Time-Resolved and Momentum-Resolved Resonant Soft X-ray Scattering on Strongly Correlated Systems

Time-Resolved and Momentum-Resolved Resonant Soft X-ray Scattering on Strongly Correlated Systems Wei-Sheng Lee Stanford Institute of Material and Energy Science (SIMES) SLAC & Stanford University

Collaborators ALS, Lawrence Berkeley Lab Z. Hussain,, Y. D. Chuang, W. Yang Stanford University and SIMES, SLAC Z. X. Shen T. P. Devereaux, B. Moritz, C. C. Chen (Theory group)

Strongly Correlated Electron System New ground states. Emergent Phenomena! Correlations! New ground states created due to the correlations among the many particles. Many solid state systems can be considered as strongly correlated d systems, especially the transition metal oxides.

Understand the Quantum Matter of Electrons. Superconductivity Fractional Quantum Hall Effect Mott Insulator High-Tc SC Thermodynamic measurements: Resistivity, Specific heat, Penetration depth Macroscopic information. Spectroscopic measurements: Single-particle spectrum -> > Quasi particle Two-particle correlation function -> > collective excitations. Microscopic information.

Momentum resolved Spectroscopy Angle Resolved Photoemission (ARPES) : Single-particle spectrum A(k,ω) Inelastic Neutron Scattering (INS) : Spin fluctuation spectrum S(q,ω) Resonant X-ray X Scattering (RXS) : Charge excitations, χ(q, (q,ω=0)

Momentum resolved Spectroscopy Angle Resolved Photoemission (ARPES) : Single-particle spectrum A(k,ω) Inelastic Neutron Scattering (INS) : Spin fluctuation spectrum S(q,ω) Resonant X-ray X Scattering (RXS) : Charge excitations, χ(q, (q,ω) Successful techniques in 3 rd generation synchrotron light source.

Opportunities provided by SXR at LCLS Soft X-ray X regime (500-2000 ev) Access to resonant scattering channels of L edge of transition metal oxides (2p-3d) Ultra-short Soft X-ray X pulses (~300 fs) Study the electronic states in time domain High pulse intensity Pulse-by by-pulse data collection (also a remedy to the pulse jittering problem) Time-resolved pump-probe probe resonant soft X-ray X scattering experiments!

Time-resolved & q-resolved q Soft X-ray X Scattering on Novel Materials Resonant X-ray X Scattering q-resolved RIXS Photon beam Powerful tool to detect the charge ordering. Energy loss information of the charge excitations.

Resonant X-Ray X Scattering Setup Capability summary: Sample cryostat/manipulator has 3-3 translation (X,Y,Z) & 2-rotation 2 degrees of freedom (θ,φ).( Low T capability 15K < T < 400K. Detectors (CCD) moves in both horizontal (360 degrees) & vertical (45 degrees) scattering planes. All motions are motorized. Simplest q-resolved q scattering probe. Suitable as the first q-resolved q X-ray X scattering experiment.

Scientific example: Charge Ordering Charge Density Wave Strips Orbital ordering, Charge ordering & Magnetic ordering Checkerboard pattern K. J. Tomas et al., PRL. 92, 237204 (2004) T. Hanaguri et al., Nature 430, 1001 (2004).

Detecting Q using RXS Sr 14 Cu 24 O 41 P. Abbamonte et al, Nature 431, 1078 (2004). q of the charge ordering can be probed by resonant elastic scattering. Resonant process enhances the Bragg scattering of the responsible charges. Successfully identify Charge Ordering in many transition oxides, such as Cuprates, Manganites,, etc.

Time Evolution of Charge Ordering Charge ordering melts after the pump. Detect the Brag peak using RXS to see how the charge ordering state reforms along the time axis.

Time Evolution of Charge Ordering Relaxation time scales? Oscillations?

Q-resolved RIXS Soft X-ray emission Photon in 1 2 3 4 Five ports for mounting the spectrograph to perform momentum-resolved IXS; enough momentum transfer to cover ~75% BZ at Mn L edge and 100% BZ at Cu L edge 5 Å -1 0.60 #5 0.75 Photon beam momentum transfer Δq 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 #4 #3 #2 #1 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 fraction of the Brillouin zone 10 5 0-5 -10-5 (0,0) (π,0) (π,π) 0 5 0.05 0.05-15 -10-5 0 5 10 15 chamber rotation angle

q-dependent Energy Loss Δq = (0, 0) Δq = (π, π) Cu K edge RIXS Both Δq dependence and (q in q out ) dependence can provide much information about the wave function projection onto the intermediate states.

Energy Loss Feature at the Q RXS RIXS at ~ (Q x, Q y )? Q y Q x Whether there is any energy loss features at ordering vector? Energy loss features at Q proximity to the charge ordering in the e phase diagram?

Inelastic Neutron Scattering near Q La 1.875 Ba 0.125 CuO 4 Energy Loss near antiferromagnetic ordering (π, π) J. M. Tranquada et al., Nature 429, 534 (2004) CE ordering (2+q, 2-q), T>Tc J. W. Lynn et al., PRB 76, 014437 (2007)

Energy Loss Feature at the Q RXS RIXS at ~ (Q x, Q y )? Q y Q x Whether there is any energy loss features at ordering vector? Energy features at Q proximity to the charge ordering in the phase diagram?

Relaxation of the Charge Ordering in Both Time and Energy Domain Non-equilibrium physics in solids and its relaxation to equilibrium state is a largely unexplored region.

Summary Time-resolved resonant soft X-ray X scattering on solids (strongly correlated systems) Resonant X-ray X Scattering Simplest q-resolve q scattering probe. Aiming for studying the charge ordering phenomena in time domain. Q- resolved Resonant Inelastic X-ray X Scattering Measuring the electronic states in both energy and time domain.

Comments and Discussions are welcome!