Magnetoelastic excitation spectrum in the rare-earth pyrochlore Tb2Ti2O7

Changes in elastic moduli as evidence for quadrupolar ordering in the rare-earth frustrated magnet Tb2Ti2O7

“…[25], and supported by the low-temperature evolution of the lowestenergy part of the neutron spectrum. The presence of magnetoelastic modes at considerably higher energies is consistent with the large magnetoelastic coupling parameter [26][27][28][29].…”

“…Furthermore, there is no direct evidence of the nature of the phase transition, which currently could be described as a hidden order: There is a specific-heat anomaly and redistribution of spectral weight in the excitation spectrum, but no measurable order parameter. Strong coupling between various crystal-field and phonon excitations has been evidenced by terahertz spectroscopy [26] and inelastic neutron scattering [27][28][29], implying the importance of quadrupolar degrees of freedom.…”

Magnetic-field control of magnetoelastic coupling in the rare-earth pyrochlore Tb2Ti2O7

“…The second example of a hybridized excitation that we have investigated is the magnetoelastic mode (MEM) formed by the hybridization of the first excited crystal field level (CEF1) with a transverse acoustic phonon (TAP), primarily observed by inelastic neutron scattering [15,18] and also THz spectroscopy [16]. A strongly dispersive magnetic mode appears just above CEF1 and extends up to hω ∼ 10 meV with the same dispersion relation as a transverse acoustic phonon propagating in the same direction, when T 30 K. The magnetic and phonon modes can be observed at different (equivalent) points in reciprocal space due to different selection rules for magnetic and phonon scattering, but because they have the same dispersion relation they are the magnetic and phononic parts of the same magnetoelastic mode (though generally we still refer to the magnetic part as the MEM and the phononic part as the TAP).…”

“…A strongly dispersive magnetic mode appears just above CEF1 and extends up to hω ∼ 10 meV with the same dispersion relation as a transverse acoustic phonon propagating in the same direction, when T 30 K. The magnetic and phonon modes can be observed at different (equivalent) points in reciprocal space due to different selection rules for magnetic and phonon scattering, but because they have the same dispersion relation they are the magnetic and phononic parts of the same magnetoelastic mode (though generally we still refer to the magnetic part as the MEM and the phononic part as the TAP). This hybridization has been characterized in detail in zero field [18]. It was suggested that as magnetic interactions become important, the single-ion excitation CEF1 develops into four cooperative exciton branches, E 1 − 4.…”

“…One candidate is the lattice, which has various anomalous properties at low temperature [11][12][13][14], and is suggested to be strongly coupled to the spins [15,16]. Indeed, three examples of couplings between excited crys-tal field states and phonons have been observed recently in Tb 2 Ti 2 O 7 : a magnetoelastic optical mode (MEOM) formed by the coupling of the third excited crystal field level (CEF3) to a transverse optical phonon (TOP) [17]; a magnetoelastic mode (MEM) formed by the hybridization of the first excited crystal field level (CEF1) with a transverse acoustic phonon (TAP) [15,16,18]; and a MEOM formed by the coupling of CEF1 to a lower-lying optical phonon [16]. The effect on these excitations of a magnetic field applied in different crystal symmetry directions has begun to be studied.…”