FERROMAGNETIC PROPERTIES OF HEXAGONAL IRON-OXIDE COMPOUNDS WITH AND WITHOUT A PREFERRED ORIENTATION

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• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 13
• Document Creation Date: November 9, 2016
• Document Release Date: February 22, 1999
• Sequence Number: 8
• Publication Date: August 1, 1952
• Content Type: REPORT

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LABORATORIA
N.V. PHILIPS' GLOEILAMPENFABRIEKEN
EINDHOVEN (HOLLAND)
FERROMAGNETIC PROPERTIES
OF HEXAGONAL IRON-OXIDE COMPOUNDS
WITH AND WITHOUT A PREFERRED ORIENTATION
G. W. RATHENAU, J. SMIT and A. L. STUYTS
GEPUBLICEERD IN: ZEITSCHRIFT FUR PHYSIK, 133, 250-260, SEPTEMBER 1952
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Zcitschrift fiir Physik, Tad. 133, S. 250-260 (1952).
Ferromagnetic properties
of hexagonal iron-oxide compounds
with and without a preferred orientation.
By
G. W. RATIMINAU, J. SMnT and A. L. STUYTS.
Mit 10 Figurcn im Text.
(Eingegangen am 22. Juni 1952.)
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I3esprechung der Magnetisicrung von hexagonalen Eisenoxydverbindungen als
Uunktion der Fcklstarkc.
Ilci der I3ildung von Bloch-Wanden miisscn t'nrcgclmaLigkcitcn im Iirislallbau
Iuitspiclcn (13). Dci regelloser Icristallvcricilung and ciner hristallgroLic obcrlialb
der kritischcn kann Dcmagnctisicrung durch wandvcrschicbung schon bci positivcn
I rldstarken von ungcfahr da I, aultreten (C).
I lurch Orienticrung der Kristalle dicscr Iiiscnoxydverbindungen I crruxdure wcr-
dcn (IM)_,-N%'crte von 3 ? iI'? Gil Oc crrcicht. Durch IcornvcrgroLicrung crgibt
iclr vine starkc 1'cncusscrung tier lextur. the gedvutct wirtl (D).
.I. I nlruduclron.
A class of magnetic hexagonal iron-oxide compounds given the name
of Ferroxdure has been dealt with in detail in an earlier publication'.
The prototype of these ceramic materials has the composition BaO.6 Fe_O.,.
We shall confine ourselves in this paper to material of about this
composition.
The most important magnetic properties of this nonconducting per-
manent magnet material of high coercive force are represented in
Digs. I 3.
As is seen from Fig. I, the saturation magnetization I, at room
temperature is about one fifth of that of metallic iron. The value of
the magnetization at low temperatures can be explained, as was shown
in 1, as being caused by non-compensated antiferromagnetism. Fig. 2
for time crystal anisotropy constant K shows that the forces binding
the spins to the direction of the hexagonal axis are very strong. K is
defined by the equation for the magnetic energy
h Iti sin'- l-J Il'stnr1U ?- . (I)
where (1 stands for the angle between the direction of the magnetization
and the hexagonal axis of a single crystal. As is not unreasonable to
1 \ ENT, J. J., G. W. RATm3NTu, G. W. GORTER and G. W. VAN OosTEIt,moeT:
Philips Tcclut. Rec. I3. 194 (1952.
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Ferromagnetic properties of hexagonal iron-oxide compounds. 251
for which the magnetization 15000
,,.,,,,.l- --I-, u - - 70000
dom the value 0.96K/IS sig- 7500 ---t - 75000
01 I I
700 -700 0 700 200 300
T
Fig. 2. Constant of crystal anisotropy K of BaFe,,O,, as a
function of temperature.
taneous rotation of the 70000
SninS- For nn --1.,1r. ?.F na .,~ 20000
the following significance.
