Resonant scattering at the Ru L-edges Ph. Leininger, B. Bohnenbuck, I. Zegkinoglou, J. Strempfer, C. S. Nelson and B. Keimer
Ruthanate materials Outline Rich phase diagram: x=0: TMI (357 K) and AFM below 110 K (small FM component) x=2 metallic and superconducting below 1.5 K (unconv. spin triplet) - T and doping dependent Structural distortions - Strong e- correlations - Spin-orbit coupling O. Friedt et al. Phys. Rev. B 63, 174432 (2001)
Interplay between Orbital, Magnetic and Structural degree of freedom? • Ca2RuO4 • RuSr2GdCu2O8 (Ru1212) • Ca3Ru2O7
Ca2RuO4 (x=0) - Single-layered - a ~ b ~ c/2 - K2NiF4-type structure strongly distorted (s. g. : Pbca) Ru-Oapical bond rotated around the long c Octahedron tilt around an axis lying in the RuO2 plane
c
b
a
- 44Ru4+: 4d4 configuration
- Antiferromagnetic ordering: 2 magnetic modes: ‘A-centered’ mode [(100) (La2CuO4 type),(011)]: TN = 110K ‘B-centered’ mode [(010) (La2NiO4 type)]: TN = 150K - S = 1 (low spin state) - m along b (m = 1.3μB < 2μB )
Braden et al., PRB 58, 847 (1998)
Resonant X-Ray Diffraction (RXD) How to investigate the structural and magnetic properties? X- ray scattering incoming x-ray coupled to : - electronic charge - magnetic moment (m) orbital magnetization density ≠ spin density: Not the case for neutron incoming x-ray ~ absorption edge Æ Resonant enhancement of magnetic scattering (electric dipole transitions) Ru L edges: - Intermediate energy range - Probe directly the d bands
RXD : Ru L2 edge APS 4ID-D (100)
L2 edge L2’ edge
(011)
Temperature Dependence at (100) (100) L2 edge
Novel phase
E = 2.9685 keV (L2) • Magnetic transition at TN=110 K • Second phase transition at ~260 K
L2’ edge
E = 2.9725 keV (2nd resonant pic) • No anomalies up to 320 K -> excitations to unoccupied states (eg) I. Zegkinoglou et al.,PRL 95, 136401 (2005)
110 K
260 K
Temperature Dependence at (011)
• Identical temperature dependences at (011) and (100) • New phase is characterized by the same
propagation vector as the low-temperature antiferromagnetic state Origin of this new phase?
Origin of the new phase
Polarization dependence at (100) only σ-π’ contribution Æ no charge scattering
260 K Muon spin rotation: Octahedral tilt angles: no anomaly at 260 K Æ no tilt order origin
260 K
Braden et al., PRB 58, 847 (1998)
no magnetic moment above TN Æ no magnetic origin
Orbital Order is responsible for phase transition at 260 K at (100) and (011)
Orbital Order: Theoretical Predictions
•Hotta et al. [3-orbital Hubbard model, el-ph interactions] -> Antiferro-orbital-ordering (AFO) : explain XAS experiments Doubling periodicity in a b (½ ½ 0): not observed experimentally • Anisimov et al., Jung et al. [first principle cal.: LDA+U, σ and XAS] : -> 4dxy Ferro-orbital (FO) ordering • Kubota et al. (RXD: interference technique) -> Ferro-O ordering • Lee et al.: (optical spectro. and multi-orbital Hubbard model) -> Phase coexistence of AF-O and F-O ordered states
Still an contradiction between theory and experiment
zx yz xy Ru: 4d4 (degenerate)
T and azimuthal dependence at (110) No charge and magn. peak in Pbca
Ψ 2θ
No anomalies up to Troom
σ-π‘ and σ - σ ≠ 0
- T and polarization dependence ≠ from (100 & 011) - Azimuthal dependence well reproduced by tilt order model (symmetry consideration)
Resonant scattering at (110) due to tilt order
RuSr2GdCu2O8 (Ru1212) • Tetragonal structure (P4/mmm)
Cu
a=b=3.836 Å, c=11.563 Å • Octahedra rotated about c and
to c
• Alternating - superconducting Cu-O layers (TC≅ 35 K) • Ru ions order AF below TN≅ 136 K
O Ru O Cu
• Gd: AF, TN = 2.5 K
||m|| = 1.18 µB predicted along c Magnetic ordering ?
