Roger Pynn. Lectures 11: Neutron Spin Echo

Transcription

1 by Roger Pynn Lectures : Neutron Spin Echo

2 The Goal of Neutron Spin Echo is to Break the Inverse Relationship between Intensity & Resolution Traditional define both incident & scattered wavevectors in order to define E and Q accurately Traditional use collimators, monochromators, choppers etc to define both k i and k f NSE measure as a function of the difference between appropriate components of k i and k f (original use: measure k i k f i.e. energy change) NSE use the neutron s spin polarization to encode the difference between components of k i and k f NSE can use large beam divergence &/or poor monochromatization to increase signal intensity, while maintaining very good resolution

3 The Principles of NSE are Very Simple If a spin rotates anticlockwise & then clockwise by the same amount it comes back to the same orientation Need to reverse the direction of the applied field Independent of neutron speed provided the speed is constant The same effect can be obtained by reversing the precession angle at the mid-point and continuing the precession in the same sense Use a π rotation If the neutron s velocity, v, is changed by the sample, its spin will not come back to the same orientation The difference will be a measure of the change in the neutron s speed or energy

4 In NSE*, Neutron Spins Precess Before and After Scattering & a y Polarization Echo is Obtained if Scattering is Elastic z x π/ F S π/ π F S Initially, neutrons are polarized along z Allow spins to precess around z: slower neutrons precess further over a fixed path-length Elastic Scattering Event Rotate spins to z and measure polarization Rotate spins into x-y precession plane Final Polarization, P = cos( φ φ) Rotate spins through π about x axis Allow spins to precess around z: all spins are in the same direction at the echo point if ΔE = 0 * F. Mezei, Z. Physik, 55 (97) 45

5 For Quasi-elastic Scattering, the Echo Polarization depends on Energy Transfer If the neutron changes energy when it scatters, the precession phases before & after scattering, φ & φ, will be different: To lowest order, the difference between φ & φ depends only on ω (I.e. v v ) & not on v & v separately The measured polarization, <P>, is the average of cos(φ - φ ) over all transmitted neutrons I.e. 3 3 ) ( using h Bdm mv Bd v v Bd v v Bd v mv v m v π ω λ γ ω γ δ γ γ φ φ δ ω = = = h h = ω λ ω λ ω λ φ φ ω λ d d Q S I d d Q S I P ), ( ) ( ) )cos(, ( ) ( r r

6 Neutron Polarization at the Echo Point is a Measure of the Intermediate Scattering Function r I( λ) S( Q, ω)cos( φ φ ) dλdω r P = r S( Q, ω)cos( ωτ ) dω I( λ) S( Q, ω) dλdω Bd m 3 where the "spin echo time" τ = γbd λ (T.m) πh I(Q,t) is called the intermediate scattering function Time Fourier transform of S(Q,ω) or the Q Fourier transform of G(r,t), the two particle correlation function NSE probes the sample dynamics as a function of time rather than as a function of ω The spin echo time, τ, is the correlation time r = I(Q,τ) λ (nm) τ (ns) 40 86

7 What does a NSE Spectrometer Look Like? IN at ILL was the First

8 Neutron Polarization is Measured using an Asymmetric Scan around the Echo Point Echo Point Neutron counts ( per 50 sec) Bd Current in coil 3 (Arbitrary Units) The echo amplitude decreases when (Bd) differs from (Bd) because the incident neutron beam is not monochromatic. For elastic scattering: γm P ~ I( λ)cos. h {( Bd) ( Bd) } λ dλ Because the echo point is the same for all neutron wavelengths, we can use a broad wavelength band and enhance the signal intensity

9 Field-Integral Inhomogeneities cause τ to vary over the Neutron Beam: They can be Corrected Solenoids (used as main precession fields) have fields that vary as r away from the axis of symmetry because of end effects (div B = 0) solenoid B According to Ampere s law, a current distribution that varies as r can correct the field-integral inhomogeneities for parallel paths Similar devices can be used to correct the integral along divergent paths Fresnel correction coil for IN5

