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90

FLUX SWITCHING MECHANISMS

IN FERRITE CORES AND THEIR

DEPENDENCE ON CORE GEOMETRY

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
i a a/fof

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NATIONAL BUREAU OF STANDARDS

technical ^lote

90

MAY 1961

FLUX SWITCHING MECHANISMS

IN FERRITE CORES AND THEIR

DEPENDENCE ON CORE GEOMETRY

George William Reimherr

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

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TABLE OF CONTENTS

Page

ABSTRACT 1

I. INTRODUCTION 1

II. MODELS OF FLUX REVERSAL 3

Domain Wall Motion 3

Incoherent Rotation 6

Coherent Rotation 8

III. MEASUREMENT OF SWITCHING TIME AND

APPLIED MAGNETIC FIELD 13

IV. EXPERIMENTAL VALUES OF SWITCHING

COEFFICIENTS 16

Results Found by the Present Author l6

Results Found by Other Investigators 16

V. SHAPING OF FERRITE CORES 17

VI. ERRORS OF MEASUREMENT 19

Errors in H 19

Errors in T 20

Errors in Comparative Measurement 21

VII. RESULTS AND CONCLUSIONS 22

SELECTED BIBLIOGRAPHY 25

APPENDIX 43

in
LIST OF FIGURES

Figure Page

1 The Spiral Model (5) 31

2 Flux Reversal in Thin Films by Coherent

Rotation . 32

3 Appearance of the Film in Fig. 2 When

Wrapped up to Form a Hollow Cylinder 33

4 Assumed Cross Section of Core Used to

Demonstrate the Coherent Rotational

Model in Ferrite Toroids • • 33

5 Experimental Layout for Obtaining Switching

Curve Data 34

6 Reciprocal Switching Time Versus Applied

Field for a Ferromagnetic Tape Toroid and

Ferrite Core Types F. and F(- 35

7 Reciprocal Switching Time Versus Applied

Field for Ferrite Core Types F, and F, 36

8 Reciprocal Switching Time Versus Applied

Field for Ferrite Core Type F? 37

9 Appearance of a Ferrite Core, (a) As Received

Commercially; (b) After Being Ground into a Square Cross Section 38

10 Reciprocal Switching Time Versus Applied Field

for 3 Type F. Cores of Different Cross Section • • 39

11 Reciprocal Switching Time Versus Applied Field

for 2 Type F,. Cores of Different Cross Section • • 40

12 Reciprocal Switching Time Versus Applied Field

for 2 Type F, Cores of Different Cross Section • • 41

13 Reciprocal Switching Time Versus Applied Field

for 2 Type F,. Cores of Different Cross Section- • 42

IV
FLUX SWITCHING MECHANISMS IN FERRITE CORES

AND THEIR DEPENDENCE ON CORE GEOMETRY

by

George William Reimherr

ABSTRACT

Plots of reciprocal switching time against applied

magnetic field for ferrimagnetic or ferromagnetic cores

usually show two or three interconnecting straight line

segments. Different theoretical flux reversal mechanisms have been proposed for each segment. Descriptive

models of these mechanisms are presented. Switching

curves are shown for seven ferrite cores of different

composition, and for a ferromagnetic tape core. The

inverse slope of the switching curve known as the switching coefficient, was calculated for these cores and it is

shown to agree well with values given by other experimenters and by theory.

Experiments were made to ascertain whether the

flux reversal mechanisms are affected by core geometry.

Nine ferrite cores were separated into four groups. The

cores of each group had identical chemical composition

and originally had nearly equal cross sections and

identical switching curves. The cores of each group

were then ground into different cross sections, at least

one being rectangular and the other being square or circular, and switching curves were again taken of these

cores. No effect of geometry upon the flux reversal

mechanisms was found. Several factors which may

affect the switching coefficient are given.

SECTION I INTRODUCTION

The mechanism of rapid magnetic flux reversal has received

considerable attention both because of its intrinsic importance in

understanding the behavior of ferromagnetic and ferrimagnetic

materials, and because of the desire to decrease the time required

to store or to retrieve information in magnetic memory systems of

electronic computers. The cores used in magnetic memory systems

are generally of ferrite materials having rectangular d. c hysteresis
loops characterized by steep sides and almost flat tops. It is with

this type of ferrite that this investigation is most concerned.

A relation found to hold when ferrite cores, metallic ribbon

cores, or thin films are subjected to sufficiently high current

pulses of short duration is the switching equation of Menyuk and

Goodenough (1),

(Hx - H )t = S (1) o w '

in which

H = the applied magnetizing force

H = the projected threshold magnetizing force when switching

the core in a given mode

T = the switching time. It is defined in the present investigation

as the duration of electrical pulse needed to switch

irreversibly 90% of the flux that is switched irreversibly

when completely reversing the magnetic state

S = the switching coefficient, a constant over a restricted

range of applied field

The above-mentioned equation can be put into another form; namely,

4 = -s-

<H - Ho>(E> W

Hence, a plot of reciprocal switching time against applied

magnetizing force should yield a straight line with a slope equal to

the reciprocal of the switching constant. However, if the range of

applied field is extended sufficiently, one may obtain three connecting

lines for a ferrite, each having a different slope. This suggests that

different modes (or mechanisms) of flux reversal are dominant over

various regions of the switching curve.

Various models have been proposed to account for these switching

mechanisms. '»»'»* '" The model of flux reversal for the lowest

region of field intensity corresponds to that of domain wall motion.
At higher regions of field intensity, a model corresponding to an

incoherent rotation of the electronic spins is proposed while at still

higher field intensities, a model corresponding to a coherent

rotation of electronic spins has been presented.

