2Ge2O7: Application of Chemical Pressure to the Enigmatic Spin-L

“…However, experimental studies revealed a lack of static order or spin freezing in Tb 2 Ti 2 O 7 down to 70 mK [3,4], and more recently 57 mK [5]. Subsequently, enormous efforts have been undertaken to uncover the origin of the spin liquid state in Tb 2 Ti 2 O 7 .A further complication in Tb 2 Ti 2 O 7 is the coupling of magnetic and lattice degrees of freedom [6][7][8][9]. It has been suggested that hybridized magnetoelastic excitations may be responsible for the suppression of magnetic order in Tb 2 Ti 2 O 7 [10].…”

“…A further complication in Tb 2 Ti 2 O 7 is the coupling of magnetic and lattice degrees of freedom [6][7][8][9]. It has been suggested that hybridized magnetoelastic excitations may be responsible for the suppression of magnetic order in Tb 2 Ti 2 O 7 [10].…”