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What's Cool About Neutron Scattering -- the Basics with a bias toward Magnetism

What's Cool About Neutron Scattering -- the Basics with a bias toward Magnetism. Jim Rhyne Deputy Leader for Science Lujan Neutron Scattering Center Los Alamos National Laboratory. 2006 Lujan Summer Students July 24, 2006. LA-UR-06-4041. Magnetism Solves All Your Problems. New Physics Here!.

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What's Cool About Neutron Scattering -- the Basics with a bias toward Magnetism

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  1. What's Cool About Neutron Scattering -- the Basics with a bias toward Magnetism Jim Rhyne Deputy Leader for ScienceLujan Neutron Scattering Center Los Alamos National Laboratory 2006 Lujan Summer StudentsJuly 24, 2006 LA-UR-06-4041

  2. Magnetism Solves All Your Problems New Physics Here! Ref. Sharper Image, Nov. 2002

  3. On to Neutron Scattering PhenomenaOutline -- References • Neutron Sources • General Concepts of Scattering • Diffractometers and Diffraction • Magnetic Diffraction • Reflectometry • Inelastic Scattering • Diffuse Scattering • References: • Neutron Diffraction, G.E. Bacon, 5th edition, Oxford Press, 1975 • Theory of Neutron Scattering From Condensed Matter, S.W. Lovesey, Oxford Press 1984 • Introduction to the Theory of Neutron Scattering, G.L. Squires, Dover, 1996. • Solid State Physics, N.W. Ashcroft, N.D. Mermin, Holt, Rinehart & Winston, 1976

  4. What Can Neutrons Do? Neutrons measure the space and time-dependent correlation function of atoms and spins – All the Physics! • Diffraction (the momentum [direction] change of the neutron is measured) • Atomic Structure via nuclear positions • Magnetic Structure(neutron magnetic moment interacts with internal fields) • Disordered systems - radial distribution functions • Depth profile of order parameters from neutron reflectivity • Macro-scale structures from Small Angle Scattering (1 nm to 100 nm) • Inelastic Scattering (the momentum and energy change of the neutron is measured) • Dispersive and non-dispersive phonon and magnon excitations • Density of states • Quasi-elastic scattering

  5. What do we need to do neutron scattering? • Neutron Source – produces neutrons • Diffractometer or Spectrometer • Allows neutrons to interact with sample • Sorts out discrete wavelengths by monochromator (reactor) or by time of flight (pulse source) • Detectors pick up neutrons scattered from sample • Analysis methods to determine material properties • Brain power to interpret results

  6. Lujan Neutron Scattering Center Isotope Production Facility Weapons Neutron Research Facility Proton Storage Ring Proton Radiography 800 MeV Proton Linear Accelerator Sources of neutrons for scattering? • Nuclear Reactor • Neutrons produced from fission of 235U • Fission spectrum neutrons moderated to thermal energies (e.g. with D20) • Continuous source – no time structure • Common neutron energies -- 3.5 meV < E < 200 meV • Proton accelerator and heavy metal target (e.g., W or U) • Neutrons produced by spallation • Higher energy neutrons moderated to thermal energies • Neutrons come in pulses (e.g. 20 Hz at LANSCE) • Wider range of incident neutron energies

  7. There are four National User Facilities for neutron scattering in the US Intense Pulsed Neutron Source (7 kw) National User Facilities HFIR 1966 NCNR 1969 IPNS 1981 Lujan 1985 (SNS 2006) NIST Center for Neutron Research Local/Regional Facilities (University Reactors) MIT Missouri … Spallation Neutron Source (first neutrons in May -- operational instruments late in 2006) (1000 kW) Manuel Lujan Jr. Neutron Scattering Center (100 kW) High-Flux Isotope Reactor

  8. Neutron scattering machines • Spectrometers or diffractometers • typically live in a beam room • are heavily shielded to keep background low and protect us • receive neutrons from the target (or reactor) • correlate data with specific neutron wavelengths by time of flight • accommodate sample environments (high/low temperature, magnetic fields, pressure apparatus)

  9. Neutron Scattering’s Moment in the Limelight

  10. Restelli What is neutron scattering all about? Source

  11. General Properties of the Neutron • The kinetic energy of a 1.8 Å neutron is equivalent to T = 293K (warm coffee!), so it is called a thermal neutron. • The relationships between wavelength (Å) and the energy (meV), and the speed (m/s, mi/hr) of the neutron are: e.g. the 1.8 Å neutron has E = 25.3 meV and v = 2200 m/s = 4900 mi/hr • The wavelength if of the same order as the atomic separation so interference occurs between waves scattered by neighboring atoms (diffraction). • Also, the energy is of same order as that of lattice vibrations (phonons) or magnetic excitations (magnons) and thus creation of annihilation of a lattice wave produces a measurable shift in neutron energy (inelastic scattering).

