P. Vavassori -Ikerbasque, Basque Fundation for Science and CIC - - PowerPoint PPT Presentation

SLIDE 1

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

FT-2: Magneto-optics and Magneto-plasmonics Part 1

• P. Vavassori
• Ikerbasque, Basque Fundation for Science and CIC nanoGUNE Consolider,

San Sebastian, Spain.

SLIDE 2

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Outline

Magneto-optics Brief overview of the Magneto-optical Kerr effects (MOKE) Advanced MOKE: vector magnetometry Magnetic nanostructures micro-MOKE Approach 1: focused beam Approach 2: microscopy MOKE from diffracted beams: simple theory of diffracted MOKE in conjunction with micromagnetics and MFM from magnetometry to magnetic imaging

SLIDE 3

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

John Kerr 1824 - 1907 Michael Faraday 1791 - 1867 s p s p s p Reflected Light z θ x Transmitted Light Polarization Plane Sample

The MagnetoOptical Effect

x z y p s p s θ θ x z y p s p s θ θ

But, what happens if we applied a magnetic field??

→ → → →

  =      

s s p s s p p p

r r R r r

SLIDE 4

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

The Magneto-Optical Effect

→ → → →

  =      

s s p s s p p p

r r R r r

xx xy xz yx yy yz zx zy zz

                  

x z y Hy p s p s θ θ x z y Hx p s p s θ θ Hz

Polar and Longitudinal Configuration Transverse Configuration

Reflectivity matrix Dielectric Tensor

SLIDE 5

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

MOKE

The magneto-optic Kerr effect (MOKE) is widely used in studying technologically relevant magnetic materials. It relies on small, magnetization induced changes in the

• ptical

properties which modify the polarization or the intensity of the reflected light. Macroscopically, magneto-optic effects arise from the antisymmetric, off-diagonal elements in the dielectric tensor.

       

ss sp ps pp

r r r r

Sample

rpp = r0

pp+ rpp M  my

rps  - mx - mz rsp  mx-mz

Fresnell reflection coefficients

iTM rTM pp

E E r =

iTE rTM ps

E E r =

iTM rTE sp

E E r =

iTE rTE ss

E E r =

          − − − = ˆ          

x y x z y z

i i i i i i

             =  ˆ

x = 0 Q mx; y = 0 Q my; z = 0 Q mz;

• Non-destructive;
• High sensitivity;
• Finite penetration depth (~ 10 nm);
• Fast (time resolved measurements);
• Laterally resolved (microscopy);
• Can be easily used in vacuum and

cryogenic systems;

• J. Kerr, Philosophical Magazine 3 321 (1877)
• Z. Q. Qui and S. D. Bader, Rev. Sci. Instrum. 71, 1243 (2000)
• P. Vavassori, APL 77 1605 (2000)

SLIDE 6

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

MOKE origin: classical picture Lorentz force

SLIDE 7

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Here, x (r) is the spin-orbit parameter or coupling constant, which depends on the gradient of the electrostatic potential of the nuclear charges. Its values are of the order of 10-100meV and, thus, the spin-orbit interaction is much weaker than the exchange interaction (≈ 1eV).

Electron theory of Magneto-Optics

Microscopically, the coupling between the electric field of the propagating light and the electron spin in a magnetic medium occurs through the spin-orbit interaction splitting of

• ptical absorption lines (Zeeman effect).

SLIDE 8

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Electron theory of Magneto-Optics

SLIDE 9

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Microscopic origin of Magneto-Optics s+ and s-

Selection rules Optical transitions between the d-orbitals and the p-orbitals

Only transition from m = 1 to m = 0 are considered for simplicity

SLIDE 10

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Microscopic origin of Magneto-Optics

SLIDE 11

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Microscopic origin of Magneto-Optics

SLIDE 12

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Microscopic origin of Magneto-Optics

SLIDE 13

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Microscopic origin of Magneto-Optics

SLIDE 14

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Microscopic origin of Magneto-Optics

SLIDE 15

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Electron theory of Magneto-Optics

• Magnetization→Splitting of spin-states (Exchange)

– No direct cause of difference of optical response between LCP and RCP

• Spin-orbit interaction→Splitting of orbital states

– Absorption of circular polarization→Induction of circular motion of electrons

• Condition for large magneto-optical response

– Presence of strong (allowed) transitions – Involving elements with large spin-orbit interaction – Not directly related with Magnetization

MOKE results from a lifting of orbital degeneracy due to spin-orbit interaction (SOI) in the presence of spontaneous spin polarization.

