Polarized Neutron Scattering Werner Schweika European Spallation Source ESS, Lund, Sweden FZJ, Research Centre Jülich SwedNess/NNSP, Tartu Estonia, September 19 th 2017
The neutron Quarks Charge 0 Charge Spin Spin 1/2 u 2/3 1/2 d -1/3 1/2 Neutron is a spin ½ particle , the spin is tied to a magnetic moment . γ n µ N = g n Sµ N µ n = e ~ µ B ≡ e ~ compare γ n = − 1 . 913 µ N ≡ 2 m p 2 m e neutron interacts with nuclei Its spin interacts with spin of nuclei Its magnetic moment interacts with magnetic moments of unpaired electrons => Structure and dynamics of atoms and magnetic moments Why polarized neutron scattering? to see more and to separate scattering terms
Do it with polarized neutron scattering? Magnetic neutron scattering - unpolarized Detection of Antiferromagnetism by Neutron Diffraction 1949 Shull et al. Nobel prize 1994 “for the development of neutron diffraction technique” (111) alternating layers MnO spin structure from intensities spins || to [100] Shull et al. PR 1951 in (111) planes Shaked et al. PRB 1988 || to Goodwin et al. PRL 2006 paramagnetic spin fluctuations polarized neutron scattering provides more information intensities and polarization
Outline Neutron spins in magnetic fields Ø experimental devices => instruments Ø Scattering and Polarization Moon, Riste, Koehler Ø spin-dependent nuclear interaction Ø magnetic interaction Ø Blume-Maleyev Equations Ø examples Ø Ø outlook for ESS
Neutron spins in magnetic fields Larmor precession Zeeman splitting ω L = − γ B = µ x B torque ~ ω L Bloch equation of motion QM: no nutation
Neutron beam polarization with respect to magnetic field average of spins: -1 < P < 1 normalized difference of intensities neutron spin up and down 0 < P < 1
Absorption and transmission Polarized He-3 filter - SEOP Spin-exchange-optical pumping Tunable efficiency by pressure and volume - Laser polarizes Rb typically good for thermal neutrons exchange with K then 3 He-spin - - very homogeneous field 3 He cells used at JCNS
Scattering constructive interference of nuclear b and magnetic scattering amplitudes p σ ± ∝ ( b ± p ) 2 Lecture 7 - Magnetic Bragg scattering e.g. Heusler crystals, Cu 2 MnAl (111), P= 0.95 single ferro domain needed, low reflectivity see in following: Moon, Riste, Koehler
Scattering constructive interference of nuclear and magnetic scattering - Total reflection by of magnetic “super-mirrors” (Mezei, Schärpf) Vielfachschichten Bragg-diffraction from an 800 multi-layer structure of varying layer thickness d 600 TiN : Fe 50 Co 48 V 2 multi-layer structure d [Å] 400 Substrat: Si 200 Gd FeCoV TiN 0 0 50 100 layer # Lage #
Scattering constructive interference of nuclear and magnetic scattering - Total reflection by of magnetic “super-mirrors” (Mezei, Schärpf) p Θ ± c = λ n ( b ± p ) / π Surface of FeSi multilayers much better polarization at the interface of Si : FeSi multilayers Source: Swiss Neutronics
Guide fields travel direction S z B constant B neutron B t-dependent Asymptotic behaviour adiabatic field change slowly varying “strong” B(t) fast precession around B B 1 B 2 = - B 1 sudden change no change of S z but change wrt B Meissner shield, General behaviour current sheet Solve Bloch equation of motion
Guide fields nutators, xyz-coils
Flipper Objective: change neutron polarization with respect to the applied field Adiabatic and non-adiabatic changes of P || B Cryo-flipper H coil precession Cryo-flipper precession Meissner coil shield superconducter 𝞺 - flipper
Spin-echo technique flip reversal of B P A B B sample spin-echo => Relaxation times
Larmor diffraction with flip reversal of B spin-echo absolute d -spacings with <10 -4 accuracy sample k G k’ B Larmor diffraction
Triple axis instrument with polarization analysis Moon, Riste and Koehler (1969) Guide fields Polariser Guide field Heusler crystal Analyzer Detector Flipper Flipper Electromagnet Sample
IN12 @ ILL Triple axis instrument with polarization analysis CryoPad: zero field sample environment
Outline Neutron spins in magnetic fields Ø experimental devices => instruments Ø Scattering and Polarization Ø spin-dependent nuclear interaction Ø magnetic interaction Ø Blume-Maleyev Equations Ø examples Ø Ø outlook for ESS
Coherent nuclear scattering now including initial and final spin states Differential scattering cross section d Ω = ( m n d σ 1 st Born approximation 2 π ~ ) 2 | < k 0 S 0 | V | kS > | 2 Point like nucleus Conservation of momentum and plane wave scattering = b ( Q ) Scattering amplitude – transition matrix element A ( Q ) = < S 0 Z | b ( Q ) | S Z > = b ( Q ) < S 0 Z | S Z > = b ( Q ) no spin-flip spin-flip = 0
Coherent & incoherent scattering coherent incoherent spin and isotope
Spin dependent interaction + → → + Spin J = I ± 1 / 2 Multiplicities 2 J +1 Two possibilities Probabilities Scattering length b + Triplet b − Singlet b + − b − 2 I + 1 ≡ B b 2 = p + p − ( b + − b − ) 2 inc ≡ ¯ b 2 − ¯ b 2 spin b 2 = c A c B ( b A − b B ) 2 ≡ ¯ b 2 − ¯ b 2 isotope inc coherent incoherent
How about spin states after scattering?
