Experiments on a specimen with large domains

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Submitted on 1 Jan 1951

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Experiments on a specimen with large domains

K.H. Stewart

To cite this version:

EXPERIMENTS ON A SPECIMEN WITH LARGE

DOMAINS

By

K. H. STEWART.

Sommaire. 2014 Un monocristal de ferro-silicium était

façonné de manière à faciliter la formation de _grands domaines. Son cycle d’hystérèse était _composé, en _{grande partie,} d’un seul saut de Barkhausen

qu’on a étudié en détail et discuté en termes de mouvements des parois des domaines.

LE _JOURNAL DE PHYSIQUE ET LE RADIUM. TOME 12, MARS

_1951,

PAGE 32ö.

1. Introduction. - Most

ferromagnetic

specimens

contain a _very

_large

number of domains

_arranged

in a

_complicated

three-dimensional

_pattern.

It

is difficult to find

_simple

laws

_connecting

the

magnetic

behaviour of such

_specimens

with the

behaviour of the idealized isolated domains which

we can treat

theoretically.

There is therefore

special

interest in

_experiments

with

_specimens

whose domain structure is

_simple.

There are two

known _ways of

_{obtaining really simple}

structures

Fig. I.

The first is the one discovered about 20 _{years ago} and used

_by

Preisach

_[1],

Sixtus and Tonks

_[2]

and

_others;

this is the method where a wire of a

material with

_{positive magnetostriction}

is

_placed

under tension so that the wire is

_{always magnetized}

along

its

_length

either

_positively

or

_negatively

and the

_change

from one state to the other takes

place by

the _passage

_along

the wire of a

_{single 180°}

domain wall.

_{By studying}

the movement of this wall a

_good

deal of information has been obtained about the

_properties

of the wall and the factors

controlling

its movement.

The second

_simple

_type

of domain structure

was found

_{recently by}

Williams and

_{Shockley [3]}

(1949)’

They

used a

_{single crystal}

of silicon-ron

that was

_carefully

cut into a

_rectangular

block

with a

_rectangular

hole

_through

the _centre, all the

faces

_{being parallel}

to

_{(100) planes}

of the

_crystal.

It was found that the

_specimen

was

_normally

divided into

_only

8

domains,

shown in

_plan

in

_figure

r,

each domain

_{extending right through}

the

_crystal.

Changes

in

_{magnetization}

occurred

_by

the movement

of the central 180° wall

_dividing

the domains

for-,

ming

a clockwise

magnetic

circuit from those

forming

an anticlockwise one. An exact

corres-pondance

was found between the movement of

this

wall,

made visible

_by

the Bitter

_pattern

tech-nique,

and the

_changes

in flux measured

_{electrically.}

It is this second

_experimental

_arrangement

for

_obtaining

_simple

domain structures that was

used in the work to be described.

2.

_Preparation

of the

_{specimen. -}

_The

spe-cimen was a

_{single crystal}

of 3 _per 100 silicon-iron of external dimensions about I cm X

_0.75

cm X

o.!~

cm

pierced

by

a hole o.5 cm X o.2 ~ cm. The faces were all

_carefully

worked until

_they

were within one

_degree

of

_{(100) planes.}

In the

_early

_stages

the

_optical

reflections from etch

_pits

were used as a

_guide

to the orientation. A more exact test for the final

_stages

was

_{provided by}

the Bitter

figures

formed when colloidal

_magnetite

was

_applied

to the

surfaces;

if the orientation was not

_perfect,

" _{fir tree "}

patterns

were formed as described

_by

Williams,

Bozorth and

_Shockley

_[4]

and their direction indicated the way in which the

crystal

had to be worked in order to correct the orientation. In most of this work Bitter

_patterns

were obtained after

_preparing

the _{surfaces in the usual way}

_bey

electrolytic polishing,

but an alternative

_method,

which may have useful

_applications

in other

work,

was also

_developed.

In this method the surfaces

were

_prepared

_by

mechanical

_polishing

and the

consequent

strains,

which

_normally

_prevent

obser-vation of

_satisfactory

_patterns,

were removed

_by

annealing

the

_specimen.

