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Martin RotterMagnetism in Complex Systems Magnetic Neutron Scattering Martin Rotter, University of Oxford

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Martin RotterMagnetism in Complex Systems Contents Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering

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Martin RotterMagnetism in Complex Systems Neutrons and Magnetism Macro-Magnetism: Solution of Maxwell´s Equations – Engineering of (electro)magnetic devices Atomic Magnetism: Instrinsic Magnetic Properties Micromagnetism: Domain Dynamics, Hysteresis MFM image Micromagnetic simulation m m m m m m Hall Probe VSM SQUID MOKE MFM NMR FMR SR NS

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Martin RotterMagnetism in Complex Systems Single Crystal Diffraction E2 – HMI, Berlin Q O k neutrons: S=1/2 μ Neutron = –1.9 μ N τ = 885 s (β decay) k=2π/ λ E=h 2 /2M n λ 2 =81.1meV/λ 2 [Å 2 ]

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Martin RotterMagnetism in Complex Systems Atomic Lattice Magnetic Lattice ferro antiferro

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In 1949 Shull showed the magnetic structure of the MnO crystal, which led to the discovery of antiferromagnetism (where the magnetic moments of some atoms point up and some point down). The Nobel Prize in Physics 1994

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Martin RotterMagnetism in Complex Systems T N = 42 K M [010] T R = 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Experimental data D4, ILL Calculation done by McPhase

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Martin RotterMagnetism in Complex Systems T N = 42 K M [010] T R = 10 K q = (2/3 1 0) GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase

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Martin RotterMagnetism in Complex Systems T N = 42 K M [010] T R = 10 K q = (2/3 1 0) GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase

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Martin RotterMagnetism in Complex Systems T N = 42 K M [010] T R = 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Experimental data D4, ILL Calculation done by McPhase

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Martin RotterMagnetism in Complex Systems T N = 42 K M [010] T R = 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Experimental data D4, ILL Calculation done by McPhase

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Martin RotterMagnetism in Complex Systems T N = 42 K M [010] T R = 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction GdCu 2 Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Experimental data D4, ILL Calculation done by McPhase Goodness of fit R p nuc = 4.95% R p mag = 6.21%

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Martin RotterMagnetism in Complex Systems The Scattering Cross Section Scattering Cross Sections Total Differential Double Differential Scattering Law S.... Scattering function Units: 1 barn= m 2 (ca. Nuclear radius 2 )

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Martin RotterMagnetism in Complex Systems M neutron mass k wavevector |s n > Spin state of the neutron P sn Polarisation |i>, |f> Initial-,final- state of the targets E i, E f Energies of –‘‘- P i thermal population of state |i> H int Interaction -operator S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984 (follows from Fermi`s golden rule)

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Martin RotterMagnetism in Complex Systems Interaction of Neutrons with Matter

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Martin RotterMagnetism in Complex Systems Magnetic Diffraction Difference to nuclear scattering : Formfactor... no magnetic signal at high angles Polarisationfactor... only moment components normal to Q contribute

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Martin RotterMagnetism in Complex Systems Formfactor Q= Dipole Approximation (small Q):

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Martin RotterMagnetism in Complex Systems A caveat on the Dipole Approximation Dipole Approximation (small Q): E. Balcar derived accurate formulas for the S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984 Page

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Martin RotterMagnetism in Complex Systems NdBa 2 Cu 3 O 6.97 superconductor T C =96K orth YBa 2 Cu 3 O 7-x structure Space group Pmmm Nd 3+ (4f3) J=9/2 T N =0.6 K q=(½ ½ ½), M=1.4 μ B /Nd Calculation done by McPhase... using the dipole approximation may lead to a wrong magnetic structure ! M. Rotter, A. Boothroyd, PRB, 79 (2009) R140405

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Martin RotterMagnetism in Complex Systems nuclear structure factor has to be known with high accuracy only for centrosymmetric structure (no phase problem) spin density measurements are made in external magnetic field, comparison to results of ab initio model calculations desirable ! Measuring Spin Density Distributions P n B P n B Nuclear Magnetic Structure Factor “Flipping Ratio”: Forsyth, Atomic Energy Review 17(1979) 345 polarized neutron beam sample in magnetic field to induce ferromagnetic moment -> magnetic intensity on top of nuclear reflections -> nuclear-magnetic interference term:

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Martin RotterMagnetism in Complex Systems Dreiachsenspektometer – PANDA Dynamik magnetischer Systeme: 1.Magnonen 2.Kristallfelder 3.Multipolare Anregungen Inelastic Magnetic Scattering

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Martin RotterMagnetism in Complex Systems k k‘k‘ Q G hkl q Three Axes Spectrometer (TAS) constant-E scans constant-Q scans

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Martin RotterMagnetism in Complex Systems PANDA – TAS for Polarized Neutrons at the FRM-II, Munich beam-channel monochromator- shielding with platform Cabin with computer work-places and electronics secondary spectrometer with surrounding radioprotection, 15 Tesla / 30mK Cryomagnet

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Martin RotterMagnetism in Complex Systems

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Martin RotterMagnetism in Complex Systems Movement of Atoms [Sound, Phonons] Brockhouse E Q π/a The Nobel Prize in Physics 1994 Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays

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Martin RotterMagnetism in Complex Systems Movement of Spins - Magnons 153 T=1.3 K MF - Zeeman Ansatz (for S=1/2)

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Martin RotterMagnetism in Complex Systems Movement of Spins - Magnons Bohn et. al. PRB 22 (1980) 5447 T=1.3 K 153

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Martin RotterMagnetism in Complex Systems Movement of Spins - Magnons Bohn et. al. PRB 22 (1980) 5447 T=1.3 K a 153

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Martin RotterMagnetism in Complex Systems Movement of Charges - the Crystal Field Concept Hamiltonian E Q charge density of unfilled shell Neutrons change the magnetic moment in an inelastic scattering process: this is correlated to a change in the charge density by the LS coupling …”crystal field excitation”

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Martin RotterMagnetism in Complex Systems Movements of Atoms [Sound, Phonons] a τ orbiton Description: quadrupolar (+higher order) interactions a τ orbiton 1970 Movement of Spins [Magnons] ? Movement of Orbitals [Orbitons]

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Martin RotterMagnetism in Complex Systems PrNi 2 Si 2 bct ThCr 2 Si 2 structure Space group I4/mmm Pr 3+ (4f2) J=4 -CF singlet groundstate -Induced moment system -Ampl mod mag. structure T N =20 K q=( ), M=2.35 μ B /Pr 10meV Blancoet. al. PRB 45 (1992) 2529

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Martin RotterMagnetism in Complex Systems PrNi 2 Si 2 excitations Blanco et al. PRB 56 (1997) Blanco et al. Physica B 234 (1997) 756 Neutron Scattering Experiment Calculations done by McPhase

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Martin RotterMagnetism in Complex Systems Calculate Magnetic Excitations and the Neutron Scattering Cross Section Linear Response Theory, MF-RPA.... High Speed (DMD) algorithm: M. Rotter Comp. Mat. Sci. 38 (2006) 400

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Martin RotterMagnetism in Complex Systems Summary Magnetic Diffraction Magnetic Structures Caveat on using the Dipole Approx. Magnetic Spectroscopy Magnons (Spin Waves) Crystal Field Excitations Orbitons

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How much does an average European citizen spend on Neutron Scattering per year ? NESY- Fachausschuss “Forschung mit Neutronen und Synchrotron-strahlung” der Oesterr. Physikalischen Gesellschaft, CENI – Central European Neutron Initiative (Austria, Czech Rep., Hungary) – membership at ILL (Institute Laue Langevin) Funding is strongly needed to build the ESS, the European Spallation Source Epilogue

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Martin RotterMagnetism in Complex Systems Martin Rotter, University of Oxford

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Martin RotterMagnetism in Complex Systems McPhase - the World of MagnetismMcPhase - the World of Magnetism McPhase is a program package for the calculation of magnetic properties ! NOW AVAILABLE with INTERMEDIATE COUPLING module ! Magnetization Magnetic Phasediagrams Magnetic Structures Elastic/Inelastic/Diffuse Neutron Scattering Cross Section

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Martin RotterMagnetism in Complex Systems and much more.... Magnetostriction Crystal Field/Magnetic/Orbital Excitations McPhase runs on Linux & Windows it is freeware