  12. COMPARATIVE PROPERTIES OF X-RAY AND NEUTRON SCATTERING Property X-Rays Neutrons Wavelength Characteristic line spectra such as Cu K= 1.54 Å Continuous wavelength band, or single  = 1.1  0.05 Å separated out from Maxwell spectrum by crystal monochromator or chopper Energy for  = 1 Å 1018 h 1013 h (same order as energy of elementary excitations) Nature of scattering by atoms Electronic Form factor dependence on [sin]/ Linear increase of scattering amplitude with atomic number, calculable from known electronic configurations Nuclear, Isotropic, no angular dependent factor Irregular variation with atomic number. Dependent on nuclear structure and only determined empirically by experiment Magnetic Scattering Very weak additional scattering ( 10-5) Additional scattering by atoms with magnetic moments (same magnitude as nuclear scattering) Amplitude of scattering falls off with increasing [sin ]/ Absorption coefficient Very large, true absorption much larger than scattering abs  102 - 103 increases with atomic number Absorption usually very small (exceptions Gd, Cd, B …) and less than scattering abs  10-1 Method of Detection Solid State Detector, Image Plate Proportional 3He counter

  13. Golden Rule of Neutron Scattering • We don’t take pictures of atoms! • Job preservation for neutron scatterers – we live in reciprocal space Atoms in fcc crystal Intensity

  14. How are neutrons scattered by atoms (nuclei)? • Short-range scattering potential: • The quantity “b” (or f) is the strength of the potential and is called the scattering length – depends on isotopic composition • Thus “b” varies over N nuclei – can find average defines coherent scattering amplitude leads to diffraction – turns on only at Bragg peaks • But what about deviations from average? This defines the incoherent scattering • Incoherent scattering doesn’t depend on Bragg diffrac. condition, thus has no angular dependence – leads to background (e.g., H)

  15. Scattering of neutrons by nuclei • A single isolated nucleus will scatter neutrons with an intensity (isotropic) • I = I0 [4b2] where I0 = incident neutron intensity, b = scattering amplitude for nucleus • What happens when we put nucleus (atom) in lattice? • Scattering from N neuclei can add up because they are on a lattice • Adding is controlled by phase relationship between waves scattered from different lattice planes • Intensity is no longer isotropic – Bragg law gives directional dependence • Intensity I (Q, or ) is given by a scattering cross-section or scattering function

  16. Observed Coherent Scattering • Intensity of diffracted x-ray or neutron beam produces series of peaks at discrete values of 2 [or d or K (also Q)] Note: d = /(2 sin) or K = 4sin/  = 2/d are more fundamental since values are independent of  and thus characteristic only of material. Benzine Pattern (partial) Note: Inversion of scales - 2  f(1/d)

  17. Scattering Cross-section • The measured scattered intensity in a diffraction experiment is proportional to a scattering function S(Q), which is proportional to a scattering cross-section I(2,d,or Q)  S(Q)   = solid angle • In turn the cross-section  |A(Q) • A*(Q)| A = scattering anplitude • In second Born approximation (kinematic limit) A  Fourier transform of scattering length density (r) = (α atom) with the sum over j atoms at position Rj • then The scattering factor f(Q) is the fundamental quantity describing the scattering of radiation from the material • f takes different forms depending on the type of radiation • f varies in magnitude depending on the scattering atom or magnetic spin

  18. Scattering Factors f • . • The Fourier transform character of the scattering factor f means that the radial extent of the scattering center density aj( r) will dictate its Q dependence. • x-rays scatter from the electron cloud of dimensions comparable to  or d (1/Q) • Neutrons scatter from the nucleus  10-5 the dimension of  or d

  19. Scattering Factors f, cont’d • For x-rays the magntude of f is proportional to Z • For neutrons nuclear factors determine f, thus no regular with Z (different isotopes can have different f s) Shaded (negative) -->  phase change For neutrons conventionally f = b (Scattering length - constant for an element)

