Neutron Scattering of Magnetic excitations - E21

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Neutron Scattering of Magnetic excitations - E21

Neutron Scattering ofMagnetic excitationsMagnetic excitations, magnons, and spin chainsby Ibrahima DialloTechnische Universität MuenchenWednesday, February 6, 13


OutlineProperties of the NeutronSpin, spin waves, and magnonsElastic/Inelastic Scattering and instrumentationNuclear and Magnetic interactionsPerovskite exampleWednesday, February 6, 13


Properties of the NeutronMassChargeMagnetic monopole momentElectric dipole momentSpinMagnetic dipolar momentBrückel, Heger, Richter (2007)Wednesday, February 6, 13


Spin Waves (magnons)All electrons carry a spin of 1/2Intuitively, spin is the rotation of electrons about their axis.Spins produce a dipolar magnetic field (bar magnet like)University of MuenterWednesday, February 6, 13


Spin Waves (magnons)All electrons carry a spin of 1/2Intuitively, spin is the rotation of electrons about their axis.Spins produce a dipolar magnetic field (bar magnet like)University of MuenterWednesday, February 6, 13


Spin Waves (magnons)DiamagnetismParamagnetism (Li, Mo, Ta)Ferromagnetism (Fe, Ni, Co, and their alloys)Antiferromagnetism (Hematite, Cr, FeMn,NiO)Spin glassFerrimagnetism (YIG, FeO ferrites, Mn)University of MuenterWednesday, February 6, 13


Elastic ScatteringIn an elastic scattering event, a momentum istransferred from the neutron to the sample, but theinternal state of the sample remains unchanged.Wednesday, February 6, 13


Ineslastic ScatteringInelastic scattering of neutrons creates or annihilates anexcitation inside the sample, so that both the energy ofthe neutron and the internal state of the sample arechanged. Both flight direction and energy must be tracked.Wednesday, February 6, 13


Ineslastic ScatteringTriple Axis SpectrometerTime of Flight SpectrometerSpin Echo SpectrometerMax-Planck Institute for Solid State ResearchWednesday, February 6, 13


Ineslastic ScatteringTriple Axis SpectrometerTime of Flight SpectrometerSpin Echo SpectrometerMax-Planck Institute for Solid State ResearchWednesday, February 6, 13


Ineslastic ScatteringTriple Axis SpectrometerTime of Flight SpectrometerSpin Echo SpectrometerMax-Planck Institute for Solid State ResearchWednesday, February 6, 13


Magnetic and Nuclear ScatteringNuclearstrong interaction of particle physics responsible for binding neutrons and protons in thenuclei.MagneticInteraction between dipolar moments of neutrons and magnetic field of unpairedelectrons.Wednesday, February 6, 13


Cross sectionElastic caseInteraction with magnetic fieldEnergy conservationSpin only interactionInelastic caseSpin only magnetic scatteringFirst Born approximationStructure FactorWednesday, February 6, 13


Magnetic and Nuclear ScatteringNeutron magneticinterference effectBoth magnetic and nuclear scatteringcontribute to a Bragg reflection.Neutron spin filterThe reaction proceeds through anintermediate state S=0. Thus, theabsorption cross section for neutronswith spins antiparallel is thereforeabout three orders of magnitude largerthan if neutron and 3 He spins areparallel.Wednesday, February 6, 13


Polarized Neutronshttp://www.orau.org/council/02presentations/klose.pdfWednesday, February 6, 13


Magnetic and Nuclear ScatteringMagnetic interactions, described by F(Q), decreases towards large Q, whereas there is no formfactor for nuclear scattering. Strong reflections with large Q must therefore be nuclear in origin.Magnetic Bragg peaks vanish at the magnetic ordering temperature (the Curie temperature Tcfor ferromagnets, or the Néel temperature Tn for antiferromagnets). Nuclear Bragg peaksvanish at the melting temperature, which is typically larger than the ordering temperature.The neutron spin operator does not appear in the cross section for coherent nuclear scattering.The neutron spin state is therefore unaffected by nuclear scattering. By contrast, magneticneutron scattering can be (but does not have to be) associated with a spin-flip of the neutron.Utilize the different temperature dependences of the two contributions, since the nuclearscattering normally changes relatively slowly with temperature.If this is not adequate, perform polarized neutron scattering, in which the spin states of theincoming and scattered neutrons are determined, making it possible to isolate the scattering ofpurely magnetic origin (Moon, Riste and Koehler 1969).Wednesday, February 6, 13


PerovskitesKoehler, Woolen, and Wilkinson, Phys. Rev. 118.58 (1960)Wednesday, February 6, 13


PerovskitesKoehler, Woolen, and Wilkinson, Phys. Rev. 118.58 (1960)Wednesday, February 6, 13


PerovskitesKoehler, Woolen, and Wilkinson, Phys. Rev. 118.58 (1960)Wednesday, February 6, 13


PerovskitesKoehler, Woolen, and Wilkinson, Phys. Rev. 118.58 (1960)Wednesday, February 6, 13


SummaryNeutrons have a small dipole moment that causes themto scatter from magnetic fields produced by electrons.Magnetic scattering cross section is similar in magnitudeto the nuclear cross section.Polarized neutrons and transition temperatures allow thedistinction of nuclear and magnetic events.Neutrons are the probe for investigating magneticproperties.Wednesday, February 6, 13


ReferencesS. W. Lovesey, Theory of neutron scattering from condensed matter, vol. 1 and 2, Oxford University Press, 1984Koehler, Woolen, and Wilkinson. Phys. Rev 118, 58 (1960)J. T. Haraldsen et al., Phy. Rev. B. 71, 064403 (2005)M. Zayed, Thesis, Ch. 5 ”Pressure induced quantum phases” (2010)M. Albrecht and F. Mila, Europhys. Lett. 34, 145 (1996)M. Bee, Quasielastic Neutron Scattering: Principles andApplications in Solid State Chemistry, Biology and Materials Science, Adam Hilger, Bristol and Philadelphia(1988)http://www.uni-muenster.de/Physik.AP/Demokritov/en/Forschen/Forschungsschwerpunkte/mBECwasw.htmlhttp://www.orau.org/council/02presentations/klose.pdfWednesday, February 6, 13


Wednesday, February 6, 13Thank You!

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