Quantum fluctuations are expected to lead to highly entangled spin-liquid states in some two-dimensional spin-1/2 compounds. We have synthesized and measured thermodynamic properties and muon relaxation rates in Cu-based two-dimensional triangular-lattice spin liquids, one of which is the least disordered of this kind synthesized hitherto. Its measured properties can all be simply characterized by scale-invariant time-dependent fluctuations with a single parameter. The specific heat divided by temperature and muon relaxation rates are both temperature-independent at low temperatures, followed by a logarithmic decrease with increasing temperature. Even more remarkably, $sim$57% of the magnetic entropy is missing down to temperatures of textit{O}(10$^{-3}$) the exchange energy, independent of magnetic field up to $gmu_BH > k_BT$@. These properties are intrinsic. They are evidence that quantum fluctuations lead either to a gigantic specific heat peak from topological singlet excitations below such temperatures, or to an extensively degenerate topological singlet ground state. This is an ultra-quantum state of matter.
تحميل البحث