  We investigate the necessary conditions for the emergence of complex,
noncoplanar magnetic configurations in a Kondo lattice model with classical
local moments on the geometrically frustrated Shastry-Sutherland lattice and
their evolution in an external magnetic field. We demonstrate that
topologically nontrivial spin textures, including a new canted flux state, with
nonzero scalar chirality arise dynamically from realistic short-range
interactions. Our results establish that a finite Dzyaloshinskii-Moriya (DM)
interaction is necessary for the emergence of these novel magnetic states when
the system is at half filling, for which the ground state is insulating. We
identify the minimal set of DM vectors that are necessary for the stabilization
of chiral magnetic phases. The noncoplanarity of such structures can be tuned
continually by applying an external magnetic field. This is the first part in a
series of two papers; in the following paper the effects of frustration,
thermal fluctuations, and magnetic field on the emergence of novel noncollinear
states at metallic filling of itinerant electrons are discussed. Our results
are crucial in understanding the magnetic and electronic properties of the
rare-earth tetraboride family of frustrated magnets with separate spin and
charge degrees of freedom.
