Simultaneous ordered phase of ferroelectric and magnetic order parameters is called “multiferroic” [1]. Cycloid spin order can induce ferroic polarization pattern, and many examples were found over the past decades. RMn2O5 is one of the examples, which has complicated magnetic and dielectric successive phase transitions. The spin order pattern was confirmed as cycloid structure [2], and two mechanisms, SxS and S.S, were confirmed [3]. In this talk, we will show how the cycloid spin order pattern is induced based on a magnetic space group. One example is YMn2O5. YMn2O5 has qM=(1/2,0,1/4) magnetic propagation vector, and then qL = (0,0,1/2) lattice modulation vector. Thus, crystal space group is Pb21m with a0xb0x2c0 unit cell, and magnetic space group is PBb21m with 2a0xb0x4c0 unit cell. This magnetic space group naturally induces cycloid spin structure and then macroscopic ferroelectric polarization. Information of magnetic space group helps to reduce the number of fitting parameters tremendously for magnetic structure analysis and also to consider the spin structure change associated with polarization reverse.
References
[1] H. Katsura et al. Phys. Rev. Lett. 95, 057205 (2005).
[2] Y, Noda, et al, J. Phys. Condens. Matter 20, 434206 (2008).
[3] S. Wakimoto et al., Phys. Rev. B 88, 140403(R) (2013).