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Soft magnetic materials,from statics to radiofrequencies
Victorino FrancoSevilla University. Spain
Current trends in Magnetic Refrigeration Magnetocaloric materials:
– Giant magnetocaloric materials– Second order phase transition materials– Nanostructured materials– Multiphase materials and composites
Modeling the magnetocaloric effect Experimental techniques for the
characterization of magnetocaloric materials Magnetic refrigeration devices Related topics on thermomagnetic energy
harvesting
Confirmed invited speakers J. I. Betancourt Reyes (UNAM); E.H. Bruck (Delft University of Technology); G.P. Carman (UCLA); A. Fujita (Tohoku University); Z.W. Liu (South China University of Technology); V.K. Pecharsky (Ames Laboratory); M.H. Phan (University of South Florida); A. Rowe (University of Victoria); J. L. Sánchez Llamazares (IPICYT); K. Skokov (Technische Universität Darmstadt); K. G. Suresh (IIT Bombay).
http://www.mrs.org/imrc-2013-cfp-7b/
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Introduction– 5 key questions in a nutshell: What, which,
where, when, why Optimization of soft magnetic properties
– Coercivity: disorder is not a bad quality all the time.
– Frequency response: losses– Do we always need the highest
permeability?: high frequency powerconversion
Example of sensor application: GMI
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Soft magnets in theglobal market
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
JMD Coey, J. Alloy. Compd. 326 (2001) 2
Where are they used?
Magnetic shielding (passive) Flux concentrators Sensors, anti-theft systems Power conversion
– Transformers, inductors– Motors, generators
Victorino Franco. European School of Magnetism. Cargèse (France) 2013Tesla car; induction motor
What we need
High saturation magnetization– composition
Low coercivity– microstructure
High Curie temperature High permeability (most of the times) Frequency response low losses
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Evolution of softmagnetic materials
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
JMD Coey, Magnetism and Magnetic Materials, Cambridge University Press, 2010
M.A. Willard, M. Daniil, K.E. Kniping, Scripta Mater. 67 (2012) 554
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
M.E. McHenry, M.A. Willard, D.E. Laughlin, Prog Mater Sci 44 (1999) 291
Warning: The importance of the demagnetizing field
M H
appl demag
demag
H H H
H NM
a applM H
( ) ( ) (1 )a appl a a aH H NM H N H H N
(1 )
a N
Material:Internal field“intrinsic” susceptibility
Measurement:Applied fieldApparent susceptibility
1 a NIf N or the susceptibility are large,Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Small applied fields for samples with highpermeability
M(T) for differentapplied fields
(1 )
a N
(1 ) 0appl appl applH H NM H N N H
1 a N
150 200 250 300 3500
1
2
3
10
15
20
25
30
M
(mem
u)
T (ºC)
field (Oe):1 10 100 1000 5000 10000
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
OPTIMIZATION OF COERCIVITY
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Domain wall pinning and defects
Potential energy E of thewall (per area unit):– Random function of
position• Local stresses• Defects
180º domain wall of area A moving a distance x– Magnetization change from
-M to M– Energy change
Equilibrium:0
0
( 2 ) 0
2
i
i
d E H Mxdx
dEH Mdx
02 iH Mx
R.C. O’Handley, “Modern magnetic materials: principlesand applications”. John Wiley and Sons, 1999
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Grain size and coercivity
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
G. Herzer, J. Magn. Magn. Mater. 112 (1992) 258
Reduce defects to decrease coercivity
Grain size and coercivity
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
G. Herzer, J. Magn. Magn. Mater. 112 (1992) 258
SIMPLE ANALOGIES TO EXPLAINTHE SMALL CRYSTAL SIZE RANGE
(AKA: understanding the random anisotropy model without formulae)
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Who will feel theirregularities?
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Floor of Colegiata de Santa María de Arbas, León (Spain)
The key is the different length scale (irregularities vs. shoes)
Refrigerator magnets
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Side view
Reverse side
Front (decorated side)
Field lines
Domains
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Refrigerator magnetsSide view
Reverse side
Front (decorated side)
Field lines
Domains
Characteristic lengths
Two characteristic lengths along the direction of movement:– Substrate (separation between stripes)– Mobile piece
Parallel orientations:– Lsubstr. ~ separation between stripes– Lmobile ~ Lsubstr. – Movement significantly alters the energy of the system
Perpendicular orientations:– Lmobile ~ size of the mobile piece– Lsubstr.<< Lmobile– We cannot detect, macroscopically, energy differences
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Two different correlationlengths
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Correlation lengths
structural magnetic
Let’s quantify
Select randomly theorientation of particles
Choose magneticcorrelated areas of different sizes
Displace the correlatedarea thoughout the“sample”
Measure the dispersionin energy
Average multiple times
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
0 2 4 6 8 100.0
0.2
0.4
0.6
0.8
1.0
Em
ax-E
min (a
.u.)