A short discussion of each of the three models for flux reversal

will follow. It is interesting to note that these models apply as well

to the flux reversal mechanisms in metallic ribbon cores and thin

films as they do to ferrite cores. While the model of domain wall

motion seems to be generally accepted, one is cautioned that the flux

configuration considered in the rotational models should not be

considered as an exact description of the actual flux reversal process

SECTION II MODELS OF FLUX REVERSAL

Domain Wall Motion. The existence of regions within a ferromagnetic or ferrimagnetic substance in which all the net electronic

magnetic moments are essentially aligned, has been fairly well

established. These regions are called domains. A magnetic

material when in the un-magnetized state may be composed of very

many of these domains, the magnetization vectors within different

domains being in different directions so that there is no over-all

magnetization exhibited by the material.

Adjacent domains are separated by transition regions within

which the magnetization gradually changes direction from that of one

domain to that of the adjacent domain. These regions of transition

are called "domain walls" or "Bloch walls". In iron, a Bloch wall

_4

is of the order of 10 mm thick, corresponding to several hundreds

of inter-atomic spacings; a domain itself may be of the order of

0. 001 to 0. 1 mm.

When a magnetic material is initially subjected to an external

magnetic field whose amplitude equals or exceeds somewhat the

coercive force of the material, those domains which happen to be
favorably oriented with respect to the external field will grow at the

expense of the neighboring domains by virtue of movement of domain

walls. "When the specimen is completely saturated in the direction of

the applied external field, the moving domain walls which brought

about this situation have been annihilated, either by combining with

other walls or by running off the edge of the grain.

Now suppose the external field "H" is reduced to zero and then is

given some small value in the reverse direction sufficient to initiate

flux reversal in the specimen. For flux reversal by domain wall

motion, it is necessary for domains of reversed magnetization to

form; i.e. , to be "nucleated". If the specimen were a perfect single

crystal, this would require extremely high fields, due to the strong

internal anisotropy fields which supply a torque opposing such change.

However, imperfections in the actual specimen give rise to internal

fields which allow nucleation of reverse magnetization at much lower

values of applied field. Any commercial magnetic material will have

many nuclei for the formation of domain walls such as crystal

boundaries, lattice defects, and surface irregularities.

In. general, domains of reverse magnetization form as H is

lowered from +H to -H . A requirement for a maximum coercive n rectangular B-H loop is that no nucleation take place as H decreases

from H to -H (1). Once the walls are nucleated at max coercive

points of crystal imperfection, they find themselves tied down by

these same imperfections so that it takes a finite applied field in the

reverse direction to break the fields away from the imperfections.

Thus imperfections are responsible for low coercive forces as they

nucleate domains of reverse magnetization; however, they keep the

coercive force from being zero by stabilizing the domain walls.

The average velocity of the domain walls when the external

field equals the coercive force is about zero. If the external field

exceeds the coercive force, the domain walls are thought to

accelerate very rapidly to an average velocity which is maintained
until the walls collide with one another or with a grain boundary.

Damping of the motion of the domain walls arises from two

factors. The first factor is the presence of eddy currents. This

factor is of no practical consequence in ultra-thin metallic tapes of

1/8 mil thickness, or in commercial ferrites since their resistivity

5

is typically of the order of 10 ohm cm. The second cause of damping is the relaxation contribution which arises from the delayed

response of the atomic spins to a force which would change their

direction; it is an inherent quality of the magnetic material (1).

An expression for the domain wall velocity v is given in

reference (2) as

4yA(H-Hol) v = (3) (7a

where

y = magneto mechanical ratio of the electron

A = exchange factor (10 erg/cm for ferrites)

<7 = wall energy (about 1 erg/cm for most ferrites)

a = a damping constant, obtained in microwave resonance

experiments

If a domain has an average initial width d, then the reversal

time t will be the time it takes the walls to go a distance d/2.

It follows that

S

= T(H -V "w£- (4)

This is not the only expression for Sw, present in the literature.

One may refer, for example, to reference (3) or (4). All three

expressions, however, have in common the fact that Sw , is

proportional to the product of the distance a domain wall moves, and

the damping constant. It appears to be generally accepted, today,

that at low values of external drive fields, flux reversal occurs by

domain wall motion.
Incoherent Rotation. As the external drive field continues to

increase above the coercive force, a break in the switching curve

is noted, followed by a straight-line region for intermediate values

of drive field. In this region of drive field, it is thought (4)

that a switching process by incoherent rotation more nearly agrees

with experiment than does the domain wall motion model.

If flux reversal occurs by domain wall motion, then intuitively,

one might expect S to be quite sensitive to the structure of the

ferrite, since it is proportional to d, the average distance a wall

moves before colliding with another wall. However, Sw? (the

switching constant for incoherent rotation) has been found to be

relatively independent of the grain size or even of the ferrite used

(4). A variation in grain size from 2 to 1500 microns, or a change

in chemical composition between ferrites, and, if the 1/8 mil permalloy material is considered, a change from ferrimagnetic to ferromagnetic material, caused a variation in Sw? by only a factor of

three (4). This type of reasoning led to an abandonment of the domain

wall motion mechanism in favor of an incoherent rotational model

for the intermediate region of the switching curve.

A potential difficulty with any rotational model is that during

flux reversal, large demagnetizing fields can result from the

discontinuity of the magnetization at the boundary of the magnetic

material. This implies that very large driving fields should be

necessary for flux reversal by spin rotation; however, the experimental value of the projected threshold field is typically on the order

of only a few oersteds (note for example H _ values in Table I).

