194 -------PHILlPS TEüHNICAL REVIEW ,VOL. 13, No. 7

,. FERROXDURE, A CLASS OF ~W PERMANENT MAGNET MATERIALS

by J',-J. WENT"'), G. W. RATHENAU, E. W. GORTER and G. ,W. van OOSTERHOUT.

621.318.12: 538.246.2

Present permanent magnet materials are ingeneral metallic alloys mostly containing nickelor cobalt or both. Eerroxdure, the class of new permanent magnet materials' developed in thePhilips Rèsearch Laboratories at Eindhoven consists of oxidic ceramics which :do notcontain any nickeÎ or cobalt. The interesting and typical properties of these materials and someapplications of Ferroxdure are treated in the three parts of this article., ,

Introduetion

I. MOST IMl'ORTANT PROPERTIES OF FERROXDURE

t'r

Ferromagnetic oxides have been the object ofextensive research' in the Philips Laboratorlesfor many years, The reader of this journal has' ,had ample opportunity to get informed about oneclass .of those materials known' by the name of:Ferroxcuhe. As was already often stated informer 'publications 1, 2) Ferroxcube materials arecharacterized by possessing a high electric resistivitytogether with a high magnetic permeability. Be-cause of the latter property Ferroxcube materialsbelong to the class ofthe magnetically soft materi-als: Ferroxcube is extremely well suited for use inhigh frequency inductances, high frequency trans-formers etc. 1) 2).

During the last two years another class of ferro-magnetic oxides has been studied extensively atthe Philips Research Laboratorles at Eindhoven.These oxides are magnetically har d, i.e':'they canbe used as materials for permanent magnets.

, The remarkable fact about these pxides is that theydo not contain any nickel or cobalt, in contradis-tinction to most other permanent'magn~t materials.This. fact is' of great economic importance as the'setwo metals are expensiye ,an:d at present difficultto obtain. The representatives of this class of newmaterials have heen given the name of Fer r 0 x-dure.

\

Cha~a~teristies of magnetically soft and hard materials

, While magnetically soft materials art) mainly characterized,by their perméability and by the' losses they introduce whenthey are placed ~ an altemating magnetic field ; quite different

~) Now with N.V. K.E.M.A., Arnhem (Netherlands).1) J. L. Snoek, Philips teehn. .Rev, 8, 353, 1946; J. L.

Sn 0 ek, New developments in ferromagnetic materials,Elsevier's Publishing Camp. Amsterdam, New-York 1947;J. J. Went and E. W. Garter, Philips techno Rev.13,1951 (No. 7.). The latter article is in the following quotedas A.', J

'2) W. Six, shortly to appear in Philips techno Rev. '

properties ar!l characteristic for magnetically har a materials.Therefore, before entering into details we wish to give a very'Short survey of the quantities which' are frequently used indealing with magnetically hard materials. This is most' con-veniently done with the aid of figure la 3). In this figure themagnetization J [4,:n;J] is given as a function of the effective fieldHi 4). As is well known, the magnetization of a ferromagneticmaterial is in generalnot uniquely determined by the effective'field. This means e.g, that if a ferromagnetic is magnetizedto its saturation magnetization, and subsequently the effectivefield is brought to zero in a continuous way, a certain magneti-zation remains, the remanent magnetization Jr. The effectivefield in the direction opposite to the remanent magnetizationthat must be applied in order to reduce the magnetization tozero is called the J-coercive field (often also the coerciveforce); it is indicated by 'the symbol JHc• In the particularcase shown in fig. la JHc is of the same order of magnitude asJr [4,:n;Jr]. A similar coercive field, the B-coercive field denotedby the symbol nHc, can be defined, which according to a com-pletely analogous definition is necessary to reduce the

3) For a more detailed discussion of most quantities see e.g.J. J. Wen t, Philips techno Rev. 10, 246, 1948.

4) The effective field is the difference between the externalfield H and. the demagnetizing field NJ/f.lo [N'J] whereN[N/] is the factor of demagnetization in the directionof the field. Unless explicitly stated differently, in thefollowing H will be used to denote the effective field.

