  Ferromagnets in contact with a topological insulator have become appealing
candidates for spintronics due to the presence of Dirac surface states with
spin-momentum locking. Because of this bilayer Bi$_2$Se$_3$-EuS structures, for
instance, show a finite magnetization at the interface at temperatures well
exceeding the Curie temperature of bulk EuS. Here we determine theoretically
the effective magnetic interactions at a topological insulator-ferromagnet
interface {\it above} the magnetic ordering temperature. We show that by
integrating out the Dirac fermion fluctuations an effective
Dzyaloshinskii-Moriya interaction and magnetic charging interaction emerge. As
a result individual magnetic skyrmions and extended skyrmion lattices can form
at interfaces of ferromagnets and topological insulators, the first indications
of which have been very recently observed experimentally.

Materials Science;Mesoscale and Nanoscale Physics;Strongly Correlated Electrons;High Energy Physics - Theory