Thermodynamics of ferrimagnetic double chains withz-znearest-neighbor interactions

We propose a general treatment involving the transfer-matrix method for solving ferrimagnetic double chains made up of two spin sublattices (s,s’ ${)}_{\mathit{N}}$ showing a z-z exchange coupling between nearest neighbors for several types of unit cell (for practical purpose we shall consider s=1/2). The whole physics of the infinite chain is contained in the largest-modulus eigenvalue ${\mathit{v}}_1$ of the 4×4 transfer matrix. When s’>1/2 we develop in the zero-field limit the secular polynomial (depending on ${\mathit{v}}_1$ and the field B) up to the ${\mathit{B}}^2$ term. By equating it to zero, we get the parallel magnetic susceptibility. When s’=1/2 the secular polynomial is simpler, and it is possible to obtain closed forms by using a differentiation method. We study successively the influence of intrachain and interchain nearest-neighbor interaction on the magnetic behavior for two types of unit cell. Some results appear to be of interest for the discussion of weak-interacting-chain lattices. This model is then applied to the one-dimensional compound VO(${\mathrm{HPO}}_4$)⋅${4\mathrm{H}}_2$O, which exhibits (1/2,1/2${)}_{\mathit{N}}$ double chains coupled by a zigzag interaction path and shows frustration effects.