# of correlated particles (x1000)
1000 10000
0.03
0.04
0.05
0.06
0.070.080.09
1N
Random anisotropymodel
*
3
* 4 6 *3/
KKN
LNl
K K l A
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
K. Suzuki, in Handbook of Advanced Magnetic Materials, Springer, 2006, pp. 339-373
G. Herzer, J. Magn. Magn. Mater. 112 (1992) 258
Finemet alloy
Composition: Fe73.5Si13.5B9Cu1Nb3
Magnetically softer after nanocrystallization– Two phase nature
– Influence of the addition of Cu & Nb
• Segregation of Cu-rich clusters
• Rejection of Nb at the crystal interfaces
Importance– Technological applications (magnetic sensors, anti-theft systems,
etc.)
– Fundamental studies in magnetism
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
25 nm
Production of amorphousalloys I: melt spinning
Video courtesy of Joseph F. Huth IIIMAGNETICS, div. of SPANG & CO.
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Crystallization behavior
Fe76Si10.5B9.5Cu1Nb3
Devitrification takes place in two main stages– 1st exotherm: -Fe,Si– 2nd exotherm: Fe2B, ...
Compositional effects– Substitution of Fe by Cr
or Mo• Enhancement of the
stability of the amorphousphase
700 800 900 1000
dH/d
t ( k
W /
kg )
T ( K )
0.0
0.1
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Microstructure
25 nmAmorphous
Nanocrystalline
Fully crystallized
40 60 80 100
2 (º)
40 60 80 100
2 (º)
40 60 80 100
2 (º)
25 nm
350 nm
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Thermomagneticmeasurements
400 600 800 1000
0
20
40
60
80
100
120
140
ba cM (
a. u
. )
T ( K )
As cast sample (a):– Tc(Amorphous)– Onset of Crystallization– Tc(Fe,Si)
Nanocrystalline (b,c):– Tc(residual amorphous)– Tc(Fe,Si)
Fully crystallized (d):– Tc(Fe,Si) (change in % Si)– Tc(Fe2B)– Tc(boride type phase)
400 600 800 1000
0
20
40
60
80
100
120
140
aM (
a. u
. )
T ( K )400 600 800 1000
0
20
40
60
80
100
120
140
dba cM (
a. u
. )
T ( K )
V. Franco, C.F. Conde, and A. Conde, J. Magn. Magn. Mater. 185 (1998) 353
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Coercivity
400 600 800 10000
10
20
30
40
2000
4000
HC (
A / m
)
Ta ( K )Stress relaxation
Nanocrystallization onset
Averaging of anisotropy
2nd crystallization stage
V. Franco, C.F. Conde, A. Conde, L.F. Kiss, J. Magn. Magn. Mater. 215 (2000) 400
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
High temperature softmagnetic nanocrystallinealloys Can we keep the soft magnetic
properties at higher temperatures? Limitations:– Microstructural evolution– Magnetic softness
Individual nanoparticles– Superparamagnetism
• No hysteresis• Overlapping of magnetization curves• Limited by anisotropy energy (TB)
Nanocrystalline alloys?
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Superparamagnetism in nanocrystalline alloys
Low temperature: blocked state (ferromagneticmatrix)
High temperature: superparamagnetic relaxation– Not controlled by blocking temperature, but by the
ferromagnetism of the matrixVictorino Franco. European School of Magnetism. Cargèse (France) 2013
400 600 800 1000
0
20
40
60
80
100
nanocrystalline
as cast
M (
a. u
. )
T ( K )
Superparamagnetic relaxation
Requisites:– No hysteresis– Overlapping of
magnetization curves Limited by:
– Anisotropy energy (TB)
– Decoupling of the grains– 2nd crystallization stage
0.0 0.5 1.0 1.5 2.00.0
0.5
1.0
615K 630K 648K 670K 687K
M(T
)/Ms (T
)
Ms(T) · H / T
V. Franco, C.F. Conde, A. Conde, L.F. Kiss, J. Magn. Magn. Mater. 215 (2000) 400
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Cr-containing Finemet alloy
Thermal stability is enhanced
Cryst. volume fraction is reduced
Smaller mean grain size800 850 900 950 1000
0.1
T (K)
Fe63.5Cr10Si13.5B9Cu1Nb3
V. Franco et al., J. Appl. Phys. 90 (2001) 1558
Thermomagnetic properties
300 400 500 600 700 800 900 10000.0
0.2
0.4
0.6
0.8
1.0
cbaM (a
.u.)
