Magnetism in Complex Systems 2009 Magnetic Neutron Scattering Martin Rotter, University of Oxford Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Contents Introduction: Neutrons and Magnetism Elastic Magnetic Scattering Inelastic Magnetic Scattering Martin Rotter Magnetism in Complex Systems 2009

Neutrons and Magnetism Macro-Magnetism: Solution of Maxwell´s Equations – Engineering of (electro)magnetic devices 10-1m 10-3m 10-5m 10-7m 10-9m 10-11m Hall Probe VSM SQUID MOKE MFM NMR FMR SR NS Micromagnetism: Domain Dynamics, Hysteresis MFM image Micromagnetic simulation. Atomic Magnetism: Instrinsic Magnetic Properties Martin Rotter Magnetism in Complex Systems 2009

Single Crystal Diffraction E2 – HMI, Berlin neutrons: S=1/2 μNeutron= –1.9 μN τ = 885 s (β decay) k=2π/ λ E=h2/2Mnλ2=81.1meV/λ2[Å2] k Q O Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Atomic Lattice Magnetic Lattice ferro antiferro Martin Rotter Magnetism in Complex Systems 2009

The Nobel Prize in Physics 1994 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).

Magnetic Structure from Neutron Powder Diffraction GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Martin Rotter Magnetism in Complex Systems 2009

Magnetic Structure from Neutron Powder Diffraction GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Martin Rotter Magnetism in Complex Systems 2009

Magnetic Structure from Neutron Powder Diffraction GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Martin Rotter Magnetism in Complex Systems 2009

Magnetic Structure from Neutron Powder Diffraction GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Martin Rotter Magnetism in Complex Systems 2009

Magnetic Structure from Neutron Powder Diffraction GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction Experimental data D4, ILL Calculation done by McPhase Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Martin Rotter Magnetism in Complex Systems 2009

Magnetic Structure from Neutron Powder Diffraction GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Powder Diffraction Rpnuc = 4.95% Rpmag= 6.21% Experimental data D4, ILL Calculation done by McPhase Goodness of fit Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 Martin Rotter Magnetism in Complex Systems 2009

The Scattering Cross Section Scattering Cross Sections Total Differential Double Differential Scattering Law S .... Scattering function Units: 1 barn=10-28 m2 (ca. Nuclear radius2) Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 M neutron mass k wavevector |sn> Spin state of the neutron Psn Polarisation |i>, |f> Initial-,final- state of the targets Ei, Ef Energies of –‘‘- Pi thermal population of state |i> Hint Interaction -operator S. W. Lovesey „Theory of Neutron Scattering from Condensed Matter“,Oxford University Press, 1984 (follows from Fermi`s golden rule) Martin Rotter Magnetism in Complex Systems 2009

Interaction of Neutrons with Matter Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Magnetic Diffraction Difference to nuclear scattering: Formfactor ... no magnetic signal at high angles Polarisationfactor ... only moment components normal to Q contribute Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Formfactor Q= Dipole Approximation (small Q): Martin Rotter Magnetism in Complex Systems 2009

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 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 NdBa2Cu3O6.97 superconductor TC=96K orth YBa2Cu3O7-x structure Space group Pmmm Nd3+ (4f3) J=9/2 TN=0.6 K q=(½ ½ ½), M=1.4 μB/Nd ... using the dipole approximation may lead to a wrong magnetic structure ! M. Rotter, A. Boothroyd, PRB, 79 (2009) R140405 Calculation done by McPhase Martin Rotter Magnetism in Complex Systems 2009

Measuring Spin Density Distributions polarized neutron beam sample in magnetic field to induce ferromagnetic moment -> magnetic intensity on top of nuclear reflections -> nuclear-magnetic interference term: PnB Pn B Nuclear Magnetic Structure Factor Forsyth, Atomic Energy Review 17(1979) 345 “Flipping Ratio”: 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 ! Martin Rotter Magnetism in Complex Systems 2009

Inelastic Magnetic Scattering Dreiachsenspektometer – PANDA Dynamik magnetischer Systeme: Magnonen Kristallfelder Multipolare Anregungen Martin Rotter Magnetism in Complex Systems 2009

Three Axes Spectrometer (TAS) k‘ k q Q Ghkl constant-E scans constant-Q scans Martin Rotter Magnetism in Complex Systems 2009

