Magnetization non-rational quasi-plateau and spatially modulated spin order in the model of the single-chain magnet, [{(CuL)_2Dy}{Mo(CN)_8}] 2CH_3CN H_2 O

Abstract: Using the exact solution in terms of the generalized classical transfer matrix method, we present a detailed analysis of the magnetic properties and ground state structure of the simplified model of the single-chain magnet, trimetallic coordination polymer compound, $[\{(\text{CuL})_2\text{Dy}\}\{\text{Mo}(\text{CN})_8\}]\cdot\text{2CH}_3\text{CN}\cdot\text{H}_2\text{O}$, in which L$^{2-}$ is N,N’-propylenebis(3-methoxysalicylideneiminato). Due to presence of highly anisotropic Dy$^{3+}$ ion, this material is a unique example of the one-dimensional magnets with Ising and Heisenberg bonds, allowing exact statistical-mechanical treatment. We found two zero-temperature ground states corresponding to different parts of the magnetization curve of the material. The zero-field ground state is shown to be an antiferromagnetic configuration with spatial modulation of the local Dy$^{3+}$(which is proven to posses well defined Ising-like properties due to large anisotropy of g-factors) and composite $S=1/2$ spin of the quantum spin trimer Cu-Mo-Cu in the form "up"-"down"-"down"-"up". Another important feature of this compound is the appearance of the quasi-plateau at non--rational value of magnetization due to difference of the g-factors of the Cu- and Mo-ion in quantum spin trimers. The quasi-plateau is a nearly horizontal part of the magnetization curve where the corresponding zero-temperature ground state of the chain demonstrates slow, but monotonous dependence of the magnetization on the external magnetic field, while the $z$-projection of the total spin, $S_{tot}^z$, is constant