Throughout this article formulae are given using therationalizeçl G i 0 r g i system of electromagnetic units (seealso Philips techn. Rev. 10, 79, 1948). For the convenienceof those readers who are not (yet) familiar with thissystem, formulae in unrationalized cgs units (G a us ssystem) are given between square brackets. In the figuresscales for both systems of units are given.It is to be remembered that in the G i 0 r g i system B

,and J are measured in volt sec/m2 or weber/m2 (1Wb/m2== 10000 gauss)' and H in ampère/m (1000/4:n; A/m =,= 79.6 A/m corresponding to 1 oersted). .In vacuum B = f.loH, in which f.lo :=:; 4.n/l07 henry/m.

Instead of H (in A/m) often the value of ItoH (in Wb/m2)is given (f.loH = 1 Wb/m2 corresponding to 10 000 oerstedin the cgs system). In a ferromagnetic material the rela-tion B = f.lH holds, in which f.l = p.rf.lo; f.lro the relativepermeability is a dimensionless number (equal to the num-ber indicated by f.l in the cgs system), '

The value of BH, which has the dimension of an energyper unit volume, is measured in (Vsec/m2) X (A/m) =VAsec/m3 = joule/m" (1 J/m3 corresponding to 126 gauss xoersted).

, ,/ • ,._."l

.JANU.4-RY 1952 FERROXDURE (PROPERTIES) 195

magnetic induction B;" p~H + I lB == H + 4.nI] to zero: Infig. lb a demagnetization curve 5) is given for a ferromagneticfor whichthe coerci~e .fiéld is such that POJHc [JHc] is ~uchsmaller than the remanent magnetization Ir [4.nJr]. It iss!!enthat in, contradistinction to fig',la, the difference betweenJH~ and BHc is very small. As will be pointed out in greaterdetail below, the figures la and- lb are valid for the cases ofFerroxdure and "Ticonal" G (a well-known permanent magnetinatérial of very high quality G» respectively.

Neither the remanent magnetization nor the' coercivefield are the most adequate quantities to describe the qualityof a permanent magnet material, It has been customary tocharacterize the usefulness of such a material by the 'maxi-mum value (BH)mnx which the product of .the magnetic in-duction B and the effective field H can attain on the demagne-

.'",. H--..!i..

2000 1000 0 fed -2000 -1000 ' 0 oersted,J+"B-i!m:,

,

~

U

U

-U

",,,-, ,I,,

aHe f-~.J'Z~ -

-2-105 -lal OBmQ3 -a2 -UI 0' cu

- - oers

0

6

,4111?~ ft-J I,

I V i(..,

"I BHe

JHcI

.(2 1..H..

-2·Kf A-I(f, m-Q2 -0.1 G ·UI

rÓ, , ~

.. J,Bt~

gauss

t4.7T-lB12000

10000

8000

U 6000

• 0,4 4000

2000

o o

-U -2000

Wbïiii

70016

Fig. 1. Demagnetization curves for Ferroxdure (a) and"Ticonal" G (b). In a; Ir [4nIr] and JHc are of the same orderof magnitude and thus a large difference between 'JHc andBHo exists. This is not the case in b. '

5), By the demagnetization curve we mean that part bf thecomplete magnetization curve which is lying in the upperquadrant on the left. "

G) See e.g, B. JonRs ,and H. .J. Meerkamp vanEm b den, Philips techno Rev. 6, 8, 1941.

..

tization curve. TlJ.~materialwith the greatestvalue of (BH)mnxwill be able to create a given field in an air gap of a given mag-netic circuit at the cost of the smallest volume of-magneticmaterial 7). It will be clear that both a 'large remanent magne-tization and a large coercive field àre favourable for obtaininga large value of (BH)mnx. • •

Survey of the mos~ important properties 'of Ferro~-dure '

The name Ferroxdure denotes a ~lass of sintered,oxidic, magnetically hard materials. In this article tb ediscussion ,ViII be limited to three of these materials.

