Polarised neutron reflectivity Frédéric OTT Laboratoire Léon Brillouin [email protected]

Polarised neutron reflectivity

Frédéric OTTLaboratoire Léon Brillouin

[email protected]

ECNS’2003 Introductory Course

Outline Reflectivity

General principles Polarised neutrons

Instrumentation Examples Superlattices

Non colinear magnetism GMR Interface magnetism

Resources


Specular reflectivity geometry

x

z

kii r

kr

q

q4

sin


Reflectivity measurements

2 ways of varying the scattering wave-vector Angular scan – 2

Time-of-flight

k0q1

q2

k1

q1

q2k2


Neutron-matter interaction

Optical approximation.

Interaction neutron-nucleus Isotropic and ponctual

Zeeman interaction Neutron spin – magnetic field

Neutron-nucleus Neutron-magnetic field

Neutron-magnetisation

/ /V

mb g gn n n n

2 2

0 0

Vm

bn( ) ( )r r2 2

V B( ) ( )r r


Limitation : planar magnetisation M//

In the Born approximation : It can be shown that the magnetic interaction is sensitive

only to the component of the magnetisation perpendicular to the scattering wave-vector

Other approach The neutron spin interacts with B :

For continuous thin films :

Mq .

)(0 DMMHµB

//)1( MMMMD z

100

000

000

D

)( //00 MHµB


Derivation of the reflectivity

Schrödinger

Helmoltz eq. U U k2 0

Neutrons

Eigenstates

Interaction

Propagation eq.

Matrix formalism

et

Vm

b gn n 2 2

0 0

/ /

2

2mV E

km

E V22

2

et Continuity conditions


Optical index

The optical index is defined as

Snell’s law :

ddr

k2

22 0

k

mE V2

2

2

nkk

22

02

nVE

b22

1 1 n b 1

2

2

cos cos i trn cn cos

c

b

i

tr


Some valuesMatérial bn (fm) (1028 m-3) b (1013 m-2) (10-6) qc (nm-1) Remarks

H -3.73 hydrogen D (2H) 6.67 deuterium

C 6.64 11.3 75 19.1 0.19 graphite C 6.64 17.6 117 29.8 0.24 diamond O 5.80 Si 4.15 5.00 20.8 5.28 0.10 Ti -3.44 5.66 -19.5 -5.0 - Fe 9.45 8.50 80.3 20.45 0.20 Co 2.50 8.97 32.6 8.29 0.13 Ni 10.3 9.14 94.1 24.0 0.22 Cu 7.72 8.45 65.2 16.6 0.18 Ag 5.92 5.85 34.6 8.82 0.13 Au 7.63 5.90 45 11.5 0.15

H2O -1.68 3.35 -5.63 -1.43 - D2O 19.1 3.34 63.8 16.2 0.18 SiO2 15.8 2.51 39.7 10.1 0.14 GaAs 13.9 2.21 30.7 7.82 0.12 Al2O3 24.3 2.34 56.9 14.5 0.17 saphir pyrex 42 10.7 0.14 C8H8 23.2 0.61 14.2 3.6 0.084 polystyrène C8D8 106.5 0.61 65 16.5 0.18

www.neutron.anl.gov


Reflection on a substrate

ziqBziqAz

ziqBziqAz

sssss

expexp

expexp 00000

00

00''

0

0

zz

zz

s

s

Vacuum « 0 »

Substrate « s »

Z = 0

ziqtz

ziqrziqz

ss exp.

exp.exp.1 000

tqrq

tr

s1

1

0 ss

s

qq

qtand

qq

qqr

0

0

0

0 2

R r et T t 2 2

2

0

0

s

s

qq

qqR

Continuity conditions

z1 r

t


Case of a non magnetic substrate

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8

qz (nm-1)

Re

flect

ivity

qc

2

0

0 rIqq

qqr

s

s


Reflection on a thin film deposited on a substrate

(non magnetic case)

