Background:symmetry argument Mostovoy,PRL 96,067601(06) If spin order is spatially inhomogeneous, symmetry allows for the 3rd-order coupling POM and then P may appear. Φem(P,M ）= yP.[M(V·M)-(M·7)M+··], D=Φem+P2/2mE →P∝[(M·a)M-M(a.M)]
Background: symmetry argument If spin order is spatially inhomogeneous, symmetry allows for the 3rd-order coupling P∂M and then P may appear. =em+P2/2 Mostovoy, PRL 96, 067601 (06)
Background:spin configuration argument 1D chain magnet with the competition between NN FM coupling (J)and NNN AFM coupling (J)favors FSO if J'/J>1/4.(JPCM7,8605(1995) J'>0 J<0 Spin on the third site can't be consistent with the J AFM triangular-lattice AF favors FSO
Background: spin configuration argument AFM triangular-lattice favors FSO. 1D chain magnet with the competition between NN FM coupling (J) and NNN AFM coupling (J ) favors FSO if |J /J|>1/4. (JPCM 7, 8605 (1995))
Background:structures and facts RMnO3 phases T.Goto et al. 100 PRL92,257201(2004) R=Nd paramagnetic g Sm Eu 50 eR兴 A-AF incommensurate-AF ↑ commen- ↑ RMnO3 surate 0 AF- 148 146 144 ↑ Mn-O-Mn bond angle(deg) ↓
Background: structures and facts T. Goto et al. RMnO3 phases PRL 92,257201 (2004) RMnO3 phases
Background:structures and facts 1.2 (a)35K 0.8 0.6 Tb/D T.Arima et al. 02 PRL96,097202(2006) -0.500.5 b axis 12 (b) 5K 1 0.8 Q.cp TbMnO; Sixe 04 0.2 0 -0.2 .1 -0.5 0 0.5 1 b axis
T. Arima et al. PRL 96, 097202(2006) TbMnO3 Background: structures and facts
Background:structures and facts a P//c a 600 1.10 0.8 (-6 nwa) (J mol-1 K-2) Specific heat/temperature 400 1.08 0.6 15K 9K 200 0.4 1.06 0 b 600 400 400 200 200 9 15K 0 0 0 20 30 40 0 Temperature(K) 0 Magnetic field (T) Kimura,Annu.Rev.Mater.Res.37,387,2007
Background: structures and facts Kimura, Annu. Rev. Mater. Res.37, 387, 2007