Roger Pynn. Lectures 10: Polarized Neutrons

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1 by Roge Pynn Lectues 0: Polaize Neutons

2 Neuton Spin an Magnetic Moment Neuton is a femion with spin ½ & the usual spin opeatos h 0 h 0 i h 0 sx,, 0 sy 0 sz 0 i The Pauli spin opeatos ae given by s h Because of its spin, the neuton also has a magnetic moment μn x h 7 γ s nμn Whee γ n -.93 an μ N is the nuclea magneton μ n is 3 oes of magnitue smalle than the Boh magneton an antipaallel to the neuton spin J.T -

3 The Neuton Spin Wavefunction & Polaization The neuton spin wavefunction is a supeposition of up an own states The polaization components of an iniviual neuton ae the expectation values of the appopiate Pauli matix i.e. The polaization P of a neuton beam is the mean value of p in the beam Note that: b a χ ) * Im( ) * Re( b a p b a p b a p z z y y x x χ χ χ χ χ χ n n n n P z

4 Behavio of the Neuton s Spin in a Magnetic Fiel The time evolution of any two-state quantum system can be epesente by the movement of a classical vecto P γ LP B t whee γ L is the gyomagnetic atio of the neuton The solutions ae P ( t) cos( ω t) P x P ( t) sin( ω t) P y P ( t) z P (0) z L L x x (0) sin( ω t) P (0) sin( ω t) P L L x y (0) (0) whee ω L γ B L.83x0 8 a.s -. T -

5 Plug in the Numbes B(Gauss) ω L (0 3 a.s - ) N (msec - ) Tuns/m fo 4 Å neutons ~9

6 Guiing the Neuton Polaization If the iection of a magnetic fiel vaies sufficiently slowly in space, the component of neuton polaization paallel to the applie fiel is peseve. This is aiabatic polaization otation. Dawing fom Bob Cywinski

7 How oes a Neuton Spin Behave when the Magnetic Fiel Changes Diection? When H otates with fequency ω, H 0 ->H ->H, an the spin taectoy is escibe by a cone olling on the plane in which H moves Distinguish two cases: aiabatic an suen Aiabatic tan(δ) << lage B o small ω spin an fiel emain co-linea this limit use to guie a neuton spin Suen tan(δ) >> lage ω spin pecesses aoun new fiel iection this limit is use to esign spin-tun evices

8 Aiabatic otation of neuton spin ϖ L 4 γ B a/g -s φ << ϖ L t Conition to maintain polaization of the neuton beam. istance [cm] H x an H z [Oe] H x H z 0 cm 30 cm φ [ ] 00 z φ istance [cm] x fequency [a/s] Note, the elation between istance an time is vali fo a neuton with λ 4 Å. ω L /4 φ/t M. R. Fitzsimmons istance [cm] time [ms]

Non-Aiabatic Tansitions If the guie fiel iection is suenly change (i.e. the aiabaticity paamete tan δ ö, the neuton polaization vecto will pecess about the new fiel iection.

9 Non-Aiabatic Tansitions If the guie fiel iection is suenly change (i.e. the aiabaticity paamete tan δ ö, the neuton polaization vecto will pecess about the new fiel iection. If the fiel is evese, the neuton polaization is flippe with espect to the fiel Gaphic coutesy of Bob Cywinski

10 Viewgaph fom Bob Cywinski

11 Spin Flippes base on Lamo Pecession Diect cuent spin flippes combine aiabatic an non-aiabatic spin otation. B B B π/ B S en S ini B B π B S en B S ini

spin, φ, epens on the time the neuton spens in the B fiel φ ω L t γb /

12 Lamo Pecession allows the Neuton Spin to be Manipulate using π o π/ Spin-Tun Coils: Both ae Neee fo NSE The total pecession angle of the spin, φ, epens on the time the neuton spens in the B fiel φ ω L t γb / v Neuton velocity, v B Numbe of tuns. B[ Gauss]. [ cm]. λ[ Angstoms] 35.65

13 Using Soft Magnetic Films to Rotate Neuton Spins A thin film of soft magnetic mateial is place in a polaize neuton beam at an angle θ to the beam As θ is change the polaization of the neuton beam changes B H, θ neuton H.0 0 micon foil tuning cuve pol B Polaization Data: Data54_pol Moel: pi_on fit Weighting: y No weighting Chi^/DoF R^ K.0933 ± x ± Rotation Stage Angle (egees)

14 Thin Magnetic Films use as π/ an π Rotatos H g H g 0.5 M M φ γm vsin χ Rekvelt H g M χ v neuton H g M M χ neuton

15 Wavelength Inepenent Flippes can be Mae with Pemanently Magnetize Films (o Coils) B B B B B neuton Polaization films C x neuton wavelength B B Neuton Polaization C x neuton wavelength films

16 White Beam Spin Flippe A f Gaient-Fiel Spin Flippe H RF H cos(ωt) H s (z) H 0 H z ω/γ H s H eff H s H H H s H Viewgaph fom M. R. Fitzsimmons

Realization The ASTERIX f Flippe 70 W @ 96kHz 50 feet Static fiel, H s (z) [Oe] 60 40 0 00 80 60 RF

17 Realization The ASTERIX f Flippe 70 96kHz 50 feet Static fiel, H s (z) [Oe] RF fiel egion 5 cm H 3 Oe cm Distance along neuton path [cm] Viewgaph fom M. R. Fitzsimmons

