Sin título de diapositiva

Magnetic interactions and
Preisach distributions of
nanostructured barium hexaferrite
P. G. Bercoff, M. I. Oliva and H. R.
Bertorello
Facultad de Matemática, Astronomía y Física
Universidad Nacional de Córdoba
Argentina

INTEREST
To study the interaction mechanisms in Ba hexaferrite
TOOL
PREISACH MODEL
Preisach Distribution Function:
f(h c , h u )
h c : coercivity of each particle
h u : internal field seen by each particle
IDENTIFICATION: Hc
hc

FIRST ORDER REVERSAL
CURVE (FORC)
2
M( α,
β)
∂
f( α ,
β
) = −
(1)
∂ ∂
α
β
α=
h + h
u
c
β = h h
u
−
c

SAMPLES
Three samples with different microstructure
Sample Preparation Composition / Microstructure
M1
MF1
MF8
HEBM of stechiometric
Fe 2 O 3 and BaCO 3 . 1 hour
at 1000ºC in air in powder
form, then compacted.
HEBM of Fe 2 O 3 BaCO 3
and 20% α-Fe .
Compacted and 1 hour at
1000ºC in air.
HEBM of Fe 2 O 3 BaCO 3
and 20% α-Fe . 8 hours at
1000ºC in air in powder
form, then compacted.
Highly crystalline phase M
(BaFe 12 O 19 ).
D ≅ 50 nm
Phase M plus ∼20% hematite.
Partial, short-range sintering.
D ≅ 50 nm
Phase M plus ∼20% hematite.
Larger degree of sintering.
ρ ≅ 0.7 ρ theo
D ≅ 60 nm

RESULTS
We measured the FORCs of the three samples and calculated
the corresponding Preisach distribution functions using Eq. (1)
BM1

BMF1

BMF8

CHECK OF RESULTS
χ
i −calc
i
=
χ
i
tot
− χ
i
rev
=
∂M
i
− χ
∂H
i
rev
=
∞
∫
0
f(h ,h − H
c
c
i
i
)dh − χ
c
rev
BM1

BMF1

BMF8

DISCUSSION
The Gaussian-shaped
shaped Preisach distribution of M1 could be attributed to the
fact that this sample is composed only of phase M and there is no reason to
believe that the fabrication process would produce other kind of particles
distribution on the plane ( (h , h ).
c u
The multiple peaks observed in the Preisach distributions of MF1 and MF8
suggest that they represent different groups of conglomerates that invert their
magnetization at the fields h of the maxima. . It is highly probable that the
sintering process has produced c a distribution of conglomerate sizes, each
conglomerate with a well defined h value. The larger the number of particles per
c
conglomerate, the lower the corresponding h . c

We identify the coercive fields of the samples H exp with the maxima h c c of
the Preisach distributions. Then, from the modified Brown equation we can
define an effective anisotropy constant, given by:
K
eff
1
= K
1
α
K
α
ex
=
H
exp
c
M
S
2
+ N
α φ
eff
M
2
S
As the exchange length in this systems ( (l =8 nm) is lesser than D, we deduce
that there is a partial coupling between the ex particles of phase M inside each
conglomerate and there are regions of lower coercivity produced by the exchange
coupling. If we accept that there is a distribution of conglomerates with
different number of particles that invert their magnetization at different
coercive fields, we can infer that the exchange interaction in these t
systems
depends on the number of particles per conglomerate.