Neutron Optics Optics reflection refraction diffraction polarization Neutron

Neutron Optics • Optics – reflection – refraction – diffraction – polarization • Neutron Instruments – source – transport – focusing, divergence – wavelength encoding – polarization encoding CERN, 12/5/09 INSTITUT MAX VON LAUE - PAUL LANGEVIN Ken Andersen

Neutrons vs Light λ E n light < μm > e. V 1→ 4 neutrons < nm > me. V 0. 9997→ 1. 0001 θc 90° 1° Φ/ΔΩ 1019 p/cm 2/ster/s 1014 n/cm 2/ster/s (60 W lightbulb) (60 MW reactor) P spin interaction left-right 1 up-down ½ electromagnetic strong force, magnetic charge 0 0 INSTITUT MAX VON LAUE - PAUL LANGEVIN

Neutron scattering 10 barns 1 barn INSTITUT MAX VON LAUE - PAUL LANGEVIN

Neutron Sources • About 10 neutron facilities worldwide • Fission (continuous) • Spallation (pulsed) • User Facilities • ILL: – 40 instruments – 700 experiments/year – mainly solid-state physics, but also fundamental physics, chemistry, biology INSTITUT MAX VON LAUE - PAUL LANGEVIN ILL ISIS

ILL & ESRF in Grenoble INSTITUT MAX VON LAUE - PAUL LANGEVIN

Neutron Moderators cold thermal hot moderator liquid D 2, H 2, CH 4 liquid H 2 O graphite moderator temperature 15– 25 K 300 K 2000 K neutron wavelength 3→ 20Å 1→ 3Å 0. 3→ 1Å sample lengthscale 1Å→ 100 nm 0. 3→ 5Å 0. 1→ 2Å sample timescale 1 k. Hz→ 1 THz 0. 1→ 10 THz 1→ 100 THz 2. 5 m INSTITUT MAX VON LAUE - PAUL LANGEVIN

Neutron Moderators INSTITUT MAX VON LAUE - PAUL LANGEVIN

INSTITUT MAX VON LAUE - PAUL LANGEVIN

Source Optics 200 cm 20 cm 5 cm 30 cm reflective internal surfaces Max angle ≈ 1° INSTITUT MAX VON LAUE - PAUL LANGEVIN

Reflecting Surfaces incident n=1 reflected θ n’<1 refracted critical angle of total reflection θc for natural Ni, θc = λ[Å] 0. 1 INSTITUT MAX VON LAUE - PAUL LANGEVIN

Increasing the Critical Angle Interface reflection: lc θc(Ni) = λ[Å] 0. 1 l 1 Equivalent Bragg diffraction: l 2 l 3 λ = 2 dsinθ l 4 d = λ/2θ = 200 Å }d 1 }d } 2 d 3 } d 4 INSTITUT MAX VON LAUE - PAUL LANGEVIN

An Fe/Si multilayer INSTITUT MAX VON LAUE - PAUL LANGEVIN

Neutron Supermirrors • Multilayers with up to several 1000 s of layers feasible by magnetron sputtering • 4×θNi is commercially available • Layer thicknesses > 20 Å • Interlayer roughness < 3 Å – limited by roughness of substrate (1 -8 Å) • < 0. 5 m 2 deposition in one batch • Technology transfer from neutron labs to industry • Neutron guides up to >100 m INSTITUT MAX VON LAUE - PAUL LANGEVIN

INSTITUT MAX VON LAUE - PAUL LANGEVIN

Instrument Example: Powder Diffraction λ = 2 dsinθ d = λ/2 sinθ Structure Determination INSTITUT MAX VON LAUE - PAUL LANGEVIN

Monochromating by time-of-flight Choppers distance 300 Hz ~μs burst time Δλ/λ ≈ 1% INSTITUT MAX VON LAUE - PAUL LANGEVIN time

Monochromating by time-of-flight Velocity selector Δλ/λ ≈ 10% INSTITUT MAX VON LAUE - PAUL LANGEVIN

Single-crystal Monochromators Bragg’s law: λ = 2 dsinθ <hkl> fwhm < 10 -4° Dl/l → 0 ! Perfect crystal h fwhm > 0. 1 ° Dl/l = cotq. B Dq Mosaic crystal INSTITUT MAX VON LAUE - PAUL LANGEVIN 2 h