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 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Movement of Atoms [Sound, Phonons] Brockhouse 1950 ... The Nobel Prize in Physics 1994 E Q π/a Phonon Spectroscopy: 1) neutrons 2) high resolution X-rays Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Movement of Spins - Magnons 153 MF - Zeeman Ansatz (for S=1/2) T=1.3 K Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Movement of Spins - Magnons 153 T=1.3 K Bohn et. al. PRB 22 (1980) 5447 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Movement of Spins - Magnons 153 a T=1.3 K Bohn et. al. PRB 22 (1980) 5447 Martin Rotter Magnetism in Complex Systems 2009

Movement of Charges - the Crystal Field Concept + charge density of unfilled shell E Q Hamiltonian 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” Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Movements of Atoms [Sound, Phonons] 1970 Movement of Spins [Magnons] ? Movement of Orbitals [Orbitons] a a τorbiton τorbiton Description: quadrupolar (+higher order) interactions Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 PrNi2Si2 bct ThCr2Si2 structure Space group I4/mmm Pr3+ (4f2) J=4 -CF singlet groundstate -Induced moment system -Ampl mod mag. structure TN=20 K q=(0 0 0.87), M=2.35 μB/Pr 10meV Blancoet. al. PRB 45 (1992) 2529 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 PrNi2Si2 excitations Neutron Scattering Experiment Blanco et al. PRB 56 (1997) 11666 Blanco et al. Physica B 234 (1997) 756 Calculations done by McPhase Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 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 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Summary Magnetic Diffraction Magnetic Structures Caveat on using the Dipole Approx. Magnetic Spectroscopy Magnons (Spin Waves) Crystal Field Excitations Orbitons Martin Rotter Magnetism in Complex Systems 2009

Epilogue 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

Magnetism in Complex Systems 2009 Martin Rotter, University of Oxford Martin Rotter Magnetism in Complex Systems 2009

McPhase - 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 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Crystal Field/Magnetic/Orbital Excitations McPhase runs on Linux & Windows it is freeware www.mcphase.de Magnetostriction  and much more.... Martin Rotter Magnetism in Complex Systems 2009

Thanks to …… ……. and thanks to you ! 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 NdCu2 Appl. Phys. A74 (2002) S751     M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu2 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 ! Martin Rotter Magnetism in Complex Systems 2009

Bragg’s Law in Reciprocal Space (Ewald Sphere) Incoming Neutron τ=Q q 2q Scattered k k‘ O 2/l a* c*

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

Magnetism in Complex Systems 2009 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) Martin Rotter Magnetism in Complex Systems 2009

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

Three Axes Spectrometer (TAS) k Q Ghkl k‘ q Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Arrangement of Magnetic Moments in Matter Paramagnet Ferromagnet Antiferromagnet And many more .... Ferrimagnet, Helimagnet, Spinglass ...collinear, commensurate etc. Martin Rotter Magnetism in Complex Systems 2009

NdCu2 Magnetic Phasediagram (Field along b-direction) Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Complex Structures μ0Hb=2.6T AF1 μ0Hb=1T μ0Hb=0 Q= Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Complex Structures μ0Hb=2.6T F1 μ0Hb=1T μ0Hb=0 Q= Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Complex Structures μ0Hb=2.6T F2 μ0Hb=1T μ0Hb=0 Q= Experimental data TAS6, Riso Loewenhaupt, Z. Phys. (1996) 499 Martin Rotter Magnetism in Complex Systems 2009

NdCu2 Magnetic Phasediagram H||b F1    F3  c F1  b a AF1  Lines=Experiment Colors=Theory Calculation done by McPhase Martin Rotter Magnetism in Complex Systems 2009

NdCu2 – Crystal Field Excitations orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ion Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297 Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 NdCu2 - 4f Charge Density T=100 K T=40 K T=10 K Martin Rotter Magnetism in Complex Systems 2009

NdCu2 F3  F3: measured dispersion was fitted to get exchange constants J(ij) F1  AF1  Calculations done by McPhase

Magnetism in Complex Systems 2009 E. Balcar M. Rotter & A. Boothroyd 2008 did some calculations Martin Rotter Magnetism in Complex Systems 2009

Magnetism in Complex Systems 2009 Calculation done by McPhase Comparison to experiment (|FM|2-|FMdip|2)/ |FMdip|2 (%) CePd2Si2 bct ThCr2Si2 structure Space group I4/mmm Ce3+ (4f1) J=5/2 TN=8.5 K q=(½ ½ 0), M=0.66 μB/Ce Goodness of fit: Rpdip=15.6% Rpbey=8.4 % (Rpnuc=7.3%) M. Rotter, A. Boothroyd, PRB, submitted Martin Rotter Magnetism in Complex Systems 2009