I'

~

t-lB~

. .T1voof these are oxides with compositions BaFe12019

and BaFe1S027 respectively. The third material.' 'is that which at 'the moment is available on the

market under the name of Fei-roxdure, and fromnow on when speaking' simply of Ferroxdure wemean this material. It consists mainly of th~ oxideBaFe~~IOI9' . This oxide has a non-cubic, viz.hexagonal, crystal structure and has one' axis ofeasy magnetization parallel to the hexagonalaxis (i.e. the crystal anisotropy is uniaxial).The uniaxial cha~acter is essential for a large

coercive force in Ferroxdure, just as it was essentialfor the F'e'r r o x c u h e matédals to he composed ofcub i c ferrites for obtaining a low coercive force(high permeability)., 'The saturation magnetization of Ferroxdure ' is

rather low compared e.g. with that of "Ticonal" G:the values at -room t.emperature are about0,4.2 Wh1m2 :[420.0 gauss] and 1.41 WbJm2 [14.10'0gauss] 'respectively.. In a Imagnetically hard material consisting of'_crystals with one axis of preferred magnetizationoriented at random like Ferroxdure, the remanentmagnetization can in general, be shown to behalf of the saturation magnetization (cf. e.g. thearticle quoted in footnote 3)). Thus the valueof the remanent induction of Ferroxdure at roomtemperature is rather, low, compared with thatof ~'Ticonal" G, namely 0.20-0.21 WhJm2 [2000-2100 gauss] ,and 1.34 WbJm2 [13400 gauss],respectively, The cöercive .force JHc, however,is 'extremely high, namely f.loJHc = 0.2"0.32·WbJm2 [JHc'. 2000-3200 Oe], as compared withf.loIHc= 0.06 WbJm2 [IHc='600 Oe] for "Ticonal"G:

In fig. la and lb the demagnetization cll!ves forthese two materi~ls are given. The high coerciveforce of Ferroxdure combined with the ratherlow, remanent induction causes the large differencewhich is found between .JHc and BHc: The value

o

8

6

4

o

7) See e.g. A. Th. van U r k, Philips techn.: Rev. 5, 29,1940. As will he pointed out later, this statement is notso strictly true as is suggested hete, '

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196 PHILIPS TECHNICAL REVIEW VOL. 13, No. 7

Fig. 3. Rod-shapedFerroxduremagnets whichhavebeen magnetizednormal to a verticalface in sucha waythat on this facealternately north and south polesare formed.The tenpoleson the specimenat the left and the fivepoleson the specimenin the centre aremadevisibleby ironpowder.Due to the lowvalue of the permeability and the high value of thecoercive force Ferroxdure is speciallysuited for producing strong alternating polesat asmall distance from each other without the necessityof using a large extension of thespecimenparallel to the direction of the magnetization.

of (BH)max for Ferroxdure, of about 6800 J1m3

[0.85 X 106 gauss oersted] is about 6 times lowerthan the (BH)max value for Ticonal G, which isup to 45800 J/m3 [5.7xl06 gauss Oe]. This doesnot mean, however, as will be pointed out below,that the volume of magnetic material needed tocreate a certain field strength in an air gap ofgiven volume is 6 times as large as that neededwhen using "Ticon al" G. Notwithstanding the lar gervolume of Ferroxdure needed, this material oftenwill offer an economic advantage because it doesnot contain critical raw materials. Besides theeconomic advantage of Ferroxdure this materialoffers new technical possibilities. lts veryhigh electric resistivity allows it to be used inhigh frequency applications as e.g. in Ferroxcubecore transformers that need premagnetization, asdefl,ection magnets for radar tubes or for theadjustment ofthe 'ternpera'ture coefficient of the per-meability of a Ferroxcube core (cf. 2)). lts extremelyhigh coercive force and the resultant strong resis-tancc to demagnetization allow a novel approachto the design of magnetic circuits, which will bediscussed in a subsequent paper to be publishedin this journal. Besides the above applications thefollowing ones should he mentioned specifically:Loudspeaker circuits (see fig. 2),Magnets for fixing one object to another,Magnets for oil filters,

Fig. 2. Two Ferroxdure magnets as used in loudspeakercircuits magnetized in the direction of the axis. Note thedisc-shapedform of the magnets which is most suitable fora material with high coercive force and relatively lowremanence.The upper magnet is lifted by the field of thelower one. The external diameter of the rings is 8 cm.

