  While tremendous success has been achieved to date in creating both single
phase and composite magnetoelectric materials, the quintessential
electric-field control of magnetism remains elusive. In this work, we
demonstrate a linear magnetoelectric effect which arises from a novel
carrier-mediated mechanism, and is a universal feature of the interface between
a dielectric and a spin-polarized metal. Using first-principles density
functional calculations, we illustrate this effect at the SrRuO$_3$/SrTiO$_3$
interface and describe its origin. To formally quantify the magnetic response
of such an interface to an applied electric field, we introduce and define the
concept of spin capacitance. In addition to its magnetoelectric and spin
capacitive behavior, the interface displays a spatial coexistence of magnetism
and dielectric polarization suggesting a route to a new type of interfacial
multiferroic.