SLIDE 16

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

          − =

xx xx xy xy xx

      ~

xy = i0 Q mz;

( ) ( ) ( ) 0

~

2 2 2

=      +  E t c E rot rot

2 2

=                     − − − −

z y x zz xx xy xy xx

E E E n n     

xy xx

i n    =

 2

Maxwell Equation Eigenequation Eigenvalue Eigenmodes：LCP and RCP Without off-diagonal terms：No difference between LCP & RCP

( )

( )

t z nk i

e E E





−

=

( )

ˆ

2

= −  − E E n n E  n

A simple case: M || z

Different modes :different speed and attenuation

Therefore, incident light becomes elliptically polarized after propagation in a MO active material

SLIDE 17

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Phenomenology of MO effect

Linearly polarized light can be decomposed to LCP and RCP Difference in phase causes rotation of the direction of Linear polarization Difference in amplitudes makes Elliptically polarized light In general, elliptically polarized light With the principal axis rotated Different speed (phase lag) Different attenuation

SLIDE 18

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

1 2 2 2 1 2 2 1 2 1 2 1

sin sin 1 sin 1 cos n n n n n     − = − = − =

rpp = r0

pp+ rpp M  my

rps  - mx - mz rsp  mx-mz

xy = i1Q mz; xz = -i1Q my; yz = i1 Q mx; xy = -yx; zx = -xz; zy = -yz;

       

ss sp ps pp

r r r r

General case: Oblique incidence and arbitrary direction of M

SLIDE 19

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Polarization conversion

Summary of phenomenology

Ei Er Ei Er M M = 0 px px py

( )

   − =

xx yx y

p

px py

SLIDE 20

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

( )

          + =           =       =  



sin cos 1 1 ~ i r r e r r r r E

pp sp i pp sp sp pp r

K K

       

pp sp

r r Re

     

ss ps

r r Re

       

pp sp

r r Im      

ss ps

r r Im

rsp << rpp

pp sp K K

r r    cos 2 2 2 tan  

pp sp K K

r r    sin 2 2 2 sin  

 cos Re

pp sp pp sp

r r r r =        

Longitudinal and polar Kerr effect

 sin Im

pp sp pp sp

r r r r =        

2 2 2

1 cos 2 cos 2 2 tan b b r r r r

sp pp sp pp K

− = − =   

2 2 2

1 sin 2 sin 2 2 sin b b r r r r

sp pp sp pp K

+ = + =   

Elliptically polarized light Normalized representation

a b Eox Eoy x y

K K

E(z,t)

SLIDE 21

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

x y x’ y’ l/4plate h E0 E0sinh E0cosh

   E E i i j = +

0(cos

sin ) h h

Optic axis

( )

      E E i ie j E i j E i

i

' (cos sin ) cos sin ' = + = + =

− 2

h h h h



x y h E’ E

Measurement of ellipticity

E0 Er E’r M

SLIDE 22

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

l/4 l/2 45° 22.5° p s p s p s p s

wollastone

45° p s

wollastone

Measurement of ellipticity & rotation: high sensitivity

+M

• M

+M

• M

<M>=0 +M

• M

SLIDE 23

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Measurement of ellipticity & rotation: high sensitivity

SLIDE 24

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

24

Measuring K and K

Modulation polarization technique for recording the longitudinal and polar Kerr effects, which are proportional to the magnetization components mx mz..

