Understanding Multiferroic Hexagonal Manganites by Static and Ultrafast Optical Spectroscopy

Table 1

Nonvanished susceptibility tensor components for hexagonal ReMnO₃ with antiparallel coupling of corresponding Mn³⁺ spins along the z-axis.

	Space group	Tensor components 𝜒𝑖𝑗𝑘
Nonmagnetic SH; (i-type)	𝑃63𝑐𝑚	𝑥𝑥𝑧=𝑥𝑧𝑥=𝑦𝑦𝑧=𝑦𝑧𝑦,; 𝑧𝑥𝑥=𝑧𝑦𝑦, 𝑧𝑧𝑧
Magnetic SH; (c-type)	𝑃63𝑐𝑚	𝑦𝑥𝑥=𝑥𝑦𝑥=𝑥𝑥𝑦=−𝑦𝑦𝑦
	𝑃63𝑐𝑚	𝑥𝑦𝑦=𝑦𝑥𝑦=𝑦𝑦𝑥=−𝑥𝑥𝑥
	𝑃63	sum of 𝑃63𝑐𝑚 and 𝑃63𝑐𝑚