Background:microscopic mechanism Frustrated spin-orbital coupling,Dzyaloshinskii-Moriya effect between two d-orbital ions with canted spins produces a dipole. KNB theory on spin-orbital coupling giving similar prediction. D Katsura et al,PRL 95,057205(05) Sergienko et al,PRB 73,094434 (06) e p-orbitals △ P=e,×(S,×S) d-orbitals d-orbitals n≈ea(tp/△b)/cos(e,/2) double-exchange 7≈ea(tp/△b)3 MI O M2 super-exchange
Background: microscopic mechanism Frustrated spin-orbital coupling, Dzyaloshinskii-Moriya effect between two d-orbital ions with canted spins produces a dipole. KNB theory on spin-orbital coupling giving similar prediction. Katsura et al, PRL 95, 057205 (05) Sergienko et al, PRB 73, 094434 (06)
Background:mechanism Cooperative GdFeO,distortion pc-×(S:×S) P Katsura,Nagaosa,Balatsky a PRL95,057205,2005 CCW Mostovoy PRL96,067601,2006 Sergienko,Dagotto PRB73,094434,2006 Xiang et al. PRL101,037209,2008 Malashevich,Vanderbilt Kimura,Annu.Rev.Mater.Res.37,387,2007 PRL101,037210,2008
Background: mechanism Katsura, Nagaosa, Balatsky PRL95,057205, 2005 Mostovoy PRL96, 067601, 2006 Sergienko, Dagotto PRB73,094434, 2006 Xiang et al. PRL101,037209, 2008 Malashevich, Vanderbilt PRL101,037210, 2008 Kimura, Annu. Rev. Mater. Res.37, 387, 2007 Cooperative GdFeO3 Cooperative GdFeO3 distortion distortion
Origin of spiral-spin order:picture Da(rn)·[SnXS+l]E=-元x+kx2:2o(S×S) Cooperative GdFeO,distortion Mn Mn Spiral DM Polarization Dzyaloshinsky,J.Phys.Chem.Solids 4,241(1958);Moriya,Phys.Rev.120,91(1960)
Origin of spiral-spin order: picture Mn O Mn O Mn Spiral Spiral DMDM Polarization Polarization Cooperative GdFeO Cooperative GdFeO33distortion distortion Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958); Moriya, Phys. Rev.120, 91 (1960) P E=- x+kx 2: ~ (S S)
Origin of spiral-spin order:picture 3.0 paramagnetic A-AFM (b) 2.5 4x4X4 1/ 172/11 C-AFM 2/15 bic lattice 3/16 2.0 4/19 1/1 FMY 1/5 <1.5 O q=0 1/8 1/6 q=1/4 1.0 ferromagnetic downFdown FM/OD E-AFM 0.0 ,/(-J)1.0 0.5 1.5 0.5 0.0 5 0.00.10.2 0.30.40.50.6 JAF Kimura,Ishihara et al. Hotta et al. PRB68,060403R)(2003) PRL90,247203(2003)
Origin of spiral-spin order: picture Kimura, Ishihara et al. PRB68, 060403(R) (2003) Hotta et al. PRL 90, 247203 (2003)
Origin of spiral-spin order:picture 1.2 1.0 λ=0.0 CM-FE 0.8 0.6 0.4 FM(A) 0.2 0.0 0 0.1 0.2 0.3 0.4 (a) Sergienko and Dagotto PRB73,094434(2006)
Origin of spiral-spin order: picture Sergienko and Dagotto PRB73, 094434 (2006)