neutron reflectometry

Neutron reflectometry

Helmut FritzscheNRC-SIMS, Canadian Neutron Beam Centre, Chalk River, Canada

Canadian Neutron Beam Centre

Outlook

Application/advantages of neutron reflectometry

Theoretical background

Instrumental setup

Experiments:• Photoactive azobenzene films• Hydrogen storage in MgAl films• Element-specific hysteresis curves in ErFe2 / DyFe2 multilayers

Supermirrors (non-polarizing and polarizing)


What can be measured with neutron reflectometry?

Film thickness (2 – 200 nm):swelling of polymer films due to water uptake film expansion during illumination of photoactive filmsfilm expansion during hydrogen absorptiongrowth of oxide layer

In-plane structures on nm and m scale

Scattering length density profile:profile of absorbed gas/liquidinterdiffusion magnetic structuresmagnetic field penetration into superconductors


Specific advantages of neutron reflectometry

Large penetration depth (for most materials):Buried layersIn-situ measurements (cryostats, cryomagnets, high-pressure cells, furnaces)

Spin and non-spin flip reflectivity:Magnetization reversal, magnetic structure

No diamagnetic background of substrate for ferromagnetic samples:Determination of absolute magnetic moment

High sensitivity to hydrogen:Determine hydrogen profile in hydrogen storage materials

Change of contrast by using isotopes:swelling of films during water (vapor or liquid) uptake (H2O / D2O)expansion of films during hydrogen absorption (H2 / D2)


Reflection and refraction

specularly reflected

refracted

incoming wave

Physical origin:

different index of refraction for two media

medium 1: n1

medium 2: n2

Refraction: Snell‘s law

n1 sin 1 = n2 sin 2

2

1

Reflection:

r = 1

r


Reflection and refraction:the critical angle

reflectedrefracted

medium 1: n1

medium 2: n2 90°

c

Critical angle: n1 sin 1 = n2 sin 90° sin c = n2 / n1

For 1 > c : no refracted beam exists, only a reflected beam

Total reflection (100% reflectivity) occurs in the medium with the larger n


Index of refraction for light

For light with = 656 nm:

Material n c (for n2=1)

Vacuum 1.00 -Water 1.33 48.8Quartz glass 1.46 43.2Benzene 1.50 41.8

What is the index of refraction for neutrons?

Note: the index of refraction depends on the wavelength


Index of refraction for neutrons

z

Ez

}Ekin,1

V SLD

Ekin,2

bkVm

kk

nVmk

mk

2

21

21

222

221

2121

22

bm

V 22 Fermi’s pseudopotential:

m: neutron mass: neutron wavelengthb: nuclear scattering length: density of atomsb: scattering length density (SLD)


Scattering lengths

X-rays

X-rays: b Z (electron density)

Neutrons

Neutrons: no systematics

Important: not absolute number but contrast of SLX-rays and neutrons are complementary probes

0 5 10 15 20 25 300

1020304050607080

b (f

m)

atomic number

Ne

Ca

H

FeCr

Ti

ArS

SiMg

OC

BeHe

Ni

0 5 10 15 20 25 30-5

0

5

10

15

b (f

m)

atomic number

H

D

He

Li

Be

BC

N

O FNe

Na

Mg

AlSi

P

S

Cl

Ar

KCa

Sc

Ti

V

Cr

Mn

Fe

Co

58Ni

Cu


Index of refraction for neutrons:some examples

For neutrons with = 0.237 nm:

Material n b (10-4 1/nm2)

Vacuum 1.00 0Water (H2O) 1.000001 -0.561Si 0.999998 2.073Quartz glass 0.999997 4.185Heavy water (D2O) 0.999994 6.36658Ni 0.999988 13.16

Note: n 1-10-5

The deviation of nneutron from 1 is much smaller than for light,because the interaction of neutrons with matter is much weaker


Reflectometry setup on D3

S1

S2

S3S4

sample

PG filter

analyzer

detector

Focusing PG monochromator

Polarizing supermirror

Spin-down neutrons

spin flipper


Reflectometry setup on D3

S1

S2

S3S4

sample

PG filter

analyzer

detector

Focusing PG monochromator


Spin-down neutrons

spin flipper

Spin-up neutrons


The reflectometry experiment

detector

sample

slit system

q2

q: scattering vector: scattering angle

sin4

ir kkq

geometry:sample moves by detector moves by 2


The reflectometry experiment

detector

sample

slit system

q

Reflectometry:Measuring the reflected intensity as a function of q


Visualization of a reflectivity curve (Si wafer)

z

Ez

refle

ctiv

ity

q

nucbm

V 22

}

qc

bq ccc sin4

Si: c=0.11º (for =2.37 Å)58Ni: c=0.28º (for =2.37 Å)