Magnets for focussing electron beams,Electric generators and motors (see also fig. 3),Magneto-mechanic couplings.

The physical background of the various pro-perties of Ferroxdure will he discussed in greater

Ev

.. .": -." -r.

JANUARY 1952 FERROXDURE' (PROPERTIES) 197

detail in part II of this article. In ordernot to,' complicate the treatment more thannecessary we, shall discuss the physical proper-ties' of the 'main component of Férroxdure onlyand' of th~ other oxide already mentioned above,with composition BaFe~IFe~iI027' the crystalstructure and physical properties of which are verysimilar to those of BaFe12019. By, considering also,this second oxide various measurements and theore-tical conclusions obtain additional confirmatien.

In the first section of part 11 the ill a gnet ica nis 0 t rop y will be treated and it will' be shownthat the, most important part is the (magnetic)crystal anisotropy, which is extremely high. This

I

large anisotropy in combination with the relativelysmall remanent magnetization' accounts for thevery high coercive force of Ferroxdure whichwill he discussed next. At the end of part 11 thefollowing points will be discussed consecutively: theremanent induction, the demagnetizationcurve and the value of '(BH)max, and ûnally rtheelectric resistivity. ,In part III of this article the crystal structure

of the two oxides BaFe12019 and BaFelS027 willbe discussed in greater detail. It will he' seen thata close relation exists between the crystal structureand the value of the saturation magnetiza'tion ofthese two oxides.

11. PHYSICAL,BACKGROUND OF SOME PROPERTIES OF FERROXDURE, ..

Magnetic anisotropy

It was already mentioned in the introduetionthat the magnetic anisotropy, i.e. the existenceof directions of easy or preferred magnetization,is of the greatest importance for the vàlue of thecoercive field. Three different factors 'contributetowards facilitating magnetization in certain pre-ferential directions: the (magnetic) crystal ani-sotropy, the stress ani sotr opy and the shapeanisotropy. As will be shown in greater detailbelow, in the oxides treated in this paper thecrystal a'nisot r op y is large and can easily bemeasured, As regards, the stress a rri sot r op y: inA (cf. I, footnote 1)) it was shown that within a smallregion of the material it is proportional to theproduct of the linear magnetostriction constant inthe, direction of stress and the internalor external

, ,

stress. In a sintered aggregate of non-cubiccrystals large internal stresses may be expecteddue to an anisotropic coefficient of thermal expan-sion. The magnetostriction constant of Ferroxdureis not zero. ~ince, however, we have reason to believethat it will ,not greatly exceed 10-5, and ~ince itis very difficult~to make a quantitative 'estimate of'the contribution of the stress anisotropy (which infact might be appreciable) to the total anisotropy,we will tentatively leave out the stress anisotropyfrom our further discussion: it will bé seen belowthat, indeed, all relevant phenomena can be ex-plained satisfactorily by taking into account the.magnetic crystal anisotropy only.The shape anisotropy can easily be shown to be

small compared with the crystal anisotropy becauseof the low value of the saturaLon magnetization.

L

The crystal anisotropy

For both hexagonal oxides mentioned above, thecrystal anisotropy was measured .on single crystals.Itwas found in both cases that the hexagonal axisis the direction of easy magnetization. The so-calledmagnetocrystalline energy density, which describes.the tendency for a preferential orientation, can bewritten as

Ec = Klsin2 8+ K2sin4 e +... (1)

Ec is the energy (per m3 [cm3]) necessary to turn themagnetization from' the easy direction (8 -:- 0)over an angle 8. The quantities Kl' K2 are constants,'the so-called anisotropy cons t an t s. For ourpurposes it is sufficient to take into account thefirst term of the series only, so that we, have oneanisotropy constant Kl' for which we shall writeK. Thus formula (1) rea dl':

Ec = K sin2 e . (2)

The measurements of the anisotrópy constantsfor ,the, two oxides, were .performed as follows..In the case. of, BaFelS027 single crystals 'were

obtained from the melt, by' H. op. J. Wij nandY. Have n of this laboratory, that were large enough

, \to allow the measurement of the 'magnetization cur-';es in the direction of the hexagonal axis and along .