T (K)
Significant reduction of Tc
am
Nanocrystallization onset is less detectable
Tc (rem. am.)?
V. Franco, C.F. Conde, A. Conde, J. Magn. Magn. Mater. 203 (1999) 60
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Thermomagnetic properties (low T)
Tc(rem. am.) is reduced with increasing Ta– Grains should be
easily decoupled
100 150 200 250 300
0.0
0.2
0.4
0.6
0.8
1.0
Ta=798K
Ta=823K Ta=848K
'' (
a.u.
)
T (K)
0.0
0.2
0.4
0.6
0.8
1.0
' (a
.u.)
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Hysteresis loops
700 800 900 1000 110005
10
2000
4000
6000
8000
10000
Dynamical treatments Isochronal treatments
Hc (
A/m
)
Ta(K)Stress relaxation
Nanocrystallization onset
2nd crystallization stage
Averaging of anisotropy?
V. Franco et al., IEEE Trans. Mag. 38 (2002) 3069
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Hysteresis loops
Coercivity has a maximum around room temperature
It is displaced to lower temperatures as crystalline volume fraction increases – Tc(res. Am.)
100 200 300 400 500 600 700
0
10
20
30
40
50 Xc
7 %16 %20 %
Hc (O
e)
T (K)
V. Franco et al., Phys. Rev. B 66 (2002) 224418
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Superparamagnetic relaxation
0 160 320 480 640
0.0
0.2
0.4
0.6
0.8
1.0
630 K 650 K 670 K 690 K 710 K
M(T
)/Ms(T
)
H/T (A m-1 K -1)
Ta px Dx (nm) <> (103 B) D (nm) 775 K undetectable undetectable 18 7 5.2 0.7800 K 0.066 9 2 41 6 6.8 0.5825 K 0.197 12 2 112 6 9.6 0.5850 K 0.385 13 2 113 6 9.6 0.5 V. Franco et al., J. Appl. Phys. 90 (2001) 1558
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Dipolar interactions between SPM nanoparticles
-1000 -500 0 500 1000-1.0
-0.5
0.0
0.5
1.0
H (Oe)
M/M
s
-1000 -500 0 500 1000-1.0
-0.5
0.0
0.5
1.0
H (Oe)
M/M
s
Sample with px=20 %, measured at 400 K
V. Franco et al., Phys. Rev. B 66 (2002) 224418; Phys. Rev. B 72 (2005) 174424Victorino Franco. European School of Magnetism. Cargèse (France) 2013
*0kT H*( )
HM N Lk T T
*1
1app T
T
Production of amorphousalloys II: mechanicalalloying
Powders can be compacted toobtain the final shape
For the samenominal composition, properties are different fromthose of melt spunalloys
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
0.00 0.05 0.10 0.15
0.00
0.05
0.10
0.15 Collision point
Detachment point
Y (m
)
X (m)
Initial ball position
-0.02 0.00 0.02-0.02
0.00
0.02
Detachment pointat the collision time
Collision point
Detachment point
Initial ball positionY (m
)
X (m)
Ipus et al, Intermetallics 16 (2008) 470
Influence of the startingphasesFe75Nb10B15 composition prepared using:
– crystalline boron (c-B alloy) – amorphous boron (a-B alloy)
(Fe75Nb10)100 composition (n-B alloy)
10 15 20 25 30 35 402 [degrees]
Exerimental Fitted Boron R-3m (34%) (N3)(NB9H11) (18%) Amorphous halo (48%)
inte
nsity
[a.u
.]
