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

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 ($x\ge x_c=-0.0025$) and spin-liquid ($x\le x_c$) states, where the magnetic field along the [001] axis is a tuning parameter which induces the magnetic ordered state.

6 pages, 3 figures