Neutron scattering a probe for multiferroics and magnetoelectrics

Transcription

1 1 Neutron scattering a probe for multiferroics and magnetoelectrics V. Simonet Institut Néel, CNRS/UJF, Grenoble, France

2 Outline of the lecture 2 The neutron as a probe of condensed matter Properties Sources Environments Scattering processes Diffraction by a crystal Nuclear, magnetic structures Instruments type Examples Inelastic scattering Phonons, spin waves, localized excitations Instruments type Examples Polarized neutrons Longitudinal, spherical polarization analysis Examples

3 Outline of the lecture 3 The neutron as a probe of condensed matter Properties Sources Environments Scattering processes Diffraction by a crystal Nuclear, magnetic structures Instruments type Examples Inelastic scattering Phonons, spin waves, localized excitations Instruments type Examples Polarized neutrons Longitudinal, spherical polarization analysis Examples

4 4 Properties: The neutron as a probe of condensed matter Subatomic particle discovered in 1932 by Chadwik First neutron scattering experiment in 1946 by Shull Neutron: particle/plane wave with and Wavelength of the order of few Å interatomic distances diffraction condition Energies of thermal neutrons k B T 25 mev of the order of the excitations in condensed matter Neutral: probe volume, nuclear interaction with nuclei

5 5 Properties: The neutron as a probe of condensed matter carries spin ½: sensitive to spins of unpaired electrons probe magnetic structure and dynamics possibility to polarize neutron beam Scattering length X rays neutrons Better than XR for Light or neighbor elements Z Neutron needs big samples

6 6 The neutron as a probe of condensed matter Two types of neutron sources for research: neutron reactor (ex. ILL Grenoble 57 MW), spallation sources (ex. ISIS UK 1.5 MW) FISSION SPALLATION 235 U U, W, Hg

7 7 Various environments : Temperature: 15 mk-700 K High magnetic fields up to 15 T (D23, ILL) Pulsed fields up to 30 T (IN22, ILL) Pressure (gas, Paris-Edinburgh, clamp cells) up to 30 kbar Electric field CRYOPAD zero field chamber for polarization analysis CRYOPAD The neutron as a probe of condensed matter D23@ILL 15 T magnet

8 8 The neutron as a probe of multiferroics and magnetoelectrics Microscopic probe of atomic positions magnetic arrangements related excitations Example: orthorhombic RMnO 3 Goto et al. PRL (2005) Complex magnetic structures spirals, sine waves modulated, incommensurate Link with atomic positions Complex phase diagrams (T, P, H, E) Hybrid excitations: electromagnons Domains manipulation under E/H fields Chirality determination and manipulation ferroelectric

9 Scattering processes 9 Counts neutrons scattered by sample in solid angle dω for energy transfer Cross section in barns (10-24 cm 2) after integration on energy and solid angle detector 2θ sample dω Inelastic scattering E f2 >E i k f2 > k i Scattering vector Elastic scattering E f =E i k f = k i Q=2sinθ/λ Inelastic scattering E f1 <E i k f1 < k i Incident neutrons E, k i

10 Scattering processes 10 Fermi s Golden rule Interaction potential Sum of nuclear and magnetic scattering Energy conservation

11 Scattering processes 11 Sum of nuclear and magnetic scattering Interaction potential very short range isotropic b Scattering length depends on isotope and nuclear spin Interaction potential Longer range (e - cloud) Anisotropic dipolar interaction: neutron magnetic moments with magnetic field from unpaired e - Spin contribution Orbital contribution

12 Scattering processes 12 d 2 σ dωde = k f ( 1 k i 2π ) j,j neutron with the scattering amplitude A j (0)A j (t)e i Q R j (0) e i Q R j (t) e iωt dt neutron nucleus j electron i Projection of the Magnetic moment _ to isotropic maximum intensity for

