Helical Spin Order in SrFeO 3 and BaFeO 3 Zhi Li Yukawa Institute for Theoretical Physics (YITP) Collaborator: Robert Laskowski (Vienna Univ.) Toshiaki Iitaka (Riken) Takami Tohyama (YITP) Z. L. et al., PRB, 85, 134419 (2012) Z. L. et al., PRB, 86, 094422 (2012) 2013.2.12@GCOE symposium ,Kyoto University
Outline 1. Introduction 2. Motivation and Purpose 3. Helical spin order in BaFeO 3 by first principles and model calculation 4. Phase transition driven by pressure 5. Open question: Helimagnet under magnetic field 5. Conclusion
Cubic provskite A FeO 3 O Fe A =Ca, Sr, Ba A 2+ O 2- A Fe 4+ high valence 3d 4 Zaanen-Sawatzky-Allen diagram [Can. J. Phys. 65, 1292 (1987)] [A. E. Bocquet et al ., PRB 45 , 1561 (1992)] U eff U eff = E (3d 5 ) + E (3d 3 )-2 E (3d 4 ) ~ 7eV cuprates A FeO 3 D eff = E (3d 5 L) - E (3d 4 ) p-band ~ - 3eV metal negative D material D eff
Introduction Hallmark of AFeO 3 (A=Ca, Sr, Ba):Helical spin order and p -type metal, i.e. O2 p electron makes main contribution to conductivity In spherical coordinate, spin moment as : (sin cos , sin sin , cos ) S S i i i i i i For helical spin order, the constraint is: q 0 r i i i Propagating vector defined in reciprocal space q ( 1 , 0 , 0 ) q A-type helical spin ( 1 , 1 , 1 ) G-type helical spin q
Motivation and Purpose Experiment: Lattice parameter SrFeO 3 : 3.85 Å T N (K) q (2 π /a) BaFeO 3 :3.97 Å CaFeO 3 115 0.167(1,1,1) BaFeO 3 SrFeO 3 134 0.112(1,1,1) BaFeO 3 110 0.06(1,0,0) (*) A-type N. Hayashi et al., Angew. Chem. Int. Ed. 50, 12547 (2011)
DFT calculation • Helical spin order predicted by local spin density approximation plus Hubbard U (LSDA+U) with generalized Bloch boundary condition 20 10 U=3.0eV, J=0.6eV U=3.0eV, J=0.6eV 16 SrFeO3-A 8 BaFeO3-A SrFeO3-G BaFeO3-G 12 6 D E( )(meV) Physics D E( )(meV) behind the 4 8 difference 2 between 4 SrFeO 3 0 and 52T 0 BaFeO 3 ? -2 0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20
DFT calculation The density of state (DOS) of FM state in BaFeO 3 is calculate by LSDA+U, U=3.0eV and J=0.6eV 1.O2 p makes the main contribution to density around the Fermi Level 4 2. Half-metallic 2 0 3. The system can be simplified as -2 t2g eg -4 conducting electron coupled to (a) DOS(states/eV/Cell) -6 4 localized electron by Hund coupling O2p Hole 2 0 E F (b) -2 -6 -4 -2 0 2 4
Model calculation It is reasonable to understand the calculated result from the double exchange model. H H H dp SE SrFeO 3 BaFeO 3 H J S S SE SE i j ij M. Mostovoy, Phys. Rev. Lett. 94, 137205 (2005)
Phase transition driven by pressure • Lattice effect FM HM FM T. Kawakami et al., unpublished FM HM
Phase transition driven by pressure • Lattice effect by calculation (a) SrFeO 3 15 24 BaFeO 3 (a) 3.97-G LDA+U 3.85-G LSDA+U 3.85-G U=4.0 eV, J=0.9 eV 3.80-G U=4.0 eV, J=0.9 eV 10 16 3.80-G 3.75-G 3.75-G 3.70-G 3.70-G 5 8 D )=E( )-E(0) (meV) 0 D (meV) 0 -5 (b) (b) 6 10 3.97-A 3.85-A 3.85-A 3.80-A 3.80-A 3.75-A 3.75-A 3.70-A 3 5 3.70-A 0 0 0.00 0.04 0.08 0.12 0.16 0.20 0.00 0.04 0.08 0.12 0.16 0.20
Phase transition driven by pressure DOS 9 BaFeO 3 (a) 3.5 LSDA+U 6 U=4.0 eV, J=0.9 eV 2 3 ( ) pd 3.4 E D D 0 M ( B/Fe) DOS (states/eV/Cell) -3 3.3 4 ( ) a=3.97 Å pd E S (b) t2g 4 3.97 D 2 eg U 3.85 O2p 3.2 2 3.80 3.75 0 3.1 3.70 local moment -2 a=3.70 Å 0.00 0.04 0.08 0.12 0.16 0.20 -8 -6 -4 -2 0 2 Energy(eV)
Open question magnetic phase diagram and electronic transport in helimagnet SrFeO 3 under external field MnSi S. Mühlbauer et al ., Science, 323,915(2009) S. Ishiwata et al ., Phys. Rev. B 84, 054427 (2011)
Conclusion 1. Both SrFeO 3 and BaFeO 3 present helical spin order at ambient pressure resulting from the competing double exchange between conducting electron and superexchange between localized electron, though the wave vector in BaFeO 3 is shorter because of weakened double exchange resulting from larger lattice parameter. 2. Ferromagnetic phase transition will happen in both SrFeO 3 and BaFeO 3 under high pressure because of enhanced hybridization
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