18 Pefomance of the Asteix f Flippe Intensity [a.u.] Polaize beam specta in 00 () (--) (-) (-) () (--) flippes 99% efficient fo λ > 4Å. ()/(SF) polaization ~94% fo λ > 4Å. 0-6 poton flash Wavelength [Å] Viewgaph fom M. R. Fitzsimmons

19 Pouction of Polaize Beams Polaizing filtes Usually 3 He these ays, although pumpe potons an ae eaths have been tie Goo fo polaizing lage, ivegent neuton beams Depen on goo polaization of filte mateial Polaizing monochomatos Mainly Heusle alloy (Cu MnAl) these ays Goo when beam monochomatization is also equie (e.g. TAS) Supemios Vey efficient, boa-ban polaizes cavities o benes ae excellent fo pepaing polaize beams Disavantage is that wie angula beam ivegence equies evices with non-unifom tansmission

20 Polaizing Filtes The polaization an tansmission ae given by: P tanh( Nt); whee p p ( T e ) / an Nt o cosh( Nt) p ( ) / 0 Pouction of polaize 3 He at ILL

21 Making a Polaizing Neuton Monochomato In a Bavais cystal, the magnetization may be witten as a Fouie seies: This may be combine with the matix element fo nuclea scatteing to give an effective scatteing length given by: Consie a situation in which the magnetization at each lattice site is along z, the quantization iection of the neuton spin, an to Q Fom the esults on the pevious slie, the effective scatteing lengths ae: an thee is no spin flip scatteing If we can fin a FM cystal fo which the nuclea an magnetic scatteing lengths ae equal we can use it to monochomate an polaize neutons Facto Fom the Magnetic is ). )exp( ( ) ( whee ). exp( ) ( ) ( iq m Q F M iq R Q F Q M B M Q F b b. ) ( ˆ 0 μ γ iq R e b. ) ( ˆ : v v Fo ; ) ( ˆ : u u Fo 0 0 z B z B M Q F b b M Q F b b μ γ μ γ

22 Schematic of a Polaizing Monochomato x z Q y Unpolaize Incient Neutons u v Q B Sample Magnetization u scatteing potential is ve if neuton spin is paallel to M i.e. its magnetic moment is anti-paallel to M thus, if polaize eflection occus, the neuton spin must be paallel to M Polaize Scattee Neutons

23 Vetically focussing Heusle alloy monochomato fo polaize neutons A. Feun, R. Pynn, W. G. Stiling an C. M. E. Zeyen; Physica 0B, 86 (983) Viewgaph fom Bob Cywinski

24 Neuton Reflection fom Magnetic Mios Since, fo a satuate feomagnet, we can wite the magnetic scatteing in tems of an effective scatteing length, we can euce a combine nuclea an magnetic SLD fo such a mateial ρ ˆ b ( bcoheent ± b volume volume magnetic We can make a mio that polaizes a neuton beam by choosing the nuclea an magnetic SLDs to be equal. ) Although the schematic of this pocess looks much like the polaizing monochomato, the eflection angles ae much smalle. We also have moe contol ove the mio than the monochomato because only the aveage composition mattes we on t nee to ely on natue to han us the answe The fist polaizing mio was emonstate by in 95 by Hughes an Bugy

25 Viewgaph fom Bob Cywinski

26 Viewgaph fom Bob Cywinski

27 ( n) n nm 0. nm Polaizing supemios up Si own m m Polaize neuton eflectivity R Fe/Si R -- Fe/Si R 3θ c SM R -- 3θ c SM Polaization (tansmission) Q min 0.0 Å - Q max Å Q [Å - ] F. Mezei an P.A. Dagleish, Comm. on Phys.,, 4 (977) Q [Å - ]

28 Patial Coss Sections II coh SI mag NSF z SI mag SF z II coh SI mag NSF y SI mag SF y II coh SI mag NSF x SI mag SF x α α α α ) (cos 3 ) (sin 3 ) (sin 3 ) (cos Blume, Phys. Rev. 30, 670 (963); Moon, Riste an Koehle Phys. Rev. 8, 90 (969

Flippe on is SF PG(004) coheent scatteing Is always NSF Nuclea spin incoheent scatteing

29 Polaize Neuton Scatteing Vaious Cases Isotopic incoheent scatteing fom Ni is NSF. Flippe off is NSF. Flippe on is SF PG(004) coheent scatteing Is always NSF Nuclea spin incoheent scatteing fom Vanaium is /3 SF. Flippe off is NSF coss section Paamagnetic scatteing fom MnF. With P//Q, all mag scatteing is SF. With P^Q ½ mag scatteing is SF an ½ is NSF

30 Science with Polaize Neutons Most measuements ae mae with - polaization analysis Magnetic fiel is applie to sample an neuton spin component is analyze in the fiel iection Diffaction Flipping atio measuements of fom factos, electon spin ensity istibutions usually with single cystals 3-iectional polaization analysis of iffuse scatteing SANS Polaize Neuton Reflectomety (PNR) Depth epenent vecto magnetomety in thin films Inelastic scatteing Magnetic excitations an fluctuations Genealize polaization analysis is also possible No magnetic fiel on sample; incient neuton spin in contolle iection; analyze neuton spin along any iection Vecto istibution of magnetization in single cystals

31 Viewgaph coutesy of Bob Cywinski

32 Viewgaph coutesy of Bob Cywinski

33 Viewgaph coutesy of Bob Cywinski

( )( )( ) ( ) + ( ) ( ) ( )

( )( )( ) ( ) + ( ) ( ) ( ) 3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13