Neutron Refractometry - B Kreimer

Neutron reflectometry

Introduction & application to oxide interfaces

B. Keimer

Max-Planck-Institute for Solid State Research

• neutron reflectometry: part of “interface toolbox”

• state-of-the-art instrument available

for Max Planck users & collaborators

motivation

outline

• self-contained introduction: neutron scattering & reflection

• small selection of applications to (oxide) interfaces

Neutron scattering

strong (nuclear) interaction

elastic lattice structure

inelastic lattice dynamics

magnetic (dipole-dipole) interaction

elastic magnetic structure

inelastic magnetic excitations

neutron

excitation: E= E2-E1

q=q2-q1

interaction

E1 q1

E2 q2

Neutron sources

FRM-II Garching, Germany

research reactor

neutron flux

Maxwellian profile

energy ~ 30 meV

continuous spectrum

Neutron sources

SNS Oak Ridge, USA

spallation source

pulsed beam

Elastic neutron scattering

Elastic neutron scattering

Born approximation

Elastic nuclear neutron scattering

Bragg peaks at reciprocal lattice vectors K

nuclear structure factor

scattering length b ~ size of nucleus ~ 10-15 m depends on isotope

Scattering cross section: x-rays versus neutrons

N.B. b for deuterium is negative

http://www.ncnr.nist.gov/AnnualReport/FY2003_html/RH2/fig2.png

Neutron radiography

two metallic cylinders attached by an adhesive only the adhesive is seen on the neutron radiograph http://einrichtungen.physik.tu-muenchen.de/antares/

Elastic magnetic neutron scattering

Elastic magnetic neutron scattering

Elastic magnetic neutron scattering

non-spin-flip

“classical electron radius” magnitude comparable to b

one electron

σz → σx , σy spin-flip (not possible for nuclear scattering)

average for unpolarized beam

Elastic magnetic neutron scattering

one atom approximated as magnetized sphere, magnetization density M(r)

Elastic magnetic neutron scattering

polarization factor magnetic structure factor

magnetic reciprocal lattice vectors

generalization for collinear magnets

Bragg peaks

from here on, assume collinear magnetism, one atom per unit cell for simplicity

Example one-dimensional antiferromagnet

Example one-dimensional ferromagnet

interference between nuclear and magnetic scattering

Nuclear-magnetic interference

cross section depends on spin direction

use nuclear-magnetic interference to create spin-polarized neutron beam

ferromagnetic Bragg peak

with

Reflection from interfaces

conveniently discussed in terms of classical ray optics

index of refraction for neutron wave inside material

example isotopically pure 62Ni can drastically change scattering power without changing chemistry & physics

perspectives not yet explored for hard materials

example natural Ni

similar to x-rays but δ can be negative for neutrons

example natural Ti

Reflection from interfaces

Reflection from interfaces

Reflection from interfaces

Reflection from interfaces

Fresnel reflectivity

Reflection from interfaces

contrast matching important for soft matter but also: hydrogen profiles in hard materials

Neutron guides

engineer layer sequence such that effective critical angle increases

supermirror

Neutron guides

http://www2.fz-juelich.de/iff/datapool/iffnews/news_28-04-2009_bild1.jpg

neutron guide hall @ FRM-II

NREX reflectometer

state of the art instrument

owned and operated by Max Planck Society

privileged access to beamtime

Thomas Keller

+49-89-289-12164

[email protected]

Nonuniform density distribution

contribution to R whenever density changes analog of magnetic form factor in diffraction

“kinematic” approximation ignore multiple reflections

example film on substrate

Multiple reflections

Multiple reflections

kinematic approximation recovered

0

waveguide effect resonant enhancement of neutron wavefunction inside layer

can use this effect to enhance contribution of single buried layer to reflectivity

Multiple reflections

multilayers

numerical calculations: Parratt formalism

image adapted from Hoppler et al., Nature Materials 2009

Reflection from graded interfaces

analogous to Debye-Waller factor in diffraction

Reflection from graded interfaces

quality of surfaces, buried interfaces can be determined by reflectometry

example Nb film

Fresnel

70 Å surface roughness Felcher et al. PRL 1984

Reflection from ferromagnets

magnetic scattering amplitude

H || z

neutron spin operator determined by magnetic field

electronic magnetic moment component perp.to Q-vector

η

ordinary ferromagnet

no neutron spin flip

M || H

Reflection from ferromagnets

H || z η

M

magnetization components H, Q

e.g. spin canting at interface, strong anisotropy

neutron spin flip

Spin-polarized neutron reflectometry

polarizing mirror

nuclear-magnetic interference effect total scattering amplitude four different reflectivities for single interface: R++, R--, R+-, R-+ reflection, transmission amplitudes in Parratt calculations become matrices

