Magnetic Neutron Scattering Collin Broholm Johns Hopkins Institute

Magnetic Neutron Scattering Collin Broholm Johns Hopkins Institute for Quantum Matter

Overview of Tutorial v Neutron spin meets electron spin v Magnetic neutron diffraction v Inelastic magnetic neutron scattering v Polarized neutron scattering v Summary

Magnetic properties of the neutron 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

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 similar in strength to nuclear scattering It is sensitive to atomic dipole moment perp. to

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

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

Magnetic neutron diffraction Time independent spin correlations Periodic magnetic structures elastic scattering 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

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

Not so simple Heli-magnet : Mn. O 2 c a b and Insert into diffraction cross section to obtain characterize structure

Diffuse Elastic Magnetic Scattering Pinch points

Understanding Inelastic Magnetic Scattering: Isolate the “interesting part” of the cross section The “scattering law” is defined as For systems in thermodynamic equilibrium Detailed balance Total moment & 1 st moment satisfies sum-rules

Weakly Interacting spin-1/2 pairs in Cu-nitrate

Sum rules and the single mode approximation When a coherent mode dominates the spectrum: Sum-rules link and : Scattering data Single model 0. 5 0. 4 0 2 4 q (p) 0 2 4 6

Spin waves in a ferromagnet Magnon creation Gadolinium Magnon destruction Dispersion relation Magnon occupation number ACNS 6/29/10

Spin waves in an antiferromagnet Dispersion relation ACNS 6/29/10

Continuum magnetic inelastic scattering Inelastic scattering is not confined to disp. relations when ü a thermal ensemble of excitations is present ü and do not uniquely specify excited state Cu(C 4 H 4 N 2)(NO 3)2 S=1/2

& the generalized susceptibility Compare to the generalized susceptibility They are related by a fluctuation-dissipation theorem We convert inelastic scattering data to • Compare with bulk susceptibility data • Expose non-trivial temperature dependence • Compare with theories to

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

Polarized neutron scattering YBa 2 Cu 3 O 7 by Mook et al. PRL (1993) magnetic Nuclear

Summary • The neutron has a small dipole moment causing scattering from electrons • Magnetic scattering is similar in magnitude to nuclear scattering • Elastic magnetic scattering probes static magnetic structure • Inelastic magnetic scattering probes dynamics correlations through • Spin resolved scattering distinguishes magnetic and nuclear processes and spin components