10 Neutrons in Condens ed Matter Res earch 0000 Energy Transfer (mev) Spallation SPSS - Chopper - Chopper Spectrometer ILL - w ithou t s pin -ec ho ILL - with s pin-ech o Elastic Scattering [Larger Objects Resolved] Micelles Polymers Proteins in Solution Viruses Metallurgical Systems Colloids Aggregate Motion Polymers and Biological Systems Coherent Modes in Glasses and Liquids Molecular Motions Membranes Proteins Critical Scattering Diffusive Modes Spin Waves Electronphonon Interactio ns Crystal and Magnetic Structures Crystal Fields Slower Motions Resolved Molecular Reorientation Tunneling Spectroscopy Itinerant Magnets Hydrogen Modes Mo lecu lar Vibrations Lattice Vibrations and Anharmonicity Amorphous Systems Neutron Induced Excitations Momentum Distributions Accurate Liquid Structures Precision Crystallography Anharmonicity Surface Effects? Q (Å - ) Neutron Spin Echo has significantly extended the (Q,E) range to which neutron scattering can be applied

11 Neutron Spin Echo study of Deformations of Spherical Droplets* * Courtesy of B. Farago

12 The Principle of Neutron Resonant Spin Echo Within a coil, the neutron is subjected to a steady, strong field, B 0, and a weak rf field B 0 B cos(ωt) with a frequency ω = ω 0 = γ B 0 Typically, B 0 ~ 00 G and B ~ G B (t) In a frame rotating with frequency ω 0, the neutron spin sees a constant field of magnitude B The length of the coil region is chosen so that the neutron spin precesses around B thru an angle π. The neutron precession phase is: φ exit neutron = φ = φ exit RF entry RF + ( φ φ entry RF φ entry neutron entry neutron + ω 0 ) d / v S entry S exit rotated S π exit B entry B

13 t B = t A + l AB +d v B t B 0 = t A + l AB +d v B'!t B!t A +! d v B 0! l AB +d v!t t C!t C! l AB +d v C t C 0 = t C + d v!t C 0! d v 0!t C! l AB +d v C' D = t C + l CD+d v 0!t D! d v 0!t C! l AB +d v t t D 0 = t C + l CD+d v 0!t D 0!( l AB +d v D' l CD+d v 0 ) Neutron Spin Phases NRSE spectrometer in an NRSE Spectrometer* A B C D n B= B=0 B 0 B 0 Sample B=0 B0 B0 B= d l AB d d l CD d t A t A t t B t C t C t t D Table. Spin orientation t Phase field B r neutron Spin phase S Time t A!t A 0 A t A 0 = t A + d v!t A 0!t A +! d v A' Echo occurs for elastic scattering when l AB + d = l CD + d D * Courtesy of S. Longeville

14 H = 0 Just as for traditional NSE, if the scattering is elastic, all neutron spins arrive at the analyzer with unchanged polarization, regardless of neutron velocity. If the neutron velocity changes, the neutron beam is depolarized

15 The Measured Polarization for NRSE is given by an Expression Similar to that for Classical NSE Assume that v = v + δv with δv small and expand to lowest order, giving: P = r I( λ) S( Q, ω)cos( ωτ NRSE ) dλdω r I( λ) S( Q, ω) dλdω where the "spin echo time" τ NRSE = γb Note the additional factor of 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 0 ( l m + d) πh λ 3

16 An NRSE Triple Axis Spectrometer at HMI: Note the Tilted Coils

17 Measuring Line Shapes for Inelastic Scattering Spin echo polarization is the FT of scattering within the spectrometer transmission function ω An echo is obtained when d dk ( Bd) k ( Bd) k = 0 N k = N k Q Normally the lines of constant spinecho phase have no gradient in Q,ω space because the phase depends only on k The phase lines can be tilted by using tilted precession magnets ω Q

18 By Tilting the Precession-Field Region, Spin Precession Can Be Used to Code a Specific Component of the Neutron Wavevector If a neutron passes through a rectangular field region at an d k // k angle, its total precession phase χ k will depend only on k. ω L = γb φ = ω t L = γb d = vsin χ KBd k B with K = 0.9 (Gauss.cm.Å) - Stop precession here Start precession here

19 Phonon Focusing For a single incident neutron wavevector, k I, neutrons are scattered to k F by a phonon of frequency ω o and to k f 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 Q 0 scattering surface k I k F k f Precession field region k f

