Hidden Order and Quantum Spin Liquid States in the Pyrochlore Magnet Tb₂Ti₂O₇

Abstract

A hidden order that emerges in the frustrated pyrochlore Tb_2+xTi_2-xO_7+y with T_c = 0.53 K is studied using neutron scattering, specific heat, magnetization measurements on a high-quality single crystal. Semiquantitative analyses based on a pseudospin-1/2 Hamiltonian for ionic non-Kramers magnetic doublets demonstrate that it is a long-range order of electric quadrupole moments intrinsic to the Tb³⁺ ions. This is the first example of electric quadrupole order in frustrated magnetic systems, and opens new research directions for "frustrated quadrupole systems". It is also found that the elusive spin liquid state of the nominal Tb₂Ti₂O₇, studied for more than a decade, is most likely a U(1) quantum spin-liquid state.