Dielectric properties - Philippe Leininger

angle dependent j. 1. FM j. 2. AFM. Cu. O. Ferroelectricity and magnetism ≠ origin. → Weak magnetoelectric ... No electrical phase transition below T. N. P ∞ e.
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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