We review recent theoretical progress in our understanding of electron-driven novel magnetic phases on frustrated lattices. Our specific focus is on Kondo-lattice or double-exchange models assuming finite magnetic moments localized at the lattice sites. A salient feature of systems with SU(2) symmetric local moments is the emergence of noncoplanar magnetic ordering driven by the conduction electrons. The complex spin textures then endow the electrons a nontrivial Berry phase, often giving rise to a topologically nontrivial electronic state. The second part of the review is devoted to the discussion of metallic spin ice systems, which are essentially frustrated Ising magnets with local spin ordering governed by the so-called ice rules. These rules are similar to those that describe proton configurations in solid water ice, hence the name "spin ice". The nontrivial spin correlations in the ice phase give rise to unusual electron transport properties in metallic spin-ice systems.
Zooming in on heavy fermions in Kondo lattice models