Most

_annealing

methods

326

produce

a film of tarnish on the

_polished

surface,

but

_{by annealing}

in a _very

_high

vacuum,

provided

by

a _{diffusion pump, this}

_difficulty

was avoided

and

_{well-polished,}

strain-free surfaces were

pro-duced. The

_patterns

obtained

_by

this method

were as

_sharp

and clear as those obtained after

electrolytic polishing.

After

_working

all the faces to the desired

orien-tation,

coils were wound on the

_specimen

to measure

its

_magnetic

_properties.

The field was

_provided

by

means of an 18 turn coil wound

uniformly

round

the

_specimen

and flux

_changes

were measured

_by

a r o turn coil on one

limb,

connected to a ballistic

galvanometer.

w

3. ~

_Experimental

_study

of the

_{hysteresis loop}

of the

_{specimen. -}

The

_{hysteresis loop}

measured

in _{the way}

_just

described is shown in

_figure

2. The

Fig. 2. - 1-H, Curve of the specimen.

most

_striking

feature is the

_{large instability}

in fields

of about o.o5 Oe. This can be

_regarded

as a

_single

Barkhausen

_{jump corresponding}

to reversal of the

magnetization

in about half the total volume of

the

_crystal.

_{We may} assume, for purposes of

discussion,

that the

_instability

in the

_{magnetization}

curve

_corresponds

to the _{passage of} a domain wall

such as that shown in

_{figure I}

from one

_position

of stable

_equilibrium

to

another,

so that a

_study

of the 11

jump

"

will

_give

information about the factors

_controlling

wall movement.

_{Unfortunately}

the Bitter

_patterns

obtained on the

_specimen

in

various states of

_{magnetization}

did not _{reveal any}

definite domain _structure; all that could be seen was a number of isolated 11 _{fir trees} "

on

_parts

of

the surface where the orientation was not

_quite

perfect.

It is therefore not

_possible

to _say

_eactly

what

_{rearrangement}

of domains

_corresponded

to the

_large

Barkhausen

_jump

of

_figure

2,

though

the

size of the

_jump

_{makes it clear that very}

_large

domains,

with volumes of the order of

_1/10

cc. were

involved. It is

_possible

that,

since this

_specimen

was much thicker than that used

_by

Williams and

Shockley,

the main domain

_boundary

was in a

plane parallel

to the surface shown in

_figure

I

rather than

_{perpendicular}

to this surface as in

Williams and

_Shockley’s

_experiments.

The

_change

in

_{magnetization}

between A and B in

_figure

2 was found to take

_place

_{quite slowly.}

It

_could,

in

_fact,

be arrested after it had started

by switching

off the

_magnetic

field. If the field

was then increased

_again

the

_jump

would re-start at a lower field than the

_{original starting}

field,

so

that the true

_{magnetization}

curve is

re-entrant,

as shown

_by

the full line in

_figure

2. ~ The re-entrant

curve could

_{plotted roughly by}

manual control of the

_field,

as

_just

_described,

but a better idea of

the form of the curve could be obtained

by

_using

an automatic control

_apparatus

shown in

figure

3.

Fig. 3. - Circuit of field control device.

H1, main field _{coil; H2, auxiliary} field coil; B, flux coil; G, galvanometer; L, lamp; P, photocell; A, d. c. _amplifier.

A flux

_measuring

coil on one limb of the

_crystal

was connected to a

_sensitive,

short

_period

galva-nometer.

_Light

reflected from the

_galvanometer

mirror fell on a

_photocell

which controlled the current

flowing

in a

_auxiliary

field

_winding

on the

_specimen.

The whole

_arrangement

behaved

_{practically linearly}

so that the field

_{provided by}

the

_auxiliary

coil was

proportional

to the

_galvanometer

deflection and hence

to the rate of

_change

of

_{magnetization}

in the

_crystal.

327

such a direction as to _{oppose the}

_change.

Thus,

if the main field was

_adjusted

to

_bring

the

_crystal

to

_point

A

_figure

2 and cause the

_jump

to _start, the

_{galavanometer}

deflected,

and

_{by altering}

the

auxiliary

field,

changed

the total field in the

directions

required

to slow down or

_stop

the

_{jump. Large}

amplification

was used so that a small rate of

_change

of

_{magnetization produced}

a

_large

_change

in the

auxiliary

field and the latter was thus

_always

_kpet

very near to the value

_required

for

_equilibrium

of

the domain wall. In this _{way it} was

_possible

to

follow the " true "

_{magnetization}

curve shown

by

the full line in

_figure

2. With the field control device in

_operation

the wall movement was _very

slow,

the whole unstable

_change

from A to B in

figure

2

taking

about 5 min.

