School of Physics & Astronomy FACULTY OF MATHS & PHYSICAL SCIENCES

Christopher Marrows

c.h.marrows@leeds.ac.uk

@ChrisMarrows

Dzyaloshinkii-Moriya interactions and chiral

magnetism (in B20 epilayers and)

at ferromagnet/heavy metal interfaces

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Acknowledgements

• N. A. Porter, C. S. Spencer, P. Sinha, J. Carter-

Gartside, A. Hrabec, A. Wells, G. Burnell, T. A. Moore,

M. B. Ward, R. M. D. Brydson – University of Leeds, UK

• M. D. Robertson – Acadia University, Canada

• A. Dobrynin – Diamond Light Source, UK

• S. McVitie, M.-J. Benitez & D. McGrouther – University

of Glasgow, UK

• C. J. Kinane, T. R. Charlton, and S. Langridge – STFC

Rutherford Appleton Laboratory, UK

Funding gratefully received from:

Spin-Orbit Coupling

Interesting phenomena in magnetism

Magnetic Properties

• Magnetocrystalline anisotropy

• Dzyaloshinkii-Moriya interaction

Magneto-Optical Properties

• Magnetooptic Kerr effect

• X-ray magnetic circular dichroism

Magnetotransport Properties

• Anisotropic magnetoresistance

• Anomalous Hall effect

• Spin Hall effect

• Tunnelling anisotropic magnetoresistance

…. Image: wikipedia.org

Dzyaloshinskii-Moriya Interaction requires structural inversion asymmetry + SOC

Fert et al. Nature Nano. 8, 152 (2013)

Al-Sharif, J. of Phys: Cond. Matter, 13, 2807 (2001)

surface interface bulk

Yu Nat. Vol 465| 17 June (2010) Meckler PRL 103, 157201

(2009)

W(110)/Fe(2 ML) Fe0.5Co0.5Si

Cu(100)/Fe/Ni

Chen PRL 110, 177204

(2013)

crystal lacks

inversion symmetry

e.g. B20 unit cell

asymmetric layers (with

different SOC) around FM

break inversion symmetry

monolayers of metal on

heavy element

substrate

Bulk DMI: B20 systems

B20 bulk crystal phases

Mühlbauer et al., Science 323, 915 (2009)

Wilson, Thesis (2013)

Skyrmion crystal

MnSi

SANS

Chiral Magnetic Skyrmions

Topologically stable vector field object

“Combed hedgehog”

Emergent electrodynamics arising from Berry phase

Each skyrmion = φ0 of fictitious magnetic flux

Moving skyrmions => effective electric field

Skyrmion Crystal

Tony Skyrme FRS

Sir Michael

Berry FRS

Fe0.5Co0.5Si - Yu Nature (2010)

B20 alloys

N. Manyala et al, Nature Materials 3(4), 255 (2004)

Wilhelm et al., PRL 107, 127203 (2011)

Kanazawa et al., PRL 106, 156603 (2011)

FeSi -

paramagnetic

narrow gap

semiconductor

MnSi -

helimagnetic metal

FeGe -

‘high’ temp.

helimagnetic

metal

Fe1-xCoxSi

- helimagnetic

doped

semiconductor

MnGe -

short period

helimagnetic

metal

transition metal

monosilicides

transition metal

monogermanides

CoSi –

diamagnetic metal

Sputtered FeGe

XRD and magnetometry

28 30 32 34 36 38 4010

0

101

102

103

104

Si

111

inte

nsit

y (

co

un

ts)

2( )

FeGe

111

FeGe co-sputtered at ~470 °C

in Ar:H2(4%) at 3 mTorr

textured films in (111) orientation

High ordering temperature: 276 K

0.0 0.5 1.0 1.5 2.00

100

200

300

-1.2 -0.8 -0.4 0.0 0.4 0.8 1.2

-300

-150

0

150

300

0 50 100 150 200 250 3000

100

200

300

270 280 2900

3

6

9

150 K

M (

kA

/m)

0H (T)

310 K

5 K

240 K

M (

kA

/m)

0H (T)

IP

OOP

Ms (

kA

/m)

T(K)

0

3

6

9

a

c

Porter et al. Phys Rev B (2014)

B20 helimagnets under field

a) E. Karhu, Structural and Magnetic Properties of Epitaxial MnSi(111) Thin Films, PhD thesis (2012)

b) Wilson et al. Discrete helicoidal states in chiral magnetic thin films, Phys. Rev. B 88, 214420 (2013)

Helimagnet in an applied field

• For a magnetic field applied parallel to

Q a conical phase forms

• In a bulk crystal if H is not parallel to Q,

Q will align to the field

• In a thin film there is a uniaxial

anisotropy that fixes the direction of the

helix

• An in-plane applied field distorts the

helix shape into a helicoid

H

∥ 𝑄

b)

a)

Polarised neutron reflectometry

• Interference fringes produced from reflections

and reflections within film

• Shift due to different polarisations of neutrons

experiencing a different scattering potential

• Structure parameters determined above Tc and

kept constant (e.g. scattering length density, film

thickness, etc.)

