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The concepts of frustrated lattices are exemplified on spinel compounds AB2X4, where the magnetic ions can occupy the tetrahedrally coordinated A-sites or the octahedrally coordinated B sites. The B sites form a corner-sharing network of terahedra, the famous pyrochlore lattice which is strongly geometrically frustrated. Chromium oxides, like ZnCr2O4 are representative examples, with exotic spin structures and new elementary excitations at low temperatures: "Geometrons" are excitations of independent spin cluster behaving analogous to molecular magnets. In the chromium sulfides and selenides the lattice becomes slightly expanded, weakening the direct antiferromagnetic exchange and increasing the ferromagnetic Cr-X-Cr exchange, yielding strong bond frustration. Multiferroic ZnCr2Se4, which is dominated by strong ferromagnetic exchange but undergoes a transition into spiral spin order, will be discussed as relevant example. In this compound the appearance of strong negative thermal expansion documents the strong frustration of the spin degrees of freedom. In week external magnetic fields in ZnCr2Se4 ferroelectricity is induced pointing towards strong magnetoelectric effects. In this so-called spin-driven multiferroics new elementary excitations can be observed, namely "electromagnons", which are spin waves gaining dipolar spectral weight via a strong spin-phonon coupling. In addition, the antiferromagnetic compounds undergo spin-driven Jahn-Teller effects, documented by low-temperature phonon splittings, which can easily be detected via optical spectroscopy.
The A-sites in the spinels form a diamond lattice, which is constructed of two interpenetrating fcc lattices. Depending on the ratio of the strength of the exchange interactions within one sublattice and in between the two sublattices strong frustration dominates. In this case magnetic spin order is suppressed in a broad range of parameters and the compounds exhibit unusual ground states including spiral spin liquids. The physics of A-site spinels is elaborated on compounds like MnSc2S4 and FeSc2S4, as well as on the alumino spinels, AAl2O4, with A = Mn, Fe and Co. The iron spinels are Jahn-Teller active but do not undergo long-range Jahn-Teller distortions. According to recent theoretical approaches it is speculated that FeSc2S4 is close to a quantum critical point, where spin and orbital order is suppressed as function of spin-orbit coupling. The statics and dynamics of the spin lattice at low temperatures are studied by neutron scattering experiments, which document the evolution of the complex ground states on decreasing temperatures. |
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