POLARIZER Glan-Thompson PHOTOELASTIC MODULATOR (50kHz) ORIGINAL ELLIPTICTY MODULATED ELLIPTICTY PREAMPLIFIED PHOTODIODE POLARIZER HeNe LASER p-polarized beam s-p polarized reflected beam (elliptical polarization)

y x

Lock-in

Electromagnet

E

More details in: P. Vavassori, Appl. Phys. Lett. 77, 1605 (2000)

K K

spol  - mx – mz ppol  mx- mz

SLIDE 25

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Io

Transverse Kerr effect

Laser Polarizer Detector p-polarized light (TM)

M

Er = rpp Eo rpp = ro

pp + rm ppmy

Ir = Er (Er)* Ir = Io+ DIm DIm/Io a my

The reflected beam is p-polarized. Variation of intensity and phase.

y

• Y. Souche et al.

JMMM 226-230, 1686 (2001); JMMM 242-245, 964 (2002). M

fm Dfm a my E E

Polarizer l/4

SLIDE 26

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Supplementary information Examples of application of MOKE for magnetic characterization of materials and nanosctructures

SLIDE 27

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Vector analysis of reversal

H M My Mx x y My Mx

• 1.0
• 0.5

0.0 0.5 1.0

• 1.0
• 0.5

0.0 0.5 1.0

• 10000
• 5000

5000 10000

• 1.0
• 0.5

0.0 0.5 1.0

my mx mz

Field (Oe)

MgO Fe(300 nm) NiO(1.4 nm) Fe(7 nm) 180-nm-thick CoNiO

• 10000
• 5000

5000 10000 30 60 90 120 150 180 210 240 10000 5000

• 5000
• 10000

180 210 240 270 300 330 360 390 420

• 10000

10000 0.5 1.0 10000

• 10000

0.5 1.0

Branch up

out in

Rotation angle (deg.)

out in

Branch down

Rotation angle (deg.)

Field (Oe)

m

Field (Oe)

m

Field (Oe)

• F. Carace, P. Vavassori, G. Gubbiotti, S. Tacchi, M. Madami, G. Carlotti, and T. Okuno,

Thin Solid Films 515/2, 727 (2006).

• A. Brambilla, P. Biagioni, M. Portalupi, P. Vavassori,
• M. Zani, M. Finazzi, R. Bertacco, L. Duò, and F. Ciccacci, Phys. Rev. B. 72, 174402 (2005).
• P. Vavassori, Appl. Phys. Lett. 77, 1605 (2000) .

Reconstruction of the magnetization vector during the reversal

SLIDE 28

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Element sensitivity (and layer sensitivity)

XMCD x-ray magnetic circular dichroism (FeL3 Py hysteresis loop and CoL3 thresholds), → chemical and magnetic sensitivity

Py Cu Co

230 nm 10 nm

• 1000
• 500

500 1000 0.1725 0.1730 0.1735 0.1740 0.1745 0.1750 Rotation MOKE signal (arb. units) Field (Oe)

• 1000
• 500

500 1000 0.065 0.066 0.067 0.068 0.069 0.070 0.071 0.072 0.073 0.074 0.075 Ellipticity MOKE signal (arb. units) Field (Oe)

MOKE XMCD

• 1000
• 500

500 1000

• 5.4
• 5.2
• 5.0
• 4.8
• 4.6
• 4.4
• 4.2
• 4.0

Fe Signal Field (Oe)

• 1000
• 500

500 1000

• 2.0
• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 Co Signal Field (Oe)

Simulations

• 1000
• 500

500 1000

• 0.006
• 0.004
• 0.002

0.000 0.002 0.004 0.006 Permalloy MOKE signal (arb. units) Field (Oe)

• 1000
• 500

500 1000

• 0.004
• 0.003
• 0.002
• 0.001

0.000 0.001 0.002 0.003 0.004 Cobalt MOKE signal (arb. units) Field (Oe)

JOURNAL OF PHYSICS D-APPLIED PHYSICS 41, 134014 (2008)

SLIDE 29

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

20 40 60 80 100

• 0,010
• 0,005

0,000 0,005 0,010 0,015

Py

S Rotation P Rotation s Ellipticity P Ellipticity Radiants Incidence Angle (degrees)

20 40 60 80 100

• 0,04
• 0,02

0,00 0,02 0,04 0,06

Co

S Rotation P Rotation s Ellipticity P Ellipticity degrees Incidence Angle (degrees)