The value of the field at _{any instant could be}

obtained from the currents

_flowing

in the main and

_auxiliary

coils and the

_{magnetization}

could be found

_{by applying}

a field

_{large enough}

to cause

saturation in one direction or the other and

_observing

the ballistic

_galvanometer

throw. A continuous record of the

_changes

in field and

_{magnetization}

was obtained

_by

_recording

_{photographically}

the deflection of the

_galvanometer

of the

_{field-controlling}

device. This deflection was

_proportional

to the

auxiliary

field and also

_{approximately proportional}

to the rate of

_change

of

_{magnetization.}

The area

between a trace of

_galvanometer

deflection and the time axis thus measured the total

_change

in magne-tization while the

_height

of the trace measured the field. Three

_typical

traces are shown in

_figure

_4.

Fig. 4.

They

were all taken under the same conditions but it will be seen that

_they

are not

_identical,

although

their main features are the same.

4.

_{Interpretation}

of the

_hysteresis

_loop.

-The

_irregular

traces shown in

_{figure 4}

and the

com-plete

hysteresis

loop

of

_figure

2, which can be

derived from

them,

provide

a

_good

illustration of the processes of

hysteresis,

which in normal materials

are on too small a scale to be accessible _to

expe-riment.

_According

to the

_accepted

account of

hysteresis

the movement of domain walls is

_opposed

by

« obstacles » which can _{be caused in various ways}

I

by irregularities

of stress or structure in the material.

,

The _{energy of the material} can thus be

_represented,

as a function of the

_position

of the

wall,

by

an

irre-gular

curve such as that shown in

_figure

5. If

Fig. 5.

an

_{increasing magnetic}

field is

_applied,

the wall will move from its

_{original equilibrium position}

at o

_along

the dotted

_path

shown in the

_figure,

the horizontal

_portions

of the

_path

_representing

irreversible movement from one obstacle to the

next. Reversal of the field

will,

of course, take

the wall back

_along

a different

_path

as shown in

figure

5. In most materials the scale of the obs-tacles is so small that a

_practically

smooth

_hysteresis

curve is obtained but in the

_{single crystal specimen,}

with its

_large

domains,

the scale is so much

_enlarged

that we can observe the

_irregular

motion of the walls in some detail.

It is not

_suggested

that the traces in

_{figure 4}

show the full detail of the obstacles the wall has

to overcome. The limitations of the

_apparatus,

particularly

the inertia of the

_{galvanometer,}

would

prevent

any

irregularities

of small

_wavelength

from

_being

observed. The

_irregular

traces shown

are, in

fact,

_only

smoothed versions of the still more

complicated

curves that would be obtained in an

ideal

_experiment.

The fact that the traces obtained

are not

_{quite reproducible,}

after

_taking

moderate

precautions

to ensure

_constancy

of

conditions,

suggests,

however,

that the smaller obstacles are

variable,

_presumably

because

_they

are _very

sensi-tive to local stress or

_temperature

_{fluctuations,}

and hence that an

_experiment

with

_higher

«

_resolving

power » would

give

further information

only

in statistical form.

