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

Elastic study of electric quadrupolar correlation in the paramagnetic state of a frustrated quantum magnet $\rm Tb_{2+\it δ}Ti_{2-\it δ}O_7$

“…The softening is caused by quadrupole fluctuation while the hardening suggests that the ground state degeneracy was lifted by a phase transition. This up-turn is consistent with the previous reports [20], and can be attributable to the quadrupolar ordering transition [19].…”

“…Figure 7 summarizes the obtained results. Consistent with the previous reports [19,20], our Tb-rich single crystal showed elastic anomaly at about 0.4 K, manifesting a long-range quadrupole ordering. We have compared the observed elastic constant and magnetostriction with the calculated data based on a single-ion model.…”

“…These equations mean that two methods in this study are complementary and suitable for probing quadrupole fluctuation and quadrupole moment, respectively. By performing ultrasound measurement down to below 0.4 K, we have found a clear anomaly in elastic constant at the quadruople ordering temperature of 443 mK, being consistent with a previous works [19,20]. We show strong quadrupolar correlation persists up to ≈ 10 K by comparing experimental data and calculation.…”

“…In addition to a magnetic dipole moment, these doublets carry a large electric quadrupolar moment, which couples to local strain. Recently, quadrupole order has been discerned around 0.5 K [19,20] for Tbrich Tb 2+δ Ti 2−δ O 7 crystals. These findings implies that quadrupolar moment plays an important role in this system.…”

“…Tb 2 Ti 2 O 7 shows prominent magnetoelastic responses such as significant elastic softening [20,22,23], giant magnetostriction [22,24,25], suppressed thermal conductivity [26], thermal Hall effect [27,28], and dynamical hybridization of phonon and crystalline electric field (CEF) states [29][30][31]. These experiments suggest that pure spin models are not enough to capture the physics of Tb 2 Ti 2 O 7 , and quadrupolar degree of freedom and its coupling to the lattice has to be considered carefully.…”