20 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

21 An NRSE Triple Axis Spectrometer at HMI: Note the Tilted Coils

22 Nanoscience & Biology Need Structural Probes for -00 nm CdSe nanoparticles Peptide-amphiphile nanofiber 0 nm holes in PMMA μ μ 0μ Actin Si colloidal crystal Structures over many length scales in self-assembly of ZnS and cloned viruses Thin copolymer films

23 Tilted Fields for Diffraction: SANS B χ χ π/ π φ π/ φ B d θ Any unscattered neutron (θ=0) experiences the same precession angles (φ and φ ) before and after scattering, whatever its angle of incidence Precession angles are different for scattered neutrons φ = P = KBd KBd and φ = k sin χ k sin( χ + θ ) KBd cos χ dq. S( Q).cos Q k sin χ cos( φ φ ) KBd cos χ cos θ k sin χ Polarization proportional to Fourier Transform of S(Q) r = KBd cos χ /( k sin χ) Spin Echo Length,

24 NSE Angle Coding Illustrated for SANS Make the number of spin precessions depend on the neutron s direction of travel instead of (only) its speed.. precession field precession field δθ δθ π/ θ 0 π θ 0 π/ d ω = γb L φ = ω t L φ φ = γb d v sin( θ + δθ ) KλBd cosθ0 π sin θ 0 0 = ( δθ δθ ) KλBd π sin( θ + δθ ) 0 Kλ Bd cosθ0 Q (π sinθ ) 0 = Qζ P / P0 = S( Q)cos( Qζ ) dq / S( Q) dq

25 The Classical Picture of Spin Precession spin polarizer st spin-echo arm sample position nd spin-echo arm +B O -B O spin analyser P = DIFFERENT PATH LENGTHS FOR THE DIFFERENT TRAJECTORIES! Viewgraph sequence by A. Vorobiev

26 spin polarizer Spin Echo Scattering Angle Measurement (SESAME) No Sample in Beam sample position +B O -B O spin analyser 0.5 P DEPOLARIZED i 0.5 BEAM! 0 0 ALL SPINS ARE PARALLEL: FULL POLARIZATION P i = P f SPIN-ECHO 0.5 P f 0 ALL SPINS ARE PARALLEL AGAIN: POLARIZATION IS BACK

27 spin polarizer Spin Echo Scattering Angle Measurement (SESAME) Scattering by the Sample +B O -B O spin analyser 0.5 P i 0 FULL POLARIZATION P i > P f 0.5 P f 0 DEPOLARIZATION!

28 Spin Echo Scattering Angle Measurement (SESAME) Scattering of a Divergent Beam spin polarizer spin analyser +B O -B O 0.5 P i 0 FULL POLARIZATION the same depolarization P i > P f independently of initial trajectory 0.5 P f 0 DEPOLARIZATION!

29 Spin-echo angular encoding: the experiment Θ 0.5 P i 0 FULL POLARIZATION P f P i,0 0,8 0,6 0,4 0.5 P f 0 0, 0, δ~cotθ [nm]

30 How Large is the Spin Echo Length for SANS? Bd/sinχ (Gauss.cm) λ (Angstroms) χ (degrees) r (Angstroms) 3, ,000 5, ,500 5, ,500 5, ,500 It is relatively straightforward to probe length scales of ~ micron

31 HMI Experiments: π/. Precession film 3. Sample 4. π 5. Iron plate

32 High Angular Resolution using SESAME 5 Thin, magnetized Ni 0.8 Fe 0. films on silicon wafers (labelled, & 4) are the principal physical components used for this new method. 3 4 High angular resolution is obtained using Neutron Spin Echo. P/P Patterson function for PS spheres (measurement & theory) Spin Echo Length (nanometers) A 00 nm correlation distance was achieved for SANS intensity off0 on0 offminuson channel omega = 0. degrees Intensity Specular neutron reflection (blue) was separated from diffuse reflection with high fidelity. Black and red data include diffuse scattering PSD Channel Diffuse Specular theta = 0.4 degrees

33 Conclusion: NSE Provides a Way to Separate Resolution from Monochromatization & Beam Divergence 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 I.e. measuring the energy line-widths of phonon excitations The method is likely to be used in future to improve (Q) resolution for elastic scattering Extend size range for SANS (SESANS) May allow x gain in measurement speed for some SANS exps Separate specular and diffuse scattering in reflectometry Measure in-plane ordering in thin films (SERGIS)