Single-crystal Monochromators Germanium 333 d-spacing 1. 089 Å Copper 111 2. 087 Å Silicon 111 3. 135 Å Graphite 002 3. 355 Å 5. 35 Å stage 1 Kintercalated graphite 002 stage 2 Kintercalated graphite 002 8. 74 Å INSTITUT MAX VON LAUE - PAUL LANGEVIN

Focusing guide ~ 100 cm 2 samples < 1 cm 2 INSTITUT MAX VON LAUE - PAUL LANGEVIN

Focusing Devices Crystal monochromators Graphite 002 Copper 200 Supermirror optics Kirkpatrick-Baez mirrors Focusing guides INSTITUT MAX VON LAUE - PAUL LANGEVIN

Monochromator Focusing A B θB 2 INSTITUT MAX VON LAUE - PAUL LANGEVIN

Monochromator Focusing A B θA θB 2 INSTITUT MAX VON LAUE - PAUL LANGEVIN

Limitations of focusing • Liouville’s theorem: phase-space density is constant – Increase in spatial density implies a reduction in angular density – worse resolution INSTITUT MAX VON LAUE - PAUL LANGEVIN

Limitations of focusing • Liouville’s theorem: phase-space density is constant – Increase in spatial density implies a reduction in angular density – worse resolution • Source brightness ~ 1014 n/cm 2/ster/s – ΔΩ ≈ 10 -3 ster – Δλ/λ ≈ 1% • Flux impinging on sample < 108 n/s – strongly limited by Poisson statistics • Sometimes S/N can be more important INSTITUT MAX VON LAUE - PAUL LANGEVIN

Polarization Optics B • Magnetism “Spin-up” (+) +½ħ – neutron magnetic moment interacts with that of unpaired electrons – magnetic scattering depends strongly on relative orientation of neutron spin, electron spin and momentum transfer – unambiguous separation of magnetic and nuclear scattering -½ħ “Spin-down” (-) • Precession techniques – polarization vector precesses around field direction – frequency ~ B – phase measurement gives time spent in field neutron speed INSTITUT MAX VON LAUE - PAUL LANGEVIN

Polarizing Supermirrors B=0 B Si Fe Si • with B B INSTITUT MAX VON LAUE - PAUL LANGEVIN

Polarizing Crystals Cu 2 Mn. Al (Heusler) crystal ILL is the only producer INSTITUT MAX VON LAUE - PAUL LANGEVIN

Polarized-3 He Spin-filters MEOP Metastability Exchange Optical Pumping Buffer 2, 5 l Polarised 3 He Cells Hydraulic piston 5. 2 liter compressor B 0 Discharge Optical polarimeter OPC Optical pumping Cells Mirror s Capillary Yb fiber laser 3 He bottle INSTITUT MAX VON LAUE - PAUL LANGEVIN Purifier

Polarized-3 He Spin-filters 2008 2002 where O(λ) = 7. 28× 10 -2×P[bar] ×t[cm] ×λ[Å] INSTITUT MAX VON LAUE - PAUL LANGEVIN

Polarized-3 He Spin-filters • 3 He Polarization < 80% • World leaders – Supplying 3 He filling stations, spinfilter cells & magnetic-field environments to neutron labs in UK, Australia, Germany, Taiwan, USA • Applications: – magnetic structures in single crystals – magnetic domain structures in thin films – disorder in frustrated magnetic systems – magnetic excitations in high-Tc superconductors • Medical applications – functional lung imaging (MRI) INSTITUT MAX VON LAUE - PAUL LANGEVIN

Summary • User facilities – experiments performed mainly by outside groups – ILL: 200 days/yr, 40 instruments, 700 experiments/year, 1200 users/year – mainly solid-state physics, but also fundamental physics, chemistry, biology • Sources – thermalized Maxwellian spectrum – low brightness, large sources – beam distribution by guides • Monochromatization – time-of-flight: velocity selectors, pulsing choppers – crystal monochromators: Bragg formula, perfect crystals, mosaic crystals • Focusing – sample size vs source/guide size, resolution degradation – crystal monochromators – guides • Polarization – crystal monochromators – supermirrors – polarized 3 He INSTITUT MAX VON LAUE - PAUL LANGEVIN