ultrafast magnetization dynamics - diva...

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2020

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1967

Ultrafast Magnetization Dynamics

Element-selective studies of magnetic alloys usingultra short XUV pulses

RAMEEZ SAEED MALIK

ISSN 1651-6214ISBN 978-91-513-1008-4urn:nbn:se:uu:diva-420004

Dissertation presented at Uppsala University to be publicly examined in Polhemsalen,Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 6 November 2020 at 09:00 forthe degree of Doctor of Philosophy. The examination will be conducted in English. Facultyexaminer: Prof. Dr. Uwe Bovensiepen (Department of Physics, University of DuisburgEssen).

AbstractMalik, R. S. 2020. Ultrafast Magnetization Dynamics. Element-selective studies of magneticalloys using ultra short XUV pulses. Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology 1967. 73 pp. Uppsala: ActaUniversitatis Upsaliensis. ISBN 978-91-513-1008-4.

In this thesis, I investigate the ultrafast magnetization dynamics in 3d ferromagnets and theiralloys with ultrashort laser pulses. The high harmonics generation (HHG) setup providesextreme-ultraviolet photons with energies 35-72 eV, which is the energy range where 3d metalshave their M2,3 absorption edges. By employing HHG with the transverse magneto-optical Kerreffect, the magnetization of multiple elements in a magnetic system is probed and their dynamicsare resolved separately on femtoseconds time scales.

The magneto-optical response of elemental Fe and Ni during demagnetization is investigated.This magneto-optical response is measured as an asymmetry in the intensity of reflected lightfor two opposite sample magnetization directions. Experiment and density functional theorycalculations show that for Fe, the asymmetry is strongly dependent on the particular type ofmagnetic excitation. However, for Ni, it is relatively insensitive to the magnetic excitation. Next,the element-specific magnetization dynamics of FeNi alloys are investigated. A time delay in theNi demagnetization relative to Fe is observed for all alloy compositions. This Ni-delay dependson the alloy composition and is related to changes in the exchange interactions.

Co2FeAl (CFA) Heusler alloys are unique due to their peculiar electronic structure andbecause they can exhibit very low damping. Experimentally, CFA films show a decreaseddamping with an increase in structural ordering. The demagnetization times of Fe and Coin CFA samples with different amount of ordering are similar for all samples. However, theremagnetization times exhibit a dependence on the structural ordering. Both the theoretical andexperimental damping parameters correlate well with the remagnetization times. In FeCo alloys,the damping can be changed by doping with heavy metals. Here, the magnetization dynamics ofFe65Co35 films as a function of Re doping are investigated. We find no observable change in thedemagnetization times for samples with increased damping. However, when increasing the Redoping and the damping, the remagnetization time becomes faster. Also, a fast increase of theasymmetry signal is observed at the Ru-edge during the demagnetization of FeCo. This effect isattributed to a super-diffusive spin current going from the FeCo layer to the Ru capping layer.

Last, the magnetization dynamics of a ferrimagnetic insulator is studied. The NiFe2O4

asymmetry shows oscillatory dynamics after an ultrashort laser pulse excitation. With 1.55 eVpump, these oscillations are strong. For 3.1 eV pump, demagnetization becomes dominant andthe oscillations diminish.

Keywords: magnetization dynamics, magnetic alloys, HHG, ultrashort laser pulses, magneto-optical Kerr effect (MOKE), Gilbert damping

Rameez Saeed Malik, Department of Physics and Astronomy, Box 516, Uppsala University,SE-751 20 Uppsala, Sweden.