0.00001

0.0001

0.001

0.01

0.1

1

0 0.5 1 1.5

qz (nm-1)

Ref

lect

ivity

dq

2

d


Example Cu(500 Å)/Cr(90 Å) on silicon

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 0.5 1 1.5 2 2.5

qz (nm-1)

Ref

lect

ivity

2/590

2/90


The neutron

spin 1/2 particle (associated magnetic moment µn

Interacts with the magnetic fields B (aligned along

z): Neutron in an eigenstate ( ) :

stays in this state Quantified neutron along (Ox) ( ) :

precession around Bz

Bz

µn

seigenstatetheareand

ou

12


Comparison nuclear and magnetic neutron scattering lengths.

Vm

b bN M 2 2

bm g M

Mn n

2 20

/ /

éléments bn (fm) bM (fm) a (barn)

Fe 9.45 5.4 2.56Co 2.49 4.5 37.2Ni 10.3 1.6 4.49Gd 6.5 - i 13.82 18.83 49700Si 4.15 - 0.17Ti -3.44 - 6.1


Polarised neutron reflectivity

It is possible to polarise neutrons

Manipulate the polarisation : neutron « flipper »

Guide field

Precession region

spin up spin down

H

beam

Guide field


Experimental set-upGuide field

polariser flipper sample

analyser detectorflipper

B+-

+-

+-

-+

M

RRRR ,,, 4 cross-sections


M // B

Sample transfert matrix

R

R

0

0

B+ +

- -M

0

1

0

0

0 R

RR

1

0

0

00

R

R

R


B perpendicular to the layer

No magnetic contrast

B+ +

- -M


M makes an angle with B

B+ +

- -

M

Sample transfert matrix

RR

RR

0

1

RR

RR

R

R

1

0

RR

RR

R

R


Magnetic domains

Neutron coherent illumination N vs magnetic domains sizes M

If N < M then (R + + R -) If N > M then no magnetic contrast

B+ +

- -

N


Field B parallel to the magnetisation

rq qq q

rq qq q

s

s

s

s

0

0

0

0

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2

q0 (nm-1)

Ref

lect

ivity

(M // B) up-up

(M // B) down-down

cq

cq


Fe thin film (30 nm) on a saphire substrate

M // B

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

q (nm-1)

Ref

lect

ivity

"up-up""down-down""up-up""down-down"


Spin-flip signal (M perp. B)

I I r

q q q

q q q qs s

s s

2 0

0 0

2

1

4

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2

q0 (nm-1)

Re

fle

cti

vity

(M perp. B) up-down

(M perp. B) up-up


Fe thin film (30 nm) on a saphire substrate

M perpendicular to B

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8

q (nm-1)

Ref

lect

ivity

"up-up""spin-flip""up-up""spin-flip"


Reflectivity geometry

b1

b2

b3

b4

M1

M4

M3

M2

Substrate

Incident beam


Roughness effects Roughness at the atomic level : interdiffusion between the

thin films, < 100 nm.

Intermediate roughness( de 0.1 µm à 50 µm).

A large scale roughness ( > 50 µm).

air

layer

0 0 + 0 -

Su b s tra te

Sam ple


Roughness effects

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4

qz (nm-1)

Re

flect

ivity

perfect interfaceinterfacial roughness of 2 nmalloy Si/Ni 2 nm


Resolution effects

Wavelength resolution Graphite monochromator : Multilayer monochromator :

(not adjustable) Chopper (ToF) : adjustable

Angular resolution Defined by the slits sizes

%1~/%20/%5

%20/%1

LW /2


Resolution effects

The resolution must be adjusted to be compatible with the studied sample

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 1 2 3 4 5 6 7 8

theta (degrees)

Ref

lect

ivit

y

Ni(10nm) on Silicon

Practical limit


2-axis spectrometer

po lariser flipper 1

flipper 2

analysers

detectorCollimation slits

sample

White beam

1 m

Graphitemonochromator

2


Upgraded 2-axis spectrometer

Top view

Side view

neutron guide G2

monochromator (M)

