Polarized neutron reflectometry: encore presentation M.R. Fitzsimmons Los Alamos National Lab.
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Transcript of Polarized neutron reflectometry: encore presentation M.R. Fitzsimmons Los Alamos National Lab.
Polarized neutron reflectometry: encore presentation
M.R. Fitzsimmons
Los Alamos National Lab
Outline
• Description of a polarized neutron reflectometer.
– Ingredients of a polarized neutron reflectometer.
– Measurement of wavelength with the time-of-flight technique.
– How are polarized neutron beams made?
– How are spins flipped?
• An example worked in detail.
– What is the specific question?
– Formulate experimental procedure.
– Collect data.
– Fit/interpret data.
– Publish!
• So, why use neutron scattering?
1st ingredient
• Knowledge and control of neutron beam polarization.
II
IIP
1
1
F
FP
I
IF
Spin up Spin down
A need for well polarized neutron beams.
0 100
5 10-6
1 10-5
1.5 10-5
-100 0 100 200 300
++ (spin up)
-- (spin down)
Depth (y) into the sample [Å]
[Å-2
]
Fe
Si
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 0.05 0.1 0.15 0.2
R++ (P = 100%)R-- (P = 100%)
R--
R++
Pol
ariz
ed n
eutr
on r
efle
ctiv
ity
Q [Å-1]
R++ (P = 100%)--
R++ (P = 82%)
R-- (P = 82%)
Strongly magnetic materials best served by well polarized neutron beams.
2nd ingredient
• Capability to measure the intensity and polarization of the neutron beam reflected by a sample.
3rd ingredient
• Ability to measure intensity and polarization of the scattered beam as a function of wave vector transfer parallel and perpendicular to the sample surface.
Measuring with the time-of-flight technique.
Neutron guides
A neutron will stay inside the guide provided:
c
Glass
58Ni
For Ni: /ź1.0 c
º23.0~
Producing clean cold neutron beams.
2
<4Å
>4Å
Bragg’s law satisfied when <2d100
Principle of a Be filter
c
>14Å
<14Å
Principle of a frame overlap mirror
101
102
103
104
105
4 6 8 10 12
20 30 40 50 60N
eutr
ons
cou
nte
d
wavelength [Å]
time-of-flight [ms]
101
102
103
104
105
4 6 8 10 12
SpectrumReflectivity of Si
20 30 40 50 60
Neu
tron
s co
unte
d
wavelength [Å]
time-of-flight [ms]
Reflectometry a good match.
101
102
103
104
105
4 6 8 10 12
20 30 40 50 60
Neu
tron
s co
unte
d
wavelength [Å]
time-of-flight [ms]
with polarization analyzer
10-4
10-3
10-2
10-1
100
0.005 0.01 0.015 0.02 0.025 0.03
Ref
leci
tivity
of S
i
Q [Å-1]
Si
(100
) B
e ed
ge
(110
) B
e ed
ge
)sin(4
Q
Covering an extended range in Q
10-5
10-4
10-3
10-2
10-1
100
101
102
0 0.05 0.1 0.15 0.2
2 = 0.58°2 = 1.02°2 = 2.02°2 = 4.62°2 = 7.96°
Spi
n F
lip R
efle
ctiv
ity
Q [A-1]
10-5
10-4
10-3
10-2
10-1
100
101
102
0 0.05 0.1 0.15 0.2
Spi
n F
lip R
efle
ctiv
ity
Q [A-1]
6 minutes
4 minutes
24 minutes
160 minutes
600 minutes
How are polarized neutron beams made?
Answer: any magnetic film will polarize a neutron beam to some degree.
