Exchange Magnetostriction in Disordered 2D Ising Ferromagnets

We investigate volume and shape magnetoelastic strains of a 2D anisotropic Ising alloy with partial atomic order. Three possible origins of shape strain are distinguished: (i) anisotropy of elastic constants, (ii) anisotropy of magnetic bonds and (iii) anisotropy of the spatial derivatives of magnetic bonds. None of these mechanisms vanishes above the Curie temperature. Equilibrium strains are expressed in terms of anisotropic spin-spin nearest-neighbours correlation functions. These functions are calculated against temperature, both in ferromagnetic and paramagnetic phase. Shape strain decreases monotonously with temperature for the mechanisms (i) and (iii), and has a maximum near the Curie temperature for the case (ii). The results may be relevant for multilayer magnetic systems.