© Rameez Saeed Malik 2020

ISSN 1651-6214ISBN 978-91-513-1008-4urn:nbn:se:uu:diva-420004 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-420004)

1988

2020 4 · 1013 1002009

100 1

100

1996

s �

m

< mz >= −2μ

�< s >

m s

3

l

< mz >=μ

�< l >

m H

E = −m ·H = − e2

4πε0m2ec

2r3·

�

3 10− 100

T

∼ 100 H i

1928

H i

ψφ r1 r2 χ r1 r2

ψ(1, 2) = −ψ(2, 1)

E = −2(J�2

)s1 · s2J E −E

2 E − E

i, jH

H = −2∑i>j

JijSi · Sj

J↑ ↑ J

↑↓

3

3

μμ

2.2 μ 1.7 μ 0.6 μ

3

3EF EF

3

31

m = μB(N↑ −N↓)

D↑ D↓

N↑ =∫ EF

−∞D↑(E)dE

N↓ =∫ EF

−∞D↓(E)dE

EF

I

I ·D(EF ) > 1

3

t= −γμ0 ×H

γ HH

H

d

t= −γ ×H − α

M

(× d

t

)

α

2.12H

Hα

H

α

3

TT T

3

G G

3

T

CedTe

dt= −Gel(Te − Tl)−Ges(Te − Ts) + P (t)

CsdTs

dt= −Ges(Ts − Te)−Gsl(Ts − Tl)

CldTl

dt= −Gel(Tl − Te)−Gsl(Tl − Ts)

G GG C , ,

�M

M= −A2τE −A1τM

τE − τM

− t

τM −τEA1 −A2

τE − τM

− t

τE

A1

A2

ττ

|↑〉|↓〉

|↑〉 |↓〉

dm

dt= Rm

Tl

Tc

{1−m

(m

Tc

Te

)}

m = m(t) = M(t)/Ms TT T

R

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2CVat

(μat/μB)E2D

a

� T /μμ

τ�

τ�

τ α

τM ∝ �

kBTC

1

α

α

α

μ(ω)

ε(ω)

D = ε0 ε(ω) ·ED ε0

E

ε

ε =

⎛⎝ εxx εxy εxz−εyx εyy εyz−εzx −εzy εzz

⎞⎠

ε

σ ε = 1 + i4πω σ ωε

σ

ε =

⎛⎝ εxx εxy 0−εxy εxx 00 0 εzz

⎞⎠

n2s = εxx

n2p = εxx +

(εxy)2

εxx

np ns

Is± =I0

[θi − n θrθi + n θr

]2

Ip± =I0

[θr − n θiθr + n θr

± 2 θi θin2(n θi + θr)2

εxy

]2

I0 θiθr

εxy

I(+)p

εxy I(−)p

A =I(+)p − I

(−)p

I(+)p + I

(−)p

∼= 2Re

[2 (2θi)εxy

n4 2 θi − n2 + 2 θi

]

θiθi 45◦

M2,3

3

80035

352.0 5 1.010

1980

∼ 15− 20> 1014 W/cm2

3.17U U

Up =e2E2

o

4mω2

e E ωm

I + 3.17UI

40 − 723

4

8020

≈ 3.1

Inte

ntist

y ( a

rb.u

nits) Ip+

Ip-(a)

0.3

0.2

0.1

0.0

-0.1

Asy

mm

etry

706560555045Energy (eV)

(b) Fe Co

≈ 54 ≈ 60

±Ip)

A(E) =I+(E)− I−(E)

I+(E) + I−(E)

1−x x

5

I±(E)E

∼ 3.1

∼ 1.55

0.200.150.100.050.00

-0.05-0.10

Asym

met

ry

70605040Energy (eV)

odd odd & even Theory

(c) Fe 0.6

0.4

0.2

0.0

-0.2

Asym

met

ry

70605040 Energy (eV)

odd odd & even Theory

(d) Ni

Inte

nsity

(arb

.uni

t)

70605040 Energy (eV)

I+ I-(a) Fe

Inte

nsity

(arb

.uni

t)

70605040Energy (eV)

I+ I-

(b) Ni

I±(E)40−72

5466

5466

A ∝ M

66

54

1.0

0.9

0.8

0.7

0.6

Norm

alize

d Asy

mmet

ry

0.50.40.30.20.10.0-0.1Delay (ps)

66 eV 63 eV 60 eV 57 eV 54 eV 51 eV 47 eV 44 eV

(a) Ni

1.1

1.0

0.9

0.8

Nor

mali

zed A

sym

met

ry

1.00.80.60.40.20.0Delay (ps)