Fe
Si
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 0.02 0.04 0.06 0.08 0.1
Pol
ariz
ed n
eutr
on r
efle
ctiv
ity
Q [Å-1]
R++
R--
10-5
10-4
10-3
10-2
10-1
100
0 0.02 0.04 0.06 0.08 0.1Pol
ariz
ed n
eutr
on tr
ans
mis
sivi
ty
Q [Å-1]
R++
R--
-1
-0.5
0
0.5
1
0 0.02 0.04 0.06 0.08 0.1
Pol
ariz
atio
n (r
efle
ctio
n)
Q [Å-1]
-1
-0.5
0
0.5
1
0 0.02 0.04 0.06 0.08 0.1
Pol
ariz
atio
n (t
rans
mis
sio
n)
Q [Å-1]
Q ~ 0.005 Å-1
A “first” PNR experiment
D.J. Hughes and M.T. Burgy, Phys. Rev., 81, 498 (1951).
Results supported Schwinger’s model of neutron moments as current loops and the predicted dependence on B not H (in contrast to Bloch’s model).
Spin down Qc Spin up Qc
Polarizing supermirrors.
10-5
10-4
10-3
10-2
10-1
100
0 0.02 0.04 0.06 0.08 0.1
R++ Fe/Si
R-- Fe/Si
R++ 3c SM
R-- 3c SM
0 1 2 3 4
Pol
ariz
ed
neu
tron
re
flect
ivity
Q [Å-1]
m
0
0.2
0.4
0.6
0.8
1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
0 0.5 1 1.5 2 2.5 3 3.5
Pol
ariz
atio
n (t
ran
smis
sio
n)
Q [Å-1]
m
Qmin
= 0.01 Å-1
Qmax
= 0.065 Å-1
Si
100 nm 0.1 nm
410)(n
dnd F. Mezei and P.A.
Dagleish, Comm. on Phys., 2, 41 (1977).
Traditional approach
[Å] Qmin
[Å-1]
Qmax [Å-
1]
5 0.01 0.065
15 0.003 0.01
0.018
Settings for = 5 Å.
An inefficient approach to simultaneously polarize multi-wavelength neutron beams.
Q
Qc(Si) = 0.01 Å-1 Qc(m=3) = 0.065 Å-1
= 5 Å
= 15 Å
Mezei polarization cavity
1. Efficient polarization of the neutron beam for > min = 4Å .
2. Maintains divergence of the neutron guide.3. Polarization of large beams, e.g., 25 mm
by 130 mm.4. No deflection of beam line. Ewald’s sphere
~
sin4
Q
Q
Q
small big
The Asterix polarization cavity
Adiabatic rotation of neutron spins
0
50
100
150
200
250
0 5 10 15 20 25 30 35 40
Hx
Hz
Hx a
nd H
z [O
e]
distance [cm]
0 cm 30 cm
0
20
40
60
80
100
0 5 10 15 20 25 30 35 40
[°]
distance [cm]
x
z
0 100
2 105
4 105
6 105
8 105
1 106
1.2 106
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
|L|/4
|d/dt|
0 5 10 15 20 25 30 35
fre
quen
cy [
rad
/s]
time [ms]
distance [cm]
Note, the relation between distance and time is valid for a neutron with = 4 Å.
L
L
dt
d
B
B
Radio frequency gradient field spin flipper
0 100
1 105
2 105
3 105
4 105
0 0.1 0.2 0.3 0.4 0.5
|L|/4
|d/dt|
0 10 20 30 40 50
fre
quen
cy [
rad
/s]
time [ms]
distance [cm]
Note, the relation between distance and time is valid for a neutron with = 4 Å.
-80
-60
-40
-20
0
20
40
60
-20 -10 0 10 20
B0 -
B1
B [G
]
position [cm]
0
60
120
180
-20 -10 0 10 20
[°]
position [cm]
I. Rabi, N.F. Ramsey, J. Schwinger,Rev. of Mod. Phys., 26, 167 (1954).
Pictures of the RF gradient flipper
Polarized neutron reflectometry
z
Spin-flip cross-sections yield Mas a function of Q.
Non spin-flip cross-sections yield: M|| as a function of Q .
A qualitative interpretation of RNSF and RSF
dyeyyQr
dyeyyyQr
yiQmBA
yiQmnBA
0
0
sin)(
cos)(
QmQR
QmQRQRQSFBA
BABANSF
cos1)(
cos1)()()(2
||
y
Why neutron reflectometry?
