UT, 2011.10.8

X-ray Absorption Spectrum ofSrFeO2
SrFeO2のX線吸収スペクトル
T. Oguchi, M. Kodera Osaka University
T. Shishidou Hiroshima University
J. Mizumaki SPring-8

Dichroism• Light in different polarization experiences avarying absorption.

- Circular dichroism∆CD = W (E (+) ) − W (E (−) )- Linear dichroism∆LD = W (Ex ) − W (Ey )- Directional dichroism∆DD = W (k) − W (−k)• Absorption intensity
W (�ω, E, k)

X-ray Absorption Spectroscopy• Transition Probability by Fermi’s Golden Rule
2π �W (ω) =|�f |F̂ |i�|2 δ(εf − εi − �ω)�fE conservation- Matrix element for the electric transitions
�f |F̂ |i� = �f |e(1 + ik · r + · · · )E · r|i�= �f |F̂E1 + F̂E2 + · · · )|i�
Electric Dipole (E1)Electric Quadrupole (E2)

F̂E1 = eE · r

F̂E2 = ie(k · r)(E · r)

- Selection rules: (L,M,Ms;l,m,ms;E) → Dichroism

E1 and E2 Transitions•Matrix Element Squared|�f |F̂ |i�|2 = |�f |F̂E1 |i�|2 + |�f |F̂E2 |i�|2+2Re�f |F̂E2 |i�∗ �f |F̂E1 |i� + · · ·E1-E2 cross term•

Relative Magnitude of E2 to E1 in X-ray Region (ex. TiK edge)-−1wave number of photon: k ∼ 1Bohrfor hν ∼ 5keV

radial integral: �1s|r|4p� ∼ 20 · �1s|r |3d�2

‣ E1 is dominant, while E2 may appear visible
depending on partial DOS.

‣ E1-E2 cross term could be more interesting incertain cases such as broken inversion.

Dichroism, Symmetry and Ordering
inversion
timecharge (orbital)
reversallinearno timereversalno inversion
electric
natural, reciprocalmagnetic
magnetic
circularmagnetoelectric*
nonreciprocal,magnetochiralpurely E1 and E2transitions+ E1-E2 crosstransition*: toroidal moment order

SOCinvolved

Infinite-Layer Fe Oxides
SrFeO2

Sr or Ca

FeCaFeO2

・Planar 4-coordination

・Almost planar 4-coordination

・Space group: P4/mmm

・Space group: P-421m

・G-type antiferromagnetic

・G-type antiferromagnetic

・Néel Temperature: 473K

・Néel Temperature: 420K

・Fe magnetic moment: 3.6µB

・Fe magnetic moment: 3.3µB

Y. Tsujimoto et al., Nature 450, 1062 (2007).

OC. Tassel et al., J. Am. Chem. Soc. 131, 221 (2009).

XAS of SrFeO2 and CaFeO2Experiment (powder)

Theory (angle averaged)
1.6
1.4

XAS(a.u.)

1.2
1.0
0.8
0.6
0.4

SrFeO2CaFeO2

0.2
0.0-10SrFeO2CaFeO2

01020
ENERGY(eV)3040

XAS and DOS of SrFeO2 and CaFeO2
0.5

O-px

0.0px, pypz

Fe-p

0.03

DOS(/eV)

DOS(/eV)

0.50.00

O-px

0.0px, pypz

Fe-p

0.03
0.00

CaFeO2XAS(a.u.)

XAS(a.u.)

SrFeO2Total-100Total

E1E1E2E21020ENERGY(eV)

3040-1001020ENERGY(eV)

3040

Polarization Dependence in SrFeO2k//x, E//z

XAS(a.u.)

XAS(a.u.)k//x, E//y-100TotalTotal

E1

E1E2E21020ENERGY(eV)

3040-1001020ENERGY(eV)・Strong polarization dependence in the pre-edge region

3040

XMCD of Ferromagnetic SrFeO2 (44GPa) at Fe-K
Theory0.006

2.4k, H//z0.004

2.00.002

1.60.000

1.2XMCD-0.002

0.4-0.006

0.0k, H//x

2.0

0.002

1.6

0.000

1.2-0.002

0.8-0.004

0.4-0.006-15-551525
ENERGY(eV)

35

XAS

0.8-0.004

0.004

Experiment (powder)

45

0.0

XAS(a.u.)

XMCD(a.u.)

XAS

XMCD

• Ferromagnetic order- spin and orbital• Spin-orbit couplingDichroism, Symmetry and Ordering
inversiontime
charge (orbital)
reversallinearno timereversalno inversion
electric
natural, reciprocalmagnetic
magnetic
circularmagnetoelectric*
nonreciprocal,
magnetochiralpurely E1 and E2transitions+ E1-E2 crosstransition*: toroidal moment order

SOC
involved