Hence, the incoherent rotational model must have the property that

the demagnetizing fields can be neglected; this is attempted in the socalled "spiral" model (5).

To illustrate the spiral model, one may consider the toroid to

be equivalent to an infinite cylinder extending along the Z axis (5).

Let the external field H be applied along the negative Z direction,
and let the magnetization M be in the partially switched state so as to make an angle Q with the Z axis. See Figure 1. The angle

varies only with time, during which flux reversal occurs.

The magnetization vector does not point uniformly in any one

direction during flux reversal, but instead is presumed to form a

spiral pattern around the Z-axis as shown in Figure 1. This in turn

results in the appearance of poles of alternating sign at the boundary

of the cylinder. The surface poles form a helical pattern with a

spacing X. If X is much smaller than the diameter of the cylinder,

then the demagnetizing field due to the surface poles will be negligible

throughout most of the volume of the cylinder (5). If one allows for

the fact that there is a demagnetizing energy due to the surface poles

and if an approximate expression for this energy can be found as a

function of X, then it is possible to find a value of X which can

minimize this energy. This expression for X that minimizes the

demagnetizing energy is given in the literature (5) as the following:

1/3

(5)

. , 2tt RA

A — c\ ^

\ M

L

s where

R = radius of cylinder

A = exchange constant, 0. 15 x 10 ergs/cm for a

manganese ferrite (Mn, . Fe , , A

M = saturation magnetization in gauss

s

~~

If one lets R = 2. 5 x 10 cm, M = 240 gauss, one obtains

-4 s X ~ 2. 2 x 10 cm, which is 2 orders of magnitude smaller than the

assumed radius of the cylinder. Likewise, the fields due to the

surface poles, when the pole density is at a maximum (0 = tt/2) are

given (5) by the following expression:

H

z

= 2TrM

s e _27rd/X

cos (5f )Z (6)

-4 where d is the distance from the surface. If d ?» 3 x 10 cm, the
fields have dropped to about 0. 2 oersted. Hence, the influence of

the demagnetizing fields is mainly limited to a surface layer having

about 1/40 of the volume of the cylinder (5). A theoretical

expression for the switching coefficient, as given by this model, is

the following (4):

S = 2o fl + -L-\ 1 4-1 A (?) w 2 A

I a / \ / where

a = a damping constant taken from the Gilbert

modification of the Landau- Lifshitz equation

of motion for M (6) s ' A = the gyromagnetic ratio

A = a term whose value depends on the remanent

magnetization of the sample, and the definition

of the switching time used. It is sometimes

omitted because it usually is of the order of one (4).

It is not known with any certainty what value to choose for a

in the above mentioned equation. However, assuming a to be the

only variable, one can minimize S with respect to a, i.e. , this

would correspond to that value of S for the minimum switching time

for a given externally applied magnetic field. Setting a = 1, the

minimum value for S in this switching mode is given by 4/X or

approximately 0.2 oersted-microseconds (oe-usec). This value

agrees with experiment, as will be seen later.

Coherent Rotation. A discussion of the existence of the very

fast uniform rotational mode of switching of ferrite toroids appeared

only recently in the literature (8). It was pointed out that a model

for the rotational mode of switching of thin ferromagnetic film had

recently been postulated (7) and had given a best explanation of the

experimental observations (7) when large drive fields were applied

along with a transverse magnetic field. An attractive postulate is

that a similar mechanism of flux reversal could also apply to

ferrite toroids. Since flux reversal in a thin film is easier to

8
visualize than it is for a ferrite toroid, a brief discussion of the

coherent rotation model for a thin film will precede that for a

toroid.

Consider a thin film with a uniaxial anisotropy in the plane of

the sample. Let the external field be applied along the easy axis

of magnetization. The magnetization in the film will then also line

up in this direction. Now let the external magnetic field be reversed

in sign, but still lie along the easy axis of magnetization in the sample.

If the magnetization in the sample is to reverse by uniform rotation,

then the magnetization of the whole sample can be represented as a

single vector which rotates within the plane of the film. However, in

the present situation, this cannot occur because the magnetization

and applied field are colinear the initial net torque on the magnetization is zero. Hence, for sufficiently high fields, flux reversal must

occur by the slower process of incoherent rotation in which it is- assumed that the magnetization does not precess as a whole, but

that the phase of the precession varies with position in the sample

(7). This is similar to the incoherent rotation model for ferrite

cores.

Consider the situation, however, if a small transverse magnetic

field is applied along the plane of the film, but at right angles to the

drive field and to the easy axis of magnetization. A small component

of the magnetization now is at right angles to the external drive

field. Now let the direction of the external drive field be reversed.

There is now a net torque causing the whole magnetization to

revolve in a vertical direction. This creates a strong demagnetizing

field which in turn causes the whole magnetization to revolve as a

single vector within the plane of the film. The fast reversal process

may therefore be interpreted physically as a precession of the

magnetization in the plane of the film around this demagnetizing

field (8). The switching process is shown in Figure 2.
With this background, the case for the ferrite toroid will now be

presented as given in reference (8).

If high speed flux reversal is to occur in ferrite toroids; it

appears that a flux configuration must be induced that gives rise to a demagnetizing field around which the bulk of the flux may process.

For this purpose, the "helical mode" is presented. As was done for

the incoherent rotation model, the case of the toroid shall be

approximated by considering it to be a cylinder of infinite length.

Suppose one takes the thin film in Figure 2 and wraps it up to

form a hollow cylinder; the flux lines have now become helical with

the small radial component, as in Figure 3. One may superpose

many such hollow cylinders of decreasing radii in order to obtain a

solid cylinder. The flux configuration is therefore uniform in the

sense that the magnetization components are independent of position

in the cylindrical coordinate system (8).

