By
Roger Pynn*
Los Alamos National Laboratory and University of California at Santa Barbara
*With contributions from B. Farago (ILL), S. Longeville (Saclay), and T. Keller (Stuttgart) Ne utro ns in Co n de ns e d Matte r Re s e arc h
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S pPaSllSa t-i oCnh o- pCpheorp Sppeer ctro meter N eutron ILL - w itho u t s pin -ec ho Induced Itine rant Hyd rog en Excitations ILL - w ith s p in -e ch o Magnets 100 Modes Crystal Momentum Elastic Scattering Fields Distributions Molecular Coherent Spin Vibrations M odes in Wa ves Glasses La ttice Vibra tions ) and Liquids and V Elec tron-
e 1 Molecular phonon A nharmonicity
m Intera ctions
( M otions [Larger Objects Resolved] Accurate Liquid Structu res r Metallu rgical C rystal and Mem branes e Micelles Polymers Systems Magnetic Amorphous Precision Crystallography f Proteins Systems s Proteins in Solution Colloids Structures Anharmonicity n
a Viruses Critic al r Sca ttering Slower T 0.01 M otions y
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n Aggregate Modes E Motion Polymers Molecular and Reorie nta tion 10-4 Biological Tunneling Systems Spectroscopy
Surface Effects ?
10-6 0 .0 01 0.01 0 .1 1 10 100 -1 Q (Å ) Neutron Spin Echo has significantly extended the (Q,E) range to which neutron scattering can be applied The Underlying Physics of Neutron Spin Echo (NSE) Technology is Larmor Precession of the Neutron’s Spin
• The time evolution of the expectation value of the spin of a spin-1/2 particle in a magnetic field can be B determined classically as: r ds r r = gs Ù B Þ w = g B s dt L g = -2913 * 2p Gauss -1.s -1
• The total precession angle of the spin, f, depends on the time
the neutron spends in the field: f = w Lt
3 -1 -1 B(Gauss) wL (10 rad.s ) N (msec ) Turns/m for 4 Å neutrons 10 183 29 ~29 How does a Neutron Spin Behave when the Magnetic Field Changes Direction?
When H rotates with
frequency w, H0->H1 ->H2…, and the spin trajectory is described by a cone rolling on the plane in which H moves
• Distinguish two cases: adiabatic and sudden • Adiabatic – tan(d) << 1 – large B or small w – spin and field remain co-linear – this limit used to “guide” a neutron spin • Sudden – tan(d) >> 1 – large w – spin precesses around new field direction – this limit is used to design spin-turn devices Larmor Precession allows the Neutron Spin to be Manipulated using Spin-Turn Coils (p or p/2)
• The total precession angle of the spin, f, depends on the time the neutron spends in the B field
f = w Lt = gBd / v
d
Neutron velocity, v
B
1 Number of turns = .B[Gauss].d[cm].l[Angstroms] 135.65 Thin Magnetic Films used as p/2 and p Rotators
Hg Hg
1
1 M 0.5 0.5 M 0
-1 0 -0.5 -0.5 -1 -0.5 0 -1 -0.5 -1 0 0.5 -0.5 0 -1 gMd 0.5 0.5 -1 f = 1 -0.5 1 0 0.5 1 1 vsin c
H Hg g M M M c v d c neutron neutron 30 m Permalloy (Ni0.8 Fe0.2) Films on Silicon Wafers used as Spin Turn Devices In NSE*, Neutron Spins Precess Before and After Scattering & a y Polarization Echo is Obtained if Scattering is Elastic x z p/2 p/2 F S p F S
Allow spins to Rotate spins Elastic Initially, precess around z: to z and Scattering neutrons slower neutrons measure Event are polarized precess further over polarization along z a fixed path length
Rotate spins Rotate spins into Allow spins to precess through p about x-y precession plane around z: precession angle x axis of all neutrons is the same Final Polarization, P = cos(f1 -f2 ) at echo point if DE = 0 * F. Mezei, Z. Physik, 255 (1972) 145 For Quasi-elastic Scattering, the Measured Neutron Polarization depends on Energy Transfer • If the neutron changes energy when it scatters, the precession