  20. What Controls the Scattering Amplitude? • I(Q)  S(Q)  |A(Q) • A*(Q)| [Measured scattered intensity, S = scat.func.] • where faj = atomic scattering factor [cm-1] • Magnitude of A(Q) is controlled by [|A(Q) • A*(Q)| called Structure Factor] • f values for various atoms in lattice • destructive interference of waves scattering from atoms at various lattice sites (calculation of above sum over atoms in lattice reveals this) • fcc lattice (000, 0½½ , ½0½, ½½0) bcc lattice (000, ½½½) • A(Q) = 4 fa for hkl all odd or A(Q) = 2 fa for h+k+l even hkl all even • A(Q) = 0 otherwise A(Q) = 0 otherwise

  21. Applications of Powder Diffraction Methods • Scattering instruments, line shapes, resolution • Rietveld Structure Refinement Analysis • Magnetic Structures and Diffraction • Diffuse Scattering

  22. Powder Diffraction Experimental View • Two types of diffactometers • Fixed Wavelength Diffraction (x rays, neutrons at a Reactor [HFIR, NCNR]) • Variable wavelength (white beam neutrons) [beam may be pulsed (LANSCE [20 Hz], IPNS [30 Hz], SNS [60 Hz]) or continuous (PNS, Geneva)] • Objective (determine “d” or “2”) Bragg Law  = 2d sin • d = /(2 sin ) • pulse neutron source - vary , keep  fixed • x-ray or reactor neutron source -- vary , keep  fixed

  23. = f(t) so d=/(2sin)= f(t)/(2sin) short t  short  small d; long t  long  large d COMPARISON OF POWDER DIFFRACTION INSTRUMENTS*** Bragg Scattering: l = 2d sin q [we need “d”] *** • Reactor Source -- Monochromator selects near mono-energetic neutrons, detector moves (2q) to collect discrete • (l fixed, vary q) diffraction data • Pulse Source -- White beam of moderated neutrons used, neutron time-of-flight selects wavelength, detectors grouped in banks, no moving parts (q fixed, vary l)

  24. Rietveld Profile RefinementLeast Squares Fitting Procedure for Powder Data • Input Data • Powder scattering pattern data • Trial structure space group and approximate lattice parameters and atomic positions • Line shape function and Q-dependence of resolution • Output Results • Lattice Parameters • Refined atomic positions and occupancies • Thermal parameters (Debye Waller) for each atom site • Resolution parameters • Background parameters • R factors of fit (and other measures of fit precision) • Preferential orientation, absorption, etc. • More than one phase can be separately refined

  25. Magnetic Powder Diffraction • Neutron has a magnetic moment -- will interact with any magnetic fields within a solid, e.g., exchange field • Magnetic scattering amplitude for an atom (equivalent to b) where g = Lande “g” factor, J = total spin angular momentum, f = magnetic electrons form factor • Magnetic scattering comes from polarizedspins (e.g., 3d [Fe] or 4f [RE]) not fromnucleus -- Therefore scattering amplitudeis Q-dependent (like for x-rays) via f • at Q = 0 for Fe  = gJ = 2.2 Bohr magnetonsp = 0.6 (comparable to nuclear b = 0.954)all in units of 10-12cm • Refinement gives moment magnitudes oneach site and x,y,z components(if symmetry permits) Mn+2

  26. Experimental Calculated MoreLocalizedMoment LessLocalizedMoment Form Factors

  27. K Magnetic Powder Diffraction II • In diffraction with unpolarized neutrons (polarized scattering is a separate topic) the nuclear and magnetic cross sections are independent and additive: • q2 is a “switch” reflecting fact that only the component of the magnetic moment   scattering vector K (or Q) contributes to the scattering

  28. Ferromagnet (parallel spins) Single Magnetic site (e.g., Fe, Co, Tb) Scattering only at Bragg peak positions (adds to nuclear), but not necessarily all (q2 switch) Multi Site Ferromagnet (e.g. Y6Fe23 (4 distinct Fe sites) -- no new peaks in scattering Antiferromagnet (parallel spins with alternate sites reversed in direction) equivalent to new magnetic unit cell doubled in propagation direction of AFM Purely magnetic scattering peaks at half Miller index positions (e.g., 1,1,1/2) Overall net magnetic moment adds to 0 [job security for neutrons!!] Basic Types of Magnetic Order and Resulting Scattering a c

  29. Other more complex antiferromagnetic cells (multi-site, but on each site  = 0) Ferrimagnet (multi-site cell) Spins parallel on each site Sites can reverse spin direction   0 on each site, but overall  could = 0 Ferromagnetic type scattering pattern --No new peaks FM layers along (0001) (111) FM Sheets A B C D bcc site antiparallel to corners AFM line along (111) Magnetic Structures, cont’d.

