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We study high-field phase diagram and low-energy excitations ofthree-dimensional quantum helimagnets. Slightly below the saturation field, theemergence of magnetic order may be mathematically viewed as Bose-Einsteincondensation (BEC) of magnons. The method of dilute Bose gas enables anunbiased quantitative analysis of quantum effects in three-dimensionalhelimagnets and thereby three phases are found: cone, coplanar fan and anattraction-dominant one. To investigate the last phase, we extend the usual BECapproach so that we can handle 2-magnon bound states. In the case of 2-magnonBEC, the transverse magnetization vanishes and long-range order occurs in thequadrupolar channel (spin-nematic phase). As an application, we map out thephase diagram of a 3D helimagnet which consists of frustrated J1-J2 chainscoupled by an interchain interaction J3.

Dilute-Bose-Gas Approach to ground state phases of 3D quantum helimagnets under high magnetic field