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Martin RotterMagnetism in Complex Systems Important Publications referencing McPhase: M. Rotter, S. Kramp, M. Loewenhaupt, E. Gratz, W. Schmidt, N. M. Pyka, B. Hennion, R. v.d.Kamp Magnetic Excitations in the antiferromagnetic phase of NdCu 2 Appl. Phys. A74 (2002) S751 M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu 2 Compounds using McPhase J. of Applied Physics 91 (2002) 8885 M. Rotter Using McPhase to calculate Magnetic Phase Diagrams of Rare Earth Compounds J. Magn. Magn. Mat (2004) 481 M. Doerr, M. Loewenhaupt, TU-Dresden R. Schedler, HMI-Berlin P. Fabi né Hoffmann, FZ Jülich S. Rotter, Wien M. Banks, MPI Stuttgart Duc Manh Le, University of London J. Brown, B. Fak, ILL, Grenoble A. Boothroyd, Oxford P. Rogl, University of Vienna E. Gratz, E. Balcar, G.Badurek TU Vienna J. Blanco,Universidad Oviedo University of Oxford Thanks to …… ……. and thanks to you !

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O a*a* c*c* Bragg’s Law in Reciprocal Space (Ewald Sphere) Incoming Neutron τ=Q Scattered Neutron k k‘

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Unpolarised Neutrons - Van Hove Scattering function S(Q,ω) for the following we assume that there is no nuclear order - =0: Splitting of S into elastic and inelastic part

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Martin RotterMagnetism in Complex Systems A short Excursion to Fourier and Delta Functions.... it follows by extending the range of x to more than –L/2...L/2 and going to 3 dimensions (v0 the unit cell volume)

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Neutron – Diffraction Lattice G with basis B : „Isotope-incoherent-Scattering“ „Spin-incoherent-Scattering“ Independent of Q: Latticefactor Structurefactor |F| 2 one element (N B =1):

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Martin RotterMagnetism in Complex Systems k k‘k‘ Q G hkl q Three Axes Spectrometer (TAS)

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Martin RotterMagnetism in Complex Systems Arrangement of Magnetic Moments in Matter Paramagnet Ferromagnet Antiferromagnet And many more.... Ferrimagnet, Helimagnet, Spinglass...collinear, commensurate etc.

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Martin RotterMagnetism in Complex Systems NdCu 2 Magnetic Phasediagram (Field along b-direction)

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Martin RotterMagnetism in Complex Systems Complex Structures AF1 Q= μ0Hb=0μ0Hb=0 μ 0 H b =1T μ 0 H b =2.6T Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499

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Martin RotterMagnetism in Complex Systems Complex Structures F1 Q= μ0Hb=0μ0Hb=0 μ 0 H b =1T μ 0 H b =2.6T Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499

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Martin RotterMagnetism in Complex Systems Complex Structures F2 Q= μ0Hb=0μ0Hb=0 μ 0 H b =1T μ 0 H b =2.6T Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499

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Martin RotterMagnetism in Complex Systems NdCu 2 Magnetic Phasediagram H||b F3 AF1 F1 a b c Lines=Experiment Colors=Theory Calculation done by McPhase

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Martin RotterMagnetism in Complex Systems NdCu 2 – Crystal Field Excitations orthorhombic, T N =6.5 K, Nd 3+ : J=9/2, Kramers-ion Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297

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Martin RotterMagnetism in Complex Systems T=10 KT=40 KT=100 K NdCu 2 - 4f Charge Density

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NdCu 2 F3 AF1 F1 F3: measured dispersion was fitted to get exchange constants J(ij) Calculations done by McPhase

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Martin RotterMagnetism in Complex Systems M. Rotter & A. Boothroyd 2008 did some calculations E. Balcar

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Martin RotterMagnetism in Complex Systems M. Rotter, A. Boothroyd, PRB, submitted CePd 2 Si 2 Calculation done by McPhase Comparison to experiment (|F M | 2 -|F M dip | 2 )/ |F M dip | 2 (%) Goodness of fit: R p dip =15.6% R p bey =8.4 % (R p nuc =7.3%) bct ThCr 2 Si 2 structure Space group I4/mmm Ce 3+ (4f1) J=5/2 T N =8.5 K q=(½ ½ 0), M=0.66 μ B /Ce

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