• A helicoid profile is used to generate the

magnetic scattering length density and a fit is

performed

a) http://www.isis.stfc.ac.uk/instruments/polref/publications/polref_science_case6635.pdf

c) Wilson et al. Discrete helicoidal states in chiral magnetic thin films, Phys. Rev. B 88, 214420 (2013)

Wilson thesis (2013)

Helicoid structure:

• M is the magnetic moment

• y – depth of film

• λ is the helix wavelength

• φ0 is a fitting parameter

Specular reflection

𝜃 − 2𝜃

𝑞𝑧 =4𝜋 sin 𝜃

𝜆

Kiessig fringes b)

c)

a)

Film

Depth

H applied in plane

with sample

Different polarisations

FeGe Results

T = 50 K

670 mT

1 mT

1 mT

1.

2.

3.

1.

2.

3.

t = 69 ± 1 nm

x = 0

In-plane magnetic field

a)

Bulk λ ~ 70 nm, from fit λ = 70 ± 5 nm

FeGe and FeGe/Fe Results

FeGe FeGe/Fe

T = 50 K T = 50 K

arXiv:1506.01575

Transition Metal Substitution:

Previous Doping Studies

MnGe FeGe CoGe

K. Shibata. et al. Nature nano 8 723–728 (2013)

What happens

when you add

Co?

Previous study in Mn1-xFexGe

B20 helimagnetic material

Change in skyrmion chirality

Divergence in helical

wavelength found x ~0.8 ?

? • Ordering temperature – Blue

• Ratio of ordering temperature to helix

wavelength - Red

adding electrons

Fe1-xCoxGe Characteristics

• Samples grown by molecular beam

epitaxy

• Si(111) wafer for lattice matching

• Growth along the (111) zone axis

• Lattice matched with a 30° in-plane

rotation

Si (7 x 7) FeGe (111)

x = 0

Low-energy electron

diffraction patterns

100 eV

Msat Lattice constant Ordering temperature

α ~ 0.1-0.03% < Bulk

x = 0 to 1

~10% larger than

bulk

a) b) c)

Fe1-xCoxGe PNR Results

x = 0.36

x = 0.54

T = 50 K

T = 50 K

x λ (nm)

0 70 ± 5

0.36 115 ± 15

0.54 >170

• Helix wavelength λ increases

with Co content

• Both samples less than one

period

• Only a lower bound of 170 nm

could be set for x = 0.54

t = 65 ± 1 nm

t = 69 ± 1 nm

1 mT

Fe1-xCoxGe Results

MnGe FeGe CoGe

a), b) K. Shibata. et al. Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin–orbit

coupling, Nature Nano 8 723–728 (2013)

x λ

(nm)

Tc λ-1

(K nm-1)

0 70 ± 5 -3.9

0.36 115 ± 15 -2.0

0.54 > 170 > -0.8

Possible divergence again

in helical wavelength

Keeping negative ratio in-

line with previous study

𝜆 ∝ 𝐽/𝐷 𝑇𝑐 ∝ 𝐽

c)

d)

FeGe - magnetoresistance

Metallic ρ(T) behaviour, with no sign

of cusp at magnetic ordering

temperature.

In out-of-plane field see negative

magnetoresistance (MR) up to Hc.

Porter et al. Phys. Rev. B (2014)

Low-field MR is

indicative of

saturation of the

conical phase.

GMR-like

mechanism:

generalised

Levy-Zhang

model for DW

resistance.

FeGe – Hall effect

• OHE linear up to about 200 K

• Can be fitted by 2-band model

• AHE peaks at about 200 K

• Quadratic scaling with ρxx

=> Intrinsic or side-jump?

FeGe – anomalous Hall effect

Onoda, Sugimoto, and Nagaosa, Phys. Rev. B (2008)

FeGe

(this work)

Topological Hall effect

C. Pfleiderer and A. Rosch, Nature 465, 880 (2010)

T. Schultz et al., Nature Physics, 8, 301 (2012)

• as an electron moves adiabatically

through spatial varying spin topography its

spin orientation maps the magnetisation:

• electrons gain Berry phase as they

traverse skyrmion.

