Magnetization plateaux of frustrated antiferromagnets

Quantum magnetism represents one of the fastest growing research fields of modern condensed matter physics. Numerous experimental and theoretical investigations in this field are driven by a relentless search for exotic spin-liquid ground states realizing seemingly paradoxical ``magnet without magnetism.'' Along the way several ordered but nonetheless quite unusual states of magnetic matter have been discovered recently. In my talk I focus on the simplest of them -- collinear spin configuration which supports constant magnetization in a finite interval of the applied magnetic field, thus realizing a magnetization plateau state.