34 SESAME Apparatus on ASTERIX 30 μ Permalloy films on Si Eqpt with guide field plates in place Ferrite Magnets V-coils (π/) Mezei flipper (π) Sample

35 Implementation of of polychromatic flipper components V-coil Mezei π- flipper H guide z y I flip H z H y x time

36 Obtaining a Spin Echo Measure flip ratio as a function of flipper position With π flipper set to echo position, incline st Py film, then measure flip ratio as a function of nd film angle 4 Calculated result allows SEL to be related to lamda

37 Measurement of Dilute 96 nm-diameter Polystyrene Spheres in 3: D O/H O SESAME measures the (Q) Fourier transform of S(Q) Single Foil; 96 nm diamter PS spheres in DO/H0 3/ G( Z) G(0) = σt; P P 0 = e λ = dq y 4π S G( Z ) G(0) dq dσ ( Q G(z ) = 0, Q ) cos( Q Z) For hard spheres G(z) can be calculated exactly (black lines in figures) z S y dω z z P/P red line -- smoothed data black line -- theory - no resolution large black dots -- theory including resolution Spin Echo Length (Angstroms) Double Foil; 96 nm diamter PS spheres in DO/H0 3/ In our measurement, slits cut off the scattered intensity, so we had to include this effect in the calculated Fourier transform (black dots) P/P red line -- smoothed data black line -- theory - no resolution large black dots -- theory including resolution The SEL range corresponds to 4 Å < λ < 8.5 Å xsi (Angstroms)

38 Conclusions from Precession Film Experiments SESAME can be implemented using thin magnetic films at either CW or pulsed neutron sources Particularly good for pulsed source because spin echo length is scanned by λ Spin echo lengths up to ~ 50 nm are not hard to achieve using cold neutrons Precession fields are large (~ T) so only thin films are needed Precession field boundaries are well-defined The method has several limitations; 30 μ 00 μ Permalloy films are not readily available Film thickness homogeneity is a limitation (5-0% by electro-deposition) Small film inclinations are needed for large spin echo lengths => large films for reasonable neutron beam size Film transmission losses increase as spin echo length goes up

39 An Optical Analogy z Glass Slab: n = n 0 ; dn/dλ = - d Glass Slab with anomalous dispersion; n = n 0 ; dn/dλ = d The spatial separation, z, of the red and blue rays depends on: (a) dn/dλ; (b) the glass thickness; (c) the inclination of the slab

40 A Better Method? A better method is to use separated π flippers Implemented at Delft using thin Py films as flippers Implemented on EVA using NRSE NRSE is clumsy to pulsed sources Try triangular cross section solenoids Stay tuned.. L = mm π/ π/ π 00 mm neutron

41 Increasing the Spin Echo Length d Cutting the slab into prisms allows the spatial separation of red and blue rays to be controlled by the separation of the prisms Adding prisms with the opposite dispersion increases the separation of the red and blue rays

42 We Can Clearly Do This With Neutrons + + We can add and subtract rectangular field regions without affecting the dispersion of spin states This leaves us with a slab with twice the magnetic field We can make the slab as thick as we like by choosing the separation of the prisms along the beam line

43 We Can Do the Same Thing With Neutrons + ve magnetic field sample ve magnetic field z Prepare neutrons in a mixture of eigenstates > + > The two, correlated spin states of a neutron can be separated in space by a magnetic field with inclined boundaries When the states are recombined, they provide information about correlations between scattering events that are separated by the spin echo length, z

44 Geometry at grazing incidence α f ϕ Resolve with PSD Resolve with Spin Echo α f tight collimation coarse collimation ϕ y z x α i q x = (π/λ)( cosα f -cosα i ) q y = (π/λ) sinϕ

45 Grazing incident geometry TOP VIEW incident Θ Y +B Z X -B specular direct incident α i SIDE VIEW Z + B - B Y X specular α f = α i α f = -α i direct THE SAME POLARIZATION IN DIRECT AND SPECULAR BEAMS

46 Dewetting of polymer-blend films from Silicon AFM picture of drops of d-polystyrene/ polyparamethylstyrene on silicon Zoomed AFM picture Model of scattering length densities as seen by X-rays(GISAXS) Model of scattering length densities as seen by neutrons (GISANS) A comparative study of P. Müller-Buschbaum et al., Physica B83,53 (000)

47 a) scattering geometry. The incident beam (I) impinges on the sample surface at a shallow angle α i ; transmitted (T), specular (S) and diffuse (Y) intensities are simultaneously recorded by PSD. b) Image taken by -dimensional PSD during real experiment. The size of the incoming beam at the sample position was 30 mm.