13 Scattering processes 13 d 2 σ dωde = k f ( 1 k i 2π ) j,j neutron with the scattering amplitude A j (0)A j (t)e i Q R j (0) e i Q R j (t) e iωt dt neutron nucleus j electron i p= x10-12 cm magnetic form factor of the free ion Scattering experiment FT of interaction potential

14 Scattering processes 14 d 2 σ dωde = k f ( 1 k i 2π ) j,j neutron with the scattering amplitude A j (0)A j (t)e i Q R j (0) e i Q R j (t) e iωt dt neutron nucleus j electron i = Double FT in space and time of the correlation function of the nuclear magnetic density in and

15 Scattering processes Separation elastic/inelastic: Keeps only the time-independent (static) terms in the cross-section and integrate over energy elastic scattering

16 Outline of the lecture 16 The neutron as a probe of condensed matter Properties Sources Environments Scattering processes Diffraction by a crystal Nuclear, magnetic structures Instruments type Examples Inelastic scattering Phonons, spin waves, localized excitations Instruments type Examples Polarized neutrons Longitudinal, spherical polarization analysis Examples

17 Diffraction from a crystal 17 Nuclear diffraction crystal lattice reciprocal lattice diffraction condition (lattice) Coherent elastic scattering from crystal Bragg peaks at nodes of reciprocal lattice

18 Diffraction from a crystal 18 Nuclear diffraction with for a Bravais lattice: 1 atom/unit cell Non Bravais lattice: ν atoms/unit cell F N ( Q)=b F N ( Q)= ν b ν e i Q.r ν Nuclear structure factor Information on atomic arrangement inside unit cell

19 Diffraction from a crystal 19 Magnetic diffraction magnetic ordering may not have same periodicity as nuclear one propagation vector periodicity and propagation direction

20 Diffraction from a crystal 20 Magnetic diffraction magnetic ordering may not have same periodicity as nuclear one propagation vector periodicity and propagation direction for a non-bravais lattice Bragg peaks at satellites positions diffraction condition

21 Diffraction from a crystal 21 Magnetic diffraction magnetic ordering may not have same periodicity as nuclear one propagation vector periodicity and propagation direction for a non-bravais lattice magnetic structure factor: info. on magnetic arrangement in unit cell F M ( Q = H + τ )=p f ν ( Q)m ν,τ e i Q.r ν Magnetic moment of atom ν in n th unit cell p= x10-12 cm Fourier component associated to

22 Diffraction from a crystal 22 Magnetic diffraction: classification of magnetic structures If =0, magnetic/nuclear structures same periodicity Bragg peaks at reciprocal lattice nodes Bravais lattice =0 ferromagnetic structure Direct space Reciprocal space

23 Diffraction from a crystal 23 Magnetic diffraction: classification of magnetic structures If =0, magnetic/nuclear structures same periodicity Bragg peaks at reciprocal lattice nodes Non Bravais lattice =0 ferromagnetic structure or not Arrangement of moments in cell intensities of magnetic peaks Direct space Reciprocal space

24 Diffraction from a crystal 24 Magnetic diffraction: classification of magnetic structures If 0, magnetic satellites at Ex., antiferromagnetic structure Direct space Reciprocal space Rational Irrational, commensurate magnetic structure, incommensurate magnetic structure

25 Diffraction from a crystal 25 Magnetic diffraction: classification of magnetic structures and Sine wave modulated and spiral structures Direct space Reciprocal space Direct space Reciprocal space

26 26 Diffraction from a crystal Magnetic diffraction: classification of magnetic structures and Sine wave modulated and spiral structures Example TbMnO 3 Kenzelmann et al., PRL K<T<41 K : incommensurate sine wave modulated paraelectric T<28 K : commensurate spiral (cycloid) ferroelectric

27 Diffraction from a crystal 27 Magnetic diffraction: classification of magnetic structures Single- and multi- magnetic structures : ex canted arrangement

