Basic concepts on magnetization reversal (2)Slow dynamics and thermal related processes
Stanislas ROHARTLaboratoire de Physique des SolidesUniversité Paris Sud and CNRSOrsay, France
Introduction: Application considerations
All applications need to work at room temperatureThermal activation may become problematic for long time scales
Energy barrier criteria :
TkKVE B)6025(
Thermal activation is crutial for nanoparticles (<25 nm)It is also relevant for thin films (domain nucleation and domain wall propagation)
Thermal activation is crutial for nanoparticles (<25 nm)It is also relevant for thin films (domain nucleation and domain wall propagation)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Contents
I. SuperparamagnetismII. NucleationIII. Domain wall propagation in disordered
magnetic filmsIV. Conclusion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
3
Contents
I. SuperparamagnetismII. NucleationIII. Domain wall propagation in disordered
magnetic filmsIV. Conclusion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Energy barrier for macrospin
Stoner and Wohlfarth hamiltonian
)cos(sin 02
HSeff HMKE Easy axisM
H
Volumic quantities
-0.5
0.0
0.5
1.0
1.5
E/K
E = KV
2
2
22
1
1
221
)0()(
K
m
HHKVE
h
hhh
eee Energy barrier (field aligned with easy axis)
2/3
1
SWHHKVE
General case
Victoria PRL 63, 457 (1989)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Thermodynamics of a macrospin
cossin 02 HVKEV eff
Macrospin moment
Partition function :
HZ
ZkT
ddkTEVZ
0
sinexp
Average moment
projected on easy axis:
Isotropic case : K = 0
kTHx
xx
dkTHZ
0
0
0
1tanh
1
sincosexp2
(Langevin function)
Infinite anisotropy: =0 or
kTHxx
kTH
kTHZ
0
00
tanh
expexp
(Brillouin ½ function)
-4 -2 0 2 4
-1.0
-0.5
0.0
0.5
1.0
<>/
x=µ0µH/kT
Langevin Brillouin
Initial susceptibility
Scaling with 1/T (like Curie law)
kTor
kT
20
20
3
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Thermodynamics of a macrospin
Case with finite anistropy
t
K dxxtErfiKVkTtHHh
thErfi
thErfi
th
th
th
0
2
2
)exp()(;/;/
11
1exp2sinh2
Brillouin like
Langevin like
Usefull : at low temperatureUsefull : at low temperature
KVkT
kT1
20
Chantrell et al. JMMM 53, 1999 (1985)Fruchart et al. JMMM 239,224 (2002)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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10-3 10-2 10-1 100 101 102
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.10.025 0.25 2.5 25 250 2500
T/TB [if ln(t/0)=25]
kT/µ 0µ2
kT/KV
Superparamagnetism: Thermodynamics of a macrospin
0 30 60 90 120 150 1800.00
0.01
0.02
Pro
babi
lity
dens
ity
kT/KV = 0.1 0.2 0.3 0.5 1.0 5.0 isotropic (sin)
Occupancy probability for a Stoner‐Wohlfarth model (H = 0)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Temperature induced switchingPhenomenological: Arrhenius law
Switching time )/exp(0 kTE
0E calculated with the macrospin approch
attempt time (~1 ns) : linked with magnetization dynamics
Néel’s model : (Phonon and magnetostriction approach)
GkTVDMG
mHe
Se
K
23 2
01
0
Young’s modulus magnetostrition Fluctuation of the demag. field
Néel Ann. Geophys.5, 99 (1949)
Brown’s model : (Langevin fluctuation of a macrospin)
kTVHMH KS
K
212 0
021
0
well
Brown Phys. Rev. 130, 1677 (1963)See also Coffey et al. PRL 80, 5655 (1998)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Temperature induced switching)/exp(0 kTE
