A spin liquid is a new state of matter with topological order where the spin moments continue to fluctuate coherently down to the lowest temperatures rather than develop static long-range magnetic order as found in conventional magnets. For spin liquid behavior to arise in a material the magnetic Hamiltonian must be "frustrated" where the combination of lattice geometry, interactions and anisotropies gives rise to competing spin arrangements in the ground state. Theoretical Hamiltonians which produce spin liquids are spin ice, the Kitaev honeycomb model and the kagome antiferromagnet. Spin liquid behavior however in real materials is rare because they can only approximate these Hamiltonians and often have weak higher order terms that destroy the spin liquid state. Ca10Cr7O28 is a new quantum spin liquid candidate with magnetic Cr 5+ ions that possess quantum spin number S= 1 /2. The spins are entirely dynamic in the ground state and the excitation spectrum is broad and diffuse as is typical of spinons which are the excitations of a spin liquid. In this paper we determine the Hamiltonian of Ca10Cr7O28 using inelastic neutron scattering under high magnetic field to induce a field polarized paramagnetic ground state and spin-wave excitations that can be fitted to extract the interactions. We further explore the phase diagram by using inelastic neutron scattering and heat capacity measurements and establish the boundaries of the spin liquid phase as a function of magnetic field and temperature. Our results show that Ca10Cr7O28 consists of distorted kagome bilayers with several isotropic ferromagnetic and antiferromagnetic interactions where unexpectedly the ferromagnetic interactions are stronger than the antiferromagnetic ones. This complex Hamiltonian does not correspond to any known spin liquid model and points to new directions in the search for quantum spin liquid behavior.
INTRODUCTIONConventional magnets in condensed matter typically develop long-range magnetic order when cooled to low temperatures [1]. Below their ordering temperature the magnetic moments develop a static component which acts as the order parameter for the phase transition and the spin ordering is observable as magnetic Bragg peaks which characterize the type of order. The excitations are usually spin-waves which are collective oscillations of the spins about their ordering directions. The transition can be described by Landau theory where symmetry is broken and the new phase is characterized by a local order parameter [2].It was recently realized that some states of matter are characterized by topological order, rather than by symmetry breaking and a local order parameter [3]. This important discovery promises new, exotic and potentially useful properties that could be of relevance e.g. to information technologies. For example topological order gives rise to coherent states which can be highly robust to the usual perturbations that destroy coherence in ordinary states due to the non-local nature of their correlations.One potential applicati...