. different directions perpendicular to, it 1)::. Thehexagonal axis appeared to be the only direction ofpreferred magnetization, as no anisotropy within thebasal plane could be detected ~t room temperature.

1) G.W. Ra thena u and J. L. .Sn oek, Philips Res. Rep.1, 239, 1945-'46.

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198 PHILIPS TECHNICAL REVIEW VOL. 13, No. 7

'-.'

The' :field strengths used were not large enough ~osaturate the crystal along the difficult direction. Thecrystal anisotropy was calculated by extrapolatingthe magnetization in the difficult direction to higher:field strengths and measuring- 'the area betweenthe .magnetization curves in. the easy and difficultdirections, this area being the work necessary toturn ;the saturation magnetization from the easyto the difficult direction of magnetization.

For BaFe12019 no single crystals were availablewith dimensions-Iarge enough to allow the.measure-ment of the magnetization curves to be performedin exactly the same way. The following procedurewas employed. As the basal plane is well developedfor these oxides, small crystals obtained frompolycrystalline material could easily be fixed on aglass plate in such a way that the hexagonalaxes were perpendicular to'the plate, as was con-firmed by X-ray diffraction. From _the results ofthe measurements performed on these specimens(fig. I) the anisotropy constant couldbe calculated 2).Infi,g.2 the values of J( for the two oxides are plot-ted against temperature. In table I the values 'ofJ( at room temperature for BaFe12019 are comparedwith those for some well-known ferromagnetics.

-Ho 2000 4000 6000 8000 /0000 /2000 oersted'!!:

-

-5

II. .-Ij'

~/'

".Y'".s>-

, -H/05 2,/05 J./65 4,/05 ,/05 6'111. 7'/05 IN05 9-/05 ~

0

cgsmg/cm3

10·/0

erf7,5,/0 60

so: 40

2,5,/0 20

oo ll2 q4 us as ~O l2~

-faH 70003

Fig. 1. Magnetic moment per unit' mass a as a function ofa magnetizing fieldH at room temperature for a single crystalof BaFe1201D.Curve indicated by 11: H is parallel to the easyaxis. Curve indi~ated by .1: H is perpendicular to the .ensyaxis.

"

Table J. The value of 1( Îlt room temperature for differentmaterials 3).

, Material K1/m3 [erg/cm'']

3 X 105O,lSX 10&4 X 105

[3 X 106][0.15 X 10°][4, xlOO]

.'

2) It was assumed that the anisotropy within the basal planemay be neglected as in BaFe1s027'which seems a reasonableassumption, considering the very close resemblance ofthe crystal structures and the experience with other hexa-gonal crystals; such as cobalt.

w.;ecfijT

<,--~ t:'!..~ ~:Fef027

'BT~8a~I~OI9~,

'\I

~

ergëiii:J

o-200 -/00 400 50~

70012o /00 200 300

Fig. 2. Anisotropy constant K as 'a function of temperature.

/

Another method of measurement is to allow a crystal toperform torsional oscillations in a strong magnetic field insuch, a way that the axis of preferred orientation oscillatesin a plane containing the direction: of the magnetic field. Byvarying the field and extrapolating to fieldsof infinite strengththe anisotropy constant K as well as the saturation magneti-zation can be calculated from the period of the oscillations.The results are in approximate agreement with those givenin fig. 24).

Coercive force

There are many factors which determine in acomplicated way the coercive force in the generalcase of a massive ferromagnetic. As Ferroxdureis a sintered material consisting of more or lesssmall crystals with an extremely high crystal aniso-tropy, which have random orientation, a somewhatsimpler situation may be expected 5). In order tosimplify the argument we shall start with' rathercrude assumptions ab'out the demagnetizationprocess and estimate on this basis the coerciveforce. After comparison with experiment we shallcorrect our model so as to obtain better agreementwith reality . It will be seen that the value of the'coercive force obtained with the aid of the firstassumptions gives a limit above whi~h the coercive, force can in no way be raised.