• Berry phase

• Considering Berry phase as an AB phase in

an emergent magnetic field, we expect a Hall

effect

• one quantum Φ0 of emergent flux per

skyrmion.

1 1

2 2

1 1

2 2

topological

Total Hall effect

ordinary

Hall bars patterned

by photolithography,

hard mask, ion

milling.

our devices

V

Total Hall effect

ordinary extraordinary/anomalous

• deflection of carriers due

to magnetic material:

• EHE often a larger than

the OHE

• arising from spin orbit

coupling

Total Hall effect

ordinary topological extraordinary/anomalous

FeGe – topological Hall effect

Huang et al. PRL, 108, 267201 (2012)

our 80 nm film: THE over

full temperature range Huang et al. - Johns Hopkins

0.0 0.5 1.0 1.5 2.00

50

100

150

200

xy

x

y,

(n

.cm

)

0H (T)

5 K

-40

-20

0

tx

y (n

.cm

)

Porter et al. Phys. Rev. B (2014)

Giant THE in Fe0.7Co0.3Si

Combined two techniques:

1. 4 wire Hall measurements

2. SQUID-VSM magnetometry

by scaling the magnetisation to fit

the Hall data one can extract the

THE as the difference.

Largest THE to date: 820 ncm.

Useful for electrical detection of

skyrmions?

T = 5 K

J = 4 108 A/m2 (results insensitive to J down to 2 104 A/m2)

Prior THE measurements

Discovered in MnSi – few nΩcm ~200 nΩcm in MnGe: 2 nm skyrmions

Recent comprehensive study by Ritz et al. in MnSi – up to 50 nΩcm

Neubauer et al., Phys. Rev. Lett. 102, 186602 (2009).

Lee et al., Phys. Rev. Lett. 102, 186601 (2009). Kanazawa et al., Phys. Rev. Lett. 106, 156603 (2011).

THE isotherms =>

Skyrmion phase diagram

THE shows two contributions:

• Broad, weakly hysteretic background (few 100 mT)

• Sharp, hysteretic extremum (~50 mT)

Giant THE

Huang et al. PRL, 108, 267201 (2012)

Y. Li et al., arXiv:1209.4480v1 (2012)

Dyadkin et al., Phys. Rev. B 84, 014435 (2011)

Karhu et al., Phys. Rev. B 84, 060404 (2011)

Manyala et al., Nature 404, 581 (2000)

skyrmion

separation

emergent gauge

(one flux quanta)

ordinary Hall

coefficient

relative skyrmion

density

(~1 if dense)

spin polarization

of the current

𝜚𝑥𝑦𝑇 = 𝑛𝑃𝑅0𝐵eff

𝐵eff~4

3

𝜙0𝑎2

why is the effect so large?

20 40 60 80 1000

50

100

T (K)

0H

(mT

)

-0.8 -0.4 0.0 0.4 0.8

T

xy (.cm)

0.0 0.1 0.2

-0.8

-0.4

0.0

0H (mT)

T x

y (

.cm

)

5 K

x = 0.3

film, x = 0.3

Giant THE

skyrmion

separation

emergent gauge

(one flux quanta)

ordinary Hall

coefficient

relative skyrmion

density

(~1 if dense)

spin polarization

of the current

high spin polarization 0.77

𝜚𝑥𝑦𝑇 = 𝑛𝑃𝑅0𝐵eff

𝐵eff~4

3

𝜙0𝑎2

Huang et al. PRL, 108, 267201 (2012)

Y. Li et al., arXiv:1209.4480v1 (2012)

Dyadkin et al., Phys. Rev. B 84, 014435 (2011)

Karhu et al., Phys. Rev. B 84, 060404 (2011)

Manyala et al., Nature 404, 581 (2000)

20 40 60 80 1000

50

100

T (K)

0H

(mT

)

-0.8 -0.4 0.0 0.4 0.8

T

xy (.cm)

0.0 0.1 0.2

-0.8

-0.4

0.0

0H (mT)

T x

y (

.cm

)

5 K

x = 0.3

film, x = 0.3

Giant THE

skyrmion

separation

emergent gauge

(one flux quanta)

ordinary Hall

coefficient

relative skyrmion

density

(~1 if dense)

spin polarization

of the current

high spin polarization 0.77

doped

semiconductor

x = 0.30,

n ~ 1 1022 cm-3

𝜚𝑥𝑦𝑇 = 𝑛𝑃𝑅0𝐵eff

𝐵eff~4

3

𝜙0𝑎2

low carrier concentration

(high Hall coefficient)

Huang et al. PRL, 108, 267201 (2012)

