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Surprise(s) in magnets without net moments

We are all familiar with ferromagnetic and antiferromagnetic materials, in which the localized ionic moments (in case of ionic insulators) or the electronic spins (in case of metals) go into a long-range ordered state with a net macroscopic moment (in case of ferromagnets) or a net macroscopic sublattice magnetization (in case of antiferromagnets). However this behaviour is far from ubiquitous even in ionic insulators with well-developed local moments. Indeed, there are many ionic insulators in which the dominant interactions between the local moments compete with each other, leading to a cooperative paramagnetic state with no ordering of the moments down to the lowest temperatures accessible to experiments. The physics of such magnets without net moments has some interesting and surprising aspects, which are touched upon in this brief review.