Indirect Exchange Interactions in Orthorhombic Lanthanide Aluminates

Magnetic exchange interactions in orthorhombic lanthanide monoaluminates LnAlO_3, Ln = Sm-Yb have been determined semiempirically within the Anderson model of exchange in insulators. The constants of magnetic exchange have been evaluated assuming indirect exchange between pairs of nearest $Ln^{3+}-Ln^{3+}$ ions via $4f^{n} \rightarrow 4f^{n-1}5d$ excitation and ionic polarization. The transfer integrals have been approximated by two-centre overlap integrals between four-term analytical $4f^{n}$ radial wave functions of $Ln^{3+}$ ions. The results have been compared with the available experimental Néel temperatures in the same compounds. It has been found that in most cases the indirect exchange interactions present substantial contributions to the energy of the antiferromagnetically ordered state in $LnAlO_3$.