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

Magnetism Solves All Your Problems New Physics Here! 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, 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

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? Lujan Neutron Scattering Center WNR Facility Proton Radiography 800 MeV Proton Linear Accelerator Isotope Production Facility Proton Storage Ring 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

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

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? Restelli Source

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).

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  

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

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)

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

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)

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)

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 polarized spins (e.g., 3d [Fe] or 4f [RE]) not from nucleus -- Therefore scattering amplitude is Q-dependent (like for x-rays) via f at Q = 0 for Fe  = gJ = 2.2 Bohr magnetons p = 0.6 (comparable to nuclear b = 0.954) all in units of 10-12cm Refinement gives moment magnitudes on each site and x,y,z components (if symmetry permits) Mn+2

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

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 K 

Basic Types of Magnetic Order and Resulting Scattering 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!!] a c

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

Ga1-xMnxAs 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) J. Blinowski et al, Phys. Rev. B 67, 121204 (2003)

Ga1-xMnxAs 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 N2 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=14mev, =2.4Å i = 2dmsin m |ki| = 2/i f = 2dasina |kf| = 2/f

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

SUPPLEMENTARY SLIDES

Using Powder Diffraction Input Information -- Structure Determination 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 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] (VonDreele, Jorgensen & Windsor)