Commercialamorphousboron
Crystallineboron
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
J.J. Ipus, J.S. Blázquez, V. Franco, A. Conde, J. Appl. Phys. 113 (2013) accepted
Global microstructure IXRD patterns
0 1 2 3 40
3
6
9
12
15
bcc-
Nb
phas
e fra
ctio
n [%
]
t [h]
n-B alloy c-B alloy a-B alloy
Bcc Nb phase dissapears after 4 h miling Amorphous phase developed only in B
containing alloysVictorino Franco. European School of Magnetism. Cargèse (France) 2013
XRD results
1 100
1
2
e [%
]
milling time [h]
0
20
40
60 n-B alloy c-B alloy a-B alloy
D [n
m]
0,286
0,288
0,290
0,292
a [n
m]
0 10 20 30 400,0
0,2
0,4
0,6
0,8
1,0
crys
talli
ne fr
actio
n
milling time [h]
c-B alloy a-B alloy
Faster amorphization in a-B alloy Microstructural parameters of crystalline
phase almost stabilized after 4 h millingVictorino Franco. European School of Magnetism. Cargèse (France) 2013
TEM sample preparation
Powder particle selected
(Focused Ion Beam)
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Ipus et al, Phil. Mag. 89 (2009) 1415
TEM sample preparation
Deposition of a protective Pt layer
Pt layer
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Ipus et al, Phil. Mag. 89 (2009) 1415
TEM sample preparation
After cutting with Ga ion beam
sample
bridge
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Ipus et al, Phil. Mag. 89 (2009) 1415
TEM sample preparation
Sample attached to a Cu grid
Cu grid
Pt deposition
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Ipus et al, Phil. Mag. 89 (2009) 1415
TEM sample preparation
Final thinning using Ga ion beam
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Ipus et al, Phil. Mag. 89 (2009) 1415
TEM sample preparation
Bright field TEM image of the sampleVictorino Franco. European School of Magnetism. Cargèse (France) 2013
Ipus et al, Phil. Mag. 89 (2009) 1415
Local microstructure
Amorphous matrix with boron inclusions and dispersed -Fe type nanocrystals
400 nm
10 nm-1
(0 0 2)
(1 1 1)
SAD amorphousmatrix
CBEDcrystallineinclusion
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Microanalysis
200 300 400 500
Matrix
E [eV]
Boron particle
coun
ts [a
.u.]
Spectrum Line
Inclusions highly enriched in boronPresence of boron in the matrix
Compositionalprofiles: line spectra
Spot spectra
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Hysteresis loops
-10000 0 10000-200
-100
0
100
200
M [e
mu/
g]
H [Oe]
0,5 h 4 h 6 h 20 h 40 h
n-B alloy
-10000 0 10000-200
-100
0
100
200
M [e
mu/
g]
H [Oe]
c-B alloy
-10000 0 10000-200
-100
0
100
200
M [e
mu/
g]
H [Oe]
a-B alloy
-100 -50 0 50 100
-10
0
10
M [e
mu/
g]
H [Oe]
a-B alloy
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Saturationmagnetization
0,0 0,2 0,4 0,6 0,80
40
80
120
160 c-B alloy (350 rpm) c-B alloy (150 rpm) a-B alloy
MS [e
mu/
g]
XC
0 10 20 30 400
40
80
120
160
n-B alloy c-B alloy a-B alloy
milling time [h]
MS [e
mu/
g]
0 10 20 300
40
80
120
160
n-B alloy c-B alloy a-B alloy
MS [e
mu/
g]
<HF> [T]
MS decreases as amorphous phase developsLinear correlation between MS and <HF>Two slopes in MS vs Xc should indicate different rates of B incorporation into the matrix
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Coercivity
Coercivity initially increases and further on decreases
10 20 30 400
30
60
90
120 n-B alloy
HC [O
e]
milling time [h]
a-B alloy c-B alloy
S Ceff
c
M HKp
Herzer, IEEE Trans Mag 26, 1397 (1990)
0.64cp
for cubic shape particles
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Magneticanisotropy
10 20 30 400
30
60
90
120 n-B alloy
HC [O
e]
milling time [h]
a-B alloy c-B alloy
0,0 0,4 0,8 1,2 1,60
4
8
12
p c Kef
f [10
3 (J/m
3 )]
microstrains [%]
c-B alloy a-B alloy n-B alloy
Initial increase due to the increase of microstrains
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Magneticanisotropy
10 20 30 400
30
60
90
120 n-B alloy
HC [O
e]
milling time [h]
a-B alloy c-B alloy
0,0 0,5 1,0 1,50
10
20
30
Kef
f2 [107 (J
/m3 ]
XC2 D3 Keff
3/2 [10-18(J/m)3/2]
2 2 2 3 3 22
1 3 2
3 32 2
C effeff S ma S mi
X D KK K
A
Shen, Phys. Rev. B 72, 014431 (2005); Ipus Phys. Express 2, 8 (2012)
Reduction after 6h due to crystal refinement
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
LOSSES
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Hysteresis losses
