djhuang@nsrrc.org.tw Di-Jing Huang Nat'l Synchrotron Radiation Research Center, Taiwan Dept. of Physics, Nat'l Tsing Hua University, Taiwan Chairon 2008, SPring8, Japan Oct. 3
Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray Absorption Basic Experimental Setup Applications - Chemical analysis - Orbital polarization - Magnetic Circular Dichroism 2. Resonant Soft X-ray Scattering Introduction Basic of resonant X-ray scattering Examples: Magnetic Transition of a Quantum Multiferroic LiCu₂O₂
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Interaction of photons with matter:
Photoelectric effect Photoabsorption Scattering/diffraction • lattice structure: arrangement of atoms • electronic states • magnetic order • excitations (electronic states or phonons) 4 dg × ∑ | Ψ , | A · P | Ψ , | 2 · δ ( E f − E f − Photo-absorption If k · r << 1，Dipole approximation: e ik r ~ 1 + ik · r ~ -iωt i(k · r − ω t ) ~  EE polarization of x-ra – E, – hv)  ∞ ∑ | (f | ε · r | i ) | ² · δ ( E, – E, – hv) f |ɛ · P | i ⟩ | ´ · δ ( E ſ imω 〈 / 〉 e · r 〈 i〉 ε {/|[A,r]|i}= {| = {| = {| |r|i}= if [V (r),r] = 0 K-edge XAS can be accurately described with ls → np single-particle methods. L-edge XAS: the single-particle approximation 2p → 3d breaks down and the pre-edge structure is affected by the core hole wave function. The multiplet effect exists. K 6 1s Dipole transition 2π M ... Absorption probability: δ(hω – E f M y ∞ 〈 f 〉ε・ î 〉 ε · î = e ¸ sin θ cos θ + e ¸ sin θ sin θ + e ¸ cos θ î = (sin θ cos φ, sin θ sin φ, cos θ ) ε・Γ Selection rule: Δ m, L. circularly polarized Y 1 1 : Δ m 1 = +1 R. circularly polarized For  2p → 3d: M ij ∞ (2) p 3dn+1 ε·r 2p 3d •Two absorption "peaks" from 2p → 3d: •Absorption cross section is proportional to numbers of d holes and density of states in the core level. L-edge XAS provides information on the chemical state, orbital symmetry, and spin state of materials. In transition-metal oxides soft x-ray absorption & scattering TM: 2p → 3d 1s → 2p Ö direct, element-specific probing of electronic structure of TMO 10
Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray Absorption Basic Experimental Setup Applications - Chemical analysis - Orbital polarization - Magnetic Circular Dichroism 2. Resonant Soft X-ray Scattering Introduction Basic of resonant X-ray scattering Examples: Magnetic Transition of a Quantum Multiferroic LiCu 2 O 2
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Measurement of Soft X-ray absorption 12
Photoexcitation and Relaxation
Measurement of Soft X-ray absorption 15
Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray Absorption Basic Experimental Setup Applications - Chemical analysis - Orbital polarization - Magnetic Circular Dichroism 2. Resonant Soft X-ray Scattering Introduction Basic of resonant X-ray scattering Examples: Magnetic Transition of a Quantum Multiferroic LiCu 2 O 2
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L-edge XAS provides information on the chemical state, orbital symmetry, and spin state of materials. 17 Polarization of Synchrotron Radiation Right-handed circularly polarized 18 Soft X-Ray Magnetic Circular Dichroism in Absorption Soft X-ray MCD in absorption provides a unique means to probe: element-specific magnetic hysteresis orbital and spin moments magnetic coupling. There are two ways to obtain a MCD spectrum: 1)  Fixing M, measure XAS with left and right circular lights. 2)  Fixing the helicity of light, measure XAS with two opposite directions of M. 20
Ferromagnetism in one-dimensional monatomic metal chains M. C. Malagoll1 Two-dimensional systems, such as ultrathin epitaxial films and dimensionality of a physical system is reduced, magnetic ordering.
