Zero-point entropies of spin-jam and spin-glass states in a frustrated magnet

Thermodynamics studies of a prototypical quasi-two-dimensional frustrated magnet Ba${}_2$Sn${}_2$ZnCr${}_{7p}$Ga${}_{10-7p}$O${}_{22}$ where the magnetic Cr${}^{3+}$ ions are arranged in a triangular network of bipyramids show that the magnetic zero-point entropy for $p=0.98$ is 55(1)% of the entropy expected when the Cr${}^{3+}$ moments are fully disordered. Furthermore, when combined with a previous neutron scattering study and the perimeter scaling entropy of a spin jam, the analysis reveals that with decreasing $p$, i.e., doping of the nonmagnetic Ga${}^{3+}$ ions, the variation in the magnetic zero-point entropy can be well explained by the combined effects of the zero-point entropy of the spin jam state and that of weakly coupled orphan spins, shedding light on the coexistence of the two types of spin states in quantum magnetism.