Consider a ferromagnetic single crystal saturated.in its easy direction. We now assume 'that changesin magnetization occur only by rotation of themagnetization from the easy direction, and askhow strong a field in the direction opposite to the

3) For iron, which has cubic magnetic anisotropy, equations(1) and (2) cannot be applied. The quantity K given foriron in table I refers to the difference in magnetic energyin the [100] and [UI] directions respectively.

.1) These measurements were carried out by 1. Sm i t of thislaboratory. .

&) It should be noted that a sample of the materiál as awhole is iso t rop i c ,and that only the small crystals ofwhich the sample is '~omposed are anisotropic.

i~~~~~'-' --~----~--~~~--~~~~--L

;

JANUARY 1952 '

, .FERROXDURE (PHYSICAL BACKGROUND) 199

magnetization must be to turn the magnetizationover an angle of 1800• if the magnetization is turned,over an angle e 'from the easy direction, the total_ energy density is; ,

Et = K'sin2e --:-HJs cos 19 .

, Th~" equilibrium angle 19e for a' given field 1-I is, fóund by making Et minimum with respect to 19:

(JEtiae = 0;2K sin e cos 19+ HJs sin 19= 0,

This equation has two solutions. Only thc first one,being sin ee = 0, corresponds to a stable equili-brium. The other one,

cos ee = -HJs/2K,

describes an unstable equilibrium. From this equationit can be seen that the absolute value of the fieldstrength necessary to turn the magnetization fromthe first stable position 19e=0 over a very small angle..e (so that cos e Rj 1) is 2K/Js' The field strengthdecreases with increasing angle of deviation.

, Thus on applying a field 2K;:J5 the 'magnetizationjumps. discontiuously in the direction of the field.The field strength H = 2K/Js is called the "turn-over" field strength.'In order to find the relation between this turn-over

field strength and the coercive force of an actualsample of BaFe12019,to which oxide we shall limitour discussion, the fact should be taken into accountthat such a sample is composed of many particles,the easy axes of which are oriented at random.It can be shown that in this case the coercive

force should lie at about K/Js' In jig. 3 the

wsecán3:-;==+==l::O:::==!:=~~-I-T--' erg/cm3WIVn\4 I 0 -i'--!. cgsm12,10 0 ~ 15000

2K t I(HOS t 2KJs '\ J,

8,105 10000, 1\6.1051--+----1,---, +--f-_:_-t--+\r- ,-IMOI'I---+---!---!----;I---+--_,.-\>- 5000

2-/05'1---+--11---1---1--_+---,-+--1-1'

_0200L-- __JIOO'---_JO--..1IOO--200l__--300l__---lhoo'----..___~OC

70007

Fig. 3. The quantity 2[(/J. forBaFel~ÓlDas a function oftemperaturê.

quantity 2K/Js is plotted against temperature forEaFe12Öl9' It is seen that up to a temperatureof 250 oe the coercive force estimated on' theassumption that only rotational processes occurIies near ftoH. = 0.75 Wb/m2 [H = 7500 Oe]. Theexperimental value of the coercive force, though

vëry high, is appreciably below this value, so thatour model must be modified as being 'too simple.The reason for the failure of our calculation

is that we did not take into account the, formationand the movement of Bloch 'walls: The stability' :of a Blo ch wall 'within a ferromagnetic particle'with one direction of preferential magnetization'depends on several factors 6). Let us assume that.the particle has heen magnetized to saturation:Its poles will crea_:!:ea demagnetising field. By theformation of a wall the demagnetization energy cánbe diminished by an amount that is the productof a demagnetization factor, which depends on theshape of 'the particle, the square of the intensity ofmagnetization and the volume of the particle, Ifalso an external field is applied in the' direction.opposite to the direction of previous magnctizationthe formation of the w,all 'vip. reduce the energyfurther by an amount which is proportional to theintensity of magnetizati on, to the field strength'and. to the volume of the particle. The energywhich has to be furnished in order to create the wallis dètermined by the "effective exchange", energy(Js2/Jo2)kTc; (where Tc is the Curie temperature)k is Bolt zm ann 's constant and Jo the saturationmagnetization at ze~o absolute teinperature), whichtends to keep the magnetic moments alignedparallel within the wall 7) and by the energy or'crystalline anisotropy which tends to keep themagnetic moments within tÎle wall away from thedirections of diffi~ult "magnetization. Further~oreit is proportional to the area of the wall.

