The Structure and Dynamics of Solids The Muppet’s Guide to: The Structure and Dynamics of Solids Neutron Diffraction and Magnetism

Neutron Scattering Neutron scattering is more complicated than x-rays because neutrons are defined both by their wavevector, k, and spin, s. They can be polarised - ±S Scattering cross section will depend on both the neutron-nuclear (structure) and the nuclear spin interaction with any magnetic moments

Atomic Nuclear Factor - Structure Very strong interaction because it is the same force that bind the nucleus together Approximate the scattering potential as a Fermi pseudo potential: As r0 ~10-15 m the interaction is essentially point like

Atomic Nuclear Factor - Structure The spatial density distribution of the nucleus is an infinitesimal point with respect to the neutron wavelength. Thus, nuclear scattering factor for neutrons is a constant and independent of q. No sinq/l correction

X-ray and Neutron comparison: Neutrons: X-rays: Neutrons: Point like, isotope dependent, sensitive to light elements. Contrast varied by isotope substitution. X-rays: Extended scatters, depends only on number of electrons – can’t ‘see’ light elements. Contrast change through anomalous scattering

Contrast Matching Unlike x-rays the neutron cross section is isotope dependent. Isotope b 1H, Hydrogen -3.7406(11) 2H, Deuterium 6.671(4) 3H, Tritium 4.792(27) Controlled mixing of 1H and 2H allows contrast to be changed. Very powerful technique for soft condensed matter.

Magnetic Interactions… The magnetic moment of the neutron interacts with the magnetic moment of any unpaired electrons within a crystal - and this probes the magnetic structure. energy associated with the neutron magnetic moment, mN in the internal field of the ion, H SPIN ORBIT

magnetic scattering amplitude for an ion is related to the Fourier Transform of the total magnetisation density, M(r):: As the magnetism arises from unpaired electrons in outer shells and not the nucleus there is a dependence on intensity, similar to the sin(q) / l used for x-rays

Scattering in Reciprocal Space Peak positions and intensity tell us about the structure: Underlying translational symmetry Periodicity within the sample Peak Position Peak Width Extent of periodicity Particle / Grain size Peak Intensity Atomic positions Order / disorder

Magnetic Super-Structures Ferromagnetic: Magnetic and charge have the same unit cell Anti-Ferromagnetic: Magnetic and charge have the different unit cells. Magnetic cell double nuclear cell.

RuSrGdCuO Powder Magnetic Diffraction Peaks

Conventional Wisdom Everyone knows that x-rays are good for studying structure X-rays Energies typically keV (Elastic scattering) Scatters from electrons (High Z materials) Strongly absorbed Good for imaging High Flux High resolution

Magnetic X-ray Scattering Recall the atomic scattering factor: Atomic scattering length:

From and e- to a magnetic atom As electrons are orbiting a nucleus we need to include orbital as well as spin components in the magnetic term. S(q) is the FT of time averaged spin density and L(q) the corresponding FT of the orbital density A and B are vectors which contain the polarisation dependences…. M. Blume and D. Gibbs, Phys. Rev. B 37 1779-1789 (1988)

Magnetic X-ray Scattering Pre-factor relates reduces magnetic scattering intensity by ~106. The maximum intensity is about 2counts / min above the background Counts in 225 mins. or 3¾hrs Data set takes 4 days to collect M. Blume and D. Gibbs, Phys. Rev. B 37 1779-1789 (1988) & F. de Bergevin PRL 39A(2) 1972

Realistic Magnetic X-ray scattering Make electronic interactions sensitive to the magnetic moment. X-ray Magnetic Circular Dichroism (XMCD) 2 step process that couples circular polarised x-rays to a the absorption processes in a magnetic material X-ray analogue to the Kerr effect

Electronic resonances A core electron is excited and creates a spin polarised photoelectron Exchange split final states act as a filter of the spin Magnetic sensitivity comes through the spin-orbit coupling and exchange and has strong polarisation dependence (MOKE) Courtesy W. Kuch, Freie Universität Berlin

XMCD Examples at Resonant Edges From Magnetism by J. Stöhr and H.C. Siegmann, Springer