I will talk about magnetic insulators in which the symmetry of the spin interactions leads to strong fluctuations and qualitatively new ground states. Of particular interest are frustrated quantum magnets in which long-range magnetic order is impeded because of competing interactions. The proximity of such systems to quantum critical points can lead to strong cross-coupling between magnetic order and the nuclear lattice. Case in point is a new class of multiferroic materials in which the magnetic and ferroelectric order parameters are directly coupled, and a magnetic field can suppress or switch the electric polarization [1]. Our neutron measurements reveal that ferroelectricity is induced by magnetic order and emerges only if the magnetic structure creates a polar axis [2-5]. The spin dynamics and the field-temperature phase diagram of the ordered phases provide evidence that competing ground states are essential but not sufficient for ferroelectricity. The origin of the magneto-electric coupling is not understood at present, but it may arise from strain derivatives of the isotropic exchange interactions or anisotropic exchange couplings such as Dzyaloshinskii-Moriya interactions.

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