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# Quantum spin liquid and electric quadrupolar states of single crystal Tb$$_{2+x}$$Ti$$_{2-x}$$O$$_{7+y}$$

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### Abstract

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 samples. Single crystal Tb$$_{2+x}$$Ti$$_{2-x}$$O$$_{7+y}$$ boules grown by the standard floating zone technique are shown to exhibit concentration ($$x$$) gradient. This off-stoichiometry parameter is determined by precisely measuring the lattice constant of small samples cut from a crystal boule. Specific heat shows that the phase boundary of the electric quadrupolar state has a dome structure in the $$x$$-$$T$$ phase diagram with the highest $$T_{\text{c}} \simeq 0.5$$ K at about $$x = 0.01$$. 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 $$x<x_{\text{c}} \simeq -0.0025$$, which is separated from the quadrupolar state via a first-order phase-transition line $$x=x_{\text{c}}$$.

### Author and article information

###### Journal
2015-09-15
2016-02-01
1509.04583
10.1088/1742-6596/683/1/012023