  Magnetism plays a key role in modern technology as essential building block
of many devices used in daily life. Rich future prospects connected to
spintronics, next generation storage devices or superconductivity make it a
highly dynamical field of research. Despite those ongoing efforts, the
many-body dynamics of complex magnetism is far from being well understood on a
fundamental level. Especially the study of geometrically frustrated
configurations is challenging both theoretically and experimentally. Here we
present the first realization of a large scale quantum simulator for magnetism
including frustration. We use the motional degrees of freedom of atoms to
comprehensively simulate a magnetic system in a triangular lattice. Via a
specific modulation of the optical lattice, we can tune the couplings in
different directions independently, even from ferromagnetic to
antiferromagnetic. A major advantage of our approach is that standard
Bose-Einstein-condensate temperatures are sufficient to observe magnetic
phenomena like N\'eel order and spin frustration. We are able to study a very
rich phase diagram and even to observe spontaneous symmetry breaking caused by
frustration. In addition, the quantum states realized in our spin simulator are
yet unobserved superfluid phases with non-trivial long-range order and
staggered circulating plaquette currents, which break time reversal symmetry.
These findings open the route towards highly debated phases like spin-liquids
and the study of the dynamics of quantum phase transitions.