The final step in visualizing the helical mode is to take into

account the curvature introduced by wrapping up the thin film. Asa

result of rolling up the film, the outer surface is stretched and the

inner surface is compressed, leading to a difference in the magnetic

surface charge density. This difference is assumed to distribute

between the two surfaces as volume charge in a way to obtain a

radial, position-independent demagnetizing field.

The complete configuration for this model as given in reference

(8) is therefore a cylinder in which most of the magnetization follows

a helical path. However, there is a small spatially independent

radial component. The discontinuity of the radial magnetization at

the surface of the cylinder creates a uniform surface charge

distribution, and a radial demagnetizing field arises within the

cylinder from the surface layer. The demagnetizing field lines

terminate on the volume charge of opposite sign which occurs because

V . M / in the cylinder. A flux configuration has been

selected which leads to a uniform demagnetizing field because this is

10
the analog to the uniform rotational mode in thin films. Note that the

model assumes no interaction between shells.

The helical model gives the following expression for the minimum

value of the switching time:

-8

. _ 6. 9 x 10 second

min =

, 1/2 (8)

< Ms He> where

M = saturation magnetization of the ferrits

H = excess threshold field (H-H ) e o'

Inserting a typical value for M of 240 gauss, and allowing H = 1

• s _9 e oersted gives as the minimum switching time 4. 5 x 10 second for

ferrite cores with H = 1 oersted drive field (within the framework of

this model); this would lead to a minimum switching coefficient of,

approximately .005 oersted-microseconds.

To test this flux reversal model, the authors of this model (8)

fabricated a core in which a 3 mil platinum wire loop was embedded in

the center of the cross -section of the core (Figure 4). Normally, no

current flows in the embedded wire and the flux pattern would be

perpendicular to the plane of this paper. But with a small current in

the wire, a component of the magnetization forms a circular flux

pattern concentric with the wire. This can be considered equivalent

to the case of the thin film with a transverse field as well as a normal

drive field. When all the flux assumes the circular pattern, then one

has approximately the half- switched state of the helical mode (8).

Switching curves were taken for the core with and without current

flow in the embedded wire, and a switching time definition was used

which took into account the fact that the core was already half

switched in the case of current flow in the embedded wire. A

reduction in switching coefficient from 0. 11 oe-jjisec to 0. 05 oe-usec

by applying this current seemed to be in qualitative agreement with

that experienced by applying a transverse field to a thin film.

11
One may note, however, that the observed switching coefficient

of 0. 05 oe-fxsec is still an order of magnitude greater than the

minimum value of 0.005 oe-jj.sec given by the model. The authors of

the model (8) explain this by observing that they assumed a damping

coefficient in their derivation of minimum switching time corresponding to optimum damping, and that this may not be applicable to the

real situation; also they point out that the switching coefficient

decreases as the temperature increases, and that the theoretical

minimum value of S may be approached as the Curie temperature

of the ferrite is approached. They did not obtain experimental

verification of this because so much flux switched reversibly as the

Curie temperature was approached as to make obscure the meaning

of switching time. They did point out that a minimum measured

value of S for the uniform rotational model in thin films was

w

reported as 0.01 oe-|isec in the literature (9).

A difficulty in the experimental verification of this model arose

when it was observed that no induced voltage appeared on the wire

embedded in the core when the flux reversal in the core was

presumably by the helical mode. This implied that the dynamic flux

configuration was not as simple as the proposed helical mode. The

difficulty can be resolved by a modification of the helical mode. This

is done by assuming that there can still be a coherent rotation in each

of the concentric shells; however, the direction and angular velocity

of the magnetization vector may vary from one shell to another (10).

This could explain the observed lack of induced voltage on the

embedded wire mentioned previously.

This completes the descriptive analysis of the various models for

magnetic flux reversal. The interested reader may refer to any of

the references cited previously, or to reference (11) for more

information on the subject. The next section will show a practical

experimental method to obtain switching curves for magnetic cores,

consistent with the definition of switching time used in this

investigation.

12
SECTION III MEASUREMENT OF SWITCHING TIME

AND APPLIED MAGNETIC FIELD

The experimental layout used in this investigation to measure

the data used in calculating a switching curve for a core is shown in

Figure 5. The electrical pulses necessary to switch the core are

provided by two pulse generators. The write pulse is generated by

a pulse generator having a risetime of the order of 1 millimicrosecond (m|j.sec). The read pulse reverses the magnetization in the

core from that provided by the write pulse. It is provided by a pulse

generator having a risetime of the order of 20 ir^sec.

The write pulse generator provides a variable write current up

to a little over 2 amperes. Different write pulse widths are provided

by charging a coaxial cable delay line to a voltage, V . A relay then

discharges the cable across the external load resistor, R. The step

voltage appearing across the load resistor is of duration t , twice the

delay time of the coax line. If R is made equal to Z , the

characteristic impedance of the line, the voltage across R is

V

-=— . The pulse width is given by (2),

t Q

= 2Z

q

C1 = 21\A~LC (9)

where

C = capacitance /unit length

L = inductance /unit length

1 = length of cable

and this is controlled by adjusting the length of the line. Pulse lengths

from 10. 7 to 1075 m|j.sec were available. They had fixed lengths and

hence had to be calibrated only once.

The read pulse length and amplitude were held constant and were

set so as to insure the total flux reversal of the core during every

read cycle. With the exception of the earliest cores examined, A-l,

A-2, and A- 3, this value was about 1. 4 amperes amplitude and a

13
pulse duration on the order of 7 microseconds. This amplitude was

the highest attainable with the Read pulse generator. It provided an

average driving field of about 5-1/2 oersteds.