48 Diffraction figure in transmission and reflection geometry q x q y Transmission Reflection cosϑ f -cosϑ i cosϑ f cosϕ -cosϑ i sinϑ f sinϕ cosϑ f sinϕ GISANS from copolymer droplets D(ILL), 8 hours q z sinϑ I + sinϑ f cosϕ sinϑ f + sinϑ i

49 SERGIS results: PpMS (polyparamethylstryrene):dps BLEND 3: P. Müller-Buschbaum et al. J. Phys.: Cond. Mat. 7 (005) S363 S386 GISAXS, SERGIS,0 P exp P R 0,8 0,6 SFM: Λ ~ h pancake-type droplets GISANS: no internal regular phase separation 0, L SE, nm

50 SERGIS results: Diblock Copolymer poly(styren-block-paramethylstryrene) P (S-bpMS) P. Müller-Buschbaum et al. J. Phys.: Cond. Mat. 7 (005) S363 S386 P exp P R,,0 0,8 0,6 SERGIS SFM: Λ ~ h spherical droplets GISANS: regular phase separation 0,4 0, 0, L SE, nm

51 EXPERIMENTAL DATA AND CALCULATED CORRELATION FUNCTIONS BLEND SAMPLE DIBLOCK COPOLYMER L=5 nm d=490 nm d=580 nm l DB =65 nm polarization hight, arb. un y, nm y, nm hight, arb. un. polarization y, nm y, nm

52 Measuring Correlations in Space & Time B π/ π π/ θ solenoid B 0 B 0 L solenoid - + d Use space and time resolving NSE simultaneously Large (~ T.m) solenoidal field: τ = 86 B 0.L. λ 3 ns (λ in nm) Triangular solenoids (~ 0.0 T): r = 47,000 B.d cot θ. λ nm At a reactor source, we could set r and τ independently At a pulsed source we could keep B λ constant by varying B with time after a pulse: TOF then maps out τ This would be a completely different way of measuring structural correlations using scattering (r,τ) instead of (Q,ω)

53 Preliminary Tests have been Carried Out Tests by Mezei, Farago and Falus on IN 5 at ILL Did not use triangular coils but current-carrying aluminum plates, perpendicular to the neutron beam, just inside main precession solenoids π/ π π/ Aluminum plate sample solenoid The length scale accessible on IN5 could be increased by a factor of 0 while keeping the usual dynamical range in time. The resolution function was a product: P (r)p (τ) Could scan τ from 5% to 00% of maximum value without depolarization independent of current in the sheets

54 Spin Echo Polarization versus r: P (r) The relatively rapid decrease of P(r) with r is not yet understood Fourier distance r [Å] Normalized NSE signal P(r) Current in field tilt sheets [A] Stay tuned.

55 Summary of NSE Field boundaries perpendicular to the neutron beam code neutron s speed (not it s trajectory) Correlation time (up to ~ 300 ns on IN5) scales as λ 3 Field boundaries inclined to neutron beam code neutron s trajectory Correlation length (also called the spin echo length) scales as λ Up to 5 microns correlation length has been achieved (Delft) Neither method requires highly collimated or monochromatic neutron beams NSE is suitable for long correlation times or large length scales typical of soft materials such as complex fluid films

56 Collaborators Experiments at HMI, Berlin Mike Fitzsimmons, LANL Helmut Fritzsche, Chalk River Marita Gierlings, HMI Janos Major, MPI, Stuttgart Experiments at LANSCE Mike Fitzsimmons, LANL Gian Felcher, ANL Triangular solenoids Mike Fitzsimmons, LANL Mark Leuschner, Indiana Paul Stonaha, Indiana Adam Washington, Indiana Haiyang Yan, Indiana Hal Lee, SNS