QmQR
QmQRQRQSFBA
BABANSF
cos1)(
cos1)()()(2
||
Domains are large compared to coherent region of the neutron beam.Sinha discusses the case of small domains this p.m.
f = 0.74
f
W.T Lee, et al., PRB, 65, 224417 (2002).
10-3
10-2
10-1
100
0 0.01 0.02 0.03 0.04 0.05
NSF, (++) = (--)SF
Neu
tron
Ref
lect
ivity
Q [Å-1]
<sin2> = 0.74
magnetometry reflectometry
Quantity || to H <cos> R+-R- <cos>
Quantity to H <sin> RSF <sin2>
QmQRSFBA cos1)( 2
Domains are large compared to coherent region of the neutron beam.
Table of measurements and their meanings.Measurement feature Information obtained from a sample of cm2 or
so size
Position of critical edge, Qc
Nuclear (chemical) composition of the neutron-optically thick part of the sample, often the substrate.
Intensity for Q < Qc Unit reflectivity provides a means of normalization to an absolute scale.
Periodicity of the fringes
Provides measurement of layer thickness. Thickness measurement with uncertainty of 3% is routinely achieved. Thickness measurement to less than 1 nm can be achieved.
Amplitude of the fringes
Nuclear (chemical) contrast across an interface.
Attenuation of the reflectivity
Roughness of an interface(s) or diffusion across an interface(s). Attenuation of the reflectivity provide usually establishes a lower limit (typically of order 1-2 nm) of the sensitivity of reflectometry to detect thin layers.
FeCo on GaAs: an example worked in detail.
• What is the specific question to be answered?
• Reality test: simulate possible answers.
• Formulate experimental protocol.
• Write proposal.
• Collect data.
• Interpret data.
• Write experiment report, publish results.
Magnetic vs. chemical thickness
How does the magnetization of the
FeCo/GaAs interface affect the polarization
of spin current passing through the
interface?
(1) A conducting and magnetically dead
interface is a source of unpolarized spins.
(2) Spins passing through the interface may
suffer spin flip scattering.
We need to understand the magnetic structure of the
as-prepared buried interface.
FeCo
GaAs (100) 2x4
Collaborators
LANL:S. Park
UMN:X. DongB.D. SchultzC.J. Palmstrøm
Magnetization of the sample.
-1
-0.5
0
0.5
1
-400 -200 0 200 400
Mr/M
s
H (Oe)
]101[
Fe48Co52 grown on
GaAs(100) 2x4
(As-rich) surface.
A.F. Isakovic, et al., JAP, 89, 6674 (2001).
]011[
X-ray vs. polarized neutron scattering
RoentgenChadwick
0.05 0.10 0.15 0.20
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
X-r
ay
Re
flect
ivity
Q (Å-1)
0.00 0.05 0.10 0.15 0.20 0.25
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Ref
lect
ivity
Q (Å-1)
R+
R-
X-R
ay
refle
ctiv
ity
Ne
utr
on
ref
lect
ivity
Spin
H = 1 kOeSpin
X-r
ay r
efle
ctiv
ity
neut
ron
refle
ctiv
ity
Q [Å-1] Q [Å-1]0.20.2
FeCo
GaAs (100) 2x4
203.6±0.2 197.5±0.2
X-rays
True and perceived specular reflectivity
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
FeCo on GaAs
specular
specular + diffuse
Ref
lect
ivity
Q [Å-1]
Homework: Quantify the influence on .
wavelength
Contour of constant Q
FeCr
Spin down neutron scattering
Importance of diffuse scattering illustrated.
FeCr
AF Bragg reflection
Specular component
Diffuse scattering
Scatters specularly
Scatters diffusively
Qx ~ 0.003 Å-1
nmQx
200~2
X-ray vs. polarized neutron scattering
RoentgenChadwick
0.05 0.10 0.15 0.20
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
X-r
ay
Re
flect
ivity
Q (Å-1)
0.00 0.05 0.10 0.15 0.20 0.25
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Ref
lect
ivity
Q (Å-1)
R+
R-
X-R
ay
refle
ctiv
ity
Ne
utr
on
ref
lect
ivity
Spin
H = 1 kOeSpin
X-r
ay r
efle
ctiv
ity
neut
ron
refle
ctiv
ity
Q [Å-1] Q [Å-1]0.20.2
FeCo
GaAs (100) 2x4
203.6±0.2 197.5±0.2
Uniaxial anisotropy offers a resolution.