Stability criterion : tmeasuremen
If ns1.00 1s 1min 1h 1day 1year 10 year
E/kT 23 27 31 34 40 43
Hard drive applications
This problem drives an intense effort of reseach for high anisotropy materials. Best candidates are Pt‐bases ordered alloys like FePt and CoPt (K~10 MJ/m3 in bulk phase <‐> Dlimit ~ 3 nm)See e.g. Sun et al. Science 287, 1989 (2000)
This problem drives an intense effort of reseach for high anisotropy materials. Best candidates are Pt‐bases ordered alloys like FePt and CoPt (K~10 MJ/m3 in bulk phase <‐> Dlimit ~ 3 nm)See e.g. Sun et al. Science 287, 1989 (2000)
Blocking temperature
0ln
tkKVT
BB
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Warning: it is difficult to predict TB from volumic anisotropy measurements as in nanoparticles K is generally dominated by surface effects/low coordinated atomsSee Jamet et al. PRL 86, 4676 (2001)
Gambardella etal. Science 300, 1130 (2003)
Warning: it is difficult to predict TB from volumic anisotropy measurements as in nanoparticles K is generally dominated by surface effects/low coordinated atomsSee Jamet et al. PRL 86, 4676 (2001)
Gambardella etal. Science 300, 1130 (2003)
Superparamagnetism: Characteristic time in experiments
Stability criterion : tmeasuremen
Blocking temperature
0ln
tkKVT
BB
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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• Loop measurment in SQUID ‐> ~ 10min ‐ 1h• ZFC‐FC in squid ‐> ~ 1s• magneto optical kerr effect (resistive coils) ‐> ~1s• SP‐STM / microSQUID : 100 ms• ac susceptibility : 1ms ‐ 10s• Moessbauer : 0.1 µs
In sweeping (field or temperature) experiments, charateristic time is ambiguous‐> rather speak of sweeping rate
see e.g. Kurkijarvi PRB 6 832 (1972) (field sweep)Rohart et al PRB 74, 104408 (2006) (temperature sweep)
Superparamagnetism: Rate equation model
-0.5
0.0
0.5
1.0
1.5
E/K
EEH 0
Brown’s model is difficult to use.Simpler model: rate equations
1111
ndt
dnnn
dtdn
nndt
dn
nn
111
)/exp(
with
tn
First order decay law with relaxation time ‐ If tmeas
kT
Hn
0tanh12
For constant field and temperature (switching rates are constant)
This equation can be used for any field orientation (if switching rates are known…)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Hysteresis loopSimulation of mean hysteresis loops with rate equations
Vsweep = 0.375HK/s
Vsweep = 0.375HK/s
Vsweep = 0.375HK/s
Vsweep = 3.75HK/s
Coercive field is not intrinsic‐> depend on temperature AND sweeping rate
BK
measKC
TTH
tKVkTHH
1
ln10
Scharrok JAP 76, 6413 (1994)IEEE Trans Mag 26, 193 (1999)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: experimental evidence
Anisotropy precisely determined from astroid at 35 mKVolume determined by SEM imagingFirst perfect agreement with Néel‐Brown model
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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First observation (2D) : Co (D = 25 nm) clusterWernsdorder et al. PRL 78, 1791 (1997)
In 3 D: (same Co cluster) E. Bonnet er al PRL 83, 4188 (1999)
3 nm Co cluster : M. Jamet PRL 86, 4676 (2001)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: experimental evidence
Jamet et al. PRL 86, 4676 (2001)
Vouille et al. JMMM 272‐276, e1237 (2004)(with exp. Data from Jamet et al.)
