Determination of the Magnetic Symmetry of Hexagonal Manganites by Second Harmonic Generation

Optical second harmonic spectroscopy is introduced as a powerful supplement for the determination of complex magnetic structures. Experimental efforts are simplified and new degrees of freedom are opened. Thereby, some principal or technical restrictions of neutron or magnetic x-ray diffraction experiments are overcome. High spatial resolution leads to additional information about magnetically ordered matter. As an example, the noncollinear magnetic structure of the hexagonal manganites $R{\mathrm{MnO}}_3$ ( $R=\mathrm{Sc}$, Y, Ho, Er, Tm, Yb, Lu) is analyzed. The results show that some earlier conclusions on their magnetic symmetry and properties should be revised.