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PERMEABILITY MECHANISMS IN MANGANESE
ZINC FERRITES
J. Knowles
To cite this version:
PERMEABILITY MECHANISMS IN MANGANESE ZINC FERRITES
J. E. KNOWLES
Mullard Research Laboratories Redhill, Surrey RH1 5HA, England
Résumé. — Uanisotropie de désaimantation est utilisée pour estimer les contributions relatives des
parois et des rotations à la perméabilité. Dans un ferrite à perméabilité élevée /iT et iï" sont tous
deux maxima à la température de compensation comme l'est le coefficient d'hystérésis v. Dans un ferrite à petits grains et faibles pertes fiT est alors maximal mais /iw et v sont minima. Ceci est expliqué
par le fait que l'épaisseur de la paroi devient comparable à la dimension du grain ; c'est probable-ment le mécanisme profond responsable des faibles pertes résiduelles. L'effet des spins accrochés aux joints de grain est discuté.
Abstract. — The anisotropy of demagnetization is used to estimate the relative contributions of
walls and rotations to the permeability. In a high permeability ferrite both nr and py were at a
maximum at the compensation temperature as was the hysteresis coefficient v. In a small grain, low-loss ferrite fir was then at a maximum, but #w and v were at minima. This is explained by the
thickness of the domain wall becoming comparable to the grain size, and this is probably the under-lying mechanism responsible for the low residual loss. The effect of the spins being pinned at the grain boundaries is discussed.
1. Introduction. — In considering the
magnetiza-tion process in MnZn ferrites, it is necessary to assume a model for the domain configuration. A suitable model is suggested by visual observation on square loop ferrites, which show a simple magnetic structure comprising from one to three 180° walls per grain [1] and possessing a small magnetostatic energy [2]. Globus [3] applied a similar model, used here, to soft ferrites and showed that for a spherical grain with a diametral wall :
, 4 - 1 = 2 nMljK nZ - 1 = (3 7t/4) M2S D/y (1)
where fi0 and $ in my notation refer to the intrinsic
initial rotational and 180° wall permeabilities, K = K^ + a magneto-elastic term, D is the grain diameter and y the wall energy. A method for estimat-ing no and pi™ is now described, and applied to typical ferrites. It is assumed that non-1800 walls are absent, and (erroneously) that 180° walls are thin. The results a then approximate, but nevertheless give some insight into the properties of soft ferrites.
2. Theory. — After a. c. demagnetization the domain magnetizations are left orientated around the demagnetizing field, the angular distribution being described by an unknown function D{9), being the relative density of domain magnetizations per unit solid angle making an angle 9 with the demagnetizing field. The magnetic properties then depend [4] on the angle between the direction of demagnetization and measurement, e. g. 0° (||) or 90° (_L). If in a grain with a 180° wall n is the angle between the magnetization of
a domain and the measuring field, its permeability comprises
p.* = p.r0 sin2 n and (T = ju^cos2^ .
In the parallel case n — 9, and in the perpendicular case sin2 n = 1 — sin2 6 cos2 cp where cp is the azimuthal angle. The permeability of a polycrystal is then given by the weighted mean of / / + p7, over all possible orientations of the domain magnetizations : e. g, for the || case (when sin2 r\ = sin2 9)
D(9) sin2 9.sin 6 d9 d(p
< It > = Ho T^TTi ^ F i •
D(G) sin 6 d0 dq> Jo Jo
It may then be shown that :
j«|[ = i"o F! + p%(\ - Fi) ,
Hx = Ml-F1/2) + tiFJ2.
Having measured ^ and n±, one may either :
a) Assume the form of D(9) and then calculate pf0
and po.
b) As shown in section 4, estimate p.T0 without
making this assumption.