-1
-0.5
0
0.5
1
-400 -200 0 200 400
Mr/M
s
H (Oe)
1 saturate
reduce2
Rotate 90º3
H=9 Oe
M M
Chemical thickness magnetic thickness
0.000 0.025 0.050 0.075 0.10010-6
10-5
10-4
10-3
10-2
10-1
100
Φ
H
M
Φ
H
M
[011]
Spin Spin Spin flip
Magnetic vs. chemical thickness
0.00
1.50x10-6
3.00x10-6
4.50x10-6
Scat
teri
ng le
ngth
den
sity
[Å-2
]
chemical magnetic
(a)
2 = 2.57
-50 0 50 100 150 200 250 300
0.00
1.50x10-6
3.00x10-6
4.50x10-6
2 = 3.89
2 = 3.94
Distacne from the surface [Å]
(b)
5.5 Å
202.7 Å
197.2 Å
Distance from surface [Å]
202.7 197.2
5.5Å
Chem MagFeCo FeCod d d
The FeCo/GaAs(100) 2x4
interface is not ferromagnetic
at 300 K (for this sample).
Al-oxide
FeCo
GaAs
So, why use neutron scattering?
• Profiling non-uniformity in magnetic thin films.
– Example #1: Magnetic vs. chemical thickness of FeCo on GaAs.
– Example #2: Measuring depth dependence of Tc.
– Also, lateral non-uniformity (off-specular and diffuse scattering, Sinha).
• “Small” moment detection and discrimination.
– Example #3: Small moments in (Ga, Mn)As on GaAs.
– Example #4: Small moments in the presence of big moments, Co on LaFeO3.
• A different kind of vector magnetometer.
– Example #5: Asymmetric magnetization reversal and exchange bias (Schuller).
• Magnetic structure determination of anti-ferromagnets.
Example #2: Measuring Tc(z).
190-nm thick film of La0.7Sr0.3MnO3. J.-H. Park, et al., PRL, 81, 1953 (1998).
5 Å50 Å
1900 Å
Co
La0.7Sr0.3MnO3
A problem tailored-made for neutron scattering:(1) All length scales probed with one technique on the same
sample, and(2) Offers an opportunity to probe magnetization of a buried
interface (in addition to that near the surface).
Collaborators
LANL:S. ParkJ.D. Thompson
Uni-Wuerzburg:L. MolenkampG. SchottC. Gould
Neutron antennas
10-6
10-5
10-4
10-3
10-2
10-1
100
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
++ (not dead)
-- (not dead)
Ref
lect
ivity
Q [Ang-1]
Ga0.5Al0.5As
Ga0.5Al0.5As
Ga0.97Mn0.03As
GaAs
2 10 -5
4 10 -5
6 10 -5
8 10 -5
1 10 -4
1.2 10 -4
0.06 0.065 0.07 0.075 0.08 0.085 0.09 0.095 0.1
Ref
lect
ivity
Q [Ang-1]
10-4
10-3
10-2
10-1
100
0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
Ref
lect
ivity
Q [Ang-1]
10 K @ 5 kOe
300 K @ 5 kOe
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055
10 K300 K
(do
wn
- u
p)
/ (d
ow
n +
up)
Q [Ang-1]
<300 K> = 0.06(0.04)
Magnetic signature most apparent.
Model reproduces data
using a uniform distribution
of magnetization.
Example #3: Small moment detection
(1) Magnetic (neutron) scattering
length density = 7.9x10-8 Å-2 (±10%)
(2) Number density of (Ga, Mn)As
formula units = 0.025 Å-3 (to 1%).
(3) Mn concentration = 3%.
(4) Using 1-3, we calculate Mn = 4B.
(5) The measured magnetic moment
is 2x10-4 emu.