Simulation of macrospin dynamics (Brown’s model)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: Experimental observation in practical
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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‐> Single particle measurments are difficult‐> Hysteresis loops are generally long to measure‐> Single particle measurments are difficult‐> Hysteresis loops are generally long to measure
Temperature variation of initial susceptibility Field coolded‐Zero field coolded measurements
)/exp(111
1)(
0 kTEiTieq
: Pulsation of the magnetic field
dtKdTkTtwithTt
TTM
/)(/exp11)(
2
Model for zfc, measuring from low to high T
Co nanodots on Au(111) with increasing sizeRohart et al. PRL 104, 137202 (2010)
Pt clusters in different matricesRohart et al. PRB 74, 104408 (2006)See also Tamion et al; APL 95, 062503 (2009)
Superparamagnetism: beyond macrospin?Superparamagnetism and nucleation‐propagation magnetization reversalSuperparamagnetism and nucleation‐propagation magnetization reversal
0
0 )/exp()(
kTAHBraun PRL 1993(same approach as Brown 1963)
If L>> : it is possible to nucleate and propagate a reversed domain
‐Strongly depends on H (<‐> size of the critial nucleus to reverse magnetization)‐Proportionnal to L (nucleation occurs in the particle – edges are neglected)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: beyond macrospin?
Superparamagnetism and nucleation‐propagation magnetization reversalExperimental check :Superparamagnetism and nucleation‐propagation magnetization reversalExperimental check :
Single particle measurement by spin polarized STM
Monte Carlo simulation0 decrease with lenght, increase with the widthedge nucleation
Krause et al. PRL 103, 127202 (2009)
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Superparamagnetism: beyond macrospin?Superparamagnetism and spin wavesSuperparamagnetism and spin waves
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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0 200 400 600 8000
20
40
60
80
100
1 2 3 4 5 6 7 8D (nm)
Nat
0 (GHz)
E a (meV
)
Nat
0
0 200 400 600 8000
200
400
600
0 200 400 600 800
1
10
0 200 400 600 800
1
10
(b1)
(b2)
(a1)
PSDmax
PSD
(a.u
.)
Frequency (GHz)
(a)
(b)
min
PSD
(a.u
.)
Frequency (GHz)
5.180E-11
6.090E-11
Atomic scale micromagnetic calculation on Co flat nanodotsAtomic scale micromagnetic calculation on Co flat nanodots
•Homogeneous magnetization ground state•Coherent rotation at T = 0 But coherent reversal over estimates switching rates at T≠0
At finite T, high excitation modes are excitedRohart et al. PRL 104, 137202 (2010)
Explains experiments from Rohart et al. 2010 and Rusponi et al. Nature Mat. 2003
Contents
I. SuperparamagnetismII. NucleationIII. Domain wall propagation in disordered
magnetic filmsIV. Conclusion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Nucleation processes: Droplet model
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Energy :
HMtrtrrE S02 22)(
rDomain wall energy cost
Zeeman energy gain
H
r
E
rc
S
Scc
HMtE
HMrr
drdE
0
20
2
20)(
E
Important process for thin filmsEnergy barrier scales with 1/H
)/exp()( 0 kTERHR Nucleation rate
Barbara JMMM 129, 79 (1994)Vogel et al. CR Physique 7, 977 (2006)
‐> 2D problem : apply to thin films with weak disorder
Nucleation processes: Magnetization reversal in constant magnetic field
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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‐> Nucleation rate vs. Domain expansion :
)exp(1)( 00 RtNNRNNdtdN
20)( tvrtS cN
Domain nucleation
Surface of the domain nucleated at t=0
Pertienent parameter : defines if the magnetization reversal is propagation or nucleation limitedcRr
vK 0
Variation of the non reversed area for different K
Labrune et al. JMMM 80, 211 (1989)Fatuzzo Phys. Rev. 127, 1999 (1962)
RNN0
0v
Nucleation site densityNucleated domainesNucleation rate