To ascertain what percentage of the core was switched, a sense

wire was wound through the core. Whenever flux reversal occurred

in the core, a voltage pulse appeared at the sense winding. This

would go into an RC integrator which in turn was connected directly

to the scope input.

The write pulses occurred at a rate of approximately 75 cycles

per second, while the read pulses occurred at a considerably higher

rate and were not synchronized with the write pulses. The scope

sweep was triggered only by the read pulses.

The sequence of events is as follows: The core, being in the

remanent state after a series of read pulses each of which is capable

of saturating it, receives a write pulse which drives it away from

remanence. No core signal is seen, however, because the scope is

not triggered by write pulses. Then, the next read pulse completely

reverses any flux switched by the write pulse, restoring the core to

its initial state. The flux reversal in the core creates a voltage pulse

in the sense winding. This voltage pulse then goes to an RC integrator

network whose output appears on the scope because the scope is

triggered by the read pulse. The output from the integrator is

proportional to the volt -second area of the core output pulse. A

direct comparison of integrator signal height to the maximum height

(attainable by using a write pulse which is sufficient to fully reverse

the magnetization in the core) gives the fraction of irreversible flux

switched. There is a lower limit of integrator signal height below

which it becomes very difficult to take accurate readings. In the

present case, this was about 6 millivolts.

The integrator time constant, RC, was adjusted so that the ratio

of RC to the core output pulse length which was integrated remained

relatively constant for all cores in a given comparison. For all

14
ferrite cores examined in this investigation, this ratio ran between

about 20 and 27 when 90% of the core was switched irreversibly, with

the exception of the earliest set examined, cores A-l through A-3 for

which the ratio was about 11.

The flux reversal field H of the core switching curve can in

theory be found by measuring the write voltage pulse across a known

value of load resistance (53. 3 ohms in this particular case) when 90%

of the flux of the core switches irreversibly. However, a perfect

current source is not available; some back e.m. f. is generated by the

core. But since the internal impedance of the pulse generator is about

the same as that of the termination (or load) resistor, only half the

core voltage appears across the load resistor, and an evaluation for

H should appear as follows:

n(V - 1/2 V ) h - m c H Rl

where

H = applied magnetic field switching the core

R = resistance (53.3ft)

n = number of turns (4)

1 = mean magnetic path length

Vw = voltage measured across R when core is not

switching, but which could switch 90% of the

core flux irreversibly

V^ = average voltage generated by core while

switching by 90%

m

c

15
SECTION IV

EXPERIMENTAL VALUES OF SWITCHING COEFFICIENTS

Results Found by the Present Author. Shown in Figs. 6, 7, and

8 are the switching curves for 5 types of commercially available

ferrites as well as for a ferromagnetic tape core. All curves were

taken at room temperature, about 23 C. The ferrites are of the size

listed in commercial literature as 50 mil O. D. , 30 mil I. D. and 15

mil in height. The tape core consists of 8 wraps of 4-79 Molybdenumpermalloy ribbon, each wrap being 1/8 mil in thickness.

It is noted that each ferrite shows 3 straight line regions in its

switching curve, presumably corresponding to the 3 switching

mechanisms mentioned previously. The ferromagnetic tape core also

shows 3 straight line regions, although the difference between the

upper 2 line segments is so small that within experimental limits of

accuracy, the predominant switching mechanism for the upper 2

regions is probably the same; namely, incoherent rotation.

Values of the switching coefficient, S , and the projected

threshold field, H , were found from these plots and are listed in

Table I. The subscript corresponds to the switching mode; e.g. , Sw ,

is the switching coefficient for flux reversal by domain wall motion,

with H , being the corresponding threshold field, etc.

Results Found by Other Investigators. A brief look at some

values of switching coefficients as found by other investigators might

prove informative, although any rigorous comparison is impossible

because of the differences in chemical composition and (usually) the

definitions of switching time. For reversal by domain wall motion,

Table II gives an indication of the wide differences possible in Sw , and Ho,, with switching time being defined as that time which elapses

during a half reversal of the magnetization (12). Table III shows

values of Sw , for the system Mm, . ^e/ ?

\ O4 with switching time

being measured between the 10% and 90% output voltage points (3).

16
Table IV gives experimental values of switching coefficients

corresponding to flux reversal by incoherent rotation. Switching

time is defined as the time required for the reversed induction to

increase from 10% to 90% of the total flux switched (4). Note in

particular how close the values of Sw? are to each other.

Another author (10), whose definition of switching time is the

same as that of the writer, has measured the switching coefficient

corresponding to flux reversal by incoherent rotation for a wide

selection of fer rites. He found the switching coefficient to fall in

the range 0. 11 to 0.41 oe-|xsec (10). He feels this compares favorably

with the predicted minimum value of 0. 2 oe-usec.

Flux reversal of ferrites by coherent rotation has been reported

so recently that little in the way of experimental values of the

switching coefficient Sw_ is available. One author (10) did report,

however, that he obtained switching coefficients in the range 0. 04 to

0. 20 oe-usec at 23 C.

SECTION V

SHAPING OF FERRITE CORES

The previous discussion showed that values of the switching

coefficient could be found which showed good agreement with those

found, or proposed, in the literature. Of particular interest was the

coherent rotational mode of switching, because of the extremely fast

reversal times associated with it. It was decided to examine the

possibility of whether the switching process, especially that involving

the helical mode, might be affected by the geometry of the core. In

particular, it was felt that the helical mode might be enhanced by a

circular cross section in preference to, say, a rectangular cross

section having an extreme length to height ratio.

