  Quantum spin liquids (QSLs) represent a novel state of matter in which
quantum fluctuations prevent conventional magnetic order from being
established, and the spins remain disordered even at zero temperature. There
have been many theoretical developments proposing various QSL states. On the
other hand, experimental movement was relatively slow largely due to
limitations on the candidate materials and difficulties in the measurements. In
recent years, the experimental progress has been accelerated. In this topical
review, we give a brief summary of experiments on the QSL candidates under
magnetic fields. We arrange our discussions by two categories: i)
Geometrically-frustrated systems, including triangular-lattice compounds
YbMgGaO4 and YbZnGaO4, kappa-(BEDT-TTF)2Cu2(CN)3, and EtMe3Sb[Pd(dmit)2]2, and
kagome system ZnCu3(OH)6Cl2; ii) the Kitaev material alpha-RuCl3. Among these,
we will pay special attention to alpha-RuCl3, which has been intensively
studied by our and other groups recently. We will present evidence that both
supports and unsupports the QSL ground state for these materials, based on
which we give several perspectives to stimulate further research activities.
