A possible coupling mechanism between magnetism and dielectric properties in EuTiO₃

The dielectric constant of an incipient ferroelectric EuTiO₃ exhibits a sharp decrease at about 5.5K, at which the antiferromagnetic ordering of the Eu spins simultaneously appears. This fact indicates the existence of a coupling between the magnetism and dielectric properties of EuTiO₃. We propose a possible coupling mechanism between the magnetic and electrical subsystems as -g\sum_l\sum_\langle i,j \rangleq_l^2\vecS_i\cdot\vecS_j. In the framework of soft-mode theory, we have obtained analytically a dielectric constant expression related to the spin correlation of nearest neighbours of Eu ions.