The _energy lost in a

_{hysteresis cycle}

_is,

_according

to the scheme of

_figure

5,

the energy

supplied by

the field

_during

the various irreversible movements

of the wall and is measured

_by

the area between

the full curve,

corresponding

to

_{equilibrium positions}

328

energy lost in the

jump

from obstacle A to obstacle B is shown

_{by shading}

in

_figure

5. For a

_complete

cycle

the _{energy lost}

_is,

of course,

represented

by

the area within the

_complete

_{hysteresis loop.}

If it

were

_possible

to

_adjust

the field

_{quickly enough}

to maintain the wall in

_equilibrium

at all

times,

i.e. to follow

_exactly

the full curve of

_figure

5,

the

area of the

_{hysteresis loop}

would shrink to zero

and _{the total energy}

_{supplied by}

the field in

perfor-ming

a

_cycle

would also be zero. In the

_experiments

with the

_{single crystal}

_{this process} was

_actually

carried out to a limited extent. The

_hysteresis

loss of the

_crystal

measured in _{the usual way} is

represented by

the area of the outer

_loop

of

_figure

_2,

but when the

_cycle

was

_performed

with the

field-control device in

_operation

the

_hysteresis

loss,

the energy transferred from field to

_specimen,

was reduced

_by

about 12 _per 100 because the

re-entrant curve of

_figure

2 was _{followed. We may}

suppose that if an

_apparatus

with a

_quicker

_response

had been

used,

a more

_deeply

indented curve would heve been followed and the

_hysteresis

loss still further reduced. It does

not,

however,

appear very

likely

from the curves

_already

obtained that

the area of the

_loop

could

_actually

be reduced to

zero

_by

_{this process.}

Two comments _{may be made} on this. In the

first

_place

the scheme shown in

_figure

5

_implies

that _{for every}

_position

of the wall there is

_only

one value of the

_magnetic

field that can

_give

equi-librium ;

this is true for most of the mechanisms which are

_supposed

to

_produce

obstacles to wall

movement so

_long

as mechanical

_hysteresis

effects in the obstacles are

_ignored.

_{If, however,}

these

are taken into account then the curve

_showing

equilibrium

positions

will not be a

_single

line as

in

_figure

5,

but will itself be a closed

_hysteresis

loop

whose area will

_represent

a minimum below which the

_{magnetic hysteresis}

loss canot be reduced no matter how

_carefully

the field is

_adjusted.

It

is

_possible

that the re-entrant curve of

_figure

2 is

an

_approximate

delineation of this minimum

_loop.

A second

_possibility

is that the obstacle

_chiefly

responsible

for the

_hysteresis

loss,

of the

_types

considered

_by

Becker, Kersten,

Néel and

others,

are on a _very much smaller scale that those revealed in

_figure

2. In this case

_figure

5 should be drawn

as a curve

_oscillating

in random manner with a

very short

wavelength

and the observed

_hysteresis

loop

would be the

_envelope

of this curve. It would then be true that if the

_{rapidly oscillating}

curve could be followed

_exactly,

the

_hysteresis

loss would become zero, but it would be

quite

beyond

the _{power of the}

_{present apparatus}

to

follow these small-scale oscillations. The

irregu-larities that were

_actually

observed

_might

then be

attributed to some other

_hysteresis

mechanism

capable

of

_producing

a few

_{relatively large-scale}

obstacles. One

_simple

_type

of obstacle that

_might

account for the main feature of the

_hysteresis

loop

in

_figure

2, the

bending

back below the rema-nence

_point,

is the

_difficulty

of

introducing

a 180°

wall at all. If an ideal

_crystal

of the form shown

in

_figure

I were first

_magnetized

to saturation in one

direction,

a _very

_high

coercive field would have to be

_applied

before a 180° wall

_running

round the

_crystal

_{could appear.} It is well

_known,

of course,

that the coercive field

_actually

needed in a real

crystal

is

_considerably

reduced because walls can

grow out from

_regions

where there are

_slight

defects

in the

_crystal.

Even so, a finite field would

cer-tainly

be needed for the introduction of a new wall

and in the

_{particular single crystal}

under conside-ration this _{field may well have the value of} about 0.02 Oe

required

to

explain

the «

hump

»

at A in

_figure

2.

5. The

_speed

of wall movement. 2013 The

inter-pretation

of

_hysteresis

effects in terms of obstacles

to wall movement leaves

_unexplained

the actual mechanism

_by

which the

_hysteresis

_{energy is}

dissi-pated

in the material. It is shown that as a wall

moves, energy is stored up in various

f orms

until

an unstable

position

is reached and the wall moves

forward to a new stable

_position

with the release of a

certain amount of _energy. The

_speed

with which the wall moves will be determined

_by

the mechanism which

_dissipates

this _energy. If no other mechanism were

available,

the wall would move _very

_quickly

and the _energy would be emitted as

_{electromagnetic}

radiation,

but in

_practice

other mechanisms are

present

which restrict the

_speed

of wall movement to much lower values and absorb the

_{greater part}

of the

_hysteresis

_{energy. We may}

_hope

to find

out the chief

_{energy-absorbing}

_{mechanism in any}

particular

case

_by

a

_study

of the

_speed

of wall

movement. Thus _{Sixtus and Tonks’ classic} expe-riments on the

_speed

of 180° walls in nickel-iron wires can be

_interpreted,

as Snoek has

shown,

as

_indicating

that the induced

_eddy

currents control the

_speed

and convert the _{energy into heat in}

thick wires but that in thin ones this effect is

less

_important

and some

_extra,

less well

_understood,

«

frictipnal

)) mechanism must be assumed to be

acting.