phases before & after scattering, f1 & f2, will be different: 1 using hw = m(v2 - v2 ) » mvdv 2 1 2 æ 1 1 ö gBd gBdhw gBdm2l3w f -f = gBdç - ÷ » dv » = 1 2 ç ÷ 2 3 2 è v1 v2 ø v mv 2ph
• To lowest order, the difference between f1 & f2 depends only
on w (I.e. v1 – v2) & not on v1 & v2 separately
• The measured polarization,
, is the average of cos(f1 - f2) over all transmitted neutrons I.e. r òò I(l)S(Q,w)cos(f1 -f2 )dldw P = r òò I(l)S(Q,w)dldw Neutron Polarization is Measured using an Assymetric Scan around the Echo Point
r òò I(l)S(Q,w)cos(f1 -f2 )dldw r r P = r » S(Q,w) cos(wt )dw = I(Q,t) I (l)S(Q,w)dldw ò òò Bd l t m2 where the "spin echo time" t = gBd l3 (T.m) (nm) (ns) 2 2ph 1 0.4 12 1 0.6 40 2000 1 1.0 186
1500 The echo amplitude decreases
1000 when (Bd)1 differs from (Bd)2 because the incident neutron 500
Neutron counts ( per 50 sec) beam is not monochromatic. 0 0 1 2 3 4 5 6 7 For elastic scattering: Current in coil 3 égm ù P ~ I(l)cosê {(Bd)1 - (Bd)2}lú.dl ò ë h û What does a NSE Spectrometer Look Like? IN11 at ILL was the First Field-Integral Inhomogeneities cause t to vary over the Neutron Beam: They can be Corrected • Solenoids used as main precession fields have fields that vary as r2 away from the axis of symmetry because of end effects (div B = 0)
• According to Ampere’s law, a current distribution that varies as r 2 can correct the field-integral inhomog- eneities for parallel paths • Similar devices can be used to correct the integral along Fresnel correction coil for IN15 divergent paths Neutron Spin Echo study of Deformations of Spherical Droplets*
* Courtesy of B. Farago The Principle of Neutron Resonant Spin Echo B • Within a coil, the neutron is subjected to a 0
steady, strong field, B0, and a weak rf field B1(t) B1cos(wt) with a frequency w = w0 = g B0
• Typically, B0 ~ 100 G and B1 ~ 1 G
• In a frame rotating with frequency w0, the neutron spin sees a constant field of magnitude B1 • The length of the coil region is chosen so that the neutron spin
precesses around B1 thru an angle p. • The neutron spin angle changes by
2wt0 + wd/v
wt0 wt0 B1 Neutron Spin PhasesNRSE spectrometer in an NRSE Spectrometer* A B C D
Sample B= B=0 B=0 n 0 B0 B0 B0 B0 B=0 + + + + + + + +
d lAB d d lCD d t t t t A A’ t tB C C’ t tD
Echo occurs for elastic scattering when
lAB + d = lCD + d
* Courtesy of S. Longeville The Measured Polarization for NRSE is given by an Expression Similar to that for Classical NSE • Again, we assume that v’ = v + dv with dv small and expand to lowest order, giving: r òò I(l)S(Q,w)cos(wt NRSE )dldw P = r òò I(l)S(Q,w)dldw 2 m 3 where the "spin echo time" t NRSE = 2gB0 (l + d) l 2ph 2 • Note the additional factor of 2 in the echo time compared with classical NSE (a factor of 4 is obtained with “bootstrap” rf coils) • The echo is obtained by varying the distance, l, between rf coils • In NRSE, we measure neutron velocity using fixed “clocks” (the rf coils) whereas in NSE each neutron “carries its own clock” whose (Larmor) rate is set by the local magnetic field An NRSE Triple Axis Spectrometer at HMI: Note the Tilted Coils Measuring Line Shapes for Inelastic Scattering
• Spin echo polarization is the FT of w scattering within the spectrometer transmission function • An echo is obtained when Q d é (Bd) (Bd) ù N N 1 - 2 = 0 Þ 1 = 2 ê ú 2 2 dk1 ë k1 k2 û k1 k2 • Normally the lines of constant spin- w echo phase have no gradient in Q,w space because the phase depends only on k Q • The phase lines can be tilted by using “tilted” precession magnets By “Tilting” the Precession-Field Region, Spin Precession Can Be Used to Code a Specific Component of the Neutron Wavevector
d k If a neutron passes through a // k rectangular field region at an c angle, its total precession phase k ^
will depend only on k^.