28 28 Diffraction from a crystal Solving a magnetic structure Find the propagation vector (periodicity of magnetic structure): powder diffraction difference between measurements < and > T c. Indexing magnetic Bragg reflections with Refining Bragg peaks intensities moment values and Magnetic arrangement of atoms in the cell (using scaling factor from nuclear structure refinement) with programs like Fullprof, CCSL, MXD Help with group theory and representation analysis Use of rotation/inversion symmetries to infer possible magnetic arrangements compatible with the symmetry group that leaves invariant (pgm like basireps ) (cf. L. Chapon s lecture)

29 Diffraction from a crystal Techniques: powder diffractometers 29 Bragg s law Fixed θ, varying λ: time-of-flight diffractometer (spallation source) D2B@ILL Fixed λ, varying θ (or multidetector): 2-axes diffractometer (neutron reactor)

30 Diffraction from a crystal Techniques: single-crystal diffractometers Bring a reciprocal lattice node in coincidence with then measure its integrated intensity (rocking curve) 30 4-circles mode lifting arm (bulky environments) detector

31 Diffraction from a crystal Techniques: difference powder/single-crystal diffraction 31 All reciprocal space accessible in same acquisition Best to find propagation vector Sometimes not enough information to solve structure (Several Bragg peaks at at same positions) Each reciprocal space point accessible by set up positioning Usually better signal/noise More information to solve complex magnetic structures Sometimes problem with magnetic domains

32 Diffraction from a crystal 32 Purpose : solve nuclear and magnetic structures, distortion under external parameters, variation of unit cell Example: YMnO 3 Influence of AF transition on on ferroelectric order Powder diffraction : Nuclear & magnetic structures Mn-O distance variation Lee et al., PRB 2005

33 Diffraction from a crystal 33 Example: YMnO 3 Mn-O distance variation Coupling spin lattice at T N Lee et al., PRB 2005

34 Diffraction from a crystal 34 Example: Ba 3 NbFe 2 Si 2 O 14 powder and single-crystal diffraction Complex magnetic structure Powder diffraction Propagation vector =(0, 0, 1/7) b a triangular lattice of Fe 3+ triangles, S=5/2

35 Diffraction from a crystal 35 Example: Ba 3 NbFe 2 Si 2 O 14 Single-crystal diffraction 120 moments on triangles in (a, b) plane Helices propagating along c Marty et al., PRL 2008

36 Outline of the lecture 36 The neutron as a probe of condensed matter Properties Sources Environments Scattering processes Diffraction by a crystal Nuclear, magnetic structures Instruments type Examples Inelastic scattering Phonons, spin waves, localized excitations Instruments type Examples Polarized neutrons Longitudinal, spherical polarization analysis Examples

37 Reminder on phonons Displacement from equilibrium harmonic forces Inelastic scattering from a crystal Normal modes (stationary waves) Characterized by wave vector Frequency Polarization longitudinal transverse Frequency related to by dispersion relation

38 Inelastic scattering from a crystal Reminder on phonons Displacement from equilibrium harmonic forces Normal modes (stationary waves) Characterized by wave vector Frequency Polarization longitudinal transverse diatomic chain Acoustic modes Optic modes Frequency related to by dispersion relation

39 Inelastic scattering from a crystal Reminder on phonons Displacement from equilibrium harmonic forces Normal modes (stationary waves) Characterized by wave vector Frequency Polarization longitudinal transverse Frequency related to by dispersion relation p atoms/unit cell ω-scans at constant -scans at constant ω 3p-3 optic branches 3 acoustic branches

40 Reminder on phonons Inelastic scattering from a crystal Quantum description: modes=quasi-particles called phonon Creation/annihilation processes in cross-section dynamical nuclear structure factor

41 Reminder on spin waves Inelastic scattering from a crystal Spin waves as elementary excitations of magnetic compounds = transverse oscillations in relative orientation of the spins Spin waves in ferromagnet Characterized by wave vector Frequency Certain spin components involved Frequency related to by dispersion relation 1 atom/unit cell