If a single crystal is mag-
netized to saturation along
the easy direction of the
hexagonal axis an anti-
parallel field must attain
2K/IS to cause reversal of
the magnetization by simul-
times smaller at room tem- 200 -100 0 700 20D 300 YOo ?C 500
perature. In rig. 3 the Fig. I. Saturation Magnetization of BaFe1EO19 as a function
quantity 2K/IS and the erg/cms of temperature.
coercive force actually ob- 5
served for fine-grained sin x706
tered material are plotted 0
against temperature. The
field strength 2K/IS has 4 3
ymme ry, the difference
of magnetization energy in WO
different directions, given
by K, is much greater than Is
the equivalent quantity in 200
cubic crystals, which, e.g.,
for metallic iron is twenty a
expect for a crystal of low c00
t GauB
simultaneous rotation of
500
the reversal of magnetiza- 700T_2_00 300 009
Lion in an actual specimen Fig. 3. The quantity 2KJI,, for BaFe,,O,, and the coercive
force jHe of fine-grained sintered specimens as a function of
of the magnets under con- temperature (particle size of the order of one micron).
sideration cannot be solely
due to rotational processes against the forces of crystal anisotropy.
Firstly ,11, though very large, is for the greater part of the Curve
RozoRTx, R. M.: Ferromagnetism, p. 831. New York 195'1.
immediately reveals that io0 7oa o 0
of the two curves in IF ig. 3
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much smaller than 0.96 K,'Is and, secondly, the dependence on tem-
perature of both quantities is quite different r.
It thus proves necessary to explain the coercive force of the fine-
grained material and the hysteresis-loop, which will be treated more
fully in section C, by assuming the formation and movement of Bloch
walls in the small single crystals of which the material is composed.
This assumption is by no means trivial in this special case, as will
presently be shown.
B. Bloch-wall formation in small Particles.
Let us for the sake of simplicity treat asmalt single crystal ofdiameterd
containing a Bloch wall parallel to the hexagonal axis (Fig. 4b). The
Bloch wall reduces the volume
energy of demagnetization, but
its surface energy has to be fur-
stable only if the diameter ex-
ceeds a critical value2, which
turns out to be about
Fig. 4 a and b. A sphertral particle in which in al a l3krh
wall grows from the right-hand side, while in h) it
. paratrs two Weiss domains.
9a
d` 2n 712
(2)
ir being the wall energy per cm2.
For Fcrroxdurc d, is of the order of one micron at room temperature,
a grain size which can be technically obtained by grinding and milling.
It is the high crystal anisotropy K, which enters in the expression
for o, and the relatively low value of I, that cause the large critical
diameter d, For metallic iron d, would be 50 times smaller.
It is a question of considerable interest how, after saturation and
application of an external demagnetizing field, the wall enters the
sphere of Fig. 4. An energy barrier has to be surmounted. It has been
stated by KITTE1.3.4 that above a certain size, exceeding d, of equation (2),
Bloch wails will be created spontaneously, but for smaller dimensions
an external field has to be applied, the critical magnitude of which he
has calculated. We believe that this calculation needs some revision,
and that the correct critical field does not depend upon the particle
size, this being very large compared with the thickness of a Bloch wall.
I The strain energy will not be considered in what follows, since the constant
of magnetustriction on saturating along a direction of the basal plane proves to
be only about 20, to ?.
2 iiITTEL, C.: Rev. Mod. t'hvs. 21, 541 (1949).
3 KITTEL, C.: Phys. Rev. 73, 810 (1948).
9 130ZORTH, R. M.: Ferromagnetism, p. 831. New York 1951.
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Our calculation, which very closely resembles that of KITTLL, runs as
follows.
It is seen that the largest field H. is needed in the very initial stage
of the formation of the wall, so we have to consider only small angles
of deviation 0 of the spins. Therefore if the Bloch wall starts at the
surface of the sphere (Fig. 4a) the energy balance reads
K Oz?v+L,X.=(H,-P 4n Is) 1, ?I: 02 V.
(3)
Here v is the volume of the disturbed region, 1 4a I, the demagnetizing
field from the bulk acting in v, and E,,,. the exchange energy, which
can be made vanishingly small as compared with the anisotropy energy
by taking the disturbed region sufficiently broad in the beginning.
Ignoring it, one obtains for the critical field strength
H` = 2K/I,-0.33. 47cI,. (4)
Thus H, is independent of the particle size. It can be shown that the
gain in demagnetizing energy is larger if the wall starts in the middle
of the sphere. In that case the coefficient of 4 rc I, is --0.86. For a
thin plate magnetized along its normal these values are - 1.01 and
-2-02 respectively.
So we arrive at the conclusion that Bloch walls will be created in
pairs with opposite screw orientation (+ and - walls). If only the
situation with one wall is stable, the other one will disappear, turning
over the spins on its way.
For Ferroxdure the condition is satisfied that the wall thickness
(about 10_e cm) is small compared with the critical diameter (about.
