Magnetic X-rays versus Neutrons
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- George Quinn
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1 Magnetic X-rays versus Neutrons what can we learn from scattering experiments when studying magnetism? which probe to use to solve a given problem? neutrons or synchrotron x-rays? problems to be solved : magnetic structures determinations observation of magnetic order origin of magnetic moments complementary use n+x T.J. Sato et al ILL C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
2 Magnetic X-rays versus Neutrons magnetism basic and applied sciences several methods of investigation bulk measurements ordering temperature type of ordering anisotropy microscopic measurements scattering probes local probes (muons, NMR) microscopies PUG LLN team C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
3 Magnetic X-rays versus Neutrons magnetic structures arrangement of magnetic moments in solids magnetic couplings : magnetic excitations local anisotropy origin of magnetic moments: electronic shells form factors origin of magnetisation d, f, p C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
4 Scattering methods scattering versus real-space/real-time real space images comparison averaging / collecting data real time (time-resolved) methods? relevant time scales electronic levels : < sec electron-nuclei interactions : sec fast chemical reactions : sec magnetic excitations : sec spin-flip : sec domain rotations : around 10-9 sec C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
5 Time-resolved experiments ultra-fast time-resolved experiments : < sec waiting for lasers! fast time-resolved experiments : sec stroboscopic experiments (pump-probe) white-beam x-rays experiments - imaging medium time-resolution : sec photon time-correlation - coherent x-rays slow dynamics - kinetics : 10-3 sec neutron & x-ray diffraction C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
6 Scattering methods what is measured in scattering experiments? correlations in space and time reciprocal space transformation into real space what does it take to get a magnetic scattering probe? magnetic sensitivity appropriate wavelength appropriate energy chemical and electronic sensitivity neutrons, x-rays, polarised atoms,... He* beams M.Marynowsky et al. PRB 60, 6053 (1999) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
7 Neutron scattering neutron-nuclei interaction Fermi length b cm magnetic interaction spin 1/2 total magnetic moment M <L>+2<S> g n r 0 M/ cm a m = g n r 0 { Q ˆ ( M(Q) 2µ Q ˆ )} ˆ separation L/S difficult B no chemical sensitivity polarised neutrons (not for free!) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
8 Neutron scattering inelastic neutron scattering possible incident energy : few mev up to 100 mev resolution mev sec observation of collective modes (i.e. spin-waves) local excitations (crystal fields transitions) diffuse fluctuations intensity limited experiments flux at sample 10 8 n/cm 2 /s sizeable sample volumes low spatial resolution - large beams restricted access to real-time mode C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
9 X-ray magnetic scattering X-rays: weak relativistic interaction Thomson scattering electron charge scattering amplitude Zr cm spin (neutrons can see charges - Schwinger) orbital momentum X-ray polarisation effects F. De Bergevin Acta Cryst. 1981) weak scattering amplitude but flux at sample ph/mm 2 /s and L/S separation C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
10 X-ray magnetic scattering total scattering amplitude : f n ( r k, r k ',h) = f n charge ( r Q ) + f n non res ( r Q, r k, r k ')+ f n res ( r k, r k ',h) (1) charge r f n ( Q ) = n ( Q r ) ˆ. ˆ ' = n ( Q r ) 1 0 (2) 0 cos2 nonres r f n ( Q, k r, k r ')= i hq 2S mc cos S ˆ 2 (Q) sin cos ( S ˆ 1 (Q) + L 1 (Q) ) + sin S ˆ 3 (Q) S sin cos ( S ˆ 1 (Q) L 1 (Q) S ) + sin S ˆ 3 (Q) cos ( S ˆ 2 (Q) + 2sin 2 L 2 (Q) ) S C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
11 Magnetic X-rays versus Neutrons Azimuthal Q (001+) Sy S x C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
12 X-ray magnetic scattering two main points non-resonant magnetic intensities are weak and must be distinguished from charge scattering peaks (crystal structure) intensity ratio around 10-6 mc = 2.59 A1 rotation of polarisation h hq mc 2S 103 electrons are not at rest- they form bound states any consequences? C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
