  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 Heisenberg 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 with magnetic Cr5+ 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 ferromagnetic 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.
