Helical Spin Order in SrFeO 3 and BaFeO 3 Zhi Li Yukawa Institute - - PowerPoint PPT Presentation

Helical Spin Order in SrFeO3 and BaFeO3

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 BaFeO3 by first

principles and model calculation

• 4. Phase transition driven by pressure
• 5. Open question: Helimagnet under

magnetic field

• 5. Conclusion

Cubic provskite AFeO3

Fe O A

A2+ O2- A=Ca, Sr, Ba Fe4+ high valence 3d4 negative D material

Zaanen-Sawatzky-Allen diagram

[Can. J. Phys. 65, 1292 (1987)] cuprates AFeO3

Ueff Deff Ueff=E(3d5) +E(3d3)-2E(3d4)

~ 7eV

Deff=E(3d5L) - E(3d4) ~ - 3eV

[A. E. Bocquet et al., PRB 45, 1561 (1992)]

p-band metal

Introduction

Hallmark of AFeO3 (A=Ca, Sr, Ba):Helical spin order and p-type metal, i.e. O2p electron makes main contribution to conductivity In spherical coordinate, spin moment as : For helical spin order, the constraint is: Propagating vector defined in reciprocal space A-type helical spin G-type helical spin

) cos , sin sin , cos (sin

i i i i i i

S S      

i i

r q    



i

 q 

) , , 1 (   q 

) 1 , 1 , 1 (   q 

Motivation and Purpose

Experiment: Lattice parameter SrFeO3: 3.85 Å BaFeO3:3.97 Å

A-type

• N. Hayashi et al., Angew. Chem. Int. Ed. 50, 12547 (2011)

TN (K) q (2π/a) CaFeO3 115 0.167(1,1,1) SrFeO3 134 0.112(1,1,1) BaFeO3 110 0.06(1,0,0) (*)

BaFeO3

DFT calculation

• Helical spin order predicted by local spin density approximation plus

Hubbard U (LSDA+U) with generalized Bloch boundary condition

0.00 0.05 0.10 0.15 0.20

• 2

2 4 6 8 10

U=3.0eV, J=0.6eV SrFeO3-A SrFeO3-G



DE()(meV)

0.00 0.05 0.10 0.15 0.20 4 8 12 16 20

U=3.0eV, J=0.6eV BaFeO3-A BaFeO3-G

DE()(meV)



52T

Physics behind the difference between SrFeO3 and BaFeO3?

DFT calculation

The density of state (DOS) of FM state in BaFeO3 is calculate by LSDA+U, U=3.0eV and J=0.6eV 1.O2p makes the main contribution to density around the Fermi Level

• 2. Half-metallic
• 3. The system can be simplified as

conducting electron coupled to localized electron by Hund coupling

• 6
• 4
• 2

2 4

t2g eg DOS(states/eV/Cell)

(a)

• 6
• 4
• 2

2 4

• 2

2 4

O2p EF

(b)

Hole

Model calculation

It is reasonable to understand the calculated result from the double exchange model.

• M. Mostovoy, Phys. Rev. Lett. 94, 137205 (2005)

SE dp

H H H  



 

 

ij j i SE SE

S S J H

SrFeO3 BaFeO3

Phase transition driven by pressure

• Lattice effect
• T. Kawakami et al., unpublished

FM FM

HM FM HM

Phase transition driven by pressure

• Lattice effect by calculation
• 5

5 10 15 3.85-G 3.80-G 3.75-G 3.70-G (a) SrFeO3 LDA+U U=4.0 eV, J=0.9 eV 0.00 0.04 0.08 0.12 0.16 0.20 3 6 3.85-A 3.80-A 3.75-A 3.70-A

D(meV)

(b)



8 16 24 3.97-G 3.85-G 3.80-G 3.75-G 3.70-G (a) BaFeO3 LSDA+U U=4.0 eV, J=0.9 eV 0.00 0.04 0.08 0.12 0.16 0.20 5 10 3.97-A 3.85-A 3.80-A 3.75-A 3.70-A



(b)

D)=E()-E(0) (meV)

Phase transition driven by pressure

DOS local moment

• 3

3 6 9 t2g eg O2p

DOS (states/eV/Cell)

BaFeO3 LSDA+U U=4.0 eV, J=0.9 eV (a) a=3.97Å

• 8
• 6
• 4
• 2

2

• 2

2 4 a=3.70Å

Energy(eV)

(b)

D 

2

) (  pd ED

U pd ES

2 4

) ( D  

0.00 0.04 0.08 0.12 0.16 0.20 3.1 3.2 3.3 3.4 3.5 3.97 3.85 3.80 3.75 3.70



M (B/Fe)

Open question

magnetic phase diagram and electronic transport in helimagnet SrFeO3 under external field

• S. Mühlbauer et al., Science, 323,915(2009)
• S. Ishiwata et al., Phys. Rev. B 84, 054427 (2011)

MnSi

Conclusion

• 1. Both SrFeO3 and BaFeO3 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 BaFeO3 is shorter because of weakened double exchange resulting from larger lattice parameter.

• 2. Ferromagnetic phase transition will happen in both

SrFeO3 and BaFeO3 under high pressure because

• f enhanced hybridization