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)