47eV 51eV 54eV 57eV 60eV

(b) Fe

εxy

Mεxy 66

ε

40

20 2

0.2 < x < 0.8

30 − 40

19

1.00.90.80.70.6No

rm. a

symm

etry

0.60.40.20.0Delay (ps)

Fe64Ni36

d1.00.90.80.7

Norm

. asy

mmet

ry

0.60.40.20.0Delay (ps)

Fe70Ni30

e1.00.90.80.70.6No

rm. a

symm

etry

0.60.40.20.0Delay (ps)

Fe80Ni20

f

1.00.90.80.70.6No

rm. a

symm

etry

0.60.40.20.0Delay (ps)

Fe22Ni78 (Py) Fe Ni

a1.00.90.80.70.60.5No

rm. a

symm

etry

0.60.40.20.0Delay (ps)

Fe32Ni68

b1.00.90.80.70.60.5No

rm. a

symm

etry

0.60.40.20.0Delay (ps)

Fe42Ni58

c

5 μ

40

1.00

0.95

0.90

0.85 Asy

mm

etry

(A)

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1.1

1.0

0.9

0.8

0.7

0.6

0.5

Fe Ni

Fe 5μm space-Ni

a

1.0

0.9

0.8

0.7

0.6 Asy

mm

etry

(A)

0.40.30.20.10.0-0.1Delay (ps)

Fe42Ni58

b

40

30

20

10

0Fe-N

i Del

ay (f

s)

1.00.80.60.40.20.0Ni concentration

3.0 x10-3

2.5

2.0

1.5

1.0

0.5

0.0

1/TC (K

-1)

Fe-Ni Delay

c TC

-1

5 μ

700

600

500

400

300

200

100

0

D (m

eVÅ2 )

1.00.80.60.40.20.0

Ni concentration

Spin wave stiffness Neutrons SQUID (Bloch T3/2

law) Ab-initio theory (EMTO) T-MOKE (MDM)

1.0

D

DD

10 − 150 D

D

35

D

100

300

50 4

( ) ( ) ( ) ( ) 4

1

m

25

m τ ττ τR

ττ

τ

( )

→( ) 83

τ τ

τ

τ

1.00

0.95

0.90

0.85

0.80

0.75

Nor

m. A

sym

met

ry

1086420 Time Delay (ps)

A2(a)

1.000.950.900.850.800.75

A/A 0

0.80.40.0

FeCo


35% B2(b)

1.000.950.900.850.800.75

A/A 0

0.80.40.0

FeCo

1.00

0.95

0.90

0.85

0.80

0.75

0.70

Nor

m. A

sym

met

ry


72% B2(c)

1.0

0.9

0.8

0.7

A/A 0

0.80.40.0

Fe Co


83% B2(d)

1.0

0.9

0.8

0.7

A/A 0

0.80.40.0

FeCo

1

3.0

2.5

2.0

1.5

τ R (p

s)

CFA300K CFA573K CFA673K CFA773K

(b)

FeCo

30025020015010050

0

τ M (f

s)

Fe Co

(a)

4.54.03.53.02.52.0

τ R (p

s)

0 20 50 80 100B2 Ordering[%]

Fe Co

Remagnetization(d)

2.0

1.5

1.0

0.5

0.0

τ M (p

s)

Fe Co

Demagnetization(c)

ττ

→

E n↓E

n↓

(τ )−1α

→ ( )

EE

( )

( ) ( ) 83

0

5

10

15n

↑ tot(E

) (s

ts./eV

) A248% B280% B2B2L2

1

-6 -4 -2 0 2 4

E-EF (eV)

-15

-10

-5

0

n↓ to

t(E

) (s

ts./eV

)4

3

2

1

0

Dam

ping

( x

10-3

)

100806040200 B2 ordering (%)

0.55

0.50

0.45

0.40

0.35

0.30

0.25

(τr ) -1 (1/ps)

Remag time (τr )-1

Exp (α)Theory (α)