13 Resonant X-ray scattering UAs simple antiferromagnetic Bragg peak intensity as a function of photon energy large resonant effects near absorption edges enhanced intensities ~ 10 6 cts/s McWhan et al. PRB 42, 6007 (1990) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
14 Resonant X-ray scattering resonant process : probe of excited states scattering amplitude depends on the relative direction of the electrical field and the local quantization axis (magnetic moment, ) atomic scattering factors are NOT spherical tensors magnetic contrast : e - spin polarisation sensitivity to long range order Bragg peaks in scattering element selectivity electronic shell selectivity large intensities J. Hannon et al. PRL (1988) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
15 Resonant X-ray scattering res f n (k,k',h) = res fe1 + res fe2 dipole resonances z : magnetization direction f res E1 = F (0) ' if (1) (' ) z + F (2) ('z)( z) = F (0) 1 0 if (1) 0 z 1 cos + z 3 sin 0 cos2 z 1 cos z 3 sin z 2 sin 2 ( ) ( ) z 2 1 sin 2 + z3 2 cos 2 + F (2) 2 z z 2 z 1 sin + z 3 cos z 2 z 1 sin z 3 cos C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
16 Resonant X-ray scattering res (0) (1) (2) f E1 = F ' if (' ) z + F ('z)( z) connection with absorption and spectroscopy - XMCD Q=0 ' = linear polarisation (real polarisation vectors) response quadratic in z Cotton-Mouton effect circular polarisation response linear in z circular dichroism (see Faraday and MO Kerr effects) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
17 Resonant X-ray scattering strength of resonance order of transition overlap integrals spin-polarisation of intermediate states elements edge transition intermediate states energy (kev) wavelength (Å) 3d K E1,E2 4p, 3d Fe L3 E1 3d d Pt L3 E2 5d f L E1,E2 5d, 4f Gd M E1 4f f L E1,E2 6d, 5f U M E2 5f r 0 1 r r r 0 10 r 0 C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
18 Magnetic scattering methods neutrons spin 1/2 magnetic moment polarimetry large magnetic sensitivity mass moderate energy inelastic scattering low brilliance beams low spatial resolution synchrotron x-rays high brilliance beams suited for surfaces and films chemical sensitivity electronic shell sensitivity resonant process relatively weak magnetic sensitivity away from resonances magnetic inelastic scattering not feasible C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
19 Choice of experimental methods determination of magnetic structures/arrangements powder samples neutrons crystals neutrons surfaces x-rays origin of magnetic moments form factor/resonance L/S hybridisation neutrons/x-rays x-rays/ neutrons x-rays magnetic excitations neutrons so far not possible with x-rays not discussed here C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
20 Magnetic structure determinations powder diffraction : Fourier components neutrons : unique tool for magnetic structure determination powder diffraction refinement on crystals necessary technique used days and nights progress in instrumentation faster acquisition smaller sample volumes C.G. Shull at al PR 76, 1256 (1949) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
21 Magnetic structure determinations only example from synchrotron UO 2 powder experiments at Daresbury U M 4 edge S.P. Collins et al. J. Phys. Cond. 7, L223 (1995) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
22 Magnetic structure determinations single crystals - once Fourier components are known! scattering work with x-rays requires good single crystals neutrons are easier to handle low absorption and many more reflections exceptions Gd, B, GdB6 : M. Amara PRB 72, (2005) resonant x-ray magnetic scattering low energy photons - absorption sample environment cryostats magnets high pressure transmission / brilliance heat load problems with x-rays C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
23 Magnetic structure determinations special case : resolution effects magnetic diffuse scattering from single quasicrystal Zn 6 -Mg 3 -Ho 1 icosahedral polarised neutrons 2-fold 3-fold strong peaks near absent crystal Bragg peaks antiferromagnetic correlations broad distribution in Q-space neutron resolution in Q-space is adapted 5-fold T.J. Sato et al ILL C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
24 Magnetic structure determinations special case : resolution effects comparison neutrons/x-rays scattering experiments reciprocal space magnetic ordering of Pr sites PrBa 2 Cu 3 O 7- IC modulation well ordered, 900 long period, 600 Å synchrotron x-rays J.P. Hill et al. PRB 1999 neutrons (3-axis) count rates! C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
