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

Abstract

The origin of quantum fluctuations responsible for the spin liquid state in Tb2Ti2O7 has remained a long standing problem. By synchrotron-based terahertz measurements, we show evidence of strong coupling between the magnetic and lattice degrees of freedom that provides a path to the quantum melting process. As revealed by hybrid crystal electric field-phonon excitations that appear at 0.67 THz below 200 K, and around 0.42 THz below 50 K, the double vibronic process is unique for Tb 3+ in the titanate family due to adequate energy matching and strong quadrupolar moments. The results suggest that lattice motion can indeed be the driving force behind spin flips within the hybridized ground and first excited states, promoting quantum terms in the effective Hamiltonian that describes Tb2Ti2O7.Keywords: THz spectroscopy, pyrochlore, frustration, spin-lattice coupling Over the last decade, spin-ice physics has aroused significant attention [1, 2]. It emerges in pyrochlore magnets, such as Ho 2 Ti 2 O 7 or Dy 2 Ti 2 O 7 , as a result of effective ferromagnetic interactions coupling the Ising-like rare-earth magnetic moments constrained along the local 111 directions by the crystal field [3][4][5] (Fig. 1 (a,b)). This combination impedes long-range order, favoring a disordered and macroscopically degenerate magnetic state governed by an organizing principle, the socalled "ice rule," where two spins point into and two out of each elementary tetrahedron in the structure [3].The possibility that quantum fluctuations can melt the spin ice state is a topical issue. It is expected to lead to a wealth of exotic phenomena such as a quantum superposition of "two-in two-out" configurations and emergent electrodynamics with new deconfined particles [6][7][8][9][10][11].In this context, the puzzling behavior of the spin liquid Tb 2 Ti 2 O 7 has attracted much attention. 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 property that distinguishes Tb 2 Ti 2 O 7 from the other rare-earth titanates is the CEF energy spectrum of Tb 3+ . It features a first excited doublet at a low energy of ∆ ≈ 1.5 meV above the ground state [25][26][27][28][29], ...

Magnetoelastic excitation spectrum in the rare-earth pyrochlore Tb2Ti2O7

“…In recent terahertz spectroscopy measurements [83], four peaks were found in the THz spectrum: P0 (hω P0 = 1.37 meV), P1 (hω P1 = 1.71 meV), P2 (hω P2 = 2.08 meV), and P3 (hω P3 = 2.78 meV). The energies and temperature dependence of P0 and P2 suggests they are excitations between the members of the ground-state and CEF1 doublets, with equal splitting of each doublet due to magnetoelastic coupling.…”

“…However, our observation of an overall exciton dispersion closely similar to that discussed by Kao et al [42] suggests that ignoring the admixture of excited states will ultimately be unrealistic. Furthermore, given the numerous couplings between phonons now catalogued in Tb 2 Ti 2 O 7 [CEF1 and TAP to produce the MEM discussed here, CEF1 and an overlying optical mode to give a magnetoelastic optical mode (MEOM [16]) observed by a terahertz spectroscopy experiment mentioned further below [83], CEF3 and an optical phonon to produce a MEOM as described in Ref. [16])], the importance of effective coupling of multipoles by phonons [84] should also be assessed.…”

Spin-Lattice Coupling in the Quantum Spin Ice Candidate Tb2Ti2O7 Revealed by THz Spectroscopy

“…Using high-resolution synchrotron-based terahertz spectroscopy, we have probed the lowest energy excitations of Tb2Ti2O7 (see Figure 1). It is revealed that a double hybridization of crystal-fieldphonon modes is present across a broad temperature range from 200 k down to 6 K [1]. This so called vibronic process affects the electronic ground state that can no longer be described solely by electronic wave functions.…”

Terahertz Electrodynamics in Transition Metal Oxides

“…[259][260][261][262][263][264] Due to statistical identity of ground state manifolds of these materials and entropy of ice, these were termed as spin ice materials which possess 2-in 2-out spin configuration on each tetrahedron. [259][260][261][262][263][264] Due to statistical identity of ground state manifolds of these materials and entropy of ice, these were termed as spin ice materials which possess 2-in 2-out spin configuration on each tetrahedron.…”