Prospects for Ferroelectrics: 2012–2022

Table 1

Requirements for ferroelectrically-induced ferromagnetism (after Birss [51]); see also Ederer and Fennie [78].

Magnetic point group symmetry	Relationship required; between P and M	Spin canting via ferroelectricity
1	None	Allowed
𝑚^′	𝑃 parallel 𝑚^′; 𝑀 parallel 𝑚^′	Allowed
𝑚	𝑃 parallel 𝑚; 𝑀 perpendicular 𝑚	Allowed
2′	𝑃 perpendicular 𝑀; 𝑃 parallel 2′	Allowed
𝑚^′𝑚2^′	𝑃 parallel 2′; 𝑀 perpendicular 𝑚	Allowed
2 or 𝑚^′𝑚^′2	𝑃 parallel 𝑀 parallel 2	Forbidden
3 or 3𝑚^′ or 4; 4𝑚^′𝑚^′ or 6 or 6𝑚^′𝑚^′	𝑃 parallel 𝑀 parallel principal axis	Forbidden