Domain wall velocity
Nucleation processes: Magnetization reversal in constant magnetic field
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Labrune et al. JMMM 80, 211 (1989)
Nucleation processes: Coercive field and droplet model
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Raquet et al. PRB 54, 4128 (1996)
Moritz et al. PRB 71, 100402(R) (2005)Pt/Co/Pt films and nanostructures
Au/Co/Au films and nanostructures
Nucleation processes: Droplet model in reduced dimensions
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Nucleation is generally easier at the edge
Critical droplet size :
c
extextc
Sc
RwithRL
HM
2
0
11
2(same as thin films)
Magnetic configuration at the maximum energy
(Same as Braun 1993)µ0H (mT)
Energy barrie
r (eV
)
coherent
droplet
Numerical application: Parameters for Pt/Co(0.5 nm)/Pt film
JP. Adam PhD thesis, Orsay 2008 (unpublished)See also 3D theory : Hinzke and Nowak PRB 58 265 (1998)
Confined droplet model (circular dot)
Nucleation processes: Coalescence between nucleated domains
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Pt/Co(0.5 nm)/PtTime between frame : 400 sNucleation field : 5 OePropagation field : 3Oe (to reduce DW velocity)
The experiment validates the picture of nucleation/propagation
Coalescence between domains is difficultNucleation of 360° domain walls
Dipolar repulsion between domains
Saturation may be difficult to reachPoison for magnetization reversal
Bauer et al. PRL 94, 207211 (2005)See also : Schrefl, et al. J. Appl. Phys. 87, 5517 (2000) (in plane magnetization)
Hehn et al. APL 92, 072501 (2008) (in MRAM nanoelements)
50 µm
Contents
I. SuperparamagnetismII. NucleationIII. Domain wall propagation in disordered
magnetic filmsIV. Conclusion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Domain wall motion in disordered films
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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50 µm
Pt/Co(0.5 nm)/Pt with perpandicular magnetizationH = 42 OeTime between frame : 100s
Domain wall is not extended as a straight line (minimisation of length) but also feels some weak defects.
Competition between elasticity and pinning
Driving force :
Elasticity :
Pinning : pinfAKtt
H
4
(roughness, thickness variation…)
VIDEO
CreepElasticity/Pinning
competition
Depinning thermal activation
Viscous regimeDefects and disorder are
not pertinent‐> DW velocity given by magnetization dynamics
theory
f = H for magnetic DW
Domain wall motion in disordered filmsFrom Creep to viscous motion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Chauve et al PRB 62 6241 (2000)
Universal law‐> Apply to ferroelectric DW‐> Superconducting vortices‐> Charge density waves‐> Fluid propagation in porous media
Universal law‐> Apply to ferroelectric DW‐> Superconducting vortices‐> Charge density waves‐> Fluid propagation in porous media
Domain wall motion in disordered filmsPropagation and roughness
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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H << Hcrit: very small velocity DW adapts to defects Significant roughness
d
v = d/t
H >> Hcrit: large velocity Limited role of disorder Small roughness
v (m
/s)
H (Oe)
Hcrit
0 500 10001E‐101E‐91E‐81E‐71E‐61E‐51E‐41E‐31E‐21E‐11E+01E+1
H (Oe)0 500 10000
5
10
V(m/s)
S. Lemerle et al, PRL.80, 849 (1998)Velocity with universal behavior on 10 orders of magnitude.Velocity with universal behavior on 10 orders of magnitude.
Domain wall motion in disordered filmsElastic energy
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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L
Fext
x
(x,t)
For a DW length L:
~ (x,t)mean of transverse fluctuations
LL
elastic dxdxd
E2
0
2
2
Elastic energy: increase in DW length
L = 2L1‐L = 2 / L
L
L1
Roughness and fluctuation Elastic energy cost Roughness and fluctuation Elastic energy cost
