1. 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

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

4. 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

5. 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

6. 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

7. 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 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

8. 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

9. 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)

10. Neutron Scattering’s Moment in the Limelight

11. What is neutron scattering all about?
Restelli
Source

12. 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).

13. 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 
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

14. 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

15. 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)

16. 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

17. 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)

18. 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)

19. 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

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

21. 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 

22. 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

23. 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

24. 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, (2003)

25. 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)

26. 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

27. 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

28. 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

33. SUPPLEMENTARY SLIDES

35. 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)