25 Magnetism at surfaces surfaces x-rays well suited resonant magnetic scattering at low photon energy absorption length is short ( Å) UO 2 U M-edge observation of magnetic order at surfaces phase transitions G. Watson et al C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
26 Magnetism at surfaces NiO non-resonant scattering grazing incidence scattering A. Barbier et al. PRL 93, (2004) depth sensitive surface ordering well-defined 2D order Melting of S-domains C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
27 Magnetism near surfaces real interfaces are not sharp effects of underlying skin off-specular scattering neutrons and x-rays C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
28 Magnetism near surfaces thin films and devices depth sensitivity reflectivity domain correlations RXMS specular scattering circular polarisation trilayer Co(35Å)/Cr(35Å)/Co(50Å) element sensitivity Co L 3 edge angular dependence coupling between layers (Cr) U. Hillebrecht et al. Science 284, 2099 (1999) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
29 Magnetism near surfaces lateral effects off-specular signal polarised neutron reflectivity multilayers [Cr(9Å)Fe(58Å)] exchange bias disorder of antiferromagnetic objects columns through layers average size 3000Å H.J. Lauter et al. Appl.Phys.Lett. 74, S1557 (2002) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
30 XMCD Magnetic arrangements imaging soft x-ray range (low energy) circular x-ray polarisation element sensitivity XMCD & PhotoElectron Emission Microscopy PEEM imaging of magnetic domain/walls Co/Cu/Ni trilayer coupling mechanism through domain wall stray fields importance for thin film technology W. Kuch et al. PRB 67, (2003) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
31 Magnetic arrangements imaging imaging in real-time pump and probe synchronized of magnetic field pulses D. Neeb et al. J.Phys.:Cond. Matter 17 S1381 (2005) FeNi/Cu/Co trilayer in-plan field pulses soft layer domains change hard layer domains unchanged W. Kuch et al. Applied Phys. Lett., 85, 440 (2004) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
32 Magnetic structure determinations structure determination powder diffraction neutrons Fourier components moments directions details in magnetic structures resolution effects neutrons/x-rays absorption imaging x-rays surfaces x-rays skins neutrons and x-rays C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
33 Origin of magnetic moments which electrons carry magnetic moments? which atoms? which electronic bands? symmetry? structure factors : neutron scattering : x-ray scattering : where scattering arises from! but model-dependent magnetic form factors spin density maps resonant scattering chemical + electronic selectivity non-resonant scattering L/S C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
34 Origin of magnetic moments magnetic form factors neutrons : the perfect tool spherical polarimetry 3 He neutron spin filter flipping ratio measurements R = N + M N M NM N 2 ferromagnets, saturated paramagnets antiferromagnets J. Brown et al C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
35 Origin of magnetic moments spin density maps Iron C. Shull et al. J. Phys Soc. Jpn 17, BIII, 1 (1962) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
36 Origin of magnetic moments organic materials molecular magnets high Tc? couplings driven by radical and crystal packing Nitrophenyl nitronyl nitroxide Tc=0.6K S. Pillet et al. (2001) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
37 Origin of magnetic moments L/S separation magnetic form factor NiO H.A. Alperin PRL 6, 55 (1961) scaling factor in Q space inclusion of covalence and ligands orbital momentum contribution? W. Marshall and S.W. Lovesey Theory Thermal Neutron scattering C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
38 X-RAY SCATTERING total scattering amplitude : f n ( r k, r k ',h) = f n charge ( r Q ) + f n non res ( r Q, r k, r k ')+ f n res ( r k, r k ',h) (1) charge r f n ( Q ) = n ( Q r ) ˆ. ˆ ' = n ( Q r ) 1 0 (2) 0 cos2 nonres r f n ( Q, k r, k r ')= i hq 2S mc cos S ˆ 2 (Q) sin cos ( S ˆ 1 (Q) + L 1 (Q) ) + sin S ˆ 3 (Q) S sin cos ( S ˆ 1 (Q) L 1 (Q) S ) + sin S ˆ 3 (Q) cos ( S ˆ 2 (Q) + 2sin 2 L 2 (Q) ) S C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