1 m

deviator

guide (D)

focussing guide (C)

2 arm

sample position

polariser (P)analyser (A)

detector

reactor

slit (S1)

S2S3S4

flipp.F2flipper (F1)


ToF reflectometer : EROS


PNR range of studies

Multilayers Superconductors Non colinear magnetism Interface magnetism


Polarised Neutron Reflectivity

Allows the study of the magnetic configuration of a multilayer system:access to the magnetisation amplitude and direction in each layer. Determination of in-depth magnetic profiles Absolute measurement of the magnetic moment in µB

per f.u. (sum of the spin and orbital moment) But sensitivity only to the in-plane moment. Resolution of the order of 0.1µB (better on simple

systems) No sensitivity to the substrate para/dia-magnetism. No absorption, no phenomenological parameter,

absolute normalisation.


Magnetic coupling

FERRO ANTI - FERRO Non colinéaires

J1 > 0 J1 < 0 J1 > 0 et J2 < 0

2212211 SSJSSJEcouplage


PNR on super-lattices

Adapted from H. Zabel


Modulated structures Example of a modulation of period 10 nm in a layer of

thickness 200nm in YBCO/STO Index variation of 2% only :

Difference of density stœchiométrie variation Magnetisation modulation de

l’aimantation YBCO

Y: 10%Ba: 12%Cu: 30%O: 49%

10

100

1000

10000

100000

1000000

10000000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

theta (degrés)

réfle

ctiv

ité (

u.a

.)


Example: magnetisation modulation

La0.3Sr0.7MnO3 film

10

100

1000

10000

100000

1000000

0 0.2 0.4 0.6 0.8 1 1.2 1.4

theta (degrés)

réfle

ctiv

ité (

a.u

.)

up-up

down-down


Exchange coupling in super-lattices [GaMnAs/GaAs]

Super-lattice(GaMnAs)m/(GaAs)n where 8<m<16 et 4<n<8Mn doping 6-7%

A201-16-6 @ 4.2K;20mT;ZFC

10

100

1000

10000

100000

1000000

0 0.02 0.04 0.06 0.08 0.1 0.12

q (A°-1)

refle

ctiv

ity

up-up

down-downMagnetisation of 0.03 T (27kA/m)

No antiferromagnetic coupling is observed.


Magnetic ordering in multilayers[ Fe/Si ]n

K. Fronc (Polish. Acad. Sc.) GaAs//[Fe(2.4nm)Si(1.2nm)]n

magnetic AF order at 300K non collinear coupling at 200K

1

10

100

1000

10000

100000

1000000

0 0.05 0.1 0.15 0.2

q (A°-1)

réfle

ctiv

ité (

x1E

6)

up-up

spin-flip

down-down

@ 7K; 20mT

10

100

1000

10000

100000

1000000

0 0.05 0.1 0.15 0.2

q (A°-1)

réfle

ctiv

ité (

x1

E6

) up-up

spin-flip

do-do

1

10

100

1000

10000

100000

1000000

0 0.05 0.1 0.15 0.2

q (A°-1)

réfle

ctiv

ité (

x1E

6)

up-up

spin-flip

down-down

@ 200K; 20mT

@ 300K; 2.8mT


Evolution of the magnetic coupling as a function of the magnetic field

AFM component disappears with the applied [email protected] T (for 10K)

