Electronic structure, magnetic and dielectric properties in NaCu2O2 Philippe Leininger Max-Planck-Institut, Stuttgart
B. Keimer, B. Bohnenbuck, M. Rahlenbeck, A. Maljuk, C. T. Lin
MPI Stuttgart
E. Weschke, E. Schierle
Helmoltz Zentrum Berlin
J. W. Freeland
Advanced Photon Source, Argonne, USA
S. Seki, Y. Tokura
University of Tokyo, Japan Talk DPG 22.03.2010
Introduction Multiferroic Electronic and magnetic order Empty band : Ex. BaTiO3
usually exclusive
Partially filled band
Ferroelectricity and magnetism ≠ origin → Weak magnetoelectric coupling Incommensurate magnetic spiral Electric polarization P ∞ eij × (Si×Sj)
eij
H. Katsura PRL (2005)
Direct magnetoelectric coupling Si
Sj
Edge-sharing CuO2 plaquettes j1 FM
Cu-O-Cu ~90° J1~0
j2 AFM
Cu O
J1: angle dependent
α = j2 / j1 >>1
Introduction NaCu2O2: Quasi-1D structure • Edge-sharing CuO2 • Cu-O-Cu: 92.9° J2 >> J1 • Cu2+ effective moment 0.56 uB • Magnetic spiral < 12K, P = (0.5 0.227 0) • No substitutional disorder
Isostructural to LiCu2O2 Multiferroic < TN L. Capogna et al., PRB (2005)
Substitutional disorder
Origin? Magnetic order
X-ray absorption spectroscopy Orbital occupation of the valence electrons LiCu2O2 Holes on the Cu(1)
Beamline: Argonne APS- 4-ID-C
Atomic and orbital selectivity Wabs. ~||2~ |r cosθ|2
NaCu2O2 P1: 2p - 3d (Cu2+) P2: 2p - 3d (Cu+) P3: non-localized states
Cu(2): holes localized in the CuO2 planes Cu(1): no holes; 3d10
Ph. Leininger et al., PRB 2010
Magnetic susceptibility
Spiral polarized in the bc plane
Resonant x-ray diffraction Cu L edge: Study directly the d states
Beamline: UE46-PGM1 Bessy II
P=(0.5 0.227 0)
TN= 11,5 K
T=3K P = (0.5 0.227 0) TN = 11.5 K No signal @ Cu K edge Long-range correlations: 3500 Å
Dielectric properties
Résolution ΔPc ~ 0.3 µC/m²
P ∞ eij × (Si × Sj) No electrical polarization < TN
No electrical phase transition below TN
Ph. Leininger et al., PRB 2010
Conclusions NaCu2O2 (No subsitutional disorder) • Quasi-1D system with a magnetic spiral < 11.5 K • X-ray absorption spectroscopy Cu(1) → Cu+ (3d10) Cu(2) → Cu2+ (3d9) : holes polarized in the CuO2 planes • Magnetic susceptibility Magnetic spiral polarized in the bc plane • Resonant x-ray diffraction Long-range correlations • No ferroelectricity/multiferroicity (experiment)
≠
LiCu2O2
In LiCu2O2 the substitutional disorder is responsible for the ferroelectricity • Antiferroelectric order?
Introduction Multiferroic properties
Multiferroics
Electronic order a) Proper
Magnetic order Band partially filled
- Empty d band; Ex.: BaTiO3, BiMnO3
Ferroelectricity and magnetism are exclusive → No magnetoelectric coupling b) Improper Charge order (LuFe2O4: Fe2+-Fe3+) Structural transitions (RMnO3), Magnetic striction (RMn2O5) Incommensurate magnetic spiral
ΔF~ PM∂M
eij Si
P ∞ eij× (Si×Sj) Sj
Direct magnetoelectric coupling
H. Katsura et al. PRL (2005) M. Mostovoy PRL (2006)
Introduction Magnetic frustration j1 FM
Cu-O-Cu ~90° J1~0
j2 AFM
Cu O
J1: angle dependent
J2 >>J1
Classical description
α = J 2 /J1 > 0.25
Incommensurable long-range magnetic spiral
Quantum description j1 > 0
j1 < 0
Heisenberg model
H = ∑J1S j S j+1 + J2 S j S j+2 j
Frustrated Phase
Gap
No gap
FM Phase
α -0.25
Unif. Distri. RVB
0
0.241
0.5
dimer state
Magnetic properties Resonant Magnetic X-ray Scattering Resonant scattering amplitude:
f nres (k , k ' , hω) ~ k, ε
k’, ε‘
∑ c
< a G c >< c G a >
2
Ea − Ec + hω −iΓc / 2 Resonance
Dipolar approximation
⎛ ' ( 0) ' ( 0) ' (1) (1) ( 2) ⎞ = ⋅ + ⋅ + × ⋅ + × ⋅ + f nres ( ε ε ) F ( ε ε ) F ( ε ε m ) F ( ε ' ε m ) F ... F ⎟ z z xy z A eu a 2u , E1 ⎜ xy xy 1 a1B a g g ⎝ ⎠ Charge scattering
1st harmonic in a magnetic spiral
2nd harmonic
m: unit vector in the direction of the magnetic moment F: scattering tensor (depend on the atomic properties) M. Haverkort et al., arXiv: 0911.0705
Magnetic properties Polarization dependence ki ~ a kf ~ b
a ki 43.9° 46.1°
IV/IH
60
30
150
180
0
210
330
240
300 270
I ∝ −i(ε
f
× ε i )mF (1)
Spiral polarized in bc plan
b
IV~mb et IH~ mc
kf 4.6°
ma = mb= 0!
⎛ ...+ (ε ' ×ε ⋅mxy ) Fe(1) + ⎞ ⎟ ⎜ u f nres = , E1 ⎜ ⎜ (ε '×ε ⋅mz ) Fa(21) +...F (2) ⎟⎟ u ⎝ ⎠
90 120
Q
2.4°
- Long-range correlations: 3500 Å - Importance of the electronic structure in the interpretation of the RMXS data