Introduction to Neutron (and X-ray) 

Scattering Techniques 

Jeffrey Lynn

NIST Center for Neutron Research

FQM School

January, 2018
Outline

• Scattering Basics

– Cross sections, form factors, x-rays vs. neutrons

• Powder Diffraction (crystal and magnetic diffraction)

– Profile refinement, subtraction technique, polarized neutrons

• Single Crystal Diffraction (structure and magnetic)

• Small Angle Neutron Scattering (SANS)

– Nanoparticles, Vortex lattice, ferromagnetic superconductor, 

skyrmions

• Reflectometry (thin films and multilayers)

– Structural and Magnetic Depth Profile

• Inelastic Scattering

– Phonons, Magnons, Spin Ice, Spin Liquid

• Reference Materials
Main Message: Neutron (and x-ray) scattering

Neutron scattering experiments measure the flux of neutrons 

scattered by a sample into a detector as a function of the change

in neutron wave vector (Q) and energy (hω).

The expressions for the scattered neutron flux Φ depend on the 

positions and motions of atomic nuclei or unpaired electron spins.

Momentum Energy

hQ = hki - hkf E = Ei - Ef

hkn = h(2π/λn)

Φ provides information about 

all of these quantities! Φ = f{ri

(t), rj(t), Si(t), Sj(t)}

Φ(Q,hω) =

neutrons

sec–cm2

φ

E = h2kn

2/2m
Conservation of 

Momentum and Energy

Q = ki − k f

m

k

m

k

E f i

2 2

2 2 2 2  

∆ = −

QC = τ + q
Reciprocal (Scattering) Space 

Periodic array of atoms

in Real Space

d

2π/d

Real space ↔ Reciprocal (Fourier) Space
Other Probes

Ephoton (keV) = 2.0k =12.4 / λ

2 2 Eelectron (eV) = 3.8k =150 / λ

1 8.06 ( / ) 1 meV cm E hc − =

1meV 11.6 K (k T) =

B

1 / 17.3 ( / ) meV μ B = T E μ B

1meV = 0.2418 THz (E / h)

2 2 Eneutron (meV) = 2.0719k = 81.7968/ λ

λ = 1 Å: En=82 meV; Ep=12,400,000 meV; Ee=150,000 meV

300 K  25 meV
25 K

300 K

2000 K

Φ ~ v3e(-mv2/2kBT)

1

2

3

4

5

6

5 10 15

Neutron velocity v (km/sec)

0

0

Liquid Hydrogen

Heavy Water (D2O)

Hot Graphite

Maxwellian 

Distribution

“Fast” neutrons: v = 20,000 km/sec

Neutron Source: 

Moderation
Neutron and X-ray Scattering

• Both techniques collect data as functions of the energy and the momentum transferred 

from the system to the neutron or photon beam. The resulting five-dimensional data 

sets serve as powerful probes of materials. Elastic scattering elucidates the crystal 

structure, magnetic configuration, direction of the spins, symmetry of the magnetic 

state, spatial distribution of the magnetization density, and dependence of the order(s) 

parameter on thermodynamic fields such as temperature, pressure, magnetic and 

electric fields. Inelastic scattering determines the energies of the fundamental 

excitations which can be used to elucidate the nature, strength, and range of the 

interactions. 

• Both techniques can measure crystal and magnetic structures and their dynamics.

• Neutron advantages:

– Magnetic and structural scattering are comparable in strength; Elastic scattering yields quantitative 

information; energy resolution is orders-of-magnitude better than x-rays; simplicity of sample 

environment; low T accessible. Theory has solid theoretical basis.

• X-ray advantages:

– High Flux  small samples; individual domains, topography; pump probe capability; resonant x-ray 

scattering element specific; magnetic resonant x-ray scattering; RIXS
Neutron Cross Sections
Neutrons and X-rays are Complementary

Nucleus looks like a point particle  b is just a constant independent 

of scattering angle.