The first alternative will now be discussed. A simple distribution is to take the domain magnetizations to be uniformly dispersed within a double solid cone of semi-vertical angle 9m [1] so that within the cone D(9) is
constant and elsewhere D{9) = 0. To estimate 0m,
C1-28 J. E. KNOWLES assume that the low field hysteresis alises only from
wall motion. The field acting on a wall is H cos y and the loss in the grain per cycle is then (213 n) v o ~ d 3 cos3 y
where H,,, is the maximum value of the applied field and vo is the Rayleigh coefficient obtaining when y = 0. Since for vll, cos3 q = cos3 8 it follows that
jr j:
D(B) cos3 B sin B do drp= vo F 5
"11 = "0
1:'
j:
D(B) sin B d p -196-
-40 0 40 80Temperature ( O C )
and v~ = v~ F6F,. is then found cornpar- FIG. 2. - Initial permeabilities and hysteresis coefficients for a
ing the experimental ratio of v,!/v, with the ratio F5/F6, high p ferrite demagnetized parallel or perpendicular to the
evaluated for various values of 8,. measurement direction.
3. Experimental observations. - The samples were usually ungapped polished RM pot cores, as shown in figure 1, the halves being secured by adhesive applied
Solenoidal winding
Toroidal winding
FIG. 1. - General view of specimen, in the form of an RM core, with windings.
externally to the mating surfaces. A toroidal winding was used for measurement purposes, so effectively only the properties of the centre pole were measured. The same winding was used for demagnetizing in the parallel direction. A superposed orthogonal solenoidal winding was used to demagnetize in the perpendicular direction.
In order to check the method, initial observations were made on yttrium iron garnet, measurements of plI, pL, v,, and v, being made at 23 OC and - 196 OC. The coefficients v were derivedfrom the hysteresis resistance. It was found that at either temperature vll/v, z 1.7, giving 8, x 750 and pll/p, z 1.24. The calculated values of
p i
were then too large by a factor of two compared with those calculated from published values of K, and M,. The cause of this error is probably the assumption that only 1800 walls are present.The next sample examined was a high permeability MnZn ferrite with a grain size of 15 pm, the pores being situated on the grain boundaries. The results are shown in figure 2. At all temperatures vll/v, z 1.4, so
Results were then obtained for a medium permeabi- lity, low-loss MnZnTi ferrite [6] having a grain size of 6 pm, again with the pores on the grain boundaries. In this material the assumption that the grains contain only 1800 walls is likely to be well satisfied. The results are shown in figure 3. Unlike the previous example, v
- - - -Temperature ( OC )
FIG. 3. - Measured and derived magnetic parameters for a low-loss ferrite, demagnetized parallel or perpendicular to the
measurement direction.
is at a minimum near
T,,
(at - 14 OC [7]) which pro- duces a corresponding minimum in tan 6,,,/p, [S]. Also shown are the calculated values of p i (open circles) and p: : as before pb is at a maximum nearT,,,
but this no longer holds for p:. These effects probably occur because the wall thickness 6, taken as 7 JAIK,, increases near T,, and may become comparable to D. The wall as such then ceases to exist, and so there occurs a minimum in v. Quantitatively, from eq. (1) :
8, x 800 and ,u: x 1.7 pi. The peak in v [5] is near the
D
3 n M:D K 1 =1.31-.
p:=-.--
-
compensation temperature T,, (where K, changes sign)
and it was shown that pi and p: are then also at a , u 4
2 J A K ,
2 . n ~ : 6Now figure 3 shows that near T,,, p:/pb 3 1.2 so D/6 s 0.9. The observed ratio of pz/pb is then consistent with the wall thickness being comparable to the grain diameter. Away from T,,, p:/pi
=
2 (as in the high p ferrite) and the ratio D/6 is proportionally increased : i. e. 1800 walls can exist.The decreasing ratio of vl,/v, near T,,, which causes an apparent increase in Om, may be due to the hysteresis loss due to rotations, which becomes noticeable as the walls vanish. The uncertainty in
On,
does not signifi- cantly alter the results.Substituting for pro, p: and other known parameters in eq. (2), it is found that walls and rotations contribute approximately equally to pll.
