Femtosecond Dynamics of Momentum-Dependent Magnetic Excitations from Resonant Inelastic X-Ray Scattering in ${\mathrm{CaCu}}_{2}{\mathrm{O}}_{3}$

Femtosecond Dynamics of Momentum-Dependent Magnetic Excitations from Resonant Inelastic X-Ray Scattering in ${CaCu}_{2} O_{3}$

Valentina Bisogni, Stefanos Kourtis, Claude Monney, Kejin Zhou, Roberto Kraus, Chinnathambi Sekar, Vladimir Strocov, Bernd Büchner, Jeroen van den Brink, Lucio Braicovich, Thorsten Schmitt, Maria Daghofer, and Jochen Geck

Phys. Rev. Lett. 112, 147401 – Published 7 April 2014

Abstract

Taking spinon excitations in the quantum antiferromagnet ${CaCu}_{2} O_{3}$ as an example, we demonstrate that femtosecond dynamics of magnetic electronic excitations can be probed by direct resonant inelastic x-ray scattering (RIXS). To this end, we isolate the contributions of single and double spin-flip excitations in experimental RIXS spectra, identify the physical mechanisms that cause them, and determine their respective time scales. By comparing theory and experiment, we find that double spin flips need a finite amount of time to be generated, rendering them sensitive to the core-hole lifetime, whereas single spin flips are, to a very good approximation, independent of it. This shows that RIXS can grant access to time-domain dynamics of excitations and illustrates how RIXS experiments can distinguish between excitations in correlated electron systems based on their different time dependence.

Received 31 July 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.147401

Authors & Affiliations

Valentina Bisogni^1,2,*, Stefanos Kourtis¹, Claude Monney^2,3,†, Kejin Zhou^2,‡, Roberto Kraus¹, Chinnathambi Sekar^1,§, Vladimir Strocov², Bernd Büchner^1,4, Jeroen van den Brink^1,4, Lucio Braicovich⁵, Thorsten Schmitt², Maria Daghofer¹, and Jochen Geck¹

¹Leibniz Institute for Solid State and Materials Research IFW Dresden, 01069 Dresden, Germany
²Research Department Synchrotron Radiation and Nanotechnology, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland
³Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany
⁴Department of Physics, Technical University Dresden, D-1062 Dresden, Germany
⁵CNR/SPIN, CNISM, and Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

^*Present address: National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, USA. bisogni@bnl.gov
^†Present address: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany.
^‡Present address: Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, United Kingdom.
^§Present address: Department of Bioelectronics and Biosensors, Alagappa University, Karaikudi-630 003, Tamilnadu, India.

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Vol. 112, Iss. 14 — 11 April 2014

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Figure 1
(a) Experimental layout for the RIXS measurements. The scattering angle was set to 130°. (b) X-ray absorption (XAS) at Cu $L_{3}$ edge of ${CaCu}_{2} O_{3}$ . (c) ${CaCu}_{2} O_{3}$ structure in the $a b$ and $a c$ planes. (d) RIXS spectra of ${CaCu}_{2} O_{3}$ for $σ$ (black) and $π$ (red) incoming polarized light, after being normalized to the $d d$ area, between 1.3 and 2.8 eV (not shown here). The vertical offset between two consecutive spectra is proportional to the difference of the corresponding momenta [given by the $y$ scale of panel (e)]. (e) Dispersion of the magnetic peak for the two polarizations (same color code). All the data have been measured at 40 K, above the Néel transition of ${CaCu}_{2} O_{3}$ ( $T_{N} = 25 K$ ) [2].
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Figure 2
Direct magnetic RIXS processes. (a) Schematic representation of the initial state $2 p^{6} 3 d^{9}$ , i.e., the ground state of a 1D AFM $S = 1 / 2$ chain, at time $t = 0^{-}$ just before the creation of the core hole. (b) Intermediate state with one doublon and one core hole present ( $2 p^{5} 3 d^{10}$ configuration) right after the creation of the core hole at $t = 0^{+}$ . As the $3 d$ level at the core-hole site is doubly occupied and has a net spin of 0, magnetic coupling to neighboring sites vanishes. (c) Intermediate state at a later time $t = τ^{-}$ , just before the deexcitation of the core hole. On the left side, two spins next to the core-hole site have flipped due to scattering on the doubly occupied site, i.e., the “cut” in the spin chain. On the right side, spin-orbit coupling of the $2 p$ state has flipped the core-hole spin. The intermediate state doublon is subject to the core-hole potential $V_{c}$ . (d) The two-spinon excitations (red bonds) in the final state at $t = τ^{+}$ . In (c) and (d), the left (right) part illustrates the $S_{0}$ ( $S_{1}$ ) process.
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Figure 3
(a) [(b)] Spectral decomposition of total RIXS intensity $I^{σ}$ (black dotted line) into $S_{0}$ (red line) and $S_{1}$ (blue line) components for $q = - 0.47$ ( $q = 0.47$ ). The elastic signal is shown in green. (c) Comparison between the extracted $I_{S_{0}}$ spectral shapes at $q = - 0.47$ (thin line) and $q = 0.47$ (thick line). (d) [(e)] $I_{S_{0}}^{G}$ ( $I_{S_{1}}^{G}$ ) as a function of $q$ , estimated by integrating $G_{S_{0}}$ ( $G_{S_{1}}$ ) between 0.1 and 0.6 eV. Only positive $q$ data are considered [32].
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Figure 4
Theoretical magnetic RIXS response and comparison to experiment. (a) [(b)] Numerically obtained $I_{S_{0}}^{G} (| q |)$ [ $I_{S_{1}}^{G} (| q |)$ ] as a function of $τ$ , calculated with exact diagonalization (solid colored lines), and comparison to theoretical $I_{S_{0}}^{G} (| q |)$ [ $I_{S_{1}}^{G} (| q |)$ ] rescaled from numerical Bethe ansatz calculations [34] (dashed black lines). (c) $(I_{S_{0}}^{G} / I_{S_{1}}^{G}) (| q |)$ as a function of $τ$ compared to experimental data points (black squares). Calculations have been done for $J = 0.16 eV$ .
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Physical Review Letters

Femtosecond Dynamics of Momentum-Dependent Magnetic Excitations from Resonant Inelastic X-Ray Scattering in CaCu2O3

Valentina Bisogni, Stefanos Kourtis, Claude Monney, Kejin Zhou, Roberto Kraus, Chinnathambi Sekar, Vladimir Strocov, Bernd Büchner, Jeroen van den Brink, Lucio Braicovich, Thorsten Schmitt, Maria Daghofer, and Jochen Geck

Phys. Rev. Lett. 112, 147401 – Published 7 April 2014

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Femtosecond Dynamics of Momentum-Dependent Magnetic Excitations from Resonant Inelastic X-Ray Scattering in ${CaCu}_{2} O_{3}$