Kiessig fringes

A u S izd

V

0.00 0.02 0.04 0.06 0.08 0.1010-5

10-4

10-3

10-2

10-1

100

Ref

lect

ivity

q (Å-1)

Oscillations due to total film thicknessq 1/d

q=2/d

qc


Multilayer Bragg peaks

bilayer Bragg peaks at q=2/t

q = n · 2/62.8 Å-1 = n · 0.1 Å-1

0.00 0.05 0.10 0.15 0.20 0.25 0.301E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

refle

ctiv

ity

q (Å-1)

Short period oscillations:Kiessig fringes

Fe

SLD

Cr

Fe

CrSi wafer

Fe

Cr}Bilayer thickness tt = 32.8 Å + 30 Å = 62.8 ÅIn total: 20 repetitions

•••


Magnetic interaction

magnuc VVV Bbm

22 magnuc bbm

22

Hext: external magnetic fieldB : magnetic inductionµ : magnetic moment of neutrons


PNR: bulk Fe

0.00 0.05 0.10 0.151E-6

1E-5

1E-4

1E-3

0.01

0.1

1 R+

R-

Runmag

refle

ctiv

ityq (1/Å)

Different reflectivity for spin-up and spin-down neutrons

Determination of the absolute magnetic moment possible

qc- qc

+

Vnuc

BVmag

BVmag

V

spin up (R+) spin down (R-)

Vnuc


PNR: Fe/Cr multilayers

1.3 nm C r

M gO (001)

2 .5 nm Fe

x 20

d struc

B

H ex t

2 .5 nm Fe1.3 nm C r

1 .3 nm C r

M gO (001)

2 .5 nm F e

x 20

d st ruc

B

H ex t

2.5 nm F e1 .3 nm C r

d A F

0.00 0.05 0.10 0.15 0.201E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

R+

R-

refle

ctiv

ity

q (1/Å)0.00 0.05 0.10 0.15 0.20

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

R+

R-

refle

ctiv

ity

q (1/Å)

Structural peakStructural peak

AF peak

Ferromagnetic coupling:Magnetic period = chemical period

Antiferromagnetic coupling:Magnetic period = 2 x chemical period


In-situ setup for photoactive films

lenses

shutter mirror

Neutron reflectometry and Laser illumination at the same time


Results for azobenzene films

0.0 h

0.4 h2.5 h

8.0 h

Laser irradiation time

Smaller q larger film thickness


Co-sputtering of MgAl alloy films

Mg Al Pd

Vacuum Chamber

<100> Si Wafer


Hydrogen absorption

Hydrogen gas cylinderAbsorption cell for thin filmson wafers with up to 100 mm diameter


Hydrogen desorptionequipment

Reflectometry furnace:

Ar atmosphere or vacuum300 K < T < 670 K

sampleheater

thermocouple


Mg0.6 Al0.4 at 298 K

0.00 0.02 0.04 0.06 0.08 0.101E-6

1E-5

1E-4

1E-3

0.01

0.1

1

exp. data simulation

Si / 52 nm Mg0.6

Al0.40

/ 10 nm Pd

Ref

lect

ivity

q (Å-1)

T = 298 K

0 100 200 300 400 500 600 700 8000.0

1.0x10-6

2.0x10-6

3.0x10-6

4.0x10-6

5.0x10-6

Si / 52 nm Mg0.6

Al0.4

/ 10 nm Pd

SLD

(Å-2

)

z (Å)

Mg0.6Al0.4PdSiO2

Si

Fit:

Pd: t = 104 Å = 4.4 ÅMgAl: t = 520 Å = 15.7 Å

0 100 200 300 400 500 600 700 8000.0

1.0x10-6

2.0x10-6

3.0x10-6

4.0x10-6

5.0x10-6

without hydrogen with hydrogen

Si / 52 nm Mg0.6Al0.4 / 10 nm Pd

SLD

(Å-2

)

z (Å)


Absorption in Mg0.6 Al0.4

• increase of film thickness by about 20%• hydrogen content is 83 at.% = 3.2 weight %

SLDbH < 0

t

0.00 0.02 0.04 0.06 0.08 0.101E-6

1E-5

1E-4

1E-3

0.01

0.1

1 without hydrogen with hydrogen

Si / 52 nm Mg0.6Al0.4 / 10 nm Pd

Ref

lect

ivity

q (Å-1)


Annealing of a desorbed Mg0.7 Al0.3 film

Pd layer does not exist anymore after 9 h:Pd diffuses into the MgAl layer

0 100 200 300 400 500 600 700 8000.0

1.0x10-6

2.0x10-6

3.0x10-6

4.0x10-6

5.0x10-6

1 h @ 473 K 3 h @ 473 K 9 h @ 473 K

SLD

(Å-2

)

z (Å)

