Spin correlations of quantum spin liquid and quadrupole-ordered states ofTb2+xTi2−xO7+y

Abstract

Spin correlations of the frustrated pyrochlore oxide Tb2+xTi2−xO7+y have been investigated by using inelastic neutron scattering on single crystalline samples (x = −0.007, 0.000, and 0.003), which have the putative quantum-spin-liquid (QSL) or electric-quadrupolar ground states. Spin correlations, which are notably observed in nominally elastic scattering, show short-ranged correlations around L points [q = ( 1 2 , 1 2 , 1 2 )], tiny antiferromagnetic Bragg scattering at L and Γ points, and pinch-point type structures around Γ points. The short-ranged spin correlations were analyzed using a random phase approximation (RPA) assuming the paramagnetic state and two-spin interactions among Ising spins. These analyses have shown that the RPA scattering intensity well reproduces the experimental data using temperature and x dependent coupling constants of up to 10 th neighbor site pairs. This suggests that no symmetry breaking occurs in the QSL sample, and that a quantum treatment beyond the semi-classical RPA approach is required. Implications of the experimental data and the RPA analyses are discussed.

Magnetoelastic excitation spectrum in the rare-earth pyrochlore Tb2Ti2O7

“…For Tb 2 Ti 2 O 7 , given these ingredients, two basic predictions are a transition to long-range magnetic order, or a cooperative Jahn-Teller transition to a nonmagnetic state. However, neither occurs; instead, depending on the sample, either a correlated, fluctuating state described as a spin liquid persists down to the lowest temperatures studied or a hidden-order transition to a possible multipole-ordered state occurs [3][4][5]. The general problems in Tb 2 Ti 2 O 7 are to understand the nature of these states, to identify how they are stabilized, and to establish if they have any particularly interesting properties such as the emergent phenomena which have become topical in the closely related (quantum) spin ices [6,7].…”

“…As mentioned, neither of these possibilities occurs, and the exact low-temperature behavior is somewhat obscured by sample-dependent properties such as the presence or absence of a heat capacity anomaly [3,[20][21][22], or different (partial) spin freezing temperatures [21][22][23][24][25]. Such sample dependence in rare-earth pyrochlores is typically attributed to very small levels of off stoichiometry [26], and detailed experimental work on samples in which the exact stoichiometry is varied according to Tb 2+x Ti 2−x O 7+y [3][4][5][27][28][29][30][31][32][33] suggests that for a small range of −0.05 x 0.04, a phase transition that is not of magnetic dipole or structural origin (i.e., a hidden order) appears at T ≈ 0.5 K and everywhere outside this critical compositional range, the spin liquid develops.…”

“…Construction of a theory of Tb 2 Ti 2 O 7 is difficult since the character of the basic degree of freedom is changing as its interactions become important; a crystal field level at 1.5 meV means that the local anisotropy [34,35] and spin correlations [5,11,[36][37][38][39][40][41] develop simultaneously below T ≈ 20 K. A theory based on Heisenberg exchange and the admixing of this level by virtual crystal field excitations (VCFEs) predicted that Tb 2 Ti 2 O 7 is a type of quantum spin ice [42][43][44], with a magnetization plateau when the field is applied along the [111] direction [44]. However, there is disagreement about the evidence for this plateau [45][46][47][48][49], which may exist at very low temperature (T ∼ 0.02 K) [48], but is lost even at typical dilution fridge temperatures (T ∼ 0.07 K) [49].…”

“…This theory is reasonably successful in accounting for thermodynamic properties and the development of a weakly dispersive excitation with a gap of ∼ 0.07 meV in the region of the transition [27,29]. By comparison with the phases of the same theory [29], it is suggested that the spin liquid is a U(1) spin liquid [7,54,55], and that the presence of a pinch point in the diffuse scattering [37] implies it is connected [5] to the predicted quantum spin ice [43]. However, other experimental phenomena, such as the small ordered magnetic moment in the hidden-order phase and the form of the diffuse scattering of the spin-liquid phase [5], cannot be explained, and the application of theories of quantum effects in pyrochlores with isolated doublet ground states [51][52][53]56] to Tb 2 Ti 2 O 7 may not be entirely successful because of the low-lying level [42,43].…”

Inelastic Neutron Scattering of Lanthanoid Complexes and Single‐Molecule Magnets

“…Inelastic neutron scattering studies have been used in these materials to determine the CF splitting of the lanthanoid(III) ions, as well as in investigation of the dynamics of these materials at different temperatures. [76][77][78][79][80][81][82][83][84][85] The CF splitting and exchange coupling in the lanthanoid dimeric Ln 2 X 9 3units of Cs 3 Ln 2 X 9 has also been extensively studied for Ln = Tb, Dy, Ho, Er, and Yb, with typical modulated Q intensity of the transitions indicative of exchange coupling observed. [19,57] The weak exchange coupling in these systems can be elucidated from fitting of scattering data to appropriate Hamiltonians.…”