The

_velocity

of wall movement was measured in the

_{single crystal}

_{specimen by recording}

photo-graphically

the

_readings

of a

_{heavily damped}

galvanometer

connected to the flux coil on the

specimen.

Measurements were made at the

begin-ning

of the movement

_only,

and in these conditions the

_galvanometer

acted as an almost

_perfect

flux-meter. The wall

_velocity

was measured as a

func-tion of

_applied

field

_by

_taking

the

_crystal

to a

_point

just

short of A in

_figure

2, and then

suddenly

applying

a

_larger

field. A

_typical

fluxmeter record

is shown in

_figure

6. The initial rate of

_change

329 curve, as

_shown,

and the wall

_velocity

was deduced

from this on the

_assumption

that the flux

_change

was due to the movement of a

_single

domain wall

Fig. 6.

of the form shown in

_{figure I .}

The results obtained for various values of the

_applied

field ares

shown

in

_figure

_7. Within the limits of

_experimental

Flgn 7.

error there is a linear relation between

_velocity

and field which can be written

V= A(H-Ho)

where A and

_{Ho are}

constants with the values

6.3 cm : s : Oe and

_o.o4g

Oe

_{respectively.}

The lower line in

_{figure 7}

was obtained

_{by repeating}

the

_experiment

with the

_specimen

immersed in

liquid

oxygen

(goo K);

the value of A and

_Ho

were

then

_5.7

cm : s : Oe and o.o56 Oe.

The linear V - H relation

_implies

that the force

controlling

the

_speed

of wall movement is one

increasing linearly

with wall

_velocity.

The velo-cities in the

_{single crystal}

are much lower than

thos that must occur in normal

_{polycrystalline}

material. These latter velocities have not been observed

_directly

but it can be inferred from

_magnetic

viscosity experiments

that

_they

are at least several hundred centimetres a second. Of the various

mechanisms that have been

_suggested

as

_controlling

wall velocities the

_only

one that would be

_expected

to

_give

_{very different velocities in}

_{polycrystalline}

iron and in the

_present

_{single crystal specimen}

is the control

_{by eddy}

currents.

_Eddy

current effects

depend strongly

on dimensions and should be much

greater

for the

_large

domains of the

_{single crystal}

than for the small ones in

_{polycrystals.}

It is difficult to calculate the exact effects of

_eddy

currents on the movement of 180~ a wall of the form shown in

_figure

I, but an order of

_magnitude

estimate can be made

_by

assuming

the wall to mave as a

_{rigid plane}

and

ignoring edge

effects. We

then have the situation shown in

_figure

8,

the wall

Fig. 8.

and the

_{crystal being supposed}

to extend

indefi-nitely

in a vertical direction. Movement of the wall will induce

_eddy

currents as indicated

_by

the

arrows and if we _{suppose that the}

_speed

of the wall is determined

_by

the condition that the field of these

_eddy

currents should be

_equal

and

_opposite

to the

_applied

field,

we obtain V = AH with .A

_{where p}

is the

_resistivity

of the

material,

Is

its saturation

_{magnetization}

and a the thickness of the

_specimen

_{perpendicular}

to the wall. The

appropriate

values for the

_single

_{crystal specimen}

are p = 5o _{x 10-6} Q _cm,

I5 =

160

gauss, a =

_o.2Q

cm so that we obtain A = 1.6 cm : s : Oe.

_Although

this is of the same order as the

_experimental

value A = 6.3 _{cm : s:}

Oe,

it is several times smaller.

The difference can

_probably

be attributed to the crude

_picture

of the motion of the wall used in the

calculation. In

_practice

the

_eddy

current field will be much less than the calculated value near

the

_edges

of the

_specimen

and the wall will thus

advance more

_rapidly

near the

_edges

and so

_give

a

greater

mean

_speed.