1 2 3 4 5 6

• 0,015
• 0,010
• 0,005

0,000 0,005 0,010 0,015 0,020

Py

S Rotation P Rotation s Ellipticity P Ellipticity degrees Photon energy (eV)

1 2 3 4 5 6

• 0,030
• 0,025
• 0,020
• 0,015
• 0,010
• 0,005

0,000 0,005 0,010 0,015 0,020 0,025 0,030 0,035 0,040 0,045

Co

S Rotation P Rotation s Ellipticity P Ellipticity degrees Photon energy (eV)

Element sensitivity (thin layer regime)

SLIDE 30

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Layer sensitivity

SLIDE 31

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

31

Ht = Ht0 Sin(2ft) H Lock-in 1: Ref.

• freq. 50-100kHz

Lock-in 2:Ref

• freq. f

mx0

mx = mx0 Sin (2ft)

MOKE transverse susceptibility: anisotropy

The quantity measured with the Lock-in2 is proportional to the transverse suceptibility ct = D0 / Ht0. It can be shown that : 1/ct = (Eo''(eq)/ <M>eq) where Eo(eq) is the total free energy and <M>eq is the average magnetization, which makes an angle eq with the EA. H = 700 Oe Ht = 35 Oe f = 156 Hz

0.0 0.4 0.8 1.2 30 60 90 120 150 180 210 240 270 300 330 0.0 0.4 0.8 1.2 1/c

M t (Oe Volt

• 1)

ea ea ea ea 1/cM

t (arb. units)

SLIDE 32

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

32

Configurational anisotropy

Flower state: higher energy Leaf state: lower energy

Even small perturbations from uniform magnetization which must exist in any nonellipsoidal magnet give rise to a (strong) angular dependence of magnetostatic dipolar energy in symmetric squared particles, which should be magnetically isotropic in the approximation of M uniform. This anisotropy is called configurational anisotropy Py squares 150 x 150 x 15 nm3

 H

fourfold symmetry, at first order, eightfold symmetry at second order

• R. P. Cowburn et al. Phys. Rev. Lett. 81, 5414 (1998)

H = 0

• P. Vavassori, et al., Phys. Rev. B 72, 054405 (2005)

SLIDE 33

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

33

Kerr microscopy: focused laser beam

Laser Detector CCD

PHYSICAL REVIEW 72, 224413 (2005)

• D. A. Allwood, et al., J. Phys. D: Appl. Phys. 36, 2175 (2003)

Py wires 175 nm wide Micro-MOKE

Py wire 200 nm wide Single loop Py wire 100 nm wide 1000 loops

SLIDE 34

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Polar Longitudinal and transverse

Kerr microscopy: imaging

M M

SLIDE 35

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Magnetometry of ultra-small nanostructure

EBID electron beam induced deposition Scanning electron microscopy image of the set of EBID cobalt structures

SLIDE 36

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

APPLIED PHYSICS LETTERS 100, 142401 (2012) t = 20 nm

single sweep measurement sensitivity of approximately 1 x10-15 Am2 sensitivity of 10-12 to 10-13 Am2 for the latest generation of SQUID magnetometer

t = 5 nm

9 averages Single sweep

Magnetometry of ultra-small nanostructure

SLIDE 37

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Diffraction of light by an array

"Diffracted-MOKE: What does it tell you?",

• M. Grimsditch and P. Vavassori J. Phys.: Condensed Matter 16, R275 - R294 (2004).

As is well known for optical gratings, when a beam of light is incident upon a sample that has a structure comparable to the wavelength of radiation, the beam is not only reflected but is also diffracted. If the material is magnetic, one may ask whether the diffracted beams also carry information about the magnetic structure.