In order to show that in isolated particles ofBaFe12019in the absence of an external field wallformation will occur only at relatively large crystalsizes, the critical diameter for wall formation atroom temperature is given in tableIl, together withthe maximum turn-ove~ field strength 2K/Js,for the same materials which have been compared

- Table II. The critical diameter do for wall formation inisolated spheres and the turn-over field strel_lgth 2[(/J.. -

Material do 2/-1oK/J. [2[(/J.]microris , in Wb/m2 [oersted]

BaFe120w 1.3 1.66 [16600] ,Fc 0.028 ' 0.018 [ 180]Co 0.24 0.56 [ 5600j

G) C. Kit tel, Rev. Mod. Phys. 21, 541, 194.9.7), The' "effective exchange" energy describes' formally

,the tendency for parallel alignment of magnetic momentson the same sublattice. This tendency originates from theactually existing negative superexchange interactionbetween magnetic moments on different' sublattices (cf.part Ill).

;·I't

"

"rY.''''"'~~~~------;:---~--------------------~----;''------ -, ~"""'_C7<:»;

200 'PHILlPS TECHNICAL REVIEW VOL. 13, No. 7

in table 1,8). 'I'he equation for spheres of diameterdo reads roughly 6):

Js2 4:n: d03 ':n:d02,!·t·_·_· '-=-aw

'[ .(4:0)2.~03 82'_"': :n:~02,,-], ! ""3 8 s, -:-Taw,from

If the expression for the wall energy awis substi-tuted 9) one arrives at:

{Kl!kTc [ 9 iK 1/ kTc]do= 36:n:,uo J

s'aJ

02 do = Is' V aJ

02 •

Here K is the anisotropy constant, and a thè meandistance between neighhouring ions belonging toequivalent suhlattices (cf. part Ill).

In the expression (3) for do only' the factor iK/Jsis temperature-dependent. It "follows from jig. 4,which gives this quantity for BaFe12Û19.as a fun~tionof temperature, that the critical diameter forBaFe12û19increases with temperature up to a regionnearthe Curie point. This hehaviour is differentfrom.that öf most traditional materials, for which iK/Jsdecreases with temperature. The increase with

. temperature' of du means that at a given fieldstrength in an aggregate of BaFe]2019' crystalsa smaller number' of Bloch 'walls will be presentat higher temperatures and that especially thoseBloch walls disappear which have the highest

~ __-+ ~ __-+ +-__-+ +-__~3500,~---+----~---+----+----+----+---_'2

~---+----~---+----+----+----+-~_,I_~~~~--_no~--~o----~~L----~~---~~--~400~--~~~

• ro~,.',',Fig. 4. TIié quantity VK/J. as a function of temperaturefor ;B~Fe120l0'

8) ,The comparison with iron can be of qualitative value onlyas .equations (1) and (2) are strictly speaking hotapplicable to the case of iron, which has a cubic magneticcrystal anisotropy. See also note 3). .

0) The expression given in reference G) has been altered bytaking into account that the exchange energy varies withtemperature as ';.2/J02;' '

"

energy and can therefore be ;most easily moved byan external field. Considering the mobility of oneparticular Blo ch .wall in a crystal that is imperfectdue to inclusions and lattice defects as well as dueto internal tensions .the following must -he bornein mind. The force driving the wall is proportional tothe magnetization Js on which the external fieldacts, and "the resistance against the movement ofa wall is due to local variations of the wall energy

00rsied

(3) 0,

A 50in 1/~ ~

oe

tJHc4

/ -.\ 4003,105,. I

3;"" ..x- ...