(6) Magnetic vs. chemical thickness is
394 Å vs. 397 Å.
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
not deaddeadobserved 10 K
(do
wn
- up
) / (
dow
n +
up)
Q [Ang-1]
What is exchange bias?
FM
AFM
FM
AFM
FM
AFM
FM
AFM
FM
AFM
FM
AFM
Field Cool
T < T < TN C
HFC
M
HA
Assume FM interaction favored.
W.H. Meiklejohn, C.P. Bean, Phys Rev., 105, 904(1957).J. Nogués, Ivan K. Schuller, J. of Magn. Magn. Mater., 192, 203 (1999).
PM
Some theoretical pictures
Meiklejohn & Bean Model
HE Jint
Mt
2JexS 2
a21
Mt27, 000 Oe
Problems:
• HE is too large for nearly all systems.
• HE often large for compensated AF planes.
• Example: (110) plane of bulk FeF2 is compensated &
HE~400 Oe for Fe/FeF2.
Random-field, domain state, etc., models
HCF
+’ve HE
Frustrated super exchange (AF-coupling)
+1
-’ve HE
Super exchange (AF-coupling)
-1
HCF10nm
U. Nowak et al., JMMM, 240, 243 (2002).A.P. Malozemoff, JAP, 63, 3874 (1988).
Frozen moments in the AF?
FM
AFM
qCan anything be learned at Hsat?
J. Nogués, et al., PRB, 61 1315 (2000).
Mshift
He
Mshift
He
Collaborators
LANL:A. Hoffmann (now at ANL)
IBM, Zürich:J.W. SeoH. SiegwartJ. FompeyrineJ.P. Locquet
NIST:J. DuraC. Majkrzak
Magnetization depth profiling
10 Å Pt
25 Å Co (FM)
350 Å LaFeO3 (AFM)
(100) SrTiO3 substrate
The “Nature” Sample
0
1
2
3
4
5
6
0 0.05 0.1 0.15 0.2
--++
Ref
lect
ivit
y*q
4 (
10-8 Å
-4)
q (1/Å)
10-6
10-5
10-4
10-3
10-2
10-1
100
0 0.05 0.1 0.15 0.2
--++
Ref
lect
ivit
y
q (1/Å)
F. Nolting, et al., Nature, 405, 767 (2000).
Saturation at 300K, when He=0.
0
1
2
3
4
5
6
0 0.05 0.1 0.15 0.2
--++
Ref
lect
ivit
y*q
4 (10
-8 Å
-4)
q (1/Å)
0
1
2
3
4
5
6
0 0.05 0.1 0.15 0.2
--++
Ref
lec
tivi
ty*q
4 (10
-8 Å
-4)
q (1/Å)
- 7500 Oe + 7500 Oe
No difference for +/- saturation
Results well reproducible
FM
AFM
Saturation at 18K, when HE = -20 Oe.
0
1
2
3
4
5
6
0 0.05 0.1 0.15 0.2
--++
Ref
lect
ivit
y*q
4 (
10-8 Å
-4)
q (1/Å)
0
1
2
3
4
5
6
0 0.05 0.1 0.15 0.2
--++
Ref
lev
tivi
ty*q
4 (10
-8 Å
-4)
q (1/Å)
- 7500 Oe + 7500 Oe
Field cooled in +7500 Oe
Asymmetry for + and - saturation
FM
AFM
Example #4: Detecting small moments near large moments.
• Magnetization profiles are not the same for +’ve and -’ve
saturation.
– Effect correlated with magnitude of HE, and
– direction of cooling field.
• Greatest change of the profile observed for Hsat parallel to
the cooling field.
– Implies frozen magnetization in the AF aligned anti-parallel to the cooling
field.
– Result consistent with observed negative exchange bias.
A. Hoffmann et al., PRB, 6, 406 (2002).
Influence of cooling field on the magnetic order parameter of Zn0.2Fe0.8F2
11-T superconducting magnet
250 nm thick film sample
(100) AF Bragg reflection
D. Belanger (UCSD),D. Lederman (WVU)