42 Inelastic scattering from a crystal Reminder on spin waves 1 atom/unit cell Crystal with p atoms/unit cell: p branches Spin waves in antiferromagnet (0 1 l) Quantum description: spin wave mode=quasi-particle called magnon Creation/annihilation processes in cross-section dynamical magnetic structure factor

43 Inelastic scattering from a crystal Nuclear excitations Magnetic excitations Phonons and magnons Form factor Form factor with Intensity max for and zero for Intensity maximum for Localized excitations Transition between energy levels : non dispersive signal Example crystal field excitations in rare-earth ions

44 Instruments: triple-axis Measure scattered neutrons as a function of and Inelastic scattering from a crystal Detector Analyser Sample Monochromator

45 Instruments: time-of-flight Inelastic scattering from a crystal Neutron pulses chopped from a monochromatic beam Arrival time and position on multi detector give final energy and Q

46 Inelastic scattering from a crystal Instruments: Time-of-Flight versus Triple-Axis Powder (sometimes single-crystal) t-scans at fixed 2θ Multidetector (all reciprocal space accessible in one acquisition) Resolution 1% Used for localized excitations Often not enough to analyze collective excitations Single-crystal (sometimes powder) Positioning at each points single-detector Scattering plane accessible only Resolution 5% Use to study collective excitations

47 Inelastic scattering from a crystal 47 Purposes of inelastic scattering experiments: Nuclear: Information on elastic constants, sound velocity, Structural instabilities Magnetic: Information on magnetic interactions and microscopic mechanisms yielding the magnetic order In multiferroics: Spin-lattice coupling, hybrid modes ex. electromagnons

48 Inelastic scattering from a crystal Example: hexagonal RMnO 3 When spin waves helps solving magnetic structures Different possible Mn 120 magnetic orders: impossible to distinguish with unpolarized neutrons diffraction Fabrèges et al., PRL 2009 R crystal field levels transitions depends on the two J z exchange interactions: Given by spin waves

49 Inelastic scattering from a crystal Example: YMnO 3 Spin and lattice excitations Oxygens Petit et al., PRL 2008 Phonon mode polarized along the ferroelectric c axis Mn (q 0 12) Spin wave dispersion (q 0 6)

50 Inelastic scattering from a crystal Example: YMnO 3 Petit et al., PRL 2008 Opening of a gap in phonon mode below T N locked on the spin wave mode Resonant interaction between both modes = Strong spin-lattice coupling

51 Outline of the lecture 51 The neutron as a probe of condensed matter Properties Sources Environments Scattering processes Diffraction by a crystal Nuclear, magnetic structures Instruments type Examples Inelastic scattering Phonons, spin waves, localized excitations Instruments type Examples Polarized neutrons Longitudinal, spherical polarization analysis Examples

52 Use of polarized neutrons Cross section depends on the spin state of the neutron. Polarized neutron experiment uses this spin state and its change upon scattering process to obtain additional information Polarization P = two spin state populations difference

53 Use of polarized neutrons Blume-Maleyev equations Unpolarized neutrons P 0 initial polarization P f final polarization Information about correlations between nuclear-magnetic terms, between different spin components: ex. chiral term

54 Use of polarized neutrons Principle of an experiment Select spin state and direction of incident neutron Analyze polarization of scattered beam in same direction: longitudinal polarization analysis Analyze polarization of scattered beam in any direction: spherical polarization analysis Z X Y

55 Longitudinal polarization analysis Use of polarized neutrons NSF N N N Incident beam Heussler monochromator SF C Scattered beam sample Helmotz coils Heussler Analyzed beam Separation magnetic/nuclear access to spin components M x, M y, M z Separation coherent/incoherent Access to chirality and nuclear/magnetic interference terms Detector

56 Use of polarized neutrons 56 Spherical polarization analysis CRYOPAD Zero magnetic field chamber Polarization matrix P final polarization incident polarization refine complex magnetic structure Access to non-diagonal terms of the polarization matrix probe domains