There were certain constraints imposed in this investigation which

limited the length-to-height ratios attainable. These constraints are

the following:

17
The cores had to be available commercially, and hence, came in

certain fixed sizes. Because H, on the average, is proportional to

the quotient of magnetomotive force to mean magnetic path length, the

smallest cores (as used in this investigation) required the least

current to produce a given field.

Cores of larger diameter would have required a larger number of

turns on the write winding than the 4 used with the smallest cores.

The resultant higher core impedance would have reduced the

ability of the core driving circuit to function as a current source.

Ferrite cores are fragile and are easily cracked. This sets

restraints on how thinly a core can be ground. In particular, it was

found that reducing 1 in Fig. (9a) to less than 0. 10 mm would probably

result in a cracked core.

Lastly, sufficient core material has to remain to give a workable

output signal.

Hence, the most extreme length to height ratios available were on

the order of 1:3, as noted in Table V. It was hoped that this would be

sufficient to show up any possible dependence of the flux switching

mechanism on core geometry.

Figure 9a shows a typical core, as received commercially. To

give an idea what the dimensions may be, the following readings were

taken for a typical core of type F4.

I. D. = 0. 760 mm ± 1. Z%

1 =0. 254 mm ± 3% o h =0. 368 mm ± 2. 4%

Figure 9b shows the appearance of a core ground into a square

cross section of a given cross sectional area. By this method, the

cores in Table V were fashioned. There are 4 sets of cores. The set

into which a core belongs is noted by a capital letter between A and D

such as A-l, C-2, etc. The length and height of each core cross

section is given, as well as the ratio of height to length.

18
*he uncertainties in measurement, shown in %, are actually a

sum of 2 uncertainties. The first reflects the fact that the core maybe thicker than average in one place, and thinner than average somewhere else. The second reflects an uncertainty in the absolute

determination of a given dimension, due to uncertainty in focusing,

slightly irregular core edges, etc.

SECTION VI

ERRORS OF MEASUREMENT

Errors in H. The errors in H involve measurement of the

switcning current and the mean path length. The former involves

measurement of voltage and resistance; the latter involves physical

measurement of the core and a knowledge of the flux distribution of

a partially switched core.

Voltage measurement uncertainties involve back e.m.f.

correction, vertical deflection linearity, and visual error. Had no

correction been made for the core's back e.m.f. , a 5% error in H

could have resulted; however, this correction was made, reducing

the estimated error to ±1/2%.

Voltage readings had to be taken directly from an oscilloscope

trace which was calibrated from a unit which in turn was calibrated

from a standard cell. Error estimate in vertical deflection

linearity is ±1/2%. Visual errors include errors in precision as

well as systematic error, as for example, the finite width of the

scope trace. The systematic error is believed < 1%. To estimate

the precision, each point of the switching curve of a typical core (C-2)

was experimentally examined five times. The average voltage reading for each point was found, along with the standard deviation. The

errors corresponding to a 95% confidence level were found by use of

the Student t factor. Three of the 21 points had the maximum spread,

about 1. 5%. However, if all points for all cores are considered,

there is really no preferred point for precision along the switching

curve. Therefore, the ±1. 5% spread was used for all points for all

19
cores. Therefore, visual error in voltage readings should be

< ±2 1/2% I . A consequence of the definition of switching time is that

part of the error in precision shows up also as an error in T since it represents uncertainty in choice of the 90% flux reversal point.

The series resistor was checked on an impedance bridge against

a standard resistance of equal value and known error. Both readings

coincided. Therefore, error in resistance is assumed < |±l/2%

Many readings were taken of core measurements. It was found

that both the inside and outside diameter of a typical core may vary by

±1/2% from its average value. It is felt that a reasonable value of the

uncertainty in path length due to uncertainty in core measurement is < |±1%|

.

Flux distribution in a partially switched core presumably varies

with the speed of flux reversal. Were the d. c. hysteresis loop applicable, then a 90% switched core would have practically all of the flux

reversed within the inner 90% of the core, the outer 10% remaining

virtually untouched. This was the reasoning used in this work too.

The other extreme is that the whole core could switch 90%. Perhaps,

considering the high frequencies involved, the true distribution is

somewhere between those 2 extremes, leading to an additional uncertainty in path length of about +1% (path length too low, making H

too high).

The total absolute error in H is estimated to be between +5% and

-6% for the ferrite cores, and ±5% for the ferromagnetic tape core. Errors in t. There are two categories of error involved in the

absolute determination of switching time T. The first is direct and

comes from the uncertainty in the absolute value of pulse lengths. The

second source is indirect and comes from an uncertainty in estimating

the 90% point of irreversible flux reversal, inherent in the definition

of switching time. It is estimated that for the cores used in this

investigation, a 1% error in estimating the 90% point can result in a

4% error in T.

20
There are 21 different pulse lengths used in this investigation.

Those > 96. 75 m^sec were measured visually; those less than that

were measured by integrating their volt- second output and comparing

their integrated height maximum with that of a known pulse length.

Hence, they acquired the error in the known pulse length also. All

readings were taken five times, and the deviations from the average

value were adjusted to provide a 95% confidence level. The scope

sweep calibration was made with a signal generator which in turn was

calibrated against the signal broadcast by radio station WWV. A

typical spread in the absolute determination of a short pulse length is

about ±3%; it drops below 1% for pulse lengths > 100 mp.sec.

There are several uncertainties in estimating the 90% flux

reversal point. All concern the integrator response to the core output

signal. All errors are small because the readings were taken in a

comparative sense --the 90% flux reversal integrator signal amplitude

compared with that of 100% flux reversal.