Low curvature:
L1= L/2 (1 +42 / L2)1/2
Domain wall motion in disordered filmsPinning
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Lfpin
x
(x,t)
: Correlation length of disorder
ni = pinning center density fpin : pinning force of one center
Random force of individual forces
Only density fluctuations can collectively pin the domain wall
= « collective force » coming from disorder
Pinning energy : LLnfE ipinpinning2
ipinnf 2
Domain wall motion in disordered filmsCompetition between pinning and elasticity
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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x
L
Small scales:Disorder caracteristic length
~ grain size~Transverse fluctuations
31
22
c
cL
Larkin length LC ~ 0.025 µm(for Pt/Co/Pt ultrathin films)
c
ccc L
L2
2
Two critical lengths: LC andC)()( celasticcpinningC LELEE
1E-3 0.01 0.1 1
10-13
10-12
10-11
Eelastic
Epinning
Eelastic
+Epinning
En
ergi
e (e
rg/
cm3 )
L (µm)
Domain wall motion in disordered filmsScaling law – Renormalization group theory
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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For L > Lc > nC
= 2/3 : universal exponent (for a 1D interface in motion in a 2D medium with weak disorder)
)(CLL
c
Pinning energy 12)( CLL
Cpinning EE
1
CCSSZeeman L
LHVMHLtME
Zeeman energy
22
cLelastic L
LE c Elastic energy
tLVvolumeCritical ccc :
Scaling law for fluctuations
)()( CelasticCpinningC LELEE
H
Hcrit
Domain wall motion in disordered filmsActivation energy and regime of motion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
36L. Roters, S. Lübeck and K.D. Usabel, Phys. Rev. E, 63, 026113 (2001)
In the vicinity of the depinning field
)( critHHV
CSCcrit VMEH /
)()( CZeemanCpinning LELE
pinningZeemanactivation EEE
41
-21-2
critC H
H E
E
12)( CLL
CcS EHVME
With = 2/3
Thermally activated regime in creep regime
Activation energy as a function of external field
4/1
0 )(expH
HTk
Evv crit
B
C
Flow regime µHv
Domain wall motion in disordered filmsex: Pt/Co/Pt ultrathin films
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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0 500 10001E‐12
1E‐9
1E‐6
1E‐3
1
v (m
/s)
H (Oe)
0 500 10000
5
10non irrad.
irrad.v (m
/s)
1.5 2.0 2.5 3.0
10‐6
10‐1
non irradiatedirradiated
(H/Hcrit)1/4
10‐12
v (m
/s)
Ec non irr= 46 kT Ec irr= 26 kT
For H<Hcrit/5
4/1
0 )(expH
HTk
Evv crit
B
C
Hcrit non irr= 700 Oe Hcrit irr= 230 Oe
)( critHHv for H >Hcrit
Depining regime Depining regime
Unpublished resultsSee also S. Lemerle et al, PRL.80, 849 (1998)
Creep regime Creep regime
tCo = 0.8 nm
0 500 1000 1500 20000
20
40
60
80
v (m
/s)
H (Oe)
Domain wall motion in disordered filmsex: Pt/Co/Pt ultrathin films
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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0 500 1000 1500 20000
20
40
60
80
v (m
/s)
H (Oe)
tCo = 0.5 nm
0 500 1000 1500 20000
20
40
60
80
v (m
/s)
H (Oe)
tCo = 0.6 nm
0 500 1000 1500 20000
20
40
60
80
v (m
/s)
H (Oe)
tCo = 0.7 nm
P. J. Metaxas, Phys. Rev. Lett. 99 217208 (2007)
Hv
Mobilité/ champ critique/ champ de Walker
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Mouvement visqueux observé = régime précessionnel
Paramètre d’amortissement de Gilbert ~0.25 compatible avec résultats FMR et valeurs utilisées pour des simulations numériques
Hv p 21
P. J. Metaxas, Phys. Rev. Lett. 99 217208 (2007)
changement de dynamique interne masqué par le piégeage
Hµv P
t(Co) (nm)0.5 100 470 0.240.6 210 590 0.300.7 230 705 0.320.8 220 650 0.31
H W (Oe) H dep (Oe)
Interprétation cohérente des observations expérimentales à fort champ
Evaluer Hw , confinement pris en compte
Domain wall motion in disordered filmsDivergence of energy barrier
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Evidence of energy barrier for H /Hcrit <<1
3/4
1H
EL Ljump
Ljump is defined at the energy barrier
3)(5
31
CCCSL
LC L
LLHtMEE
