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Growth and helicity of non-centrosymmetric Cu$_2$OSeO$_3$ crystals

We have grown Cu$_2$OSeO$_3$ single crystals with an optimized chemical vapor transport technique by using SeCl$_4$ as a transport agent. Our optimized growth method allows to selectively produce large high quality single crystals. The method is shown to consistently produce Cu$_2$OSeO$_3$ crystals of maximum size 8 mm x 7 mm x 4 mm with a transport duration of around three weeks. We found this method, with SeCl$_4$ as transport agent, more efficient and simple compared to the commonly used growth techniques reported in literature with HCl gas as transport agent. The Cu$_2$OSeO$_3$ crystals have very high quality and the absolute structure are fully determined by simple single crystal x-ray diffraction. We observed both type of crystals with left- and right-handed chiralities. Our magnetization and ferromagnetic resonance data show the same magnetic phase diagram as reported earlier.