10-4 cm).
We expect from this analysis that large crystals should also retain
a very high coercive force (2K/IS -2.02 ? 4n I, 7000 Oe at room tem-
perature). Since this is contrary to the experiments we must assume
that the Bloch walls are nucleated at places where the anisotropy energy
is lower due to imperfections most probably occurring at the crystal
boundaries.
C. The magnetization curve.
It has been shown in the preceeding section that in specimens of
BaO ? 6 Fe2O3. containing crystals of the order of magnitude of one
micron, single domain behaviour may be expected at room temperature
near the remanence point. At large negative field strengths walls are
probably introduced at places where the anisotropy is locally reduced.
When trying to understand the magnetization loop of fine-grained
material we have to explain at first the course of the curve representing
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1H, as it function of temperature (Fig. 3). It has been stressed in I that
the critical diameter d, of equation (2) increases with temperature as
1i4j15. This means that for a given grain diameter at elevated tem-
peratures below the region of the CURIr temperature fewer walls are to
he expected than at a lower temperature, at which a higher saturation
magnetization aids in forming them. Especially those walls which are
fixed at inclusions or regions of suitable strain, and therefore are least
mobile, will persist at higher temperatures. On the other hand the field
strength necessary to move a particular wall decreases with temperature
as lit. It is believed that these two effects, the influence of which on
the coercive force is opposed, cause the maximum in the curve 11,
versus temperature,
The material under consideration is ideal for separating the magneti-
zation processes of rotation and wall movement. While the stiffness
with respect to rotation given by 2K,11, is very large compared to 4nI5,
the wall formation and wall movement can be made rather easy by
firing the material at a high temperature and thus increasing the dia-
meter of the grains to some thousand times the critical diameter d,
Considering this case, the walls will he formed already in very small
demagnetizing fields, say zero. Due to the random orientations of the
crystals large internal demagnetizing finds are present, which cause
Bloch-wall formation already in positive external fields, leading to a
low remanence. Because an appropriate analysis is very difficult, we
shall try to approach the problem by using mean values throughout
and ignoring the pure rotation for the present (1I= : ). Without
wall formation the I -- Il curve coming from saturation should then be
the straight line 1 -- j I.
Let us consider a small ellipsoid of revolution in the matrix, which
will be assumed to have a homogeneous magnetization I in the z direc-
tion. The easy direction is along the axis of revolution (,,) and the
demagnetization coefficient in that direction is n. The angle between
and is 0. It is seen that the total internal field h; in the ellipsoid
will vanish for an external field parallel to I given by
H,(0)_ cos'-nI. (5)
For 11 ?H0(U) the ellipsoid is magnetized to saturation, but for lower
fields wall formation occurs and the magnetization decreases in such a
way that the internal field h.1 remains zero. The total magnetization
as a function of II can now be calculated by averaging over 0, and the
NVENT, J. J., G. W. RATHENAU, L. W. GORTER and G. W. VAN OOSTERHOUT:
Philips Techn. Rev. 13, 191 (1952).
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Ferromagnetic properties of hexagonal iron-oxide compounds.
peratures and therefore having
different grain sizes. In Fig. 7
the curves arc plotted for two 0 0,5 Ile 1,5 .o 25
such materials, measured at a low
nIs -
and at a high temperature, one (a) Fig. 5. Demagnetization curve calculated for an as
with small crystals and the sembly of crystals which are oriented at random. Field
strength for wall formation and displacement are
other (b) with large grains show- assumed to be zero. 2K1I, - oo .
ing that the fall-off field varies
with temperature approximately as 43r I. Curves for pure rotation
as calculated by STONER and Wol1LFAxlzT1, on inserting the values
of K and Is as measured for single crystals, are dashed.
curve of Fig. 5 is found. For H = a n 1, in all ellipsoids walls are created,
and for decreasing field the slope of the curve for the dense material
assumes the constant value 1. It is seen that the field at which an
appreciable decrease of the magnetization due to wall formation occurs
specimens fired at different tom- I, 025
in agreement with the experi- 050
ments. Fig. 6 shows curves of I
is about nls. For Ferroxdure
with its plate-like particles this
should be about 4sr I. This is
GauB
3000
` 2000
255
600,9 Oe, 8000
Fig. 6a and b. Hysteresis loops at room temperature of l3alPe,,O,, sintered at 1350 and 1400? C respectively..
