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School of Physics & Astronomy FACULTY OF MATHS & PHYSICAL SCIENCES
Christopher Marrows
@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:
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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
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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
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Bulk DMI: B20 systems
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B20 bulk crystal phases
Mühlbauer et al., Science 323, 915 (2009)
Wilson, Thesis (2013)
Skyrmion crystal
MnSi
SANS
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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)
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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
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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)
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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)
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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
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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
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FeGe and FeGe/Fe Results
FeGe FeGe/Fe
T = 50 K T = 50 K
arXiv:1506.01575
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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
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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)
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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
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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)
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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.
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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?
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FeGe – anomalous Hall effect
Onoda, Sugimoto, and Nagaosa, Phys. Rev. B (2008)
FeGe
(this work)
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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
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Total Hall effect
ordinary
Hall bars patterned
by photolithography,
hard mask, ion
milling.
our devices
V
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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
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Total Hall effect
ordinary topological extraordinary/anomalous
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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)
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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)
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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).
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THE isotherms =>
Skyrmion phase diagram
THE shows two contributions:
• Broad, weakly hysteretic background (few 100 mT)
• Sharp, hysteretic extremum (~50 mT)
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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
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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
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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
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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
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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
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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
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Interface DMI: multilayers D
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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
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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)
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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
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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
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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
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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)
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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
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DW annihilation:
polar Kerr microscopy
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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
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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
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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
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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
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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!
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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)
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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)
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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
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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
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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