Adjacent elements, heavy + light elements, isotope substitution
Neutrons and X-rays are Complementary
Neutron Cross Sections
Magnetic X-ray Cross Sections
Reciprocal Space for Powder

TiAu

glass/fluid/nano/amorphous
The scattered neutron flux Φ(Q,hω) is proportional to the space (r) 

and time (t) Fourier transform of the probability G(r,t) of finding one or 

two atoms (spins) separated by a particular distance (angle) at a 

particular time.

e G r t d rdt i Q r

 t   

( ) 3

2

( , ) ∫∫ ⋅ − ∝

∂Ω∂

∂ Φ ∝ ω

ω

σ

Time space

ω

2π/T

Ε-space

d

Real space

Q

2π/d

Q-space

~1/ξ ~1/Γ

T

Review

time

Φ Φ

ξ Γ
Neutron Scattering Techniques

• Crystallography—powder, single crystal

Atomic positions, site occupancies, lattice parameters, bond distances, meansquare vibrations as a function of T, H, P

• Magnetism

Magnetic structure, order parameter, spin directions, spin density distribution

Phase Transitions and Critical Phenomena (Scaling, Universality)

• Small Angle Neutron Scattering (SANS)

Ferromagnetic Correlations, Vortex Structures, Domain Structures, Grain 

boundaries, twin boundaries, defect structures, nanoparticles, skyrmions, ...

• Thin Film Reflectometry

Density profiles, Magnetic structures, Magnetization profiles, Surface and 

Interface properties (flatness, roughness)

Diffraction
Inelastic Scattering

Lattice Dynamics

Phonon Dispersion, Density of States

Interatomic Force constants

Mean-square vibrations

Diffusion

Spin Dynamics

Magnon Dispersion, Exchange interactions

Magnetic Anisotropy

Magnetic Fluctuation Behavior

Crystal Field Levels

Magnetic-Structural Coupling
May 2017

NIST Center for Neutron Research
RESEARCH PARTICIPANTS
Oak Ridge National Laboratory

High Flux Isotope 

Reactor 

Spallation Neutron 

Source
Different Spectrometers Cover 

Different Regions of Phase Space

Larger “objects” tend to 

exhibit slower motions.
Materials that are both 

Magnetic and 

Superconducting
Magnetic Impurities

Cause Spin depairing

M. B. Maple, Appl. Phys. 9,179 (1976) 

Magnetic Concentration

T

C

Temperature

Field

Magnetic Fields and 

Superconductivity are Antagonists
• Concentrated Magnetic Systems (Exceptions to the Rule!)

C-15 Cubic Laves phase (Ce-Ho)Ru2 (’60’s-’70’s)

• Magnetic Sublattice—Long Range Order

Chevrel Phase DyMo6S8 (’70’s)

• Ferromagnets—Competition & Coexistence

– Chevrel Phase HoMo6(S-Se)8, ErRh4B4 (’70’s – 80’s)

• High TC cuprates—Cu spin order & fluctuations

Cuprates RBa2Cu3O7 [123], R2CuO4 [214] (’80’s→...)

• Borocarbides

– HoNi2B2C, ErNi2B2C (’90’s→...)

• New Ferromagnetic Superconductors 

– Ruthenates RuSr2GdCu2O8, RuSr2(Eu-Ce)2Cu2O10; ZrZn2, UGe2 (2000’s →...)

• Sodium cobaltates (Magnetic, thermoelectric, and Superconducting) 2000’s→...

– NaxCoO2 (+ H20) [just add water for superconductivity !]

• Iron-based superconductors (2008→...)

– R(O1-xFx)FeAs; Sr1-xKxFe2As2; LiFeAs; Fe(Se1-xTex)

– 1:1:1:1 1:2:2 1:1:1 1:1

Magnetic Superconductor History

⇐

• Pure Superconductors (1911→ ...) (k ;- k )

• X Magnetic Impurities X

⇐
Magnetic Structures

Ferromagnet

Antiferromagnet

Spin Density Wave
Magnetic Structures

Ferromagnet

Antiferromagnet

Spin Density Wave
Ferromagnetic Superconductor

RuSr2GdCu2O8

• T(Ru) = 136 K

• T(Superconductivity) = 35 K

• T(Gd) = 2.5 K

• J. W. Lynn, B. Keimer, C. Ulrich, C. Bernhard, and J. L. 

Tallon, Phys. Rev. B61, 14964 (2000)
160Gd order

Phys. Rev. B61, 14964 (2000)

Antiferromagnetic Order
Ru order

Phys. Rev. B61, 14964 (2000)
Magnetic Structure

Phys. Rev. B61, 14964 (2000)

Antiferromagnetic Order

RuSr2GdCu2O8
Chevrel Phase Superconductors

[(HoS8)Mo6 Magnetic Lattice Isolated]

Tsuper = 1.8 K 5.6 K 8.6 K 

Tferro = 0.7 K 0.5 K 0.9 K

Treentrant= 0.7 K < 0 K 0.9 K

HoMo6S8, HoMo6Se8, ErRh4B4
HoMo6S8 Magnetic Diffraction Pattern

Direct Observation of Long Range Ferromagnetic Order in the 

Reentrant Superconductor HoMo6S8, J. W. Lynn, D. E. Moncton, W. 

