Absence of Magnetic Thermal Conductivity in the Quantum Spin-Liquid Candidate YbMgGaO_{4}

We present the ultralow-temperature specific heat and thermal conductivity measurements on single crystals of YbMgGaO_{4}, which was recently argued to be a promising candidate for a quantum spin liquid (QSL). In a zero magnetic field, a large magnetic contribution of specific heat is observed, and exhibits a power-law temperature dependence (C_{m}∼T^{0.74}). On the contrary, we do not observe any significant contribution of thermal conductivity from magnetic excitations. In magnetic fields H≥6  T, the exponential T dependence of C_{m} and the enhanced thermal conductivity indicate a magnon gap of the fully polarized state. The absence of magnetic thermal conductivity at the zero field in this QSL candidate puts a strong constraint on the theories of its ground state.