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Martin RotterMagnetism in Complex Systems 20091 Magnetic Neutron Scattering Martin Rotter, University of Oxford.

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Presentation on theme: "Martin RotterMagnetism in Complex Systems 20091 Magnetic Neutron Scattering Martin Rotter, University of Oxford."— Presentation transcript:

1 Martin RotterMagnetism in Complex Systems 20091 Magnetic Neutron Scattering Martin Rotter, University of Oxford

2 Martin RotterMagnetism in Complex Systems 20092 Contents Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering

3 Martin RotterMagnetism in Complex Systems 20093 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. 10 -1 m 10 -3 m 10 -5 m 10 -7 m 10 -9 m 10 -11 m Hall Probe VSM SQUID MOKE MFM NMR FMR  SR NS

4 Martin RotterMagnetism in Complex Systems 20094 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 ]

5 Martin RotterMagnetism in Complex Systems 20095 Atomic Lattice Magnetic Lattice ferro antiferro

6 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

7 Martin RotterMagnetism in Complex Systems 20097 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

8 Martin RotterMagnetism in Complex Systems 20098 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

9 Martin RotterMagnetism in Complex Systems 20099 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

10 Martin RotterMagnetism in Complex Systems 200910 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

11 Martin RotterMagnetism in Complex Systems 200911 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

12 Martin RotterMagnetism in Complex Systems 200912 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%

13 Martin RotterMagnetism in Complex Systems 200913 The Scattering Cross Section Scattering Cross Sections Total Differential Double Differential Scattering Law S.... Scattering function Units: 1 barn=10 -28 m 2 (ca. Nuclear radius 2 )

14 Martin RotterMagnetism in Complex Systems 200914 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)

15 Martin RotterMagnetism in Complex Systems 200915 Interaction of Neutrons with Matter

16 Martin RotterMagnetism in Complex Systems 200916 Magnetic Diffraction Difference to nuclear scattering : Formfactor... no magnetic signal at high angles Polarisationfactor... only moment components normal to Q contribute

17 Martin RotterMagnetism in Complex Systems 200917 Formfactor Q= Dipole Approximation (small Q):

18 Martin RotterMagnetism in Complex Systems 200918 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 241-242

19 Martin RotterMagnetism in Complex Systems 200919 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

20 Martin RotterMagnetism in Complex Systems 200920 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:

21 Martin RotterMagnetism in Complex Systems 200921 Dreiachsenspektometer – PANDA Dynamik magnetischer Systeme: 1.Magnonen 2.Kristallfelder 3.Multipolare Anregungen Inelastic Magnetic Scattering

22 Martin RotterMagnetism in Complex Systems 200922 k k‘k‘ Q G hkl q Three Axes Spectrometer (TAS) constant-E scans constant-Q scans

23 Martin RotterMagnetism in Complex Systems 200923 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

24 Martin RotterMagnetism in Complex Systems 200924

25 Martin RotterMagnetism in Complex Systems 200925 Movement of Atoms [Sound, Phonons] Brockhouse 1950... E Q π/a The Nobel Prize in Physics 1994 Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays

26 Martin RotterMagnetism in Complex Systems 200926 Movement of Spins - Magnons 153 T=1.3 K MF - Zeeman Ansatz (for S=1/2)

27 Martin RotterMagnetism in Complex Systems 200927 Movement of Spins - Magnons Bohn et. al. PRB 22 (1980) 5447 T=1.3 K 153

28 Martin RotterMagnetism in Complex Systems 200928 Movement of Spins - Magnons Bohn et. al. PRB 22 (1980) 5447 T=1.3 K a 153

29 Martin RotterMagnetism in Complex Systems 200929 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”

30 Martin RotterMagnetism in Complex Systems 200930 1950 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]

31 Martin RotterMagnetism in Complex Systems 200931 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=(0 0 0.87), M=2.35 μ B /Pr 10meV Blancoet. al. PRB 45 (1992) 2529

32 Martin RotterMagnetism in Complex Systems 200932 PrNi 2 Si 2 excitations Blanco et al. PRB 56 (1997) 11666 Blanco et al. Physica B 234 (1997) 756 Neutron Scattering Experiment Calculations done by McPhase

33 Martin RotterMagnetism in Complex Systems 200933 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

34 Martin RotterMagnetism in Complex Systems 200934 Summary Magnetic Diffraction Magnetic Structures Caveat on using the Dipole Approx. Magnetic Spectroscopy Magnons (Spin Waves) Crystal Field Excitations Orbitons

35 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, http://www.ati.ac.at/~nesy/welcome.html CENI – Central European Neutron Initiative (Austria, Czech Rep., Hungary) – membership at ILL (Institute Laue Langevin) www.ill.eu Funding is strongly needed to build the ESS, the European Spallation Source Epilogue

36 Martin RotterMagnetism in Complex Systems 200936 Martin Rotter, University of Oxford

37 Martin RotterMagnetism in Complex Systems 200937 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

38 Martin RotterMagnetism in Complex Systems 200938 and much more.... Magnetostriction Crystal Field/Magnetic/Orbital Excitations McPhase runs on Linux & Windows it is freeware www.mcphase.de

39 Martin RotterMagnetism in Complex Systems 200939 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. 272-276 (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 !

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

41 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

42 Martin RotterMagnetism in Complex Systems 200942 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)

43 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):

44 Martin RotterMagnetism in Complex Systems 200944 k k‘k‘ Q G hkl q Three Axes Spectrometer (TAS)

45 Martin RotterMagnetism in Complex Systems 200945 Arrangement of Magnetic Moments in Matter Paramagnet Ferromagnet Antiferromagnet And many more.... Ferrimagnet, Helimagnet, Spinglass...collinear, commensurate etc.

46 Martin RotterMagnetism in Complex Systems 200946 NdCu 2 Magnetic Phasediagram (Field along b-direction)

47 Martin RotterMagnetism in Complex Systems 200947 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

48 Martin RotterMagnetism in Complex Systems 200948 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

49 Martin RotterMagnetism in Complex Systems 200949 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

50 Martin RotterMagnetism in Complex Systems 200950 NdCu 2 Magnetic Phasediagram H||b F3  AF1  F1  a b c Lines=Experiment Colors=Theory Calculation done by McPhase

51 Martin RotterMagnetism in Complex Systems 200951 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

52 Martin RotterMagnetism in Complex Systems 200952 T=10 KT=40 KT=100 K NdCu 2 - 4f Charge Density

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

54 Martin RotterMagnetism in Complex Systems 200954 M. Rotter & A. Boothroyd 2008 did some calculations E. Balcar

55 Martin RotterMagnetism in Complex Systems 200955 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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