Thomlinson, G. Shirane and R. N. Shelton, Sol. St. Comm. 26, 493 

(1978).
Small Angle Neutron Scattering
HoMo6S8

Sol. St. Comm. 26, 493 (1978); PRL 46, 368 (1981); 

J. de Physique Lettres 42, L45 (1981); Phys. Rev. B24, 3817 (1981). 

Oscillatory Magnetic State with 

≈200 Å repeat distance
HoMo6S8 Order Parameter

Sol. St. Comm. 26, 493 (1978); Phys. Rev. Lett. 46, 368 (1981); 

J. de Physique Lettres 42, L45 (1981); Phys. Rev. B24, 3817 (1981). 
HoMo6Se8

~100 Å 

(10 nm)

periodicity 

TS=5.6 K

TM=0.5K

J. W. Lynn, J. A. Gotaas, R. W. Erwin, R. A. Ferrell, J. K. 

Bhattacharjee, R. N. Shelton and P. Klavins, 

Phys. Rev. Lett. 52, 133 (1984)
HoMo6Se8

Center for Neutron Research
HoMo6Se8

J. W. Lynn, J. A. Gotaas, R. W. Erwin, R. A. Ferrell, J. K. Bhattacharjee, 

R. N. Shelton and P. Klavins, Phys. Rev. Lett. 52, 133 (1984)
ErNi2B2C Spin Density Wave

TC = 11 K 

TN = 6 K

TM = 2.3 K

T=4.6 K

T=2.6 K

T=1.1 K

0.5

S. -M. Choi, J. W. Lynn, D. Lopez, P. L. Gammel, P. C. Canfield and 

S. L. Bud'ko, Phys. Rev. Lett. 86, 712 (2001)
Spontaneous Vortex Formation
Vortex Matter in Superconductor Nb 

X. S. Ling and S.-R. Park (Brown University)

S.-M Choi, D. Dender and J. Lynn, (NCNR/NIST)

Phys. Rev. Lett. 72, 3413 (1994); 86, 712 (2001); 91, 167003 

(2003).

T=4.6 K 3.05 kG

2.15 kG

1.1 kG

T (K)

H (kG)

Hc2

Hc1

3.75 kG 4.1 K 4.4 K 4.6 K

Real space depiction 

of vortex lattice
Iron-based High TC Superconductors
Crystal Structure of La(O,F)FeAs

Magnetic Order Close to Superconductivity in the Iron-based Layered La(O1-xFx)FeAs

systems, C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff II, J. L. Zarestky, H. A. 

Mook, G. F. Chen, J. L. Luo, N. L. Wang, and P. Dai, 

Nature 453, 899 (2008).
Basic Properties of Iron 

Superconductors

• Parent Materials

– Metallic (poor metal)

– Anisotropic (ranging from 5 – 30)

– Have a structural distortion (T ~ 150 K)

– Fe spins are antiferromagnetically ordered (TN ~ 140 K)

• Superconductors

– TC as high as 56 K in bulk; ~100 K? in thin films

– Anisotropic (but not nearly as much as the cuprates)

– Very high (isotropic) upper critical fields (60 T) 100 T 300 T
Iron-based superconductors under 

Investigation at the NCNR

• FeSe, Fe1+x(Se-Te), KxFe2-ySe2 (1:1) 

• LiFeAs (1:1:1)

• LaO1-xFxFeAs LaOFeAs (1:1:1:1)

• CeO1-xFxFe(As,P) CeOFeAs

• NdO1-xFxFeAs Nd...

• PrO1-xFxFeAs Pr...

