Magnetic neutron diffraction

Transcription

1 Magnetic neutron diffraction Rob McQueeney Physics 590 1

2 Magnetic moment-rare earths Progressive filling of 4f levels Strong Hund s rules Strong spin-orbit interaction Weak CEF Unpaired electrons Total angular momentum J = L + 2S µ = g J µ B J g J J e 2m e Physics 590 2

3 Transition metals Progressive filling of 3d levels Strong Hund s rules interactions Strong CEF Weak spin-orbit interaction Unpaired electrons Spin moment Orbital moment (quenched) µ = gµ B S 2S e 2m e transition metal oxygen Physics 590 3

4 Magnetic structures Exchange coupling between moments leads to ordering Direct exchange Superexchange (insulators) RKKY (metals) Dipolar Magnetic anisotropy leads to moment direction Magnetic structures defined by Propagation vector(s) Moment size Moment direction(s) Elastic scattering - Bragg s Law 2dsinθ = nλ Physics 590 4

5 1-D cartoons Physics 590 5

6 Neutron magnetism Spin-1/2 particle Magnetic moment µ n = γµ N = e 2m p n µ n /µ e m e /m p =1/2000 Physics 590 6

7 Dipole interaction Interaction between neutron and electron U = µ n B = µ 0 γe 2 σ B = γr 0 σ B 4π m e U uv = ub ps σ v p = γr 0 gsf (Q) strength z S = ˆ S ( ˆ S ˆ Q ) ˆ S n B = B L + B S Q U ++ = b ps z x y U = b + ps z U + = p(s x + is y ) U + = p(s x is y ) Only moment projection perp. to Q will scatter neutrons Physics 590 7

8 Magnetic cross-section ( γr 0 ) 2 = 291 millibarns/steradian b 2 (Fe) = 895 mb/sr Physics 590 8

9 Magnetic form factor f(q): Fourier transform of the atomic magnetization density Physics 590 9

10 Magnetic structure factor Magnetic structure factor is actually a vector quantity, but for collinear structure, can be simplified 1 F M (τ) = 2 g S d d σ d F d (Q) exp( W d )exp( iτ d) d ordered form factor moment moment direction dipole scattering DW factor dσ dω = Nr 2 0 (1 ˆ τ 2 z ) F M (τ) 2 phase factor Scattering differential cross-section for unpolarized beam More generally dσ dω = Nr 2 0 strength τ δ( Q τ) Q ˆ {M(τ) Q ˆ } 2 Fourier transform of magnetization density Physics

11 1-D Cartoons Physics

12 Determine magnetic structure Prescription Measure the magnetic propagation vector(s) Magnetic space group Limits the possible structures You need to know the crystal structure Detemine moment direction(s) (refinement) Potential problems Magnetic domains Crystallographic twinning Multiple wavevectors/multi-q structures Physics

13 Confirmation of AF structure In 1949, Clifford Shull observed additional magnetic reflections in MnO, which led to the confirmation of antiferromagnetism Shull and J. S. Smart, Phys Rev 76, 1256 (1949). C. G. Shull et al., Phys. Rev. 83, 333 (1951). Physics

14 Cone structure of Er incommensurate Alternating cone structure Spin slips from magnetoelastic effect H. Lin et al., Phys. Rev B 45, (1992). Physics

15 Cone structure of Er CAM Slip cone Cone Physics

16 Neutron polarization analysis Why use polarization? Separate magnetic/nuclear scatt. (q=0 structures) Refine structure determination (eg. canting) Separate coherent/incoherent (diffuse scattering, mag. densities) z x Q y U ++ = b ps z U = b + ps z U + = p(s x + is y ) U + = p(s x is y ) Physics

17 Instrumentation Monochromator Crystal magnetization U ++ = b ps z unpolarized polarized U = b + ps z 0 Cu 2 MnAl (111) (Heusler) Spin flippers Physics

18 Spin-flip vs. Non-spin-flip unpolarized beam polarizing mono flipper sample flipper polarizing analyzer OFF NSF(++) SF(+-) OFF ON Useful modes P Q (in-plane polarization): All magnetic scattering is SF P Q (vertical polarization): magnetic scattering can be SF & NSF Physics

19 Polarized experiments NSF NSF SF SF Separation of magnetic/nuclear Paramagnetic scattering Physics Moon, Koehler, Riste, Phys. Rev 181, 920 (1969).

20 pulsed source 3 He polarizers Heusler mono won t work for wide angle scattering Physics

21 Further references Magnetic neutron scattering G. Squires, Intro to theory of thermal neutron scattering, Dover, S. Lovesey, Theory of neutron scattering from condensed matter, Oxford, Moon, Koehler, Riste, Phys. Rev 181, 920 (1969). R. Pynn, Structural refinements GSAS FullProf Magnetic space groups Izyumov, Ozerov, Neutron diffraction of magnetic materials Sarah program (representational analysis) Physics