L21E

A2 → B2

τ

τ

α

5

0 12.620 3

54 60

45− 72∼ 54

∼ 60

Ms 65 35

12

44

54

32−72

12

6

3

44

20 1 8

12

ατ

1.00

0.95

0.90

0.85

0.80

0.7586420-2

Time Delay (ps)

6% Re

(c)

1.00

0.95

0.90

0.85

0.80

0.7586420-2

Time Delay (ps)

12% Re

(d)

1.00

0.95

0.90

0.85

0.80

0.75

Nor

m.A

sym

met

ry

86420-2Time Delay (ps)

Fe (undoped)

(a)

1.00

0.95

0.90

0.85

0.80

0.7586420-2

Time Delay (ps)

3% Re

(b)

1.00

0.95

0.90

0.85

0.80

0.7586420-2

Time Delay (ps)

6% Re

(g)

1.00

0.95

0.90

0.85

0.80

0.75

Nor

m.A

sym

met

ry

86420-2Time Delay (ps)

Co (undoped)

(e)

1.00

0.95

0.90

0.85

0.80

0.7586420-2

Time Delay (ps)

3% Re

(f)

ατ

ττ τ

403

6 12

150250

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0.0

τ R (p

s)

12840Re (%)

τR (Fe)

(b)

300

250

200

150

100

50

0

τ M (f

s)

12840Re (%)

τM (Fe)

(a)

765432 α

(x10

-3)

12840 Re (%)

τα

τ

44d

12

9

ττ

1.41.31.21.11.00.90.8

Asym

met

ry

undoped3%Re6%Re12%Re

(a)

1.000.950.900.850.80

Asym

met

ry

0.40.20.0-0.2Time Delay (ps)

1.00

0.95

0.90

0.85

Fe(Ru) Fe (Cu)

(b)

2+ 2+ 2+

2+

3+

T O3+ O

3+ T 2+

O

2+ 3+ Oh Td3+ T O

O

> 4O

d

3+ T −3.95 μ O4.10 μ 3+

2+ O 1.59 μ

2 μ

50 − 6063 − 7054 66

573+ T O

66 57O

2+ 3+

-6-4-2024 Fe (oh)

40

-4

Fe (Td)

-3-2-1012

-8 -4 0 4Energy (eV)

Oxygen

-4-202 Ni (oh)

-10-505

10 Total

DO

S (e

V-1)

O O T

εε O T

52− 58

1.55 54 57

662.4

1.55

Int.(

arb.

units

)

706560555045Energy (eV)

HHG I+ I-

(a) 0.060.040.020.00

-0.02-0.04-0.06

Asym

met

ry

706560555045Energy (eV)

NFO (MGO)

(b)

-0.4

-0.2

0.0

0.2

Re[ε x

y]

5756555453Energy (eV)

Fe (Oh) Fe(Td) Fe(both)

(c) 0.6

0.4

0.2

0.0

-0.2

-0.4

Asym

met

ry

6058565452Energy (eV)

Fe(Oh) Fe(Td)

(d)

44 − 7254 66

57ε T O

1.05

1.00

0.95

0.90

0.85

0.80

Nor

m. A

sym

met

ry

6420 Time delay (ps)

Fe (54) Fe (57) Ni

(a)

NFO/MGO (1.55 eV)

1.04

1.02

1.00

0.98

Nor

m.S

um

6420Time delay(ps)

Fe(54) Fe(57) Ni

(b)

Sum Signal (1.55 eV)

1.566

54 57I = (I+ + I−)

1.08

1.06

1.04

1.02

1.00

0.98

Nor

m.S

um

86420Time delay(ps)

Fe(54) Fe(57) Ni

(b)

1.1

1.0

0.9

0.8

0.7

0.6

0.5

Nor

m.A

sym

met

ry

86420Time delay(ps)

Fe(54) Fe(57) Ni

(a)

Sum (400 nm) NFO/MGO (3.1 eV)

3.1

∼ 2I = (I+ + I−)