39 Origin of magnetic moments X-rays : no modelling of data non-resonant x-ray scattering separation L/S measure of orbital moment in NiO V. Fernandez et al. PRB 57, 7870 (1998) L(Q) / 2 S(Q) NiO T = 300 K Q/4 = sin/ spin and orbital form factors S(Q) L(Q) sin/ similar results on NiFe 2 O 4 using XMCD G. van der Laan et al. PRB 1999 C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
40 Origin of magnetic moments other oxides counts/sec NiO Theta (deg) L(Q)/S(Q) CoO 1.0 NiO 0.5 CuO 0.0 MnO Q/4=sin/ W. Neubeck et al. J.Phys.Chem.Solids 62, 2173 (2000) large incident flux from synchrotron sources C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
41 Origin of magnetic moments resonant effects have made x-ray scattering experiments popular large resonant enhancements in particular at M edges D.B. McWhan et al. PRB 42, 6007 (1990) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
42 Resonant x-ray magnetic scattering important edges E1 l = 1 E2 l = 2 typical edges elements edge transition intermediate states wide energy range limitations Bragg cut-off absorption strength of the resonance energy (kev) E1 transition to the interesting e- levels wavelength (Å) 3d K E1,E2 4p, 3d Fe L3 E1 3d d Pt L3 E2 5d f L E1,E2 5d. 4f Gd M E1 4f f L E1,E2 6d, 5f U M E2 5f C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
43 Resonant x-ray magnetic scattering across series 3d series element K edge L1 edge L2 edge L3 edge (ev) (ev) (ev) (ev) Sc Ti V Cr Mn Fe Co Ni Cu Zn valence state TmSe Tm ions in 2 different configurations Tm 2+ and Tm 3+ C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
44 Origin of magnetic moments chemical selectivity absorption edges alloys, compounds, intermetallics heteromagnetic multilayers, U 1-x Np x Ru 2 Si 2 antiferromagnetic system incommensurate structure at x=0 (neutron scattering) magnetic intensity at (00 4+q) separation of U and Np response E. Lidström et al. PRB 61, 1375 (2000) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
45 Origin of magnetic moments element specific studies Uranium is driven by Neptunium studies : multilayers C.T. Chen at al. PRB 1993 Y.U. Idzerda PRB 1993 V. Chakarian et al. PRB 1996 N. Ishimatsu et al. PRB 1999 Fe/Gd induced moment on V in V/Fe ML M. Sacchi et al. PRB 1999 C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
46 Origin of magnetic moments Samarium RXMS E1 and E2 5d and 4f temperature dependence 100 E1 5d Peak Intensity (cts/s/200ma) E2 E1 Sm 5000 Å film ( ) T = 50 K Energy (kev) Integrated Intensity 10 E2 4f Temperature (K) A. Stunault at al. JMMM 226, 1116 (2001) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
47 Scattering experiments scattering probes have characteristic time scales energy resolution! x-rays E 1 ev fast fluctuations sec neutrons E mev slow fluctuations sec do we measure the same quantities? itinerant systems/insulators C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
48 Magnetic X-rays versus Neutrons NEUTRONS SYNCHROTRON LIGHT magnetic structure determination polycrystals imaging and timedependence devices magnetisation densities magnetic excitations local collective chemical selectivity electronic selectivity surfaces microcrystals (resonance) C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
49 Magnetic X-rays versus Neutrons neutrons are magnetic x-rays are electronic well defined domains of excellence for neutrons and x-rays magnetic structure determinations/ imaging nano-objects excitations / origin of moments x-ray methods are relatively recent and will develop gains in neutron optics are expected new neutron sources are being prepared new x-ray sources are dreamed of one probe + another probe makes more than two probes C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
50 Magnetic X-rays versus Neutrons European Campus on the ILL - ESRF site ILL ESRF C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
51 ORIGIN OF MAGNETIC MOMENTS are neutrons sensitive to electronic properties? magnetic form factor Fourier transform of magnetic electrons J. Brown et al C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
52 Origin of magnetic moments important for magnet technology important for chemistry x-rays could be used at O, N absorption edges but wavelength is too long for diffraction only Q=0 experiments (absorption, dichroism,..) no spatial information C. Vettier Institut Laue Langevin European School on Magnetism Constanta 7-16 September
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