DKF25; 140K; FC

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

-0.1 0 0.1 0.2 0.3 0.4 0.5

Field (T)

refle

ctiv

ity a

t qz

= 0

.87

nm-1

(A

FM

pea

k)

up-up

do-do

spin-flip

DKF25; 12K; [Fe (2.5nm)Si(1nm)]22

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 0.2 0.4 0.6 0.8 1Field (T)

refle

ctiv

ity a

t qz

= 0

.87

nm-

1 (A

FM

pea

k)

up-up

do-do

spin-flip


Spin-valves structures

E. Kentzinger, S. Nerger, U. Rücker, J. Voigt, O.H. Seeck, Th. Brückel(Forschungszentrum Jülich, Germany)

More academic structure

AsGa

AgFeCo

FeCoAu

Mncouche de blocage

couche libre

couche bloquée

Capteur GMR

substrat Si


In a saturating field of 0.5T

Fe0.5Co0.5/Mn (8A°)/ Fe0.5Co0.5

Moment of 2.4 µB/atom in Fe0.5Co0.5

Moment in manganese of 0.8µB/atom! Theoretically predicted

in FeCo alloys(not observed in Fe alone)

1

10

100

1000

10000

100000

1000000

10000000

0 1 2 3 4 5 6

theta (degrés)

réfle

ctiv

ité (

a.u

.)

++- -++ simul- - simul

E. Kentzinger et al., Physica B 276-278 (2000)S. Nerger et al., Physica B, to be published.


Measurement in low field

1

10

100

1000

10000

100000

1000000

10000000

0 1 2 3 4 5 6

theta (degrés)

réfle

ctiv

ité (

a.u.

)up-up

spin-flip corrected

down-down

fit up-up

fit spin-flip"

fit down-down

Quadratic coupling

B = 1.2mT

FeCo1 FeCo2

Mn


GMR optimisation

couche de blocage

couche libre

couche bloquée

Capteur GMR

substrat Si

Typical GMR structureSiO2// Ta/ NiFe/ CoFe/ Cu/ CoFe/ MnPt/ Ta

Aim to to optimize GMR sensors used in high density tape recording

PNR magnetometry characterize the system magnetically in a saturating field

(thickness and amplitudes of the magnetic moments). sweep the field H or the temperature T but restrict the

measurement to a few points of the reflectivity curve Adjust these points by letting vary only the amplitude and

direction of the magnetic moments in the multilayer model.


Hysteresis cycle

-1.5

-1

-0.5

0

0.5

1

-8 -6 -4 -2 0 2 4 6 8

B (mT)

M (

T)

along hard axis of free layer

along easy axis of free layerA

BC

D

E

F G

The easy axis of the AF layer is perpendicular to the easy axis of the free layer


PNR magnetometry Magnetisation of the different

layers as a function of the applied field

1

10

100

1000

10000

100000

1000000

0 0.5 1 1.5 2 2.5

q (nm-1)

refl

ecti

vity

(a.

u.)

Up-pUp

Down-Down

fit Up-Up

fit Down-Down

0

0.5

1

1.5

2

2.5

3

-4 -2 0 2 4

B (mT)

Flip

ping

rat

io

R++ / R- -

R-+/ R++

D (+1mT) E (1.5mT) G (6mT)

A (6mT) B (0.5mT) C (-4mT)CoFe

NiFe

CoFe

MnPt

Cu


Spin injection materialsMagnetite (DRECAM/SPCSI, J.B. Moussy et al) Fabrication of all oxide magnetic junctions Combination of Al2O3, Fe2O3, Fe3O4 layers Magnetite Fe3O4 is a potential candidate as spin-injector material Typical structure : A2O3//Fe2O3/Fe3O4/Al2O3/Fe3O4

BUT often a partial or total transformation of the Fe2O3 into Fe3O4 occurs (not visible during the deposition process using XPS or RHEED)

Collaboration : P. Bayle-Guillemaud, P. Warin, DRFMC-SP2M, CEA-Grenoble

HRTEM

[111]

[1-10]

[11-2] -Al2O3

(0001)

-Fe2O3

(0001)

Fe3O4 (111)

2.5 nm


PNR characterisation Neutron reflectivity allows to very quickly check the presence or absence of

Fe2O3 layer (by using the magnetic contrast)

Information on the magnetic moments : the transformed layer has a reduced magnetic moment

Sample 231 (T = 300K; H = 1.2 T)

0.0001

0.001

0.01

0.1

1

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

theta (°)

refle

ctiv

ityup-updown-downUP fit with Fe2O3/Fe3O4DO fit with Fe2O3/Fe3O4UP fit with Fe3O4 onlyDO fit with Fe3O4 only

Al2O3

M = 2.5 µB/f.u.