Unlike the low field hysteresis losses, the high field losses (B = 200 mT) in both ferrites shown a minimum at T,,. The anisotropy K is then at a minimum so H, is at a minimum also, irrespective of whether some of the walls disappear or not.
4. Behaviour at high frequencies. - In general, the wall permeability lags the field by an angle 6 but that
due to rotations is nearly in phase with it [3]. For 1800 walls, from eq. (2)
Eq. (3) implies that at low frequencies pll - pI > 0 and at high frequencies pll - pL
<
0. When pll = p1then from eq. (2) and (3) pll = p, = pro = p t cos 6, whatever the form of D(0). This method was applied to the high resistivity MnZnTi ferrite discussed above :
the cross-over frequencies ranged from 0.5 to 3 MHz. The values of so found are shown in figure 3 by solid circles, and agree with those obtained by assuming D(0) which suggests that the assumed distribution is a good approximation to the actual distribution.
5. The influence of the grain boundaries.
-
Our unpublished Kerr observations on a MnZn ferrite, subjected to a small alternating magnetic field, suggest that the magnetization is pinned at the grain bounda- ries as if it were subjected to a large local anisotropy there. U. Enz (unpublished) considered the case where the boundary magnetization is pinned in the z direction and a small field applied in the x direction, K, being zero. Obviously, exchange forces tend to align the spins in the interior of a grain along the z direction also. We now assume that these spins are, for small devia- tions, subjected to an anisotropy field of 2 K,/M,. Then for a spherical grain the intrinsic rotational suscepti- bilityXg
is given byand
R, = ~,/JA/K, where 2 r, = D
.
If it is assumed that introducing a 1800 wall does not alter x:, then from eq. (1) and (4) it is found that for small D/ J*,, X:/X: 2 3.5.
The total susceptibility
x
of a randomly orien- tated assembly of such grains is given byx
= (213)Xrd
+
(113) 11; whtreXr
and X: are given by eq. (4) and (1). In figure 4, X / ( ~ , 2 / 2 K,) is plotted as aFIG. 4. - Normalized susceptibility as a function of normalized grain diameter.
function of normalized grain diameter. Shown by a broken line is the curve obtaining in the absence of grain boundary pinning ; this intercepts the axis at a value of 213 so the value derived for the anisotropy is K,. The ratio D/6 must be at least two if 1800 walls are to exist, so D / J ~ K
>
14. The extrapolated solid line intercepts the axis at a value which is considerably less than 213 so the value of anisotropy then deduced is correspondingly larger.Thus this model, like that of Globus 131, gives rise to an effective anisotropy greater than the magneto- crystalline anisotropy, but the present mechanism is significant only for materials where the grain diameter is comparable to the wall thickness, and probably only for those having a small anisotropy ; i. e. MnZn ferrite.
6. Conclusion. - In both high permeability and low loss ferrites the rotational permeability was at a maximum at the compensation temperature
T,,.
In the low-loss ferrite the grain size is such that at T,, the walls in some grains disappear, giving rise to minima in the hysteresis and residual loss factors.If the spins are pinned at the grain boundaries then the performance of a ferrite with low residual loss cannot be improved by further reducing the grain size, which would reduce the rotational permeability and so increase the loss factor.
R, sinh R) R, dR
R sinh R, (4) Acknowledgements. - The author is indebted to Dr. U. Enz (Philips Research Laboratories) for making where
C1-30 J. E. KNOWLES
References
[I] KNOWLES, J. E., Proc. Phys. 75 (1960) 855. [5] N ~ E L , L., Cah. Phys. 13 (1943) 18.
[2] KNOWLES, J. E., J. Phys. D. 1 (1968) 987. [6] STIJNTJES, T. G. W., BROESE VAN GROENOU, A., PEARSON, R. F., K N O ~ L E S , J. E. and RANKIN, P., I. C. F. 1 (1970) [3] GLOBUS, A., Proceedings of SMM2, Cardiff (1975). 194.