important 7. Spin lattice models predict that an infinite one- dimensional linear chain with short-range magnetic interactions of the magnetization, thereby prohibiting long-range ferromag- not take into account kinetic barriers to reaching equilibrium or and long-range ferromagnetic order for one-dimensional mona- that the monatomic chains consist of thermally fluctuating seg- hold temperature, evolve into a ferromagnetic long-range Co chains are characterized by large localized orbital moments and  correspondingly  large  magnetic  anisotropy  energies  com-
pared to two-dimensional films and bulk Co. line represents a single step). The surface has a 6.45° miscut angle relative to the (111) direction; repulsive step interactions result in a narrow terrace width distribution centred at 20.2 Å with 2.9 Å standard deviation. b , Co monatomic chains decorating the Pt step edges (the vertical dimension is enhanced for better contrast). The monatomic chains are obtained by evaporating 0.13 monolavers of Co onto the substrate heid at T = 260 K and previously cleaned by ion sputtering and annealing cycles in ultrahigh vacuum (UHV). The chains are linearly aligned and have a spacing equal to the terrace veinth. Nature 416, 301 (2001) Figure 2 Co X-ray absorption spectra for parallel ( ω ,) and antiparallel ( ω ...) direction of light polarization and field-induced magnetization. The dichroism signal ( μ , 一μ , ) is obtained by subtraction of the absorption spectra in each panel and normalization to the L 2 peak. a , Monatomic chains; b , one monolayer; c , thick Co film on Pt(997). The sample was mounted onto a UHV variable-temperature insert that could be rotated with the respect to the direction of the external magnetic field applied parallel to the incident photon beam. Spectra were recorded in the electron-yield mode at T = 10 K and 23
Soft X-ray Absorption and Resonant Scattering
1. Soft X-ray Absorption Basic Experimental Setup Applications - Chemical analysis - Orbital polarization - Magnetic Circular Dichroism 2. Resonant Soft X-ray Scattering Introduction Basic of resonant X-ray scattering Examples: Magnetic Transition of a Quantum Multiferroic LiCu2O2
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Spin, Charge, and orbital ordering
As the photon energy ĥ ω  approaches the binding energy of one of the core-level electrons, ƒs(q,hω)= ƒ 0 (q)+ ƒ'(hω)+ iƒ"(hω) dispersion corrections 27 Advantage of Resonant Soft X-ray Scattering 28 Setup of Soft X-ray Scattering
X-ray magnetic scattering
kinetic energy m B SO H int dA K A ôt Non-resonant 2π h 2π
m c
hw mc 2 f charge ~ 10 b for ĥω ~ 600 eV Resonant σ → f | H in | n | H 2π δ( E i − E f ) h E ; + hω – E Blume, J. Appl. Phys. (1985) 30 Resonant X-ray magnetic scattering As a result of spin-orbit and exchange interactions, magnetic ordering manifests itself in resonant scattering。 Resonant soft x-ray magnetic scattering: •Cross section comparable to that of neutron scattering. •Good k resolution (Δk < 0.0005 Å -1) •Spectroscopic information. •Limited to a small k space, less bulk sensitive. 32 Soft X-ray Absorption and Resonant Scattering 1. Soft X-ray Absorption Basic Experimental Setup Applications - Chemical analysis - Orbital polarization - Magnetic Circular Dichroism 2. Resonant Soft X-ray Scattering Introduction Basic of resonant X-ray scattering Examples: Magnetic Transition of a Quantum Multiferroic LiCu 2 O 2 Magnetism: ordering of spins Magnetization can be induced by H field Ferroelectricity: polar arrangement of charges Electric polarization can be induced by E field
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34 Magnetoelectric effect Induction of magnetization by an electric field; induction of polarization by a magnetic field. - first presumed to exist by Pierre Curie in 1894 on the basis of symmetry considerations Multiferroics: materials exhibiting ME coupling Cr 2 O 3 BiMnO3 However, the effects are typically too BiFeO3 small to be useful in applications! ..... 35 Two contrasting order parameters Magnetization: time-reversal symmetry broken t ⇒ −t:   M ⇒ −M Polarization: inversion symmetry broken ⇒ − r:  P ⇒ − P, M ⇒ M r = P = qr 36 Recently discovery in the coexistence and gigantic coupling of antiferromagnetism  and ferroelectricity in frustrated spin systems such RMnO₃ and RMn₂O₃ TbMnO₃: Kimura et al., Nature 426, 55, (2003) (R=Tb, Ho , ...) TbMn2O5: Hur et al., Nature 429, 392 (2004) revived interest in “multiferroicity” Magnetism and ferroelectricity coexist in materials called “multiferroics.” •l > c l N • Frustrated magnetic systems.
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orthorhombic, Pnma a=5.734 Å, b=2.856 Å c=12.415 Å Qausi-1D spin ½ chain: •Characterization of the ground state? •Multiferroicity (Park et al. PRL98, 057601; Seki et al.,  cond-mat 0810.2533)
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Above T N , in-plane correlation ξ(T) αc e 2πρs /k BT renormalized classical behavior average J ~ 4.25 meV •The ground state of LiCu₂O₂ exhibits a long range AFM  ordering. 47 END 48 Appendix: Basic of Magnetic Circular Dichroism in X-ray Absorption Considering L-edge 2 ρ 3r2 → 3d absorption, and ignoring the spin-orbit interaction in the 3d bands, 〈l, m 〉ε · γ 〉 j, m