  We introduce a new class of isolated magnetic skyrmions emerging within
tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The
asymmetric magnetic structure of these skyrmions is associated with an
intricate pattern of the energy density, which exhibits positive and negative
asymptotics with respect to the surrounding state with a ferromagnetic moment
tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion
interaction has an anisotropic character and can be either attractive or
repulsive depending on the relative orientation of the skyrmion pair. We
investigate the stability of these novel asymmetric skyrmions against the
elliptical cone state and follow their transformation into axisymmetric
skyrmions, when the tilted ferromagnetic moment of the host phase is reduced.
Our theory gives clear directions for experimental studies of isolated
asymmetric skyrmions and their clusters embedded in tilted ferromagnetic
phases.