Y. Li et al., arXiv:1209.4480v1 (2012)

Dyadkin et al., Phys. Rev. B 84, 014435 (2011)

Karhu et al., Phys. Rev. B 84, 060404 (2011)

Manyala et al., Nature 404, 581 (2000)

20 40 60 80 1000

50

100

T (K)

0H

(mT

)

-0.8 -0.4 0.0 0.4 0.8

T

xy (.cm)

0.0 0.1 0.2

-0.8

-0.4

0.0

0H (mT)

T x

y (

.cm

)

5 K

x = 0.3

film, x = 0.3

Giant THE

skyrmion

separation

emergent gauge

(one flux quanta)

ordinary Hall

coefficient

relative skyrmion

density

(~1 if dense)

spin polarization

of the current

high spin polarization 0.77

2 / √3 = 11±1 nm

strain reduces

separation relative

to bulk (48 nm*)

doped

semiconductor

x = 0.30,

n ~ 1 1022 cm-3

𝜚𝑥𝑦𝑇 = 𝑛𝑃𝑅0𝐵eff

𝐵eff~4

3

𝜙0𝑎2

Huang et al. PRL, 108, 267201 (2012)

Y. Li et al., arXiv:1209.4480v1 (2012)

Dyadkin et al., Phys. Rev. B 84, 014435 (2011)

Karhu et al., Phys. Rev. B 84, 060404 (2011)

Manyala et al., Nature 404, 581 (2000)

low carrier concentration

(high Hall coefficient)

20 40 60 80 1000

50

100

T (K)

0H

(mT

)

-0.8 -0.4 0.0 0.4 0.8

T

xy (.cm)

0.0 0.1 0.2

-0.8

-0.4

0.0

0H (mT)

T x

y (

.cm

)

5 K

x = 0.3

film, x = 0.3

Giant THE

skyrmion

separation

emergent gauge

(one flux quanta)

ordinary Hall

coefficient

relative skyrmion density

(~1 if dense)

calculate: n ~ 0.2

spin polarization

of the current

high spin polarization 0.77

doped

semiconductor

x = 0.30,

n ~ 1 1022 cm-3

𝜚𝑥𝑦𝑇 = 𝑛𝑃𝑅0𝐵eff

𝐵eff~4

3

𝜙0𝑎2

Huang et al. PRL, 108, 267201 (2012)

Y. Li et al., arXiv:1209.4480v1 (2012)

Dyadkin et al., Phys. Rev. B 84, 014435 (2011)

Karhu et al., Phys. Rev. B 84, 060404 (2011)

Manyala et al., Nature 404, 581 (2000)

low carrier concentration

(high Hall coefficient)

2 / √3 = 11±1 nm

strain reduces

separation relative

to bulk (48 nm*)

20 40 60 80 1000

50

100

T (K)

0H

(mT

)

-0.8 -0.4 0.0 0.4 0.8

T

xy (.cm)

0.0 0.1 0.2

-0.8

-0.4

0.0

0H (mT)

T x

y (

.cm

)

5 K

x = 0.3

film, x = 0.3

Topological contribution to ρxx ?

Hysteretic dips in ρxx coincide with THE peaks

(after linear and WL background subtraction)

Only present below ~20 K

Peaks in ρxx predicted by Monte Carlo

simulations – Yi et al. Phys. Rev. B 80, 054416 (2009).

T = 5 K

Interface DMI: multilayers D

4 DW configurations in PMA films

• 2 possible magnetization re-orientation

- perpendicular to the magnetization plane (Bloch)

- in the magnetization plane (Néel)

• 2 possible chiralities for each

• Bloch wall state has

lower magnetostatic energy

N S N

S + +

- -

+ + + +

- - - -

Ku

Imaging of chiral DWs

Spin polarized

STM

SPLEEM NV center

Lorentz-TEM

Yu et al., Nature (2010)

Tetienne et al., Science (2014) Chen et al., Nature Comm.

(2013) Kubetzka et al., PRB (2003)

TEM – Fresnel mode

L

z

x

z

y

• Investigated Ta(3.2)\Pt(3)\Co(0.8)\AlOx(5.3) films

z)dz(x,Bh

eλ=(x)β yL

• Defocus microscope by Δz to reveal

contrast

• Fresnel mode at 100kV

• JEOL TEM

Calculated Contrast

Néel wall Bloch wall

• For a Bloch wall contrast

variation is always observed

• No contrast observed for

Néel wall at normal incidence

• Tilting the sample reveals

contrast

Experimental contrast

B = 0 T; θ = 30° B = 0 T; θ = 0°

• DWs are observable at θ=30

• No contrast variation is

observed at θ=0°

• Symmetric linetraces

Néel walls

DW interaction: LTEM

• L-TEM

• Domain growth until DW

meet each other and form a

360° structure

• Néel type DW confirmed in

both directions

Benitez, Hrabec et al: ArXiv (2015)