SLIDE 38

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Examples of D-MOKE loops

Peculiar structures due to

• Collective properties
• Interference effects
• P. Vavassori, et al., J Appl. Phys. 99, 053902 (2006)
• M. Grimsditch, P. Vavassori, et al., Phys. Rev. B 65, 172419 (2002)
• P. Vavassori, et al., Phys. Rev. B 67, 134429 (2003)
• P. Vavassori, et al., J. Appl. Phys. 101, 023902 (2007)
• P. Vavassori, et al.,Phys. Rev. B 59 6337 (1999)
• P. Vavassori, et al., Phys. Rev. B 69, 214404 (2004)
• P. Vavassori, et al., Phys. Rev. B 78, 174403 (2008)
• 2000 -1500 -1000 -500

500 1000 1500 2000

• 3,0
• 2,5
• 2,0
• 1,5
• 1,0
• 0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 Field (Oe) 2

nd order

• 600
• 400
• 200

200 400 600

• 0.274
• 0.273
• 0.272
• 0.271
• 0.270
• 0.269
• 0.268

Reflected D-MOKE Intensity (arb. units) Field (Oe)

H

• 2000 -1500 -1000 -500

500 1000 1500 2000

• 1,0
• 0,5

0,0 0,5 1,0 1,5 Rflected

• Norm. Signal
• Norm. Signal

Intensity (norm. signal)

• 600
• 400
• 200

200 400 600 0.838 0.840 0.842 0.844 0.846 0.848 0.850 0.852 0.854 0.856

Field (Oe) D-MOKE Intensity (arb. units) 2

nd order

H

Reflected Reflected 2nd order 2nd order

• 600 -400 -200 0 200 400 600
• 600 -400 -200 0 200 400 600

Field (Oe) Field (Oe)

3.0 2.0 1.0 0.0

• 1.0
• 2.0
• 3.0

1.0 0.5 0.0

• 0.5
• 1.0

1.0 0.5 0.0

• 0.5
• 1.0

1.0 0.5 0.0

• 0.5
• 1.0
• 2000 -1000 0 1000 2000

Intensity (norm. signal)

• 2000 -1000 0 1000 2000

Incidence Plane (xz)

H

Laser 532 nm 50 mW

E D i f f r a c t i

• n

p a t t e r n

coil coil

Photodetector

Incidence Plane (xz)

H

Laser 532 nm 50 mW

E Incidence Plane (xz)

H

Laser 532 nm 50 mW

Incidence Plane (xz)

H

Laser 532 nm 50 mW

E D i f f r a c t i

• n

p a t t e r n

coil coil

Photodetector

SLIDE 39

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Intuitive explanation of D-MOKE loops

Peculiar structures due to

• Interference effects
• Collective properties
• O. Geoffroy et al., J. Magn. Magn. Mat. 121 (1993) 516
• Y. Souche et al., J. Magn. Magn. Mat., 140-144 (1995) 2179

H

rpp = ro

pp + rm ppmy(x,y)

M M

SLIDE 40

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Physical-optics approximation provides a very simple and physically transparent description.

The electric field in the nth order diffracted beam, due to the periodic modulation of the “effective” reflectivity r’pp is:

En

d = Eo fn

fn= S r’pp exp{i n G•r} dS

where n integer, G reciprocal lattice vector and S is the unit cell.

r’pp = ropp + rmpp my(x,y,H) En

d = Eo (ropp fn nm+ rmpp fn m) with ropp(i, n, dots, subst), rmpp(i, n, dots, Q)

fn

nm= S exp{i n G•r} dxdy

non-magnetic form factor

fn

m(H)= Dot my(x,y,H) exp{i n G•r}dxdy magnetic form factor

In

d = En d (En d)*

DIn

m (my) = AnRe[fn

m]+Bn Im[fn m]

Simple theory of diffracted-MOKE

SLIDE 41

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

DIn

m a An Re[fn m] + Bn Im[fn m]

Re[fn

m]= Dot my cos(n Gx x) dS

Im[fn

m]= Dot my sin(n Gx x) dS

Im[f1

m] = 0

Saturated state  Re[f1

m] > 0

What are the differences due to?

y x

period L Unit cell

Gx = 2/L reciprocal lattice vector Diffracted spots in the scattering plane

y x y x

1st order

Im[f1

m] < 0

 Re[f1

m] = 0

Im[f1

m] > 0

 Re[f1

m] = 0

2nd order

Im[f2

m] < 0 large

 Re[f2

m] = 0

y x y x

3rd order

Im[f2

m] < 0 very large

 Re[f2

m] = 0

Two-domain state: asymmetric M distribution

SLIDE 42

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

y x

Tuning the sensitivity to selected portions of the dot!

