Ferrimagnetic long-range order caused by periodicity of exchange interactions in the spin-1 trimer chain compounds ANi3P4O14 (A=Ca,Sr,Pb,Ba)

We report magnetic properties of ANi₃P₄O₁₄ (A=Ca,Sr,Pb,Ba) . A spin-1 trimer chain with J₁-J₁-J₂ interactions exists, where J₁ and J₂ denote two exchange interaction parameters. A magnetic phase transition occurs and a small spontaneous magnetization appears at low temperatures. The temperature dependence of magnetic susceptibility above the transition temperature and the magnetic-field dependence of magnetization in high magnetic fields are consistent with quantum Monte Carlo results for a spin model that consists of trimer chains with antiferromagnetic J₁ and ferromagnetic J₂ interactions. The small spontaneous magnetization is explainable qualitatively by ferrimagnetic long-range order in the chains and by imperfect cancellation of the net magnetic moments of the chains. To our knowledge, this is the first observation of ferrimagnetic long-range order whose origin is the periodicity of the exchange interactions in chains.