Quadrupole order in the frustrated pyrochlore magnet Tb$_2$Ti$_2$O$_7$

TL;DR

This study investigates the hidden quadrupolar long-range order in the frustrated pyrochlore magnet Tb₂Ti₂O₇ using specific heat measurements and Monte Carlo simulations, revealing how magnetic fields influence its ordered states.

Contribution

It provides experimental and simulation evidence that magnetic fields suppress quadrupolar order, highlighting Tb₂Ti₂O₇'s position at the boundary between quadrupolar and spin-liquid states.

Findings

Magnetic fields above 0.3 T suppress the specific heat peak.

Monte Carlo simulations qualitatively reproduce the field effects.

Tb₂Ti₂O₇ is at a boundary between quadrupolar and spin-liquid phases.

Abstract

We have studied the hidden long-range order (LRO) of the frustrated pyrochlore magnet Tb$_2$Ti$_2$O$_7$ by means of specific-heat experiments and Monte-Carlo (MC) simulations, which has been discussed as the LRO of quadrupole moments inherent to the non-Kramers ion of Tb$^{3+}$. We have found that the sharp specific-heat peak is collapsed into a broad hump by magnetic fields above 0.3 T for $H//[001]$. This result, qualitatively reproduced by MC simulations, suggests that a field-induced magnetic state overcomes the quadrupolar LRO state, as a similar case of a classical spin ice. The present results support the interpretation that Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ is a unique material in the boundary between the quadrupolar ($x \geq x_c = -0.0025$) and spin-liquid ($x \leq x_c$) states, where the magnetic field along the [001] axis is a tuning parameter which induces the magnetic ordered state.