Temperature Lynn et al., PRB 61, R14964 (2000)
Gd
Ru
Energy dependence at (½ ½ ½)
L2 edge
L2’ edge
calculated absorption coef. from fluorescence
Temperature dependence at (½ ½ ½)
- T > 50 K x-rays and neutrons: identical TN~ 138 K
Below 50 K (superconducting state): Integrated Int. x-rays ≠ neutron Magnetic – superconducting interplay? Æ Difficult to obtain further info.
Azimuthal dependence at (½ ½ ½)
Azimuthal dependence resonant dipole magentic scattering simulation
I σ −σ ' ( 1 1 1 ) ∝ F σ −σ ' ( 1 2 2 2
I
σ −π '
( 12 12 12 )
∝F
σ −π '
2 1 1 2 2 2
)
2
( 12 12 12 )
=0
= A cos 2 Ψ − B cos Ψ + C
Hill and McMorrow, Acta Cryst. A52, 236 (1996)
Direction of magnetic moment RXD : Intensity max. when m in the diffraction plane Intensity max. when m is ~55º off from c axis
≠ powder neutron diffraction (m||c)
(111)
μ
• The direction of the magnetic moment is ~55º off the c-direction
α μp 77º
53º c cp
• From fitting of azimuthal dependence: angle between m and (111)= α = 45.6º • Calculated direction of m : (102)
Ca3Ru2O7 • Orthorhombic structure (rotation and tilting distortion) • Double layer • Paramagnetic metal at high T • AFM ordering temperature below TN = 56K • Structural phase transition at TS = 48K - Large changes of lattice constants - Increase of resistivity below TS Æ Metal insulator-like transition
Yoshida et al., PRB 72, 054412 (2005)
Æ Quasi 2D metal below 30K
- Ordering propogation vector?
Energy Dependence Bessy: KMC-1 • Large resonance enhanchement at reflections (001) and (110) • Calculated structure factor: A-type AFM structure: Ferromagnetic bilayers Antiferromagnetic coupling along c-axis
Azimuthal Dependence Simulation
I
π −σ '
I
π −π '
∝F
π −σ ' 2
= m1cosθ + m3 sinθ
∝F
π −π ' 2
= − m2 sin2θ
2
2
⎛ m1 ⎞ ⎛ cos ψ sin α ⎞ ⎜ ⎟ ⎜ ⎟ m = ⎜ m2 ⎟ = m⎜ sin ψ sin α ⎟ ⎜m ⎟ ⎜ − cos α ⎟ ⎝ 3⎠ ⎝ ⎠ Hill and McMorrow, Acta Cryst. A52, 236 (1996)
Æ Reorientation of magnetic moment at TS - T < TS: m || b - T > TS: m || a
Temperature Dependence
• Similar T-dependence at (001) and (110) • Intensity constant below TS • Drastic intensity loss at TS due to reorientation of magnetic moment • Decreasing magnetic moment in AFM-metallic phase
TS TN
Orbital Order? Raman scattering: - Large structural changes at TS and orbital-ordering RXD: No Anti-Ferro-Orbital (AFO) Order at (100), (010), (1/2 0 0),… Reason… Magnetic and Orbital Order at the same reciprocal space positions Outlook: Search for FO-Ordering: Resonant x-ray interference technique
I(90°+ΔФ) - I(90°-ΔФ)∞ 2Re[Fσσ´F*σπ]×sin2θAsin2ΔФ]
Ferro-orbital ordering => Interference term Next beamtime (few weeks)
Takashi Kiyama et al., J. Phys. Soc. Jpn., Vol. 72, 785 (2003)
Conclusions
New orbitally ordered paramagnetic phase discovered T∞ = 260 K (x=0) Tilt ordering above 260 K (x = 0) m along (102) in Ru1212 Reorientation of m at TS, No AFO-order (Ca3+) Æ Orbital order weakly coupled to crystal lattice (no structural phase transition at TOO) Æ Magnetic structure sensitive to small lattice distortions caused by doping
Collaborators C. T. Lin
MPI, Stuttgart
J.C. Lang, G. Srajer
APS, Argonne, USA
E. Schierle
HMI at BESSY, Berlin
C. Schüßler-Langeheine
Universität Köln
N. Kikugawa
National Institute for Material Science, Tsukuba, Japan
Y. Yoshida, S. I. Ikeda
National Institute of Advanced Industrial Science and Technoloy, Tsukuba, Japan
H. Fukazawa, S. Nakatsuji, Y. Maeno
Department of Physics, Kyoto University, Kyoto, Japan