0.00 0.02 0.04 0.06 0.08 0.10

1E-5

1E-4

1E-3

0.01

0.1

1

1 h @ 473 K 3 h @ 473 K 9 h @ 473 K

Ref

lect

ivity

q (Å-1)


DyFe2 / ErFe2 multilayer:element-specific hysteresis

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1E-4

1E-3

0.01

0.1

1

0H = 6.0 T

q (Å-1)

Ref

lect

ivity

1E-4

1E-3

0.01

0.1

1

fit of R- -

fit of R+ +

H = 1.0 T

1E-4

1E-3

0.01

0.1

1

R- -

R+ +

H = 0.4 TMagnetization reversal at 100 KAfter saturation at µ0H = –6 T(6 nm DyFe2 / 6 nm ErFe2)40

0 1 2 3 4 5 6-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

DyFe2

ErFe2

averageM

(T)

0H (T)

ErFe2 and DyFe2 magnetizations are not parallelDyFe2: easy-axis loopErFe2: hard-axis loop


PNR is element-specific

ErFe2 DyFe2

R+ = R-

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0 TM

ErFe2 = 0 T

q (Å-1)

Ref

lect

ivity

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0.13 TM

ErFe2 = -0.13 T

1E-4

1E-3

0.01

0.1

1 R+ +

R- -

MDyFe2

= -0.13 TMErFe2 = 0.13 T

nonmagnetic layers



0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0 TM

ErFe2 = 0 T

q (Å-1)

Ref

lect

ivity

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0.13 TM

ErFe2 = -0.13 T

1E-4

1E-3

0.01

0.1

1 R+ +

R- -

MDyFe2

= -0.13 TMErFe2 = 0.13 T

ErFe2 DyFe2

ErFe2 DyFe2

R+ = R-

~R+ ~R-H

D y F e 2

E rF e 2

nonmagnetic layers



0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0 TM

ErFe2 = 0 T

q (Å-1)

Ref

lect

ivity

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0.13 TM

ErFe2 = -0.13 T

1E-4

1E-3

0.01

0.1

1 R+ +

R- -

MDyFe2

= -0.13 TMErFe2 = 0.13 T

ErFe2 DyFe2

R+ = R-

ErFe2 DyFe2

~R- ~R+

ErFe2 DyFe2

~R+ ~R-H

D y F e 2

E rF e 2

H

D y F e 2

E rF e 2

nonmagnetic layers



0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0 TM

ErFe2 = 0 T

q (Å-1)

Ref

lect

ivity

1E-4

1E-3

0.01

0.1

1

MDyFe2

= 0.13 TM

ErFe2 = -0.13 T

1E-4

1E-3

0.01

0.1

1 R+ +

R- -

MDyFe2

= -0.13 TMErFe2 = 0.13 T

ErFe2 DyFe2

ErFe2 DyFe2

R+ = R-

~R+ ~R-

ErFe2 DyFe2

~R- ~R+

H

D y F e 2

E rF e 2

H

D y F e 2

E rF e 2

nonmagnetic layers


supermirror

goal:Extend the range of neutron reflectionbeyond the regime of total reflection

concept:continuous Bragg reflection from a multilayercomposed of bilayerswith a variation of the thickness

realization:Ni/Ti multilayer, bNi = 10.3 fm, bTi = -3.4 fm100 bilayers,qc = 2 x qc, Ni


supermirror

m-value: m = qc / qc, Ni

Ni

SLD

Ni

Ti Ti Ti

Ni

z



concept:Using the supermirror concept with a magnetic/non-magnetic bilayerThe SLD of the bilayer is index-matched for spin-down neutronsno multilayer Bragg peaks for down-neutronsSpin-up neutrons show supermirror behavior with extended critical edge

Fe/Co

SLD

spin-up neutrons

Si

Fe/Co

Si

spin-down neutrons

Fe/Co

SLD

Si Fe/Co Si

Index matching


Polarizing supermirror:Fe-Co/Si

0.0 0.2 0.4 0.6 0.8 1.0 1.20

1000

2000

3000

4000

5000

R_down R_up

refle

cted

neu

trons

(cou

nts)

(deg)

supermirror 5127u with =0.472 nm

0.0 0.2 0.4 0.6 0.8 1.0 1.20

1000

2000

3000

4000

T_down T_up

trans

mitt

ed n

eutro

ns (c

ount

s)

(deg)


Reflected intensity Transmitted intensity


Flipping ratio

0.0 0.2 0.4 0.6 0.8 1.0 1.20

20

40

60

80

100

transmission reflectivity

flipp

ing

ratio

(deg)


RRRR

Flipping ratio =

usable range25

neutron reflectometry

Documents

neutron wavelengthb

neutron mass

hydrogen profile

r spin

neutrons determination

different index of refraction

magnetic peri

n290 cindex of refraction