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Neutron Refractometry - B Kreimer
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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
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.
dich
roic
diff
eren
ce
inte
nsity
(arb
. uni
ts)
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