Using a modified Heisenberg model and a Green's function technique we have studied the influence of size d and concentration x of Sr dopants on the Curie temperature T C , saturation magnetization M S , coercivity H C and specific absorption rate (SAR) of single-domain La 1Àx Sr x MnO 3 nanoparticles. Their magnetic properties are explained based on the "magnetically death" surface layer and the competition between the ferromagnetic double-exchange and antiferromagnetic super-exchange interaction. We calculated the specific absorption rate which characterizes the efficiency of the absorption energy when the magnetic hyperthermia is applied as a therapeutic method for the treatment of tumors. A set of nanoparticles appropriate for in vivo and in vitro medical applications, such as magnetic hyperthermia and drug delivery to cancer cells, is determined. The established methodology and microscopic model are suitable to study the magnetic properties of low-dimensional systems (thin films and nanoparticles) such as La 1Àx A x MnO 3 with A ¼ Ca, Ag, Ba, Na for medical applications.