The uncertainty due to visual observation is believed to be

±1/2%; that due to vertical deflection linearity, < |±l/2%j ; that due to

the imperfect integrator, about +1/2%; i.e. , the 89. 5% flux reversal

curve was probably found instead of the 90% curve, due to the

imperfect integrator. Any error due to capacitor leakage

(C

^ 53 fiui) was neglected.

Although the estimated error in determining the 90% flux

reversal point is only -1% to + 1 1/2%, the corresponding likely error

in t is -4% to +7% for each point in the graphs. It is seen that this

is a larger source of error in t than is the absolute determination

of the pulse lengths.

Error in Comparative Me asurement. The cores of sets A to D

were made in such a way that the cross sectional area, hence the core

output signal of each core in a set, was nearly equal. Also, the ratio

of integrator RC time constant to core output signal duration was kept

practically the same for each core of a set. Therefore, the

21
comparative error between the cores of a set is small, being composed only of precision error (±1. 5%), uncertainty that the cores of a

given set originally had identical switching curves (±1/2%), and

uncertainty in flux distribution (-0. 4% for the core with the larger

mean path),

SECTION VII

RESULTS AND CONCLUSIONS

Before being ground into their various special shapes, all cores

of a given set were similar in dimension and in chemical composition

and gave identical switching curves. After being ground into their

various final shapes, the switching curves of each core of a given set

were again taken and compared between members of the same set.

The results are shown in the switching curves of Figures 10 through

13. The estimated comparative error for each point in these plots

lies between +2. 0% to -2. 4% of the H value of that point, in a direction

parallel to the H axis. Since the switching curves of the cores of a

set were already practically coincident, the comparative error was

omitted for the sake of clarity. It is seen that, within the limits of

comparative accuracy, the switching curves of all cores of a given

set are identical.

The conclusion of the investigation is that within experimental

limits, no effect of core geometry on the switching properties of the

ferrite core types examined was found. This assumes that only cores

having practically equal cross sectional areas, and hence similar core

voltage waveforms, are used. If there is a dependence of switching

mechanisms on core geometry, it evidently occurs rather suddenly

rather than gradually, and it probably requires much more extreme

shapes than those used in this investigation. Hence, the possibility

of such a dependence has not been completely eliminated by the

results of this investigation.

22
In conclusion, a listing of items which have been thought to

influence the switching coefficient, S , could include the following:

1. chemical composition - this is noted in Tables I through IV;

2. method of preparation - it is known that the grain

size and the number of voids in the ferrite are

affected by the sintering temperature and sintering

time duration. One group of investigators (2)

reported that for a ferrite composed of 35% MgO,

25% MnO and 40% Fe_0_, an increase in firing

(sintering) time generally increased grain size,

lowered the coercive force, but had little effect

on S ; w

3. temperature - the switching coefficient is temperature

dependent, and it generally lowers as the temperature

increases. As an example, the value of Sw? for the

ferrite Mn. ., ^8n 71 ^e i 7 a ^4 was f°un<l (4) to be

0. 46 oe-|j.sec, at 77 K, and only 0. 18 oe-usec, at

473°K. The Curie point for this ferrite was given as

550°K (4);

4. effect of core geometry - this writer has found no such

effect on S , within the areas of constraint mentioned w

in section V;

5. definition of switching time - the absolute value of S

obviously depends on what one uses as his definition of

switching time, T. Unfortunately, there are a number of

ways that t is defined in the literature, 3 of which were

noted in conjunction with Tables II, III and IV. Perhaps

in the future, a standard way to define T can be agreed

on by all investigators;

23
6. rise time of drive current pulse - a ferrite core can be

switched faster with a pulse having a short rise time

than with a pulse having a relatively long rise time,

assuming a similar (peak) value of external drive field.

At least one investigator (13) noted a decrease in the

switching coefficient with a faster pulse rise time;

7. effect of previous history - not only is the switching rate

dependent on the initial state of magnetization and the

applied external field, but also on the method by which

the core was brought to its initial state of magnetization.

In particular, the core output voltage waveform is

dependent on the drive field used to attain the initial

remanent state (14).

24
SELECTED BIBLIOGRAPHY

(1) N. Menyuk and J. B. Goodenough, J. Appl. Phys. 26, 9(1955),

(2) Private Communication.

(3) T. J. Matcovich and C. J. Kriessman, J. Appl. Phys. 30,

36s (1959).

(4) E. M. Gyorgy, J. Appl. Phys. 28, 1011(1957).

(5) E. M. Gyorgy, J. Appl. Phys. _29JL 1709 (1958).

(6) T. L. Gilbert and J. M. Kelley, Proceedings of the

Pittsburgh Conference on Magnetism and Magnetic

Material, June 14-16, 1955. American Institute of

Electrical Engineers, New York, 1955, p 253.

(7) F. B. Humphrey and E. M. Gyorgy, J. Appl. Phys. 30,

935(1959). ~~

(8) E. M. Gyorgy and F. B. Hagedorn, J. Appl. Phys. 30,

1368(1959).

(9) CD. Olson and A. V. Pohm, J. Appl. Phys. 29, 274(1958).

(10) W. L. Shevel, J. Appl. Phys. 30, 47s (1959).

(11) E. M. Gyorgy, J. Appl. Phys. 31, 110s (I960).

(12) J. Smit and H. P. J. Wijn, Ferrites, John Wiley and Sons

(1959), pp 341-343.

(13) B. R. Eichbaum, J. Appl. Phys. 3JU 117s (I960).