• BaFe2As2, SrFe2As2, CaFe2As2 (1:2:2)

• CaFe2As2, Under Pressure; doping 

– http://www/ncnr.nist.gov/staff/jeff
20 40 60 80 100 120 140

0

1000

2000

3000

4000

5000

6000

counts

2θ

CeFeAs0.95P0.05O 

tetragonal

P4/nmm 

175K

Neutron Powder Diffraction 

94.4 95.2

0

1000

counts

2θ

(220)t

(040)O (400)o
Crystal Structure of LaOFeAs
Magnetic Scattering from La(O,F)FeAs

PSD on

BT-7

C. de la Cruz, Q. Huang, J. W. Lynn, J. Li, W. Ratcliff II, J. L. Zarestky, H. A. Mook, G. F. 

Chen, J. L. Luo, N. L. Wang, and P. Dai, 

Nature 453, 899 (2008).
Magnetic Structure of La(O,F)FeAs
Antiferromagnetic Order LaOFeAs
Single Crystal SrFe2As2

Spin and Lattice Structure of Single 

Crystal SrFe2As2, Jun Zhao, W. 

Ratcliff-II, J. W. Lynn, G. F. Chen, J. 

L. Luo, N. L. Wang, Jiangping Hu, 

and Pengcheng Dai, Phys. Rev. B 

78, 140504(R) (2008).
F- doping Phase diagrams

J. Zhao (2008)

J. Zhao, Q. Huang, C. de la Cruz, S. Li, J. W. Lynn, Y. Chen, M. A.

Green, G. F. Chen, G. Li, Z. Li, J. L. Luo, N. L. Wang, and P. Dai, 

Nature Materials 7, 953 (2008).

CeFeAsO1-xFx
F- doping Phase diagrams

(Drew 2009)

SmFeAsO1-xFx

H. Luetkens (2008)

J. Zhao (2008)
Inelastic Scattering

Spin Waves

Low energy spin waves and magnetic interactions in 

SrFe2As2, 

Jun Zhao, Dao-Xin Yao, S. Li, Tao Hong, Y. Chen, S. Chang, 

W. Ratcliff II, J. W. Lynn, H. A. Mook, G. F. Chen, J. L. Luo, 

N. L. Wang, E. W. Carlson, J. Hu, and P. Dai, 

Phys. Rev. Lett. 101, 167203 (2008).
Spin Waves In SrFe2As2

Jun Zhao, Dao-Xin Yao, S. Li, Tao Hong, Y. Chen, S. Chang, W. Ratcliff II, J. W. Lynn, H. A. 

Mook, G. F. Chen, J. L. Luo, N. L. Wang, E. W. Carlson, J. Hu, and P. Dai, Phys. Rev. Lett. 

101, 167203 (2008).
Spin Resonance in Fe(Se0.4Te0.6)

Y. Qiu, W. Bao, Y. Zhao, C. Broholm, V. Stanev, Z. Tesanovic, Y.C. Gasparovic, S. Chang, J. 

Hu, B. Q., M. Fang, and Z. Mao, Phys. Rev. Lett. 103, 067008 (2009).
Spin Resonance Symmetry Crossover

KxFe2−ySe1−zSz

Transition from Sign-reversed to Sign-preserved Cooper-pairing Symmetry in 

Sulfur-doped Iron Selenide Superconductors, 

Qisi Wang, J. T. Park, Yu Feng, Yao Shen, Yiqing Hao, Bingying Pan, J. W. 

Lynn, A. Ivanov, Songxue Chi, M. Matsuda, Huibo Cao, R. J. Birgeneau, D. V. 

Efremov, and Jun Zhao, 

Phys. Rev. Lett. 116, 197004 (2016). 
Spin Resonance Symmetry Crossover
Neutron Investigation of the Magnetic Scattering in an Ironbased Ferromagnetic Superconductor

Jeffrey W. Lynn1, Xiuquan Zhou2, Christopher K. H. Borg2, Shanta R. Saha3, 

Johnpierre Paglione3, and Efrain E. Rodriguez2

(Phys. Rev. B 92, 060510(R) (2015)

The Preparation and Phase Diagram of Superconducting 

(7Li1-xFexOD)FeSe

Xiuquan Zhou2, Christopher K. H. Borg2, Jeffrey W. Lynn1, Shanta R. Saha3, 

Johnpierre Paglione3, and Efrain E. Rodriguez2

J. Materials Chem. C 4, 3934 (2016).

1NIST Center for Neutron Research, Gaithersburg, MD (USA)

2Department of Chemistry and Biochemistry, University of Maryland, College 

Park, MD (USA)

3Department of Physics, University of Maryland, College Park, MD (USA)

7Li1-xFexODFeSe
Coexistence of 3d-ferromagnetism and superconductivity in [(Li1-xFex)OH](Fe1-yLiy)Se, 