54 57

3.1

54

3.13.1

3.11.55

44

1.5566 54

Acknowledgments

This thesis work would not have been possible without the kind support of somany nice people aroundme. 4.5 years of PhD (1.34·1023 femtoseconds) workhad been an incredible journey for me, during which I have had the pleasureto meet with numerous great people.First of all, I am grateful to my supervisor Prof. Olof ”Charlie” Karis, for

giving me this opportunity to work as a PhD student. I am very thankful to youfor giving me the freedom and teach me to work as a independent researcher.I appreciate your efforts for all the encouragement and fruitful discussion wehad throughout this journey.My sincere appreciation goes to my co-supervisors Ronny, Yaroslav, and

Johan for their guidance, motivation, and valuable information towards thisresearch work. A special thank to youRonny, for being such an excellent advi-sor, being supportive and available all the time, whenever I needed it. I admireyour knowledge and passion for research. A special thank to you Yaroslav foryour constant support and scientific input during this PhD work.I also extend my gratitude to all my colleagues who were/are working in

the laser lab (HELIOS). I had excellent time in this lab doing late-night ex-periments. Robert, thank you for the time that we have spent together in thelab with Ronny. Fighting with the laser, making harmonics and aligning theTMOKE setup and mostly on Friday evening. Also, I am very happy to seenew faces in the lab. Hampus, Marta and Susmita, I am sure you all will havea great time in thae lab.I like to express my gratitude to Prof. Olle for your motivation, scientific

discussions and valuable opinions. You were very supportive throughout thiswhole journey. Also, from the Theory side, I would like to thank Danny andErna for their support and great team work. I am deeply thankful to our col-laborator in the Engineering Science department, Prof. Peter, Ankit, Sajid,and Rahul for all the long discussions we had regarding CFA and FeCo alloysprojects. I also like to thank our collaborator from FloridaDario for providingme very interesting Ni-ferrite samples and for wonderful scientific discussions.I want to thank all my Ph.D fellows and all other postdoc/researchers for

making our workplace and lunch room lovely and super friendly. A big thanksto you Geethu for listening to me whenever I was down. You are such a greatcolleague and an awesome friend. I am looking forward to see your PhD de-fence. Also, I am very thankful to you Mahmoud for your kind support andmotivation throughout this thesis writing phase.

60

Outside of my academic life, I would especially like to thank my very closefriendAhsan Jutt and Zagum Toor, for your moral support and love through-out this journey. Thank you for not making distance a big deal of our friend-ship. A thousand miles apart, and you both are still my best old friends. Faisal,Thank you for always making time for me, no matter how far away you are.You always supported me during my tough time in Germany and in Sweden.Anindya and Amit, I want to thank both of you for the beautiful memories

and endless love. You both have always supported me during this whole time.I have great respect for both of you from the bottom of my heart. Soon it willbe a time to learn deep learning (AI).A special thanks to youTherese for all of your patience during this time and

always stand beside me, motivating me and, most importantly listening me.Finally, I thank all my familymembers, particularlymy father SaeedAhmed

and my mother Salma Saeed, for their love, prayers, and belief in me. With-out both of you, I would not be the person I am today. A big thanks to my Bigbrothers,Waqas Saeed and Sheraz Saeed, this was not possible without theirconstant support. Today, I am standing here at this stage is only because ofyour encouragement, care, and love throughout this time.

61

32

2018

1 10−910000

20 72

400

Acta Universitatis UpsaliensisDigital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1967

Editor: The Dean of the Faculty of Science and Technology

A doctoral dissertation from the Faculty of Science andTechnology, Uppsala University, is usually a summary of anumber of papers. A few copies of the complete dissertationare kept at major Swedish research libraries, while thesummary alone is distributed internationally throughthe series Digital Comprehensive Summaries of UppsalaDissertations from the Faculty of Science and Technology.(Prior to January, 2005, the series was published under thetitle “Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology”.)

Distribution: publications.uu.seurn:nbn:se:uu:diva-420004

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2020

ultrafast magnetization dynamics - diva...

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