(14) R. W. McKay and K. C. Smith, J. Appl. Phys. 31, 133s

(I960). —

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26
Ferrite H S

°1 Wl Chemical Composition oersted oe - |isec

Mg .45Mn0.78Fe 1.77 4°' 9 °* 4

Cu0.25Mn0.75Fe2°4 °* 85 °' 4

Mg .6Ni0.4Fe2°4 3 ' 6 1. 1

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0.

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0. l

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Mn0.18Co0.02Fe2.8°4 2 ' 5 4

Co0.1Fe2.9°4 8 50

Table II. Switching Coefficients S and Threshold Fields H (12),

27
Ferrite SWl Chemical Composition oe - jxsec

MnFe

2 4

0. 55

Mnl„43Fe 1.57°4 °' 46

Mn1.84Fe 1.16°4 °' 36

Table III. Switching Coefficients for the System

Mn

(l + X)

Fe

(2-X)°4 (3) '

28
Ferrite Sw

2

Chemical Composition oe - jisec

Mn

0. 46M*0. 71Fe

l. 76°4 °* 25 to °' 35

Zn

0. 39

Mn

0. 47M*0. 34Fe

l. 62°4 °* 22

Zn

0. 02^0. 46Mg . 79

Fe

l. 62°4 °* 21

Zn

0. 08Mn

0. 64MS0. 28Fe1. 74°4 °' 23

Zn

0. 18

Mn

0. 57*^0. 16Fe

1. 79°4 °* 33

Zn0.69Ni0.29Fe 1.98°4 °' 25

(1/8 mil permalloy tape) 0. 2

Y

3

Fe

5 12 (garnet) 0.30

Table IV. Switching Coefficients S (4). w

2

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31
H.

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Figure 2. Flux Reversal in Thin Films by Coherent Rotation

32
Figure 3. Appearance of the Film in Figure 2 when Wrapped up to

Form. a Hollow Cylinder

\0o9

Figure 4. Assumed Cross Section of Core Used to Demonstrate the

Coherent Rotational Model in Ferrite Toroids

33
WRITE PULSE

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Figure 5. Experimental Layout for Obtaining Switching Curve Data

34
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16

OERSTEDS

Reciprocal Switching Time Versus Applied Field for a Ferromagnetic Tape Toroid and Ferrite Core Types F. and Fc

35
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CORE TYPE

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APPLIED FIELD, OERSTEDS

24

Figure 7. Reciprocal Switching Time Versus Applied Field for

Core Types F, and F3

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APPLIED FIELD, OERSTEDS

Figure 8. Reciprocal Switching Time Versus Applied

Field for Ferrite Core Type F-,

37
(a)

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Figure 9. Appearance of a Ferrite Core

(a) As Received Commercially

(b) After Being Ground into a Square Cross Section

38
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Figure 10. Reciprocal Switching Time Versus Applied Field for

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24

Figure 12. Reciprocal Switching Time Versus Applied Field for

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41
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Figure 13. Reciprocal Switching Time Versus Applied Field for

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42
APPENDIX

An extension of the switching curves into the region of long

write pulses - i. e. , those > 1 usee, was made for core types F.,

F,, and F c . In each case, the straight line region corresponding

to flux reversal by domain wall motion was extended until a certain

value of H was reached, following which no more than 90% of the

total irreversible flux could be switched no matter how long the

write pulse was made. Presumably, the field at the outermost

regions of the core had'fallen below the coercive force for the

ferrite material.

Figures 14 and 15 show the switching curves for all the core

types which were examined. No experimental errors are noted.

Figure 14 shows a more detailed view of the lower region of the

switching curves.

Figure 14 also reveals that there is usually a straight line

transition region between what has previously been referred to in

this investigation as the first 2 switching modes - i. e. , domain

wall motion and incoherent rotation. Various possibilities exist as

to the cause for this transition region; for example, it may be a

result of flux reversal by both domain wall motion and incoherent

rotation.

Two new types of 50-30-15 mil cores were received recently.

They are designated as core types F/ and F„, and their switching

curves are shown in Figures 14 and 15. The switching coefficients

were found to be the following, in units of oe - jxsec.

Core Type Sw, Sw

2

Sw

3

F

6 0.29 0. 19 0. 15

F

7

0.50 0.30 0.21

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45

. S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BURfeAU OF STANDARDS

A. V. Astin, Director

The so* THE NATIONAL BUREAU OF STANDARDSope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and Boulder,

Colorado, is suggested in the following listing of the divisions and sections engaged in /technical work. Tn general, each section carries out specialized research, development, and engineering in the field indicated by its title. A brief description of the activities, and of the resultant publications, appears on the inside of the front cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. Metrology. Photometry and Colorimetry. Reftactometiy. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetry and Densimetry. Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment.

Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Analytical

Chemistry. Inorganic Chemistry.

Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer

Structure. Plastics. Dental Research. Metallurgy. Thermal Metallurgy. Chemical Metallurgy. Mechanical Metallurgy. Corrosion. Metal Physics"

Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Crystal Growth.

Physical Properties . Constitution and Microstructure. Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials,

Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics.

Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog Systems*

Applications Engineering.

Atomic Physics. Spectroscopy. Radiometry. Solid Slate Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical Instru- ments. Basic Instrumentation. Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy. Molecular Kinetics. Mass Spectrometry. Molecular Structure and Radiation Chemistry.

• Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Gas Liquefaction.

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere

Research. Prediction Services. Sun-Earth Relationships. Field Engineering. Radio Warning Services. Radio Propagation Engineering. Data ReductionMnsirumentation. Radio Noise. Ttopospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center. Millimeter-Wave

Research. Mictowave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna Research. Navigation Systems. Space Telecommunications.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics. Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.
NBS