57 Use of polarized neutrons Example: YMnO 3 Longitudinal polarization analysis Spin flip: magnetism T>T N T<T N Non Spin flip: nuclear Hybrid Goldstone mode of multiferroic phase spin waves dresses with atomic fluctuations Pailhès et al., PRB 2009

58 Use of polarized neutrons Chirality and ferroelectricity Chirality: sense of spin precession in spiral or triangular arrangements Magnetic spiral order ferroelectricity with Katsura et al. PRL (2005) Mostovoy PRL (2006) Sergienko et al. PRB (2006)

59 Use of polarized neutrons Chirality and ferroelectricity Example: Ba 3 NbFe 2 Si 2 O 14 Static Chirality 2 chiralities associated to helices and triangular arrangements 4 possible chiralities (+1,+1), (-1,-1), (-1,+1), (+1,-1) Unpolarized neutron single-crystal diffraction 2 possible magnetic structures (+1,-1) and (-1,+1)

60 Use of polarized neutrons Chirality and ferroelectricity Example: Ba 3 NbFe 2 Si 2 O 14 Static Chirality Calculated vs measured final polarization single chirality Spherical polarization analysis with CRYOPAD A single possibility is selected (+1,-1) Marty et al. PRL (2008) Link with electrical polarization?

61 Example: Ba 3 NbFe 2 Si 2 O 14 Use of polarized neutrons Chirality and ferroelectricity Dynamical Chirality Chiral scattering measured Totally chiral spin wave branch measured by longitudinal polarization analysis calculated Loire et al. submitted

62 Use of polarized neutrons 62 Chirality and ferroelectricity TbMnO 3 : electric control of spin helicity in a magnetic ferroelectric (polarized neutrons) Yamasaki et al. PRL (2007) RbFe(MoO 4 ) 2 Kenzelmann et al. PRL (2007) Triangular magnetic structure 2 domains of triangular chiralities P E at T N proportional to the chirality domain unbalance

63 Use of polarized neutrons Domains in multiferroics/magnetoelectrics Ni 3 V 2 O 8 : coupled magnetic and ferroelectric domains (longitudinal polarization analysis) Cabrera, PRL 2009 YMn 2 O 5 : Electric field switching of antiferromagnetic domains (spherical polarization analysis) Radaelli, PRL 2008 P YX

64 Use of polarized neutrons Domains in multiferroics/magnetoelectrics Example: MnPS 3 T N =78 K Magnetic group 2 /m Collinear antiferromagnet with =0 allows ferrotoroidicity allows linear ME effect with non diagonal tensor in the (a, b, c*) frame cf. antiferromagnetic domains handling in linear magnetoelectric Cr 2 O 3 Brown JPCM 1998

65 Example: MnPS 3 Use of polarized neutrons Domains in multiferroics/magnetoelectrics Antiferromagnetic/ferrotoroidic domains manipulated in crossed E and H fields when cooled through T N Relative domain population Spherical polarization analysis electrodes sample Ressouche et al. PRB (2010)

66 66 What I did not speak about: Debye-Waller factor omitted in the scattering expressions Incoherent versus coherent Diffuse scattering (short-range order) reflectometry and small angle scattering: heterostructures flipping ratio technique: magnetization density map Also possible to study films Neutron diffraction study of hexagonal manganite YMnO 3, HoMnO 3, and ErMnO 3 epitaxial films Gélard et al APL (2008) Institut Néel coll. M. Loire (PhD), R. Ballou, S. de Brion, E. Lhotel Thanks to B. Grenier and E. Ressouche (CEA-Grenoble, France)

67 67 Bibliography thermal neutrons scattering, G. L. Squires, Cambridge University Press (1978). Neutrons Polarisés, Es. Kernavanois, Ressouche, Schober, Soubeyroux, EDP Sciences, (in english). Neutron Physics J. Rossat-Mignod, Eds Skold and Price, Academic Press (1987) Theory of Neutron scattering from Condensed Matter, S. W. Lovesey, Oxford, Clarendon Press (1984)