Quantum criticality will be investigated in metallic and insulating transition-metal oxides and chalcogenides. Magnetic quantum phase transitions can be tuned by external magnetic fields or by doping. In many transition-metal oxides geometrical frustration plays an important role, pushing magnetic order towards T = 0 K and leading to a wealth of novel phenomena. In some cases the pure system is at the quantum critical point and magnetic order can be induced, e. g. by marginal doping. Due to frustration there are an infinite number of ground states not related by symmetry to one another. Rather remarkably in some systems such degeneracies can be lifted by fluctuations leading to complex magnetic ordering.
The two major directions of our research will be heavy-fermion and non-Fermi liquid behaviour in itinerant transition metal oxides, as well as quantum criticality in semiconducting and insulating magnets resulting from strong frustration effects.