Probing excitations using Inelastic Neutron Scattering

1. Probing excitations using Inelastic Neutron Scattering Helen Walker Merlin Instrument Scientist Excitations and Polarised Neutrons Group ISIS

2. WHY? • To understand the macroscopic properties of a material, clearly we need to determine the structure Structure dictates function • However atoms are not static and certain properties are linked to the dynamics of the system

3. Images vs Movies

4. Phonons • Collective vibration of atoms within solid • Particles of mass m connected by springs with force constant C: • Energy of lattice vibration is quantized – phonon • Specific heat, melting, thermal & electrical conductivity, sound transmission, reflectivity of ionic crystals, superconductivity – electron-phonon coupling

5. Spin waves • Low energy excitations of ordered magnetic state – quantised oscillations of the relative orientations of spins on a lattice – called magnons, in analogy with phonons • E.g. Simple ferromagnet with neighbouring parallel spins S coupled by Heisenberg interaction J • Determining dispersion relation for more complex magnetic structures allows us to obtain the spin Hamiltonian

6. How? • What to use as scattering probe? • X-rays, electrons, or neutrons? • X-rays: • Electrons:              

7. How?  = 1 Å E = 82 meV  = 9 Å E = 1 meV • Neutrons:            

8. Triple Axis Spectroscopy • First TAS built in 1955 at Chalk River by Bertram Brockhouse (Nobel Prize for Physics 1994) 1. Monochromator: Neutrons diffracted by angle determining energy by Bragg’s Law 2. Sample: Neutrons scatter from sample where and define momentum transfer 3 2 1 3. Analyser: Neutrons diffracted through by analyser crystal, determining energy of neutrons detected

9. Pros & cons to TAS • Advantages • Can focus intensity on important point in reciprocal space minimizing size of sample required • Can use either constant q or E, depending on type of excitation being studied • Can use polarisation analysis to separate electronic and phonon signals • Disadvantages • Slow technique requiring expert attention • Monochromators and analysers  risk of spurions • Restricted to high symmetry directions  possibility of missing something important • Ill suited to spallation sources

10. Time of Flight spectroscopy • Indirect • Direct

11. Time of Flight spectroscopy • Indirect ki • Direct 2a ki -kf Q 2q Q -kf Excellent energy resolution Poor coverage at high E & low Q Poorer Q resolution Good Q coverage Energy resolution determined by moderator and chopper Excellent Q resolution

12. Direct chopper spectrometer

13. Direct chopper spectrometers worldwide ISIS: LET, MAPS MARI, MERLIN FRM2: TOFTOF HZB: NEAT NIST: DCS ILL: IN4, IN5, IN6 JPARC: 4SEASONS HRC, AMATERAS SNS: ARCS Sequoia CNCS OPAL: PELICAN

14. MARI • Spec • Ei = 7 meV to 1 (50) eV • L1 = 10 m • L2 = 4 m • 1000 3He tubes; 3° to 130° • ΔE/Ei = 2.5 - 5% • Magnetism, soft matter, liquids & disordered materials • No single crystals

15. MAPS • Spec • Ei = 40meV to 2eV • L1 = 10 m • L2 = 6m • 40000 3He PSD elements; main bank: 3° to 20°, high angle bank: 20° to 60° • ΔE/Ei = 1- 5% • Single crystal magnetism, catalysis • No fields/pressure

16. MERLIN • Spec • Ei = 10meV to 2eV • L1 = 11 m - guide • L2 = 2m • πsteradians3He PSD (gapless); x20 Maps flux x7 Maps detector coverage • ΔE/Ei = 4- 6% • Single crystal magnetism, phonons, disordered materials • Max field – 2.5T KCuF3 Lake et al, Nature Materials, 2005

17. LET • Spec • Ei = 0.5 to 20meV • L1 = 25 m - guide • L2 = 4m • πsteradians3He PSD (gapless); Same flux/coverage as Merlin • ΔE/Ei = 0.6–3.5% • Single crystal magnetism • Dilution temperatures, high fields, high pressure

18. Instrument Suite • MAPS • MARI • MERLIN Energy • (Flux) • LET

19. Double differential cross-section Number of neutrons deflected by (2,) per unit solid angle = Number of incident neutrons per unit area of beam = for between and Matrix element connecting initial & final states Probability of being in initial & final state Energy conservation for E transfer Scattering potential is either: Very short range nuclear force Dipole-dipole coupling with unpaired electrons

20. Inelastic scattering cross-sections • Nuclear scattering potential: • Phonon scattering fn: • Magnetic scattering potential: • Spin wave scattering fn: Intensity large for Q//vibration & increases with T Intensity large for Q   & fades above Torder

21. Powder Example

22. Science at ISIS Ladders with strong legs Low-dimensional magnets (such as “spin-ladders”) are useful materials for testing the predictions of many-body quantum mechanics. They also realise exciting new phases of matter. The group of Prof. A Zheludev (ETH Zurich) have measured the magnetic excitations of a S=1/2 spin-ladder with strong leg interactions. These results validate long-standing predictions from quantum field theory - but also test the limits of that approach. LET PHYSICS http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.111.107202

23. Science at ISIS New insights into high temperature superconductors Superconductors have the potential to revolutionise storage and transport of electricity. Iron-based superconductors are interesting because they offer another possible route to high superconducting transition temperatures other than the famous cuprate superconductors. Pengcheng Dai and co-workers at ISIS used the MERLIN and MAPS instruments to study the magnetic fluctuations in hole doped (electrons removed) and electron doped (electrons added) variants of the most widely studied iron-based superconductor. MERLIN PHYSICS Wang et al., Nature Communications 4, 2874 (2013)

24. Challenges • Competition coming from RIXS • High brilliance allows use of microscopic samples • Typically using keV incident energies, harder to obtain similar energy resolution • Cross-section not so well understood, mostly limited to study of cuprates, iridates and osmates

25. Pushing the limits • Spin waves in 0.3g FePS3 • Crystal field excitations in Ce-BAS from 45mg of Ce

26. Rep-rate multiplication

27. Rep-rate multiplication Distance Detectors Sample Fermi chopper Disc chopper Time

28. Challenges • Competition coming from RIXS • High brilliance allows use of microscopic samples • Typically using keV incident energies, harder to obtain similar energy resolution • Cross-section not so well understood, mostly limited to study of cuprates, iridates and osmates • Data analysis & visualisation of 4d+ data sets • Typically producing GB of data • Infrastructure requirements • Software development

29. Mantid • Sample alignment • Processing raw data • Visualising data

30. Horace