Spin-polarized neutron reflectometry

reflectometer with spin polarization analysis

http://www.ncnr.nist.gov/instruments/ng1refl/Beamline_color.bmp

allows separate measurements of R++, R--, R+-, R-+

Spin-polarized neutron reflectometry

SrRuO3 – La0.7Sr0.3MnO3 Heterostructures

Ziese, Vrejoiu et al. (Halle group) PRL 2010

SrRuO3 TC = 140 K, M SL

La0.7Sr0.3MnO3 TC = 320 K, M || SL

antiferromagnetic coupling through Mn-O-Ru bond

competing interactions at interfaces

J.H. Kim et al. (MPI-FKF)

M || Q inside SRO layer invisible to neutrons

M Q at interface through Ru-O-Mn coupling

SrRuO3 – La0.7Sr0.3MnO3 Heterostructures

LaMnO3 – SrMnO3 Heterostructures

Santos et al. (Argonne group) arXiv:1105.0223

LaMnO3 – SrMnO3 Heterostructures

Santos et al. (Argonne group) arXiv:1105.0223

spin-flip scattering canted structure

Reflection from superconductors

Pb film in Meissner state

Nutley et al. PRB 1994

Reflection from superconductors

Pb film in vortex state

Drew et al. PRB 2009

Superconductor – Ferromagnet Heterostructures

inverse proximity effect

at interface between superconductor and ferromagnet

Bergeret et al. PRB 2004

Superconductor – Ferromagnet Heterostructures

engineered waveguide structure to observe inverse proximity effect

Khaydukov et al. (Dubna group) arXiv:1005.0685

amplitude of waveguide resonance suggestive of inverse proximity effect

YBCO-LCMO interface

YBa2Cu3O7 (YBCO): high-Tc superconducor

La0.7Ca0.3MnO3 (LCMO): double-exchange ferromagnet

CuO2 layers || interface

coherence length interface very small

SC proximity effects not expected

SrTiO3 (001) substrate

Zhang et al. APL 2009

Magnetic proximity effects?

YBCO-LCO on (110) SrTiO3 CuO2 layers perpendicular to interface

Kim, Mustafa

YBCO-LCMO interface

suppression of superconductivity for YBCO layers thinner than ~ 5 nm

Sefrioui et al., PRB 2003 Holden et al. PRB 2004

suppression of metallicity

YBCO-LCMO charge transfer

charge transfer doping without chemical substitution

YBa2Cu3O6+x

La1-xCaxMnO3

YBCO-LCMO magnetic reconstruction

neutron reflectometry two interface models yield equivalent fits: - antiferromagnetically polarized layer - magnetically “dead” layer

model 1 model 2

J.H. Kim NREX @ FRM-II

Stahn et al. PRB 2005

YBCO-LCMO magnetic reconstruction

• ferromagnetic polarization of Cu in YBCO • direction antiparallel to Mn

Chakhalian et al., Nature Phys. 2006

additional information from XMCD

Chakhalian et al. Nature Phys. 2006

• superexchange coupling through Cu-O-Mn bond

Off-specular reflectometry

specular off-specular

correlations plane correlations || plane

• in-plane domain structure

• interface roughness

In-plane domain structure

FePd films

magnetic stripe domains

Qz

Qx

Fermon et al.

new magneto-structural domain state

periodicity ~ 1µm

YBCO-LCMO superlattice

T > 100 K

T < 100K

Chakhalian et al. Nature Phys. 2006

In-plane domain structure

origin: structural phase transition in STO substrate

J. Hoppler, C. Bernhard et al. Nature Mat. 2009

YBCO-LCMO superlattice on SrTiO3

novel superconductivity-induced magnetic domain structure

In-plane domain structure

LaNiO3-LaAlO3 superlattice on SrLaAlO4 simpler structure of superlattice no structural transitions in substrate

A. Frano full crystallographic description of lattice structure,

strain-induced domains

639 eV 620 eV fit

This image cannot currently be displayed.

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momentum transfer (nm-1)

experiment

model

Magnetic depth profiling by soft x-rays

Freeland et al. PRB 2010

resonant reflectometry

with circularly polarized x-rays

element-specific magnetization profile

example CaRuO3 — CaMnO3 superlattices

Neutron versus resonant x-ray reflectometry

neutron reflectometry advantages • yields total magnetization, independent of electronic structure • cross section completely understood, no calculation required • no beam heating can reach mK temperatures • isotopic labeling, sensitivity to hydrogen • Larmor phase manipulation of neutron spin, spin-echo experiments

resonant x-ray reflectometry advantages • element specific • yields valence state, orbital occupation, magnetization in one shot

(software available soon) S. Macke • higher intensity, dynamic range

Further reading