The

_temperature

_dependence

of

_{velocity provides}

further

_support

for the idea that the

_velocity

is

330

effects

_depending

on mechanical relaxation of strains. The latter would be

_strongly

_{temperature-dependent}

whereas

_eddy

current effects

_depend

_chiefly

on the

resistivity,

which,

in

_{silicon-iron,}

does not _very

greatly

with

_temperature.

The measured decrease in

_resistivity

of a

_{strip sample}

of the same material

on

_cooling

from room

_temperature

to

_go~

K was

18 per oo, while the observed decrease in the

velocity

constant A for the

_{single crystal specimen}

was 1 o _per 100. In view of the rather

_large

experi-mental errors in

_velocity

_measurement,

these values

are in fair

_agreement

with each other.

6.

_Energy

losses in

_alternating

fields.

--We may conclude from the evidence of the

previous

section that the

_speed

of the main wall movement

in the

_{single crystal specimen}

was controlled

_by

the induced

_eddy

currents and hence deduce that

these currents were the means of

_converting

into

heat an

_appreciable

fraction of the whole

_hysteresis

loss of the

_{specimen-certainly}

the _fraction repre-sented

_by

the « unstable » area between the full

and dotted curves of

_figure

2 and

probably

also

a considerable additional area

_{corresponding}

to

instabilities too small to be revealed

_by

the

_present

experimental technique.

If it is

_accepted

that at

least a

_part

of the

_hysteresis

_{energy of} a material is

_disposed

of

_{by eddy}

currents induced

_by

domain wall movement, it is

_interesting

to

_enquire

how the energy losses observed in

alternating

fields are to be

_interpreted.

It is usual to divide these losses into three

_independent

_components,

_hysteresis

loss,

eddy

current loss and

_viscosity

loss,

but if

_hysteresis

loss is to be attributed

_partly

to

_eddy

currents and if the

_viscosity

effect is also

_supposed

to be due

to

_eddy

current control of wall _movement, it is no

longer

obvious that there are three

_separate

compo-nents of loss which can be added

_together.

A

_{satisfactory interpretation}

is, however,

still

possible

in a material

_containing

_many domains. When such a material is taken round its

_hysteresis

loop slowly

we _{may suppose that each domain wall}

passes

through

its unstable

region

at a different

instant. As it does so, it will set _up, over a limited

region

of space and

time,

a

_system

of

_eddy

currents

which

_dissipates

the

_hysteresis

_energy of the indi-vidual domain. The total energy so

_dissipated

may be written

where

wH

is the

_hysteresis

loss of the

_{material, p}

its

resistivity,

In

the

_eddy

current induced

_by

the nth

domain in the volume d V at time t.

If the

_cycle

is

_performed

more

_quickly

there are

two differences. In the first

_place

if the

_applied

field

changes appreciably

during

the movement

of any domain

wall,

the

_speed

of that wall will be

affected and

_consequently

the

_eddy

currents it induces will

_change.

Each of the

terms,

I;, J2 "

...,

I ~

may therfore be

changed by performing

the

hysteresis

cycle

more

_rapidly

and the

_consequent

increase in

WH

can be identified with the «

visco-sity

loss )). In most materials the movements of

walls are so

_quick

that this effect

_only

becomes

appreciable

at radio

_frequencies.

The second effect of

_{rapidly varying}

fields is to

reduce the interval between the wall movements

of

_separate

domains until actual

_overlapping

occurs

and the

_eddy

current at _any

_point

is the sum of contributions from more than one domain. Because

the energy converted into heat

depends

on the

square of the current

_density,

this

_overlapping

will

cause an increase in the total energy lost. We can

write.

where the domains I and

2, l~

and I,

are

_supposed

to _pass

_through

these unstable

_regions

_practically

simultaneously,

while other domains remain dis-tinct. The second _term,

We,

due to

_{« overlapping »}

of

_eddy

currents can be identified with the

_eddy

current loss calculated

_according

to

_ordinary

macros-copic electromagnetic theory,

as can be verified

_by

detailed calculation for

_particular

models.

It thus appears

justifiable,

in material with many

domains,

to treat

_{hysteresis, large}

scale

_eddy

currents

and

_viscosity

as

_producing

there distinct

_components

of loss which can be added to

_give

the total loss in

an

_alternating

_magnetic

_field,

_despite

the fact that

all three

_components

_may

_{fundamentally}

be due to

eddy

currents.

