%0 Journal Article
%T Quantum spin liquid and electric quadrupolar states of single crystal Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$
%A M. Wakita
%A T. Taniguchi
%A H. Edamoto
%A H. Takatsu
%A H. Kadowaki
%J Physics
%D 2015
%I arXiv
%X The ground states of the frustrated pyrochlore oxide Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$, sensitively depending on the small off-stoichiometry parameter $x$, have been studied by specific heat measurements using well characterized single crystalline samples. Single crystal Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ boules grown by the standard floating zone technique exhibit concentration ($x$) gradient. Values of $x$ of small crystal samples cut from a boule are estimated by precisely measuring the lattice constant. The ordered phase of electric quadrupole moments shows a dome structure in the $x-T$ phase diagram with the highest $T_{\text{c}} \simeq 0.5$ K at $x \simeq 0.01$. This phase diagram suggests that the putative U(1) quantum spin liquid state of Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ exists in the range $x<x_{\text{c}} \simeq -0.0025 $ being separated from the quadrupolar state via a vertical line, $x=x_{\text{c}}$, of a first-order phase transition.
%U http://arxiv.org/abs/1509.04583v1