w L = gB
d KBd B f = w Lt = gB = vsin c k^ Stop precession here -1 with K = 0.291 (Gauss.cm.Å) Start precession here “Phonon Focusing”
• For a single incident neutron wavevector, kI, neutrons are scattered to kF by a phonon of frequency wo and to kf by neighboring phonons lying on the “scattering surface”. • The topology of the scattering surface is related to that of the phonon dispersion surface and it is locally flat • Provided the edges of the NSE precession field region are parallel to the scattering surface, all neutrons with scattering wavevectors on the scattering surface will have equal spin-echo phase Q0 scattering surface
kF k Precession field region kI f
kf^ “Tilted Fields”
• Phonon focusing using tilted fields is available at ILL and in Japan (JAERI)….however, • The technique is more easily implemented using the NRSE method and is installed as an option on a 3-axis spectrometers at HMI and at Munich • Tilted fields can also be used can also be used for elastic scattering and may be used in future to: – Increase the length scale accessible to SANS – Separate diffuse scattering from specular scattering in reflectometry – Measure in-plane order in thin films – Improve Q resolution for diffraction An NRSE Triple Axis Spectrometer at HMI: Note the Tilted Coils Nanoscience & Biology Need Structural Probes for 1-1000 nm
CdSe nanoparticles Peptide-amphiphile nanofiber
10 nm holes in PMMA
1m 2m 10m
Actin Si colloidal crystal Structures over many length Thin copolymer films scales in self-assembly of ZnS and cloned viruses “Tilted” Fields for Diffraction: SANS d c q c B B p/2 p p/2 f1 f2
• Any unscattered neutron (q=0) experiences the same precession angles
(f1 and f2) before and after scattering, whatever its angle of incidence • Precession angles are different for scattered neutrons
KBd KBd é KBd cos c ù and cos( ) cos f1 = f2 = Þ f1 -f2 » ê 2 q ú k sin c k sin( c +q) ëê k sin c ûú é KBd cos c ù P = dQ.S(Q).cos Q Polarization proportional to ò ê 2 2 ú ëê k sin c ûú Fourier Transform of S(Q)
Spin Echo Length, r = KBd cos c /(k sin c)2 How Large is the Spin Echo Length for SANS?
Bd/sinc l c r (Gauss.cm) (Angstroms) (degrees) (Angstroms)
3,000 4 20 1,000
5,000 4 20 1,500
5,000 6 20 3,500
5,000 6 10 7,500
It is relatively straightforward to probe length scales of ~ 1 micron Using “Sign Reversal” to Implement Angle Coding An element that performs a p rotation about an axis in the precession plane changes the sign of prior precession angles
f = 0….f1…-f1..(f2-f1)… f f f f f f f p neutron 1 2 3 4 5 6
Start p p p p p precession precession plane Net Precession = - f1 + f2 – f3 + f4 – f5 + f6
• Total net precession angle = (f4 + f5 + f6) – (f1 + f2 + f3) + 2(f2 – f5) • The first two terms depend on neutron velocity only, last term depends on velocity and angle of neutron trajectory – Requires suitably oriented planar p rotators (flippers) • Can be set up to encode two, mutually perpendicular, trajectory angles Conclusion: NSE Provides a Way to Separate Resolution from Monochromatization & Collimation
• The method currently provides the best energy resolution for inelastic neutron scattering (~ neV) – Both classical NSE and NRSE achieve similar energy resolution – NRSE is more easily adapted to “phonon focusing”
• The method is likely to be used in future to improve (Q) resolution for elastic scattering – Extend size range for SANS (“rescue” scattering from the beam-stop region) – May allow 100x gain in measurement speed for SANS – Separate specular and diffuse scattering in reflectometry – Measure in-plane ordering in thin films (Felcher)