M = 1.75 µB/f.u.The transformation process is not yet understood


La0.7Sr0.3MnO3 : Hysteresis cycle

-1

-0.5

0

0.5

1

-0.1 0.1 0.3 0.5

B (T)

M/M

s

0

0.25

0.5

0.75

1

0 50 100 150 200 250

T (K)

M/M

sMsat

Mrem

M at 500G

LSMO film (40 nm) deposited on a SrTiO3 substrate


Reflectivity measurements.

LSMO on MgO (68nm) LSMO on STO (56nm)

100

1000

10000

100000

1000000

0 0.5 1 (degrees)

Ref

lect

ivity

(a.

u.)

"up-up"

"dow n-dow n"

"f it up-up"

fit dow n-dow n

100

1000

10000

100000

1000000

0.2 0.4 0.6 0.8 1 1.2 1.4

(degrees)

Ref

lect

ivity

(u.

a.)

"up-up"

"dow n-dow n"

fit "up-up"

fit "dow n-dow n"


Fitting procedure

Perfect system

LSMO

STO ou MgO STO ou MgO

More realistic model

M3

M2

M1


Magnetic profile in a LSMO on STO

0

0.5

1

1.5

2

2.5

3

0 30 60 90 120 150 180

Depth in the film (A°)

M (

µB/f

.u.)

150K

200K

240K

295K

320K

vacuumSrTiO3


LSMO film (16nm) sur STO

Spin asymmetry

RR

RR

77K; 1.2T-0.2

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5

Theta (°)

Spi

n as

ymét

rie

10

100

1000

10000

100000

1000000

0 0.5 1 1.5

Theta (°)

réfl

ec

tiv

ité

up-up

down-down

fit up-up

fit down-down

300K; 1.2T-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.5 1 1.5

Theta (°)

Spi

n as

ymét

rie

spin asymetrie

fit


Magnetisation variations (LSMO(16nm)/ STO)

0

0.5

1

1.5

2

2.5

3

3.5

4

50 100 150 200 250 300 350

Temperature (K)

Aim

an

tati

on

(µB

/f.u

.)

interface STO/LSMOmilieu du film

interface LSMO/air0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150

profondeur dans le film (nm)

aim

an

tati

on

(µ

B/f

.u.)

77K117K190K250K300K


Conclusion Applications

Multilayers Non colinear magnetism Interface magnetism

Determination of magnetic profiles with a depth resolution: access to the magnetisation amplitude and direction in each layer. Determination of in-depth magnetic profiles Absolute measurement of the magnetic moment in µB per f.u.

(sum of the spin S and orbital moment L ) But sensitivity only to the in-plane moment. Resolution of the order of 0.1µB (better on simple systems) No sensitivity to the substrate para/dia-magnetism. No absorption, no phenomenological parameter, absolute

normalisation. “low” flux.


Bibliography A few recent general references

H. Zabel et al, Physica B 276-278 (2000) 17-21.« Neutron Reflectometry on magnetic thin films »

H. Zabel et al, J. Phys.: Condens. Matter 15 (2003) S505-S517.Polarized neutron reflectivity and scattering studies of magnetic heterostructures.

G.P. Felcher, J. Applied Physics 87 (2000) 5431Neutron reflectometry as a tool to study magnetism

G. Fragneto-Cusani, J. Phys. : Condens. Matter 13 (2001) 4973-4989

Other ressources www-llb.cea.fr/prism/PRISM.html http://www.neutron.anl.gov/software.html All existing reflectometers :

http://www.studsvik.uu.se/research/NR/reflect.htm

Documents

Polarised neutron reflectivity Frédéric OTT Laboratoire Léon Brillouin [email protected]