Immaginary contribution: highlight any asymmetric (y-mirror symmetry breaking) magnetic (my) behaviour Real contribution: y-mirror symmetry my

y x

period L

SLIDE 43

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Asymmetry to induce the desired vortex rotation

Narrow channel pins the magnetization

2 m

• 600
• 400
• 200

200 400 600

• 0.274
• 0.273
• 0.272
• 0.271
• 0.270
• 0.269
• 0.268

Reflected D-MOKE Intensity (arb. units) Field (Oe)

3 1 2

• 600
• 400
• 200

200 400 600 0.838 0.840 0.842 0.844 0.846 0.848 0.850 0.852 0.854 0.856

Field (Oe) D-MOKE Intensity (arb. units) 2

nd order

• 600
• 400
• 200

200 400 600

• 0.46
• 0.44
• 0.42
• 0.40
• 0.38
• 0.36
• 0.34

1

st order

D-MOKE Intensity (arb. units)

• 600
• 400
• 200

200 400 600

• 0.285
• 0.280
• 0.275
• 0.270
• 0.265
• 0.260
• 0.255

1

st order

• 600
• 400
• 200

200 400 600

• 0.231
• 0.230
• 0.229
• 0.228
• 0.227
• 0.226
• 0.225
• 0.224

Field (Oe) 2

nd order

H H H H H

• 600
• 400
• 200

200 400 600

• 3
• 2
• 1

1 2 3

Field (Oe)

2

nd order (Re[fd m] + 0.65 * Im[fd m])

• 600
• 400
• 200

200 400 600

• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5

Normalized D-MOKE signal

Reflected

Field (Oe)

H H H H H

• 600
• 400
• 200

200 400 600

• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5

1

st order (Re[fd m] + 0.8 * Im[fd m])

Normalized D-MOKE signal

• 600
• 400
• 200

200 400 600

• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5

1

st order (Re[fd m] + 0.8 * Im[fd m])

• 600
• 400
• 200

200 400 600

• 1.5
• 1.0
• 0.5

0.0 0.5 1.0 1.5

Normalized D-MOKE signal Field (Oe)

2

nd order (Re[fd m] + 0.65 * Im[fd m])

• P. Vavassori, R. Bovolenta, V. Metlushko, and B. Ilic, J Appl. Phys. 99, 053902 (2006)

Measured Calculated

SLIDE 44

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Measured D-MOKE loops from square rings

• 2000 -1000

1000 2000

• 1.0
• 0.5

0.0 0.5 1.0

Normalized Kerr signal 0th order

• 2000 -1000

1000 2000

• 1.0
• 0.5

0.0 0.5 1.0

0th order

• 2000 -1000

1000 2000

• 15
• 10
• 5

5 10 15

1st order

Field (Oe)

• 2000 -1000

1000 2000

• 3
• 2
• 1

1 2 3

1st order Normalized Kerr signal

Field (Oe)

(a) (b)

Reflected 1st order 1st order Reflected

H

H

Square lattice (4.1x4.1 m2) of Permalloy square rings (2.1 m side). Nominal width 250 nm. Thickness 30 nm.

Note intense peaks in the diffracted loops

• P. Vavassori, et al., Phys. Rev. B 67, 134429 (2003)

SLIDE 45

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Square ring structures

1 saturated state 2 onion state 4 reversed onion state 5 saturated state 1 saturated state 4 reversed onion state 5 saturated state 2 onion state

• 2000
• 1000

1000 2000

• 8
• 4

4 8 Normalized signal 1st order

Field (Oe)

• 2000
• 1000

1000 2000

• 2
• 1

1 2 Field (Oe) 1st order Normalized signal

3 horseshoe state 3 vortex state

H H

SLIDE 46

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Quenching structures in intermediate states and image them with MFM

• 1000
• 500

500 1000

• 3
• 2
• 1

1 2 3 Normalized Kerr signal Field (Oe)

H

• 1000
• 500

500 1000

• 15
• 10
• 5

5 10 15 Normalized Kerr signal Field (Oe)