_(Other

causes of

_hysteresis

and

viscosity

may, of course, be

present

in addition

to the

_{eddy currents.).}

In material with small numbers of

domains, however,

such as the

_single

crystal

specimen

described

_above,

the distinction between the «

microscopic » eddy

currents

respon-sible for the

_hysteresis

_component

of loss and the

«

_{macroscopic »}

ones

_responsible

for the normal

eddy

current

_component

can no

_longer

be made and

_special

calculations would have to be made

to

_predict

the _energy loss in an

_alternating

field.

There are

_clearly

_{many ways in which the}

expe-riments that have been described could be

_improved

and extended.

_They

were not intended as much

more than a

_{preliminary investigation,}

made in a rather limited

time,

of the

_{possibilities}

of

experi-ments ou

_specimens

of this

_type.

At the end of the

_experiments

the

_crystal

was annealed

_again

in

an

_attempt

to

_improve

its

_propreties.

331

number of small

_crystals

within the main one and

the unusual

_properties

of the

_{original specimen}

were lost.

7.

_{Achnowledgements. -}

The author would like to thank Dr H. Lawton and Dr D.

_Shoenberg

for their advice and assistance and the British Elec-trical and Allied Industries Research

Association,

which

_sponsored

_{the programme of research.}

Remarque

de M.

_Shockley.

- Dr Stewart has

proposed

that if the

_magnetic

field were

_properly

adjusted

during

changes

in

_{magnetization,}

the

magnetization

process

might

become

_entirely

rever-sible.

_Although

such a situation

_might

_prevail

if the field were

_{ajusted locally}

within the

_specimen.

For the

_specimens

of the

_type

measured at

Cam-bridge

and at Bell

_Telephone

Laboratories there will

_certainly

be irreversible _energy losses due to

the fracture of the Néel

_spikes.

The studies made

by

Williams are believed to

_represent

_very

_closely

the

_limiting

behaviour that would be obtained for

vanishing

small rates of

_change,

and these studies show two _{forms of energy losses :} one

_having

a

memory and associated with the Néel

spikes

and the other

_behaving

like a

_dynamic

friction.

Dr Stewart has also discussed the

_relationship

between domain behaviour and

_eddy

current losses. It may be worthwile to

_point

out a conclusion reached

_by

Dr Kittel and the

_speaker

based on a

consideration of the

_{collapsing cylinder}

model :

If the domain wall is

_just

inside the surface of the

specimen,

then the

_eddy

current losses are

negli-gible

for a

_given

value of on the other hand if

dt

the radius of the

_{collapsing cylinder}

is made

arbi-trarly

small,

the energy loss increases without limit for a

_given

value of

f .

Dr Kittel has

_recently

dt

carried out an

_{analysis covering}

more realistic cases which he uses in

_discussing

anomalous

_eddy

current losses and related

_problems.

Remarque

de M. Snoek. - I should like to

point

out that the mechanism

_by

which _energy is

trans-mitted from one

_spin

to another in the course of a

rotation process

involving

a

_displacement

of a

Bloch

_boundary

has not

_yet

been discussed

theore-tically.

It

_obviously

has a

_bearing

too on the

phenomenon

of

_{ferromagnetic}

resonance and the

damping

observed therein.

The

_experiments

_by

Stewart on

_boundary

dis- .

placements

in a

_{single crystal}

should be discussed in connection with the

_experiments

_by

_Dijkstra

et Sncek on

_boundary

shift in

_elastically

strained wires of nickel iron.

Remarque

de M. Roberts. - If there is

magneto-striction,

then there will be another mechanism

enabling

the direct

_dissipation

of

_magnetic

_energy of the

_spins

in the domain wall in the form of thermal lattice vibration i.e. without the intervention of

eddy

currents.

REFERENCES.

[1] PREISACH F. - Physik. Z., 1932, 33

905.

[2] SIXTUS K. and TONKS L. 2014 Phys. Rev., 1933, 43, 931.

[3] WILLIAMS H. J. and SHOCKLEY W. - _{Phys. Rev., 1949,}

75, 178.

[4] WILLIAMS H. J., BOZORTH R. M. and SHOCKLEY W. 2014