In this connection it is also interesting to note that the remanence
of hexagonal metallic Cobalt 2 is only 27% of the saturation value.
It is.seen from Fig. 6 b that the slope of the I -H curve near H = 0
is greater than the theoretical value 4/8n. This may be due to some
2000 0 2000 4000 6000 Oe 8000 -2000 0 2000 4000
H_ fl--
a b
1 STONER, E. C., and E. P. WOHLFAHRT: Phil. Trans. Roy. Soc. Lend. 240,
599 (1948).
2 BozoiTn, R. 112.: Ferromagnetism, p. 266. New York 1951.
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clustering of similarly oriented crystals, or to walls which pass through
crystal boundaries, thus leading to smaller demagnetization.
-ZGW u 6t/W 'UM oarro vu awa
H
fe
Fig. 7a and b. Hysteresis loops for tiaFc,.U,. oriental at random, measured at - tyb- and 280- C resper-
tively. of a material with small crystals, obtained by sintering at a low temperature, b) a material with
larger crystals. Dashed: demagnetization curves calculated for pure rotation.
8 2080 0 two t090 &700 X l' i ~O4W -? 17 D 4 6000 80000810000
H-- H--
a b
Fig. 8a and b. Hysteresis loops at n,om temperature measured for psewio-unicrystalline material along the
direction of preferred magnetization, to be compared with Fig. 5. a) small crystals,
b} large crystals, higher density.
For the sake of comparison Figs. ba and b show the magnetization
curves of pseudo-unicrvstalline specimens of the same material (sec-
tion D), with small and large crystals respectively. As can be expected,
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Ferromagnetic properties of hexagonal iron-oxide compounds. 257
for positive fields these curves do not show a decrease of magnetiza-
tion through wall formation (due to the formation of internal poles)
as strong as represented in Figs. 6 and 7.
In connection with the above considerations dealing with a material
for which it was assumed that rotations were absent, while wall displace-
ments could easily occur, one may ask how the magnetization curve
will be if wall formations are strictly excluded while only rotations occur.
This case can be realized by working with particle sizes much smaller
than the critical one. Whereas in the first case considered the remanent
induction for crystals with one direction of preferred magnetization
proved to be much less than half of the saturation induction, it turns
out that in the latter case it is larger. This can be understood as follows.
The remanence value of 2,r IS has been deduced by assuming that
in each particle the magnetization points in the easy direction, giving
a minimum of the energy of crystal anisotropy. The inner demagne-
tization energy, however, which has been dealt with above, may then
be large. In reality the sum of both energies has to be minimized.
Therefore the actual value of the remanence will exceed 2n IS and
corresponds to the magnetization in a positive field, smaller than 4i-ZI,
in STONER and WOHLFAHRTS curve. Due to the large value of 2K/IS the
saturation magnetization was measured on a single crystal. Therefore
we were not able to verify experimentally the above statements with
certainty.
t 1
permanen -agnet rnateiia needed to produce a B=4atJ~H
given field in a given volume of air gap is about
inversely proportional to the value (BH)max in the _H eHL o
part of the B-11 diagram, where B is positive Fig. 9. schematic 4 a I and
B curves at negative field
and H negative'. From Fig. 9 it will be evident strengths.
that the only way to raise the (BH)max value of
a material with very high coercive force IH, is to increase the remanence
4'r I, for if the coercive force for the magnetization were infinitely
is equal to half the saturation value. i~
From a technical point of view the volume of
D. Preferred orientation in the polycrystalline ceramic material.
It has been stressed that, since it is due to non-compensated anti-
ferromagnetism, the magnetic saturation of the hexagonal iron-oxide
compounds is not very large. Except for correc-
tions which are treated in section C the remanent ~'tI
magnetization of an assembly of crystals with
uniaxial magnetic anisotropy, oriented at random,
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258 G. W. RATHENAU, J. SaiiT and A. L. STUYTS:
large the coercive force for the induction 1? would be H, = 4~r I, and the
(BH)n,ax value would amount to
4nIF)2
-2
It has therefore been our aim to arrive at a preferred orientation
of the hexagonal axes, which is the direction of easy magnetization of
the small single crystals within the sintered permanent magnet bodies.