  30. Paramagnetism (T > TC ) spins thermally disordered no coherent magnetic scattering Incoherent scattering (weak) has form factor dependence Periodic Moment Structures (e.g., Er, Au2Mn) = 0, but periodic spin arrangement gives rise to magnetic scattering satellites (+, -) of nuclear Bragg peaks More Magnetic Structures • Periodic Moment Structures (e.g., Er, Au2Mn) • = 0, but periodic spin arrangement gives rise to magnetic scattering satellites (+, -) of nuclear Bragg peaks • Periodic Moment Structures (e.g., Er, Au2Mn) • = 0, but periodic spin arrangement gives rise to magnetic scattering satellites (+, -) of nuclear Bragg peaks

  31. Polarized Neutron Reflectometry Incident Polarized Neutrons Specular Reflectivity Detector Spin Polarizing Supermirror Al-Coil Spin Flipper • index of refraction: sensitive to  • scattering length density: used to model reflectivity • reflectivity: measured quantity non spin-flip Al-Coil Spin Flipper Sample spin-flip

  32. Ga1-xMnxAs J. Blinowski et al, Phys. Rev. B 67, 121204 (2003) • Dilute ferromagnetic semiconductor • Spintronics applications • Annealing increases magnetization & Tc • Interstitial Mn go to the surface! • K. W. Edmonds et al., PRL, 92, 37201, (2004) - Auger • Depth-dependence of chemical order and magnetization determined Polarized-Beam Neutron Reflectivity • Compared similar as-grown and annealed films • T = 13 K, H = 1 kOe (in plane)

  33. Ga1-xMnxAs As-Grown & Annealedt = 110 nm, x = 0.08, TC = 50 K, 120 K • Measured reflectivities & fits • Spin up & spin down splitting due to sample magnetization • Spin up reflectivities are different • “Slope” at high Q different • Fits are good • Magnetic signal: spin asymmetry • SA = (up – down) / (up + down) • Larger amplitude for annealed film • Better defined for annealed film • SLD Models (mag. & chem.) • As-grown M doubles near surface • M increases and more uniform for annealed film • Both films show magnetic depletion at surface • Drastic chemical change at annealed film’s surface • Interstitial Mn have diffused to surface! (combined with N2 during annealing)

  34. Inelastic Scattering • Inelastic Scattering (the momentum and energy change of the neutron is measured) • Dispersive and non-dispersive phonon and magnon excitations • Density of states • Quasi-elastic scattering

  35. i = 2dmsin m |ki| = 2/i f = 2dasina |kf| = 2/f Triple Axis Neutron Scattering Spectrometer Want Thermal neutrons e.g., E=14mev, =2.4Å

  36. MURR Triple Axis Neutron Spectrometer (TRIAX) Analyzer Assembly Beam Stop (pivots with drum and sample) Detector Shield and Collimator Sample Table and Goniometer Monochromator Drum

  37. Diffuse Scattering(Life Without Bragg Peaks) • Amorphous Material • No periodic lattice • May have short range ordering (SRO) of atoms (e.g. Dense Random Packing (DRP) of Spheres, tetrahedral atom clusters (e.g., Ge) • Thus no discrete Bragg Peaks, but • SRO leads to features in Intensity = S(Q) • Study Diffraction with White Beam (e.g., pulse source) X-ray S(Q) vs Q [K] for amorphous Fe80B20 and related metallic glasses (Wagner)

  38. Amorphous Structure FactorsReciprocal Space • Single component system -- Real Space Probability Distribution of Atoms is given by Fourier Transforms of S(Q): • Multicomponent system (e.g., atoms 1 and 2) S(Q) is a superposition of partial structure factors Sij(Q) [Faber-Ziman formalism] • S(Q) = <b>-2 [c12 b12 S11(Q) + c22 b22 S22(Q) + 2c1 c2b1 b2 S12(Q) including the scattering factor weightings • Partial structure factors can often be obtained by enhancing scattering from one atom component wrt another [e.g., by isotopic substitution (neutrons) or by combining x-ray (heavy atom sensitivity) and neutron (uniform sensitivity) data • Example: Amorphous metallic glass Ni80P20 [Lamparter] -- Scattering Patterns: • (1) Natural Ni [b = 1.03] • (2) Ni substituted by 62Ni [b = -0.87] • (3) Natural Ni substituted by null scattering mixture [b = 0]

  39. S(Q) with various Niatom replacements Yields Partial Structure Factors Amorphous Ni80P20 Isotopic Substitution Patterns [Lamparter] Null Ni ampl.

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