Spin liquid correlations, anisotropic exchange, and symmetry breaking in Tb2Ti2O7

Abstract

We have studied the low energy spin dynamics between 4.6 K and 0.07 K in a Tb2Ti2O7 single crystal sample, by means of inelastic neutron scattering experiments. The spectra consist in a dual response, with a static and an inelastic contribution, showing striking Q-dependences. We propose an interpretation involving an anisotropic exchange interaction in combination with a breaking of the threefold symmetry at the rare earth site. Simulations of the Q-dependent scattering in the Random Phase Approximation account well for the inelastic response.Spin liquids now attract considerable attention in modern condensed matter physics [1,2]. In a classical picture, the localized magnetic moments in such cooperative paramagnets keep fluctuating in a correlated manner, failing to develop long range order down to very low temperature. From a quantum point of view, a spin liquid ground state can be described by entangled spin wavefunctions and supports exotic fractionalized excitations also called spinons. Geometrically frustrated magnets are good candidates in the pursuit of such disordered quantum ground states [3] and one of the celebrated examples is the Tb 2 Ti 2 O 7 pyrochlore. It remains in a spin liquid state, with short range correlated fluctuating moments, down to a temperature as low as 20 mK [4,5]. Since 1999, it has been the subject of many theoretical as well as experimental works, and the origin of its spin liquid ground state is still puzzling.Tb 2 Ti 2 O 7 belongs to the same family as the Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 spin ices, characterized by an Ising anisotropy along local < 111 > axes [6]. However, the Tb 3+ crystal electric field (CEF) with trigonal symmetry [7,8] has a much lower energy gap between the ground state doublet and the first excited doublet than in spin ices (18 K instead of 200 to 300 K). It was suggested that, unlike in spin ices, this gap is small enough to allow admixture of excited crystal field states, that produces an effective ferromagnetic contribution which competes with the original antiferromagnetic interactions, and that moves Tb 2 Ti 2 O 7 towards a "quantum spin-ice" regime [9,10]. More recent general descriptions of pyrochlores introduce a minimal Hamiltonian, based on symmetry grounds, for pseudospins 1/2 (the subspace spanned by the ground doublet states |ψ ± ) [11][12][13]. These models involve an Ising exchange constant J zz responsible for the spin-ice behavior, as well as three "quantum" terms J ± , J z± and J ±± that lift the macroscopic degeneracy of the spin-ice manifold and stabilize a so called Coulomb phase or U(1) spin liquid phase, describable by an emergent U(1) gauge field. For large quantum couplings, conventional phases are stabilized against the spin liquid. Interestingly, in the particular case of non-Kramers ions (like Tb 3+ ), these phases are characterized by ordering of the 4f quadrupoles [14,15], breaking spontaneously the threefold symmetry of the crystal field. Recently, we proposed a somehow more phenomenological route to point out the relevanc...

Double vibronic process in the quantum spin ice candidate Tb2Ti2O7 revealed by terahertz spectroscopy

“…Despite effective antiferromagnetic interactions, Tb 2 Ti 2 O 7 features no long-range order [12,13], however short-range correlations are present over a broad temperature range [14][15][16]. Remarkably, the ground state supports elastic power law spin correlations [17,18], bearing some resemblance to the pinch point pattern observed in spin ices [19]. Below 300 mK, a dispersing low-energy collective mode is found to emerge from these pinch points, reaching its maximum energy at ∼0.25 meV [20].…”

“…This signal likely corresponds to fluctuations between the two |± electronic states of the crystal electric field (CEF) ground state doublet. It was interpreted as a signature of interactions between quadrupoles, highlighting the importance of those degrees of freedom [18,[20][21][22]. This is because the non-Kramers nature of Tb 3+ ions prevents magnetic exchange alone from inducing such fluctuations within the Ising-like ground state [22][23][24].…”

“…A second process is observed as high as 200 K and couples the first excited CEF state and associated transition at ∆ with a silent optical phonon mode. This double vibronic process provides a natural path for spin-lattice quadrupolar coupling that amplifies The measurements were performed using a Tb 2 Ti 2 O 7 single crystal grown by the floating zone technique previously described in [18,20]. We have measured the polarization dependent THz spectrum in the 0.2-1.0 THz (0.82-4.14 meV) energy range using both standard (SSR) [31] and coherent synchrotron radiation (CSR) [32,33] techniques.…”

Mesoscopic correlations inTb2Ti2O7spin liquid

“…The Tb 3+ short range correlated moments fluctuate 12 down to 20 mK at the time scale of the muon probe (10 −6 s). The origin of these fluctuations has been highly debated [13][14][15][16][17][18] . Several mechanisms have been proposed taking into account the non-Kramers nature of the Tb ion and the small energy gap between the ground and first excited crystal field doublets, which open the possibility of quantum spin ice behavior 19 .…”

“…Below this temperature, spin fluctuations coexist with static spin correlations and spin glass-like irreversibilities 26,27 . In single crystals, these correlations have been detected by an energy analysis of the neutron cross section 16,[28][29][30] , yielding an elastic contribution with diffuse maxima at the positions of half integer Bragg peaks. This intensity vanishes under a small magnetic field of about 0.1 T and shows some sample dependence, suggesting the influence of a minute amount of defects.…”