Terahertz magneto-optical investigation of quadrupolar spin-lattice effects in magnetically frustrated Tb2Ti2O7

Condensed matter magneto-optical investigations can be a powerful probe of a material's microscopic magnetoelectric properties. This is because subtle interactions between electric and magnetic multipoles on a crystal lattice show up in predictable and testable ways in a material's optical response tensor, which dictates the polarization state and absorption spectrum of propagating electromagnetic waves. Magneto-optical techniques are therefore strong complements to probes such as neutron scattering, particularly when spin-lattice coupling effects are present. Here we perform a magneto-optical investigation of vibronic spin-lattice coupling in the magnetically frustrated pyrochlore ${\mathrm{Tb}}₂{\mathrm{Ti}}₂{\mathrm{O}}₇$. Coupling of this nature involving quadrupolar mixing between the ${\mathrm{Tb}}³⁺$ electronic levels and phonons in ${\mathrm{Tb}}₂{\mathrm{Ti}}₂{\mathrm{O}}₇$ has been a topic of debate for some time. This is particularly due to its implication for describing the exotic spin-liquid phase diagram of this highly debated system. A manifestation of this vibronic effect is observed as splitting of the ground and first excited crystal field doublets of the ${\mathrm{Tb}}³⁺$ electronic levels, providing a fine structure to the absorption spectra in the terahertz (THz) frequency range. In this investigation, we apply a static magnetic field along the cubic [111] direction while probing with linearly polarized THz radiation. Through the Zeeman effect, the magnetic field enhances the splitting within the low-energy crystal field transitions revealing new details in our THz spectra. Complementary magneto-optical quantum calculations including quadrupolar terms show that indeed vibronic effects are required to describe our observations at 3 K. A further prediction of our theoretical model is the presence of a novel magneto-optical birefringence as a result of this vibronic process. Essentially, spin-lattice coupling within ${\mathrm{Tb}}₂{\mathrm{Ti}}₂{\mathrm{O}}₇$ may break the optical isotropy of the cubic system, supporting two different electromagnetic wave propagations within the crystal. Together our results reveal the significance of considering quadrupolar spin-lattice effects when describing the spin-liquid ground state of ${\mathrm{Tb}}₂{\mathrm{Ti}}₂{\mathrm{O}}₇$. They also highlight the potential for future magneto-optical investigations to probe complex materials where spin-lattice coupling is present and reveal new magneto-optical activity in the THz range.