Spin dependent nuclear scattering amplitude σ · ˆ A ( Q ) = h k 0 S 0 | A + B ˆ I | kS i Spin operator Pauli Matrices spin states, quantization axis z 2/3 spinflip 1/3 non-spinflip
Spin dependent nuclear scattering amplitude σ · ˆ A ( Q ) = h k 0 S 0 | A + B ˆ I | kS i No spin flip in absence of a nuclear spin for the + + and − − case for the + − and − + case A perpendicular nuclear spin flips the neutron spin! A parallel nuclear spins flip does not 2/3 of spin-incoherent scattering is spin-flip for disordered nuclear spins, independent of the direction of P
Moon, Riste and Koehler (1969) 2/3 of spin-incoherent scattering is spin-flip independent of the direction of P
Spin dependent nuclear scattering non spin-flip scattering is elastic spin-flip scattering maybe inelastic magnetic hyperfine 143 Nd order splitting H=0, disorder Spheres @ FRM-II Phys. Rev. B 78, 012411 (2008) Quiz: why are only two side peaks visible at low T?
Separation of spin incoherent scattering In the absence of nuclear polarization and magnetic scattering + d σ + d Ω isotope − inc only spin-incoherent d Ω coh + d σ d σ d Ω isotope − inc = d σ d Ω NSF − d σ d Ω SF
Polarization analysis: Spin-flip and non-spin-flip scattering Separation of spin-incoherent and coherent nuclear scattering Applications to hydrogeneous materials, soft matter, etc. PMMA DNS at FRM II small H = 1.75 b H = 80.26 b σ coh σ inc H = − 3.74 fm D = + 6.67 fm b coh b coh * Separating huge spin-incoherent background of H * Intrinsic calibration from intensities to partial pair-correlation functions to compare with MD and MC simulations A.C. Genix et al Macromolecules 39, 3947 (2006)
About spin incoherent scattering: (Spin) incoherent scattering does not contain phase information between distinct particles → single particle behavior is accessible self correlation function, Chap. 11.2) phase information on the identical particle: exp(iQ(R(t)-R 0 (t 0 ))+i ω (t-t 0 )) (Spin) incoherent scattering is isotropic if integrated in energy → calibration of multi detector instruments internal standard for absolute intensity measurements Conservation of angular momentum → Spin incoherent scattering has an effect on the neutron spin while isotope incoherent scattering does not
Liquid sodium at 840 K (homepage Otto Schärpf) www.ncnr.nist.gov a good motivation to think about how to separate scattering spin-incoherent coherent σ inco = 1 . 62b σ coh = 1 . 66b ~ ω [meV] ~ ω [meV] 0 1 2 3 4 0 1 2 3 Q [Å -1 ] Q [Å -1 ] FT (self correlation) FT (pair correlation) collective behavior single particle diffusion precursors of Bragg scattering
Outline l Introduction l Neutron spins in magnetic fields l Scattering and Polarization Spin dependent nuclear scattering magnetic scattering
Reminder Neutron spins dipole-dipole interaction with magnetic fields of unpaired electrons V M = − µ ( n ) · ( B S + B L ) V m B Constructive interference Destructive interference
initial and final spin states Choosing z as quantization axis for the + + NSF case for the − − NSF case for the + − SF case for the − + SF case coordinate system say x || Q A perpendicular component flips the neutron spin! we have seen this before: A parallel component does not direction of P, M, Q matters!
How about nuclear spin incoherent? Nuclear peaks Nuclear peaks Flipper off Flipper off spinflip Magnetic peaks spinflip spinflip Moon, Riste and Koehler (1969)
Example: MnF 2 paramagnet spinflip non spinflip spinflip non spinflip
Separation of magnetic scattering by differential methods XZ Difference: nuclear coherent and (spin) incoherent terms and background vanish for paramagnets, antiferromagnets and powders, weak fields and isotropic M | M x | = | M y | = | M z | If there is no chirality …
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