Quasistatichysteresis loop
Energy dissipated in a toroidal core overone cycle
Combining Ampere and Lenz laws
The energy lost per unit volume is givenby the area of theloop
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
0( ) ( )
t T
tW i t V t dt
0
t T
t
dBW lA H dt lA HdBdt
Increasing frequency
Loops get broader and rounder
Effect of eddy currents induced in the material
Change in Minduced voltage which opposes the flux change
Losses emerge due to the heating of the sample due to these currents
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
D.C. Jiles, J. Appl. Phys. 76 (1994) 5849
Classical eddy currents
The material isuniformly magnetized
Change in Minduced voltage which opposes the flux change
Losses emerge due to the heating of the sample caused by these currents i2R
Powe loss per unitvolume at lowfrequency
Reduce losses by:– Reduzing d– Increasing resistance
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
R.C. O’Handley, “Modern MagneticMaterials”, Willey, 2000
2 2 2
/ mclass
B dP vol
The flux change isrestricted to theenvironment of the wall
Losses depend on thevelocity of the wall– Drag field
For multiple walls, currents interfereand reduce thelosses
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Influence of inducedanisotropies
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
F. Fiorillo, C. Beatrice, J Supercond Nov Magn 24 (2011) 559
More sofisticated models
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
F. Fiorillo, C. Beatrice, J Supercond Nov Magn 24 (2011) 559
Perspectives of core lossreduction in GOSS
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
T. Kubota, M. Fujikura, Y. Ushigami J. Magn. Magn. Mater. 215-216 (2000) 69
HIGH FREQUENCY POWERCONVERSION
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Designing an inductive component
For the same voltage amplitude, the section is inversely proportional to the frequency
Go to higher frequencies in power converters to decrease the volume and weight
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
2
cos( ) cos( )o odB dI N AV NA L LI t I tdt dt l
High frequency power converters use active switching circuits and PWM– Superposition of many frequencies– Materials should have broadband capabilities
Heat dissipation in the inductors– Scaling down the surface while keeping the
dissipated heat brings thermal managementproblems
We have to add winding losses and corelosses
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Lower permeability allows larger efficiency under some circumstances
For the same induction, we need larger H (more current or more turns) for lower permeability materials
Depending if the added stored energy is larger than the additional heating, it could be beneficial
A.M. Leary, P.R. Ohodnicki, M.E. McHenry, JOM 64 (2012) 772
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
SENSORS: GIANT MAGNETO IMPEDANCE
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
-3 -2 -1 0 1 2 3
-1.0
-0.5
0.0
0.5
1.0
M/M
S
H/HK
The (very) basics of GMI
Skin penetration depth
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Giant magnetoimpedance
-8000 -4000 0 4000 8000
0.6
0.8
1.0
H (A/m)
|Z| (
)
Amorphous (as-cast)
Amorphous
(structurally-relaxed)
Nanocrystalline (annealed at the onset)
Nanocrystalline (annealed at the end)
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
GMI vs Fluxgate fieldsensors
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
Y. Honkura, J Magn Magn Mater 249 (2002) 375
Relationshipanisotropy/GMI
500 600 700 800 900
0
75
150
0.0
0.2
0.4
0.6
X
/X
Ta(K)
16 at. % Si 9 at. % Si
R
/R
500 600 700 800 90050
100
150
200
250 16 at. % Si 9 at. % Si
<HK>
(A/m
)Ta (K)
Victorino Franco. European School of Magnetism. Cargèse (France) 2013
V. Franco, A. Conde, Materials Letters 49 (2001) 256
Conclusions
Soft magnetic materials are used in numerous energy-related applications
Coercivity can be optimized by properly designing the microstructure of the materials– Random anisotropy model
High temperature soft magnetic amorphous alloys are a challenge
Amorphous and nanocrystalline alloys can be a good testing ground to develop models of multiphase magnetic systems
Victorino Franco. European School of Magnetism. Cargèse (France) 2013