C
41
critC )
H
H( EE
Jump length
Barkhausen jumps with 1/H4/3 jump lengthMotion through avalanche processes
V. Repain et al., EuroPhysicsLett 68 (2004) 10213
H= 2 Oe ( 0.01 Hcrit) Dt = 200 secondes H = 4 Oe (0.02 Hcrit) Dt =1 seconde
Domain wall motion in disordered filmsRoughness analysis
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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3/422 )()]()([)(CLL
LLxxLC
0 1 2 3 4 50.0
0.2
0.4
0.6
0.8
1.0
C2 (L
)
L/LC
)(Cc LL
LL = 2/3
Correlation on a given length L
101 102
100
101
102
103 2=4/3
<[
(x+
L)-(
x)]2 >
L (pixel)
H/Hc=
0.9 0.8 0.6 0.4 0.3 0.13 0.1 0.06
Critial exponent is independent of H (for H<0.9HC)Sligh increase of LC for H/HC>0.2
A. Mougin et al. unpublished results
Domain wall motion in disordered filmsCreep in confined geometry
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Domain wall propagation in nanowires (Pt/CoFe0.3nm/Pt)Domain wall propagation in nanowires (Pt/CoFe0.3nm/Pt)Cross over between creep motion (2D like) and hoping (1D like)
Universal scaling :
c
col
Ccol
LLw
HLwLw 4/3/
Wire width
Segment length for jump
Larkin length
w
Kim et al. Nature 458, 740 (2009)
Domain wall motion in disordered filmsMagnetization reversal with strong pining
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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Epitaxial FePt(40nm)/Pt film : presence of micromacle than pins the domain walls.
Domain wall propagation is channeled between micromacles : fast fractal‐like domain growth.Saturation needs to overcome strong pinning barriers :Slow high field saturationThermal activation (slow dynamics)
Attane et al. PRL 93, 257203 (2004)
Some readings
•Skomski and Coey Permanent magnetism (Taylor & Francis Group 1999)•Aharoni Introduction to the theory of ferromagnetism (Oxford 1996)•Skomski Nanomagnetics J. Phys. Cond. Mat. 15, R841 (2003)•Fiorani Surface effects in Magnetic Nanoparticles (Springer 2005)•P. Metaxas, PhD thesis (Creep), Orsay, 2009 : http://trove.nla.gov.au/work/39007513
Some readings
•Skomski and Coey Permanent magnetism (Taylor & Francis Group 1999)•Aharoni Introduction to the theory of ferromagnetism (Oxford 1996)•Skomski Nanomagnetics J. Phys. Cond. Mat. 15, R841 (2003)•Fiorani Surface effects in Magnetic Nanoparticles (Springer 2005)•P. Metaxas, PhD thesis (Creep), Orsay, 2009 : http://trove.nla.gov.au/work/39007513
To go further
•Toward quantum fluctuations : already observed in molecular magnets‐> quantum fluctuation and tunneling of a domain wall is still a challenge…
Wernsdorfer and Sessoli Science 284, 133 (1999)Gunther and Barbara Quantum Tunneling of Magnetization‐QTM’94 (Kluwer, Netherlands,
1995)•Magnetization reversal under spin polarized current‐> Creep law with a different driving force (spin transfert torque)
Yamanouchi et al. Nature 428, 539 (2004)
To go further
•Toward quantum fluctuations : already observed in molecular magnets‐> quantum fluctuation and tunneling of a domain wall is still a challenge…
Wernsdorfer and Sessoli Science 284, 133 (1999)Gunther and Barbara Quantum Tunneling of Magnetization‐QTM’94 (Kluwer, Netherlands,
1995)•Magnetization reversal under spin polarized current‐> Creep law with a different driving force (spin transfert torque)
Yamanouchi et al. Nature 428, 539 (2004)
Take home message
•When dealing with long time scales, thermal activation plays an essential role.•Many properties (like coercive field) depend on the time scale (field sweeping time, waiting time)…
Take home message
•When dealing with long time scales, thermal activation plays an essential role.•Many properties (like coercive field) depend on the time scale (field sweeping time, waiting time)…
Conclusion
S. ROHART : Basic Concepts on Magnetization Reversal : Slow Dynamics European School on Magnetism ‐ Targosite 2011
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