Magnetic Neutron Scattering

1. Magnetic Neutron Scattering Collin Broholm* Johns Hopkins University and NIST Center for Neutron Research Neutron spin meets electron spin Magnetic neutron diffraction Inelastic magnetic neutron scattering Polarized neutron scattering Summary *Supported by the NSF through DMR-9453362 and DMR-0074571

2. Magnetic properties of theneutron The neutron has a dipole moment mn is 960 times smaller than the electron moment A dipole in a magnetic field has potential energy Correspondingly the field exerts a torque and a force driving the neutron parallel to high field regions

3. The transition matrix element The dipole moment of unfilled shells yield inhomog. B-field The magnetic neutron senses the field The transition matrix element in Fermi’s golden rule Magnetic scattering is as strong as nuclear scattering It is sensitive to atomic dipole moment perp. to

4. The magnetic scattering cross section Spin density spread out scattering decreases at high k The magnetic neutron scattering cross section For unspecified incident & final neutron spin states

5. Un-polarized magnetic scattering Squared form factor DW factor Polarization factor Fourier transform Spin correlation function

6. Magnetic neutron diffraction Time independent spin correlations elastic scattering Periodic magnetic structures Magnetic Bragg peaks Magnetic primitive unit cell greater than chemical P.U.C. Magnetic Brillouin zone smaller than chemical B.Z. The magnetic vector structure factor is

7. Simple cubic antiferromagnet No magnetic diffraction for Real space ‘ Reciprocal Space

8. Not so simple Heli-magnet : MnO2 c b a characterize structure and Insert into diffraction cross section to obtain

9. Understanding Inelastic Magnetic Scattering: Isolate the “interesting part” of the cross section The “scattering law” is defined as for a wide class of systems It satisfies useful sum-rules Detailed balance Total moment First moment sum-rule

10. Scattering from a quantum spin liquid Dimerized spin-1/2 system: copper nitrate

11. Why a gap in spectrum of dimerized spin system J • A spin-1/2 pair has a singlet - triplet gap: • Weak inter-dimer coupling cannot close gap • Bond alternation is relevant operator for quantum critical uniform spin chain infinitesimal bond alternation yields gap

12. Spin waves in a ferromagnet Magnon creation Magnon destruction Dispersion relation Gadolinium Magnon occupation prob.

13. Spin waves in an antiferromagnet Dispersion relation

14. r ( ) and the magnetic susceptibility to • We convert inelastic scattering data to • Compare with bulk susceptibility data • Isolate non-trivial temperature dependence • Compare with theories ab k w S , Compare to the generalized susceptibility They are related by the fluctuation dissipation theorem

15. Polarized magnetic neutron scattering Specify the incident and final neutron spin state Non spin flip: Spin flip:

16. Polarized neutron scattering Nuclear isotope incoherent scattering Paramagnetic scattering MnF2 H//k H//k SF SF NSF NSF

17. Summary • The neutron has a small dipole moment that causes it to scatter from inhomogeneous internal fields produced by electrons • The magnetic scattering cross section is similar in magnitude to the nuclear cross section • Elastic magnetic scattering probes static magnetic structure • Inelastic magnetic scattering probes spin dynamics through • Polarized neutrons can distinguish magnetic and nuclear scattering and specific spin components