Ursula Pachmayr, Fabian Nitsche, Hubertus Luetkens, Sirko Kamusella, Felix Bruckner, 

Rajib Sarkar, Hans-Hennig Klauss, and Dirk Johrendt, Angew. Chem. Int. Ed. 54, 293 (2015)

(Li-Fe)OHFeSe Ferromagnetic Superconductor

TC=43 K

TC=10 K
Coexistence of 3d-ferromagnetism and superconductivity in [(Li1-xFex)OH](Fe1-yLiy)Se, 

Ursula Pachmayr, Fabian Nitsche, Hubertus Luetkens, Sirko Kamusella, Felix Bruckner, 

Rajib Sarkar, Hans-Hennig Klauss, and Dirk Johrendt, Angew. Chem. Int. Ed. 54, 293 (2015)

(Li-Fe)OHFeSe Ferromagnetic Superconductor

TS=43 K

TF=10 K
FeSe Superconducting Layer

Magnetic Layer

Incommensurate Long wavelength 

Ordered state?

Spontaneous Vortex Lattice?

Crystal Structure
X. Dong, H. Zhou, H. Yang, J. Yuan, K. Jin, F. Zhou, D. Yuan, L. Wei, J. Li, X. Wang, G. Zhang,

and Z. Zhao, J. Am. Chem. Soc. 137, 66 (2014); X. F. Lu, et al., Nat. Mat 14, 325 (2015).

Phase Diagram For (Li-Fe)OHFeSe
Neutron Diffraction

7Li1-xFexODFeSe (x ≈ 0.18) 

Neutron

T = 4 K

a= 3.7827(1) Å 

c= 9.1277(3) Å 
X. Dong, H. Zhou, H. Yang, J. Yuan, K. Jin, F. Zhou, D. Yuan, L. Wei, J. Li, X. Wang, G. Zhang,

and Z. Zhao, J. Am. Chem. Soc. 137, 66 (2014).

Phase Diagram
Phase Diagram for Deuterium
Magnetization for Tc = 18 K 

(polycrystalline sample)
Ferromagnetic Magnetization
Neutron Diffraction at 2.5 K
Difference Data (2.5 K – 50 K)
SANS I(5 K) – I(25) K

TC = 18 K
No Applied Magnetic Field
B = 0.4 T
Magnetic Superconductors

Magnetic Superconductors have a rich and interesting 

history, ranging from “shouldn’t have magnetic spins in the 

lattice” to “must have magnetic spins in the lattice” for 

High Tc

The iron-based superconductors exhibit a similar phase 

diagram to the cuprates. The ‘parent’ systems exhibit a 

ubiquitous structural transition, below which long range 

antiferromagnetic occurs. The magnetic energetics is ~200 

meV, also similar to the cuprates. The role of spin 

fluctuations in the superconducting pairing is clear. 
La1-xCaxMnO3 Phase Diagram

S-W. Cheong and C. H. Chen

Colossal Magnetoresistance, Charge Ordering, and Related 

Properties of Manganese Oxides (World Scientific, 1998), 

p. 241 (Ed. by Raveau and Rao)
J. W. Lynn, D. N. Argyriou, Y. Ren, Y. Chen, Y. M. Mukovskii, 

and D. A. Shulyatev, Phys. Rev. B76, 014437 (2007) 
Polaron Dynamics in CMR La0.7Ca0.3MnO3

J. W. Lynn, D. N. Argyriou, Y. Ren, Y. Chen, Y. M. Mukovskii, and D. A. 

Shulyatev, Phys. Rev. B76, 014437 (2007) 
Polarized Neutron Scattering Data (BT7)

Coupled Magnetic and Ferroelectric Hysteresis in Multiferroic Ni3V2O8, I. 

Cabrera, M. Kenzelmann, G. Lawes, Y. Chen, W. C. Chen, R. Erwin, T. R. 