H

(c) (b)

• P. Vavassori, M. Grimsditch, V. Novosad, V. Metlushko, B. Ilic, P. Neuzil, and R. Kumar, Phys. Rev. B 67, 134429 (2003)

SLIDE 47

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
• Y. Suzuki, C. Chappert, P. Bruno, and P. Veillet, J. Magn. Magn. Mater. 165 516 (1997)
• nly for size >> l

“effective” reflectivity An = Re[ropp* rmpp] Bn = Im[ropp* rmpp] An and Bn (i, n, dots, sub, Q) r’pp = ropp + rmpp For inhomogeneous gratings ropp = ropp, dot + ropp, sub DIn

m (my) = 2 fn nm { AnRe[fn m]+Bn Im[fn m] }

About An and Bn

An interesting characteristic of D-MOKE related to this : the absolute value of (DI/Io)n is increased up to several times the specular value. Effect due to the compensation of the non-magnetic component of the light diffracted by the magnetic dots and the light diffracted by the (non-magnetic) complementary part of the substrate.

Io,n = |ropp, dot|2 fn

nm + | ropp, sub |2 f’n nm = ( |ropp, dot|2 - | ropp, sub |2 )fn nm

SLIDE 48

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

532 nm laser

Different approach: towards Fourier imaging? 1st step

H

(1,0) (-1,0) (0,1) (0,-1) (-1,-1) (1,-1) (1,1) (-1,1)

Normal incidence: the scattering plane is defined by the selected spot

y x

Sensitivity to (mx , my) Sensitivity to mx

• 2000
• 1000

1000 2000

• 0.0465
• 0.0460
• 0.0455
• 0.0450
• 0.0445
• 0.0440
• 0.0435
• 0.0430
• 0.0425

2

nd order mx

MOKE intensity (arb. units) Field (Oe)

Vectorial D-MOKE (DIn

m)norm = An Re[fn m]- Bn Im[fn m]

(DI-n

m)norm = −An Re[fn m]- Bn Im[fn m]

Sensitivity to my

• 2000
• 1000

1000 2000

• 16.55
• 16.50
• 16.45
• 16.40
• 16.35
• 16.30

2

nd order my

MOKE intensity (arb. units) Field (Oe)

• 2000 -1000

1000 2000

• 1.0
• 0.5

0.0 0.5 1.0

0th order

• 2000 -1000

1000 2000

• 15
• 10
• 5

5 10 15

1st order

Field (Oe)

Im Re

M

z x

SLIDE 49

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
• K. Postava et al. “Null ellipsometer with phase modulation,” Opt. Express 12, 6040 (2004)

compensator analyzer photodetector photoelastic modulator polarizer laserr

Lock-in

I I2

Lock-in Re[Drm/r0] = DIm/I0 Im[Drm/r0] = Dfm/f0 Dfn

m/fn

• = Bn Re[fn

m]−An Im[fn m]

DIn

m/In

• = An Re[fn

m]−Bn Im[fn m]

DI−n

m/I−n

• = −An Re[fn

m] − Bn Im[fn m]

Df−n

m/f−n

• = −Bn Re[fn

m] − An Im[fn m]

Re[fn

m]

Im[fn

m]

D-MOKE problem fully solved

M

fm Dfm a my E E

SLIDE 50

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Samples: arrays of NiFe triangular rings

Triangular rings (2.1 m side). Nominal width 250 nm. Nominal thickness 30 nm. ZEP 520 Resist (0.3 m) PMGI Resist (0.3 m) Exposed Areas

Double Layer Resist Spin-coating EB Patterning

Si substrate

Resist Development EB Deposition (FeNi target) Lift-off process

nanoelement

Electron beam lithography

SLIDE 51

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

+ 1

• 1
• 2000
• 1000

1000 2000

• 0,002
• 0,001

0,000 0,001 0,002

• 2000
• 1000

1000 2000

• 0,003
• 0,002
• 0,001

0,000 0,001 0,002 0,003 Amplitude(mV) Field(Oe)

• 1 order Re(Drpp/rpp)
• 1 order Im(Drpp/rpp)

