Exact and density matrix renormalization group studies of two mixed spin- (12,52,12) branched-chain models developed for a heterotrimetallic Fe-Mn-Cu coordination polymer

Abstract

The mixed-spin Ising-Heisenberg and Heisenberg branched chains whose magnetic backbone consists of regularly alternating spins 1/2 and 5/2, the latter of which are additionally coupled to an extra spin 1/2 providing lateral branching, are investigated using exact analytical and density matrix renormalization group (DMRG) methods. The proposed spin-chain models capture some relevant aspects of the heterotrimetallic coordination polymer $[\mathrm{Cu}\mathrm{Mn}(\mathrm{L})][\mathrm{Fe}(\mathrm{bpb}){(\mathrm{CN})}_{2}]\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{Cl}{\mathrm{O}}_{4}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{H}}_{2}\mathrm{O}$. The mixed spin-$(1/2,5/2,1/2)$ Ising-Heisenberg branched chain is exactly solvable under the assumption of an Ising-like exchange coupling along the chain, while the lateral branching is treated as an anisotropic $XXZ$ Heisenberg exchange interaction. We determine the ground-state phase diagram and quantify a bipartite quantum entanglement between dimers at lateral branching. It is shown that the studied mixed-spin Ising-Heisenberg branched chain accurately fits available experimental data for temperature dependence of the magnetic susceptibility. The ground-state phase diagram of the analogous mixed spin-$(1/2,5/2,1/2)$ Heisenberg branched chain is obtained within the DMRG method. The ground-state phase diagrams of the Ising-Heisenberg and its full Heisenberg counterpart are contrasted. In particular, the ground-state phase diagram of the mixed-spin Heisenberg branched chain involves a special Gaussian critical point, for which a proper finite-size scaling analysis is provided to accurately estimate its location and the correlation length critical exponent.