We have succeeded in producing a preferred orientation of this kind
by orientating small single crystals of the hexagonal compounds in a
strong magnetic field and compacting them by pressing, preferably in
a magnetic field. In the subsequent firing operation the preferred
orientation is not dest-
Tabir I. roved butontlfecontrary
a,sl e, rr,~ greatly improved. This
can be shown by a corn-
bfore firing . 1500 870 1.72 parison of the remanent
after firing . . . 3100 , 420 7.4 magnetization of the
specimen in the direction
in which the orienting field had been applied and normal to it, before
and after firing. According to table 1 the ratio of the remanent
magnetizations greatly increases on firing.
This improvement of the preferred orientation by firing will be
discussed more fully below. Here it suffices to say that by orienting
the crystals the value of Fcrroxdure permanent magnets has
been increased from 09 to 3.0 times 100 GB Ore. The curves in Figs. 8a
and b give the magnetization for oriented Ferroxdure-samples which
have been fired at lower and higher temperatures respectively.
The orientation of such sintered ceramics becomes apparent when
the specimens are broken. Rupture occurs generally along the basal pla-
nes, which develop very perfectly. When the specimen is correctly
tilted with respect to a light source a pronounced reflection of light by
the basal planes can be observed. Specimens with a texture, in the form
of a cube with two faces parallel to the hexagonal basal plane of the
crystals, demonstrate --when overfircd--the existence of the texture
through the preferential growth of the crystals along the basal plane.
In Figs. 10a and b micrographs of such a specimen are seen with the
plane of the figure normal, respectively parallel, to the hexagonal axes.
The large dimensions of the crystals in the basal plane and the small
dimensions normal to it are evident.
In discussing the improvement of preferred orientation by firing,
two explanations are possible. Firstly it might be thought that the
crystals which are incorrectly oriented are generally those that have the
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Ferromagnctic properties of hexagonal iron-oxide compounds. 259
smallest dimensions and therefore disappear under the action of the
surface tension at the boundary of air and the crystals. However,
since the disappearance of the incorrectly oriented material occurs mainly
after the specimen has been sintered to about four-fifths of the X-ray
density, it seems that the following explanation is more appropriate.
It has been shown for metals that a crystal cannot absorb another
one which has about the same orientation or a twin. orientation'. The
Fig. tea and to Microphotographs of a Ferroxdure cube with oriented crystals, a) the hexagonal basal
planes being in the plane of the picture, b) the basal planes being normal to the plane of the picture. I ox .
improvement of a preferred orientation by grain. growth has also been
followed directly by electron-emission microscopy2. It turns out that
only those crystal boundaries move that have large interfacial energies
due to different orientation of neighbouring grains. If an incorrectly
oriented crystal is imbedded in. a matrix of equally oriented crystals it
"rows only if it is large compared with the crystals of the matrix. Other
wise it will be absorbed.
The condition for growth is approximately3: Did > 2yd1/yii, where
ydt is the interfacial energy of the boundary of the incorrectly oriented
r 'CIEDEMA, T. J., W. MAY and W. G. BURGERS: Acta Crystallogr. 2, 151 (1949).
LACOMBE, P., and A. BERCIIEZAN: C. R. Acad. Sci., Paris 228, 93 (1949).
2 RATHENAU, G.W., and G. BAAS: Physica, Ilaag 17, 117 (1951).
a SMITIr, C. S.: Trans. Amer. Soc. Met. ('reprint 37 (1951).
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2(i() G. W. ltArnrxAu, I. SMIT and A. L. STUYTS: Ferromagnetic properties.
large grain within the matrix of small grains, while y, is the mean inter-
facial energy between similarly oriented grains. D and d are the dia-
meters of the crystal under consideration and that of the adjacent
particles respectively.
For the plate-like Ferroxdure particles the above-calculated ine-
quality does not apply, but it is easily shown by energy considerations
that a similar relation holds also in this case. Consider, therefore, a
thin plate (thickness d, diameter D) where 0 is the angle of misfit with
respect to the surrounding, perfectly oriented, crystals of mean thick-
ness d. The misfitting particle will disappear if the total surface energy
is reduced by the absorption. This leads for D to the approximate
relation card 3yd?y? for growing, and if it is smaller then the particle
will disappear. Here yd, and y? have the same significance as above.
,d, will strongly increase with 0.
In conclusion, it may thus be expected from this analysis that in
the course of the sintering process misoriented crystals with about the
same dimensions will be absorbed by the matrix.
Lindharen (.Vc:derland), Philips' Research Laboratories, N. 1'. Philips'
C iloeilampenfabrieken.
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