Amplitude(mV) Field(Oe)

• 2000
• 1000

1000 2000

• 0,001

0,000 0,001

• 2000
• 1000

1000 2000

• 0,002
• 0,001

0,000 0,001 0,002 Amplitude(mV) Field(Oe) +1 order Re(Drpp/rpp) Amplitude(mV) Field(Oe) +1 order Im(Drpp/rpp)

Normal incidence: extraction of magnetic form factors

Dfn

m/fn

• = Bn Re[fn

m]−An Im[fn m]

DIn

m/In

• = An Re[fn

m]−Bn Im[fn m]

DI−n

m/I−n

• = −An Re[fn

m] − Bn Im[fn m]

Df−n

m/f−n

• = −Bn Re[fn

m] −An Im[fn m]

Re[fn

m]

Im[fn

m]

SLIDE 52

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

 

n m

f 

 

n m

f 

• 0.10
• 0.05

0.00 0.05

• 0.02

0.00 0.02

• 2
• 0.12
• 0.06

0.00 0.06

• 2
• 1

1 2

• 0.08
• 0.04

0.00 0.04

• 0.05

0.00 0.05 0.10

• 0.03

0.00 0.03

2

nd order horizontal

2

nd order vertical

3

rd order horizontal

Experimental

1

st order horizontal

Form factor Field (

3

rd order vertical

1

st order vertical

Exp and calculated Re[fm] and Im[fm] – horizontal and vertical plane

SLIDE 53

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
• 2000
• 1000

1000 2000

• 0,14
• 0,12
• 0,10
• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 0,08 0,10 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,020
• 0,015
• 0,010
• 0,005

0,000 0,005 0,010 0,015 0,020 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,10
• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 0,08 0,10 0,12 Re Im Amplitude Field (Oe)

1st - h 2nd - h 3rd - h 1st - v 2nd - v 3rd - v

Re and Im parts of the magnetic form factors

SLIDE 54

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

Saturated state

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

50 100 150 200 50 100 150 200

SLIDE 55

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

“Peak” state

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

50 100 150 200 50 100 150 200

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

SLIDE 56

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

50 100 150 200 50 100 150 200

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

After “peak”

SLIDE 57

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

50 100 150 200 50 100 150 200

50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200 50 100 150 200

Towards negative saturation

SLIDE 58

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
• 2000
• 1000

1000 2000

• 0,12
• 0,09
• 0,06
• 0,03

0,00 0,03 0,06 0,09 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,020
• 0,015
• 0,010
• 0,005

0,000 0,005 0,010 0,015 0,020 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,14
• 0,12
• 0,10
• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 0,08 0,10 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,020
• 0,015
• 0,010
• 0,005

0,000 0,005 0,010 0,015 0,020 Re Im Amplitude Field (Oe)

Exp and calculated Re[fm] and Im[fm] – horizontal plane

1st - h 2nd - h 3rd - h

SLIDE 59

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018
• 2000
• 1000

1000 2000

• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 0,08 0,10 0,12 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,10
• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 0,08 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,10
• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,08
• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 Re Im Amplitude Field (Oe)

• 2000
• 1000

1000 2000

• 0,06
• 0,04
• 0,02

0,00 0,02 0,04 0,06 0,08 0,10 0,12 Re Im Amplitude Field (Oe)

1st - v 2nd - v 3rd - v

Exp and calculated Re[fm] and Im[fm] – vertical plane

SLIDE 60

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

Micromagnetic simulations D-MOKE MFM (quenched To 0 field)

Magnetic imaging proved

APPLIED PHYSICS LETTERS 99, 092501 (2011)

SLIDE 61

• P. VAVASSORI European School on Magnetism (ESM-2018), Krakow 17-28 September 2018

MOKE is a powerful technique for studying technologically relevant magnetic materials. MOKE magnetometry based on microscopy provides a noninvasive probe

• f magnetization reversal for individual ultra-small nano-structures.

Concluding remarks

Next lecture: Interplay between plasma excitations and MO-activity (magnetoplasmonics).

D-MOKE is a powerful technique to investigate the collective behavior of magnetic nano-arrays.