Gentile, J. B. Leao, J. W. Lynn, N. Rogado, R. J. Cava, and C. Broholm, 

Phys. Rev. Lett. 103, 087201 (2009).
Thin Films and Multilayers
Doping Ferromagnetism in 

Antiferromagnetic Manganite Superlattices 

T. S. Santos, B. J. Kirby, S. Kumar, S. J. May, J. A. Borchers, B. B. Maranville, J. Zarestky, 

S. G. E. Te Velthuis, J. van den Brink and A. Bhattacharya, 

Phys. Rev. Lett. 107, 167202 (2011).
Interfacial Magnetism Example

A. J. Grutter, B. J. Kirby, M. T. Gray, C. L. Flint, U. S. Alaan, Y. Suzuki, and J. A. Borchers, 

Phys. Rev. Lett. 115, 047601 (2015).
Spin Ice and Magnetic Monopoles

• Observation of Magnetic Monopoles in Spin Ice, Hiroaki 

Kadowaki, Naohiro Doi, Yuji Aoki, Yoshikazu Tabata, 

Taku J. Sato, J. W. Lynn, K. Matsuhira, and Z. Hiroi, J. 

Phys. Soc. Japan 78, 103706 (2009).

• Quantum Spin Fluctuations in the Spin Liquid State of 

Tb2Ti2O7, H. Kadowaki, H. Takatsu, Y. Tabata, T. J. Sato, 

J. W. Lynn, J. Phys. Cond. Matr. 24, 052201 (2012).

• Quadrupole Order in the Frustrated Pyrochlore

Tb2+xTi2−xO7+y, H. Takatsu, S. Onoda, S. Kittaka, A. 

Kasahara, Y. Kono, T. Sakakibara, Y. Kato, B. Fåk, J. 

Ollivier, J. W. Lynn, T. Taniguchi, M. Wakita, and H. 

Kadowaki, Phys. Rev. Lett. 116, 217201 (2016).
Dy2Ti2O7 Spin Ice

B = 0.5 T T = 0.43
Topological Systems

• Topological RPdBi half-Heusler semimetals: a new family 

of non-centrosymmetric magnetic superconductors, Y. 

Nakajima, R. Hu, K. Kirshenbaum, A. Hughes, P. Syers, 

X. Wang, K. Wang, R. Wang, S. Saha, D. Pratt, J.W. 

Lynn, and J. Paglione, Science Advances 1, e1500242 

(2015).

• Large Anomalous Hall Effect in a Half Heusler

Antiferromagnet, T. Suzuki, R. Chisnell, A. Devarakonda, 

Y.-T. Liu, J. W. Lynn, and J. G. Checkelsky, Nature 

Physics (http://dx.doi.org/10.1038/NPHYS3831).
Na

Mn

O

Polarized beam inelastic scattering

Q || P Q ⊥ P

Amplitude (Higgs) Mode

Rebecca Dally, et al.,

Nature Comm.

(submitted) 

BT-7

α-NaMnO2

magnetic structure
Spin Liquid Scattering in ZnCu3(OD)6Cl2

Tian-Heng Han, Joel S. Helton, Shaoyan Chu, Daniel G. Nocera, Jose A. Rodriguez-Rivera, Collin Broholm, 

and Young S. Lee, Nature 492, 406 (2012).

6 meV

2 meV

3/4 meV

T = 1.6 K

MACS
Fractional Spin Excitations in Yb2Pt2Pb

L. S. Wu, W. J. Gannon, I. A. Zaliznyak, A. M. Tsvelik, M. Brockmann, J.-S. Caux, 

M. S. Kim, Y. Qiu, J. R. D. Copley, G. Ehlers, A. Podlesnyak, M. C. Aronson, 

Science 352, 1690 (2016).
References:

S. W. Lovesey, Theory of neutron scattering from condensed matter, Oxford: 

Clarendon Press - Oxford, 1984.

E. Balcar and S. Lovesey, Theory of Magnetic Neutron and Photon Scattering, 

Oxford: Clarendon Press, 1989.

L. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill and J. van den Brink, 

"Resonant inelastic s-ray scattering studies of elementary excitations," Rev. Mod. Phys., 

vol. 83, p. 705, 2011.

G. E. Bacon, Neutron Diffraction, Third ed., Oxford: Oxford University Press, 1975.

Magnetic Scattering, Jeffrey W. Lynn and Bernhard Keimer, in Handbook of 

Magnetism, ed. by Michael Coey and Stuart Parkin

Neutron Nuclear Properties: 

https://www.ncnr.nist.gov/resources/n-lengths/ 

https://www.ncnr.nist.gov/instruments/magik/Periodic.html

Magnetic Form Factors

https://www.ill.eu/sites/ccsl/ffacts/ffachtml.html

List of publications at http://www.ncnr.nist.gov/staff/jeff