Annihilation process

• In case of Néel wall magnetostatic charges are

created on either side of DW

• Rigidity of the Néel wall is locked by the DMI

• To annihilate the two walls this toplogical barrier must be overcome

• Annihilation is a measure of the DMI

DW annihilation:

polar Kerr microscopy

DMI in Pt\Co\AlOx

• Measurement of annihilation field

• Problem reproduced by micromagnetic

simulations

• D = 0.35 ± 0.05 mJ/m2

Hiramatsu et al., JJAP (2014)

• Value is artificially low (no thermal activation in model, assume perfect material)

MuMax3

Materials

W\Mn

W\Fe

• Epitaxially grown materials, studied in-situ Pt(111)\Ni Ir(111)\Ni

D D

• Pt(111)\Ni Ir(111)\Ni shows opposite DMI

• Do Pt\Co\Ir layers have larger DMI? Can we enhance the effective DMI?

Chen et al, Nature Comm.

(2013)

Bode et al, Nature (2007)

D

Kubetzka et al, PRB (2003)

Chen et al, Nature Comm.

(2013)

Pt(111)\Ni

Film characterization

Ta(3nm)

Pt(5nm) Co(0.8nm) Pt(3.5nm)

Ir (0Å) Ir (2.3Å) Ir (4.6Å) Ir (13Å)

• Films grown by DC sputtering

• Kerr microscopy used to measure hysteresis loops

• Out-of-plane anisotropy measured by SQUID/VSM no significant change with inserted Ir layer

Ta(3nm)

Pt(5nm)

Co(0.8nm)

Pt(3.5nm)Ir (0Å) Ir (2.3Å) Ir (4.6Å) Ir (13Å)

DD D

Experimental setup

• DW displacement measured by Kerr microscopy

δ≈2.3°

• Differential mode employed

• Displacement radially symmetric in case of

out-of-plane field

• Strong asymmetry with presence of in-plane field

B

DW velocities

100um

Ir (0Å) Ir (2.3Å) Ir (4.6Å)

• Huge asymmetry in Pt\Co\Pt

• 2.3Å of Ir lifts the asymmetry

• 4.6Å of Ir reverses the asymmetry

• Different contribution from Co\Pt and Co\Ir!

Creep regime

• Thermally activated creep regime in

general

• Where the scaling ς parameter is field-dependent

• DW energy density

Transition from Bloch wall to Néel wall

Néel wall

Simulations

Thiaville et al: EPL 100, (2012) S-B Choe et al, PRB (2013)

Modelling:

creep law including DMI fields

Right-handed chirality

Left-handed chirality

• Model well reproduces experimental data

• DMI changes sign around Pt\Co\Ir(2.5Å)

• Bloch–Néel wall transition

• D-M constant obtained by using

Transition Bloch-

right-handed Néel

Hrabec et al., Phys. Rev. B 90, 020402 (2014)

DMI in Pt\Co\Pt

Why do we observe DMI in symmetric stack?

Ta(3nm)

Pt(5) Co(0.8) Pt(3.5)

Pt (3) Co (0.7)

Pt (1)

• Epitaxial sample grown by sputtering @ >150°C

on Al2O3

Mihai et al, APL (2013)

Ta\Pt\Co\Pt stack must not be symmetric!

Crystallographic order is extremely important!

5nm

Towards exotic textures

• DW energy

Non-homogeneous ground state

Isolated skyrmions

Ta/CoFeB/TaOx

Jiang et al. arXiv:1502.08028

Pt/Co/Ta

Woo et al. arXiv:1502.07376

{Pt/Co/Ir}×N

Moreau-Luchaire et al. arXiv:1502.07853

20 40 60 80 1000

50

100

T (K)

0H

(mT

)

-0.8 -0.4 0.0 0.4 0.8

T

xy (.cm)

• examined scattering mechanisms and observed

conical phase MR and THE in textured FeGe

Porter et al., Phys. Rev. B 90, 024403 (2014)

•evidence for chiral magnetic structure in PNR and

a giant THE in Fe1-x

CoxSi.

Porter et al., arXiv:1312.1722 [cond-mat.mes-hall]

• topological protection of homochiral walls in Pt/Co/AlOx

Benitez et al., arXiv:1503.07668 [cond-mat.mtrl-sci]

•interface engineering of DMI in Pt/Co/Ir/Pt

Hrabec et al., Phys. Rev. B 90, 020402 (2014)

Conclusions