Whats Cool About Neutron Scattering the Basics with

What's Cool About Neutron Scattering -- the Basics with a bias toward Magnetism Jim Rhyne Deputy Director Lujan Neutron Scattering Center Los Alamos National Laboratory Summer Student Lecture Series June 8, 2007 LA-UR-06 -4041

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Magnetism Solves All Your Problems New Physics Here! 3 Ref. Sharper Image, Nov. 2002

On to Neutron Scattering Phenomena Outline -- References • • • Neutron Sources General Concepts of Scattering Diffractometers and Diffraction Magnetic Diffraction Reflectometry Inelastic Scattering • References: – Neutron Diffraction, G. E. Bacon, 5 th 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

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

Sources of neutrons for scattering? Isotope Production WNR Facility Lujan Neutron Scattering Center • Nuclear Reactor Facility Proton Storage Ring 235 – Neutrons produced from fission of U – Fission spectrum neutrons moderated to thermal energies (e. g. with D 20) Proton Radiography – Continuous source – no time structure – Common neutron energies -- 3. 5 me. V < E < 200 me. V 800 Me. V Proton Linear Accelerator • 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

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

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)

Neutron Scattering’s Moment in the Limelight

What is neutron scattering all about? Source Restelli

General Properties of the Neutron u u The kinetic energy of a 1. 8 Å neutron is equivalent to T = 293 K (warm coffee!), so it is called a thermal neutron. The relationships between wavelength (Å) and the energy (me. V), and the speed (m/s, mi/hr) of the neutron are: e. g. the 1. 8 Å neutron has E = 25. 3 me. V 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 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 Very weak additional scattering ( 10 -5) Nuclear, Isotropic, no angular dependent factor Irregular variation with atomic number. Dependent on nuclear structure and only determined empirically by experiment Very large, true absorption much larger than scattering abs 102 - 103 increases with atomic number Solid State Detector, Image Plate Absorption usually very small (exceptions Gd, Cd, B …) and less than scattering abs 10 -1 Property Magnetic Scattering Absorption coefficient Method of Detection Additional scattering by atoms with magnetic moments (same magnitude as nuclear scattering) Amplitude of scattering falls off with increasing [sin ]/ 13 Proportional 3 He counter

Golden Rule of Neutron Scattering u We don’t take pictures of atoms! Atoms in fcc crystal neutron scatterers – we live in reciprocal space Intensity u Job preservation for 14

How are neutrons scattered by atoms (nuclei)? u Short-range scattering potential: The quantity “b” (or f) is the strength of the potential and is called the scattering lengt u Thus “b” varies over N nuclei – can find average defines coherent scattering amplitude leads to diffraction – turns on o u But what about deviations from average? This defines the incoherent scattering u u Incoherent scattering doesn’t depend on Bragg diffrac. condition, thus has no angular 15

Scattering of neutrons by nuclei u u A single isolated nucleus will scatter neutrons with an intensity (isotropic) – I = I 0 [4 b 2] where I 0 = 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 u 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 Factors f, cont’d u u 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) For neutrons conventionally f = b Shaded (negative) --> phase change 18 (Scattering length - constant for an element)

Magnetic Powder Diffraction u u 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 u Magnetic scattering comes from polarized spins (e. g. , 3 d [Fe] or 4 f [RE]) not from nucleus -- Therefore scattering amplitude is Q-dependent (like for x-rays) via f u u at Q = 0 for Fe = g. J = 2. 2 Bohr magnetons p = 0. 6 (comparable to nuclear b = 0. 954) all in units of 10 -12 cm Refinement gives moment magnitudes on each site and x, y, z components (if symmetry permits) Mn+2 19

Form Factors u Experimental u Calculated More Localized Moment Less Localized Moment 20

Magnetic Powder Diffraction II u In diffraction with unpolarized neutrons (polarized scattering is a separate topic) the nuclear and magnetic cross sections are independent and additive: u q 2 is a “switch” reflecting fact that only the component of the magnetic moment scattering vector K (or Q) contributes to the scattering K 21

Basic Types of Magnetic Order and Resulting Scattering u Ferromagnet (parallel spins) – Single Magnetic site (e. g. , Fe, Co, Tb) – Scattering only at Bragg peak positions (adds to nuclear), but not necessarily all (q 2 switch) a u 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) c – Multi Site Ferromagnet (e. g. Y 6 Fe 23 (4 distinct Fe sites) -- no new peaks in scattering – Overall net magnetic moment adds 22 to 0 [job security for neutrons!!]

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

Ga 1 -x. Mnx. As • 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 k. Oe (in plane) J. Blinowski et al, Phys. Rev. B 67, 121204 (2003)

Ga 1 -x. Mnx. As As-Grown & Annealed t = 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 N 2 during annealing)

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

Triple Axis Neutron Scattering Spectrometer Want Thermal neutrons e. g. , E=14 mev, =2. 4Å i = 2 dmsin m |ki| = 2 / i f = 2 dasin a |kf| = 2 / f 27

MURR Triple Axis Neutron Spectrometer (TRIAX) Analyzer Assembly Beam Stop (pivots with drum and sample) Detector Shield and Collimator Sample Table and Goniometer Monochromator 28 Drum

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SUPPLEMENTARY SLIDES 33

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Using Powder Diffraction Input Information -- Structure Determination u Know instrument-dependent scattering line-shape – Gaussian for fixed – Convolution of rising and falling exponentials with Gaussian for TOF – Sample distortions (pseudo Voigt) linear comb. of Lorentzian and Gaussian u u Know or parameterize resolution and background functions Know Space Group (or a limited # choices) [coordinates of atoms in cell - may be variables x, y, z] (Von. Dreele, Jorgensen & Windsor) 35