Partition function zeros and magnetization plateaus of the spin-1 Ising–Heisenberg diamond chain

•We consider the spin-1 Ising–Heisenberg model on a diamond chain.•Exact ground-state phase diagrams are derived.•The existence of the magnetic and quadrupole moments plateaus is shown.•Distributions of the Yang–Lee and Fisher zeros have been studied.

We study the properties of the generalized spin-1 Ising–Heisenberg model on a diamond chain, which can be considered as a theoretical model for the homometallic magnetic complex [Ni3(C4H2O4)2−(μ3−OH)2(H2O)4]n⋅(2H2O)n. The model possesses a large variety of ground-state phases due to the presence of biquadratic and single-ion anisotropy parameters. Magnetization and quadrupole moment plateaus are observed at one- and two-thirds of the saturation value. The distributions of Yang–Lee and Fisher zeros are studied numerically for a variety of values of the model parameters. The usual value σ=−12 alongside an unusual value σ=−23 ​is determined for the Yang–Lee edge singularity exponents.