V, ,, l\ t'~

3'105 TI /' ,.- ,.- \,2

1"""",- .- \ \

2000.-,.- \

1J5 x' \7 \ 7000~~---- • 11I--- .....--~f----- ---- --',~,

00

0,

o 700 200 500 C'70484

Fig. 5. Coercive force JHc as a function of temperature.The drawn line applies to a very fine-grained sintered speci-men of BaF,e120lD'the broken lines to sampleswhich containlarger crystals. In the latter cases the actual values of thecoercive force are 10 times smaller 'than is read on the scale,The lowest curve was found for a very coarse grained sampleof Eerrexdure [largest extension of crystals several nim's).

300 400

and increases with the energy of anisotropy andthe intensity of magnetization. It thus follows thatthe mobility of one particular wall in an externalfield depends on temperature as 1(-'/. (fig. 2). Ob-viously the modei of isolated spheres is not strictlyapplicable to Ferroxdure. However, Ferroxdureis a sintered material, the density of which is about10% below that calculated for the case of theabsence of pores (X-ray-value) 10).We believe that:the interplay. of the decrease of jhe number ofwalls and the jncrease of the mobility of a particularwall with temperature is mainly responsible forthe maxi~um in:the curve of the coercive forceJHc vs terii1..<1f:\áJ:;'e, as shown in jig. 5.

As to the actual crystal size -for which wallformation can be avoided and accordingly a highcoercive force can be obtained, it is seenfrom table II,that the rough calculation arrives at dimensionsof about one micron. It has been verified experi-mentally by grinding a coarse-grained polycrystal-

10)Calculated by dividing the weight of the unit cell by itsvolume, (2Wm/NA)Îtca21!3, where c is the cell dimensionalong the c-axis, a is the cell. dimension along the a-axis,Wm is the molecular weight and NA· is Av 0 gad r 0 ' snumber. • ,

J.i;\NUARY 1952'.

F~RROXDURE (PHySICAL ~~CKGROU_ND) 201

line sample cf Ferroxdure of approximate compo-sition BaFe12019 to different grain sizes (cf. table Ill)that. the coercive force at room temperatme in-creases' rapidly when dimensions of one micron. are approached,

polycrystalline specimen;crystal diameter > 300 !.l

specimen ground; diameter ofparticles about 100 !.l

specimen ground; diameter ofpartieles about 3 !.l '

0.0050 [50]

0.0075 [75]

• 0.1240 • [124,0]

In sintered \specimens of BaFe12019 the largest, coercive forces' are' obtained in samples which arefired in such a way as to avoid as much as possible

. the growth of large crystals.

Remanence

The remanent magnetization of a hard magneticmaterial consisting of crystals with one directionof easy magnetization oriented at random shouldbe one haIf of the saturation magnetization. Thishas'been found to be true. for sintered Ferroxdureof the approximate composition BaFe12019 at tem-peratures up to 400°C, as can be seen fromfig. 6.

IJ

~I,<,

r-,<,

~<,r-,

~............. J5-. 1'--...

.1~ I~q 4tr.1r~

I. -............. r\0

D,5 5000

4000

3000

a 2000

000

-200 -100 300o 100 20070014

Fig. 6. The remanent magnetization Jr of sintered Ferroxdureof the approximate composition BaFe12010 and the saturationmagnetization J. of BaFe12010 of about the sarne densityas functions of temperature. Note that the-relation Jr = ij.~~w~ .

. The value ofthe remanent u;,duction Br=Jr=ear[Br = 4nJr = 4near] depends on the apparentdensity (e) of the material. (In this formula ar isthe saturation magnetic moment per unit mass inWh m/kg [gauss cm3/gram] and hence independent,

,

of.the density.) The, X-ray density ;l0) of the mate-rial is 5300 kg/m3 [5.3 g/cm3] -and the highest in-duction would he obtained with material havingthis maximum density. This density, however,cannot be obtained without the growth of crystalsappreciably larger than oJ?e m,icr(m, so that thehighest remanent induction can only he obtainedat- the cost of a lower coercive force and vice versa.Therefore a compromise is sought and the density.is kept below 5300 kg/m3 [5.3 g/cm3].

o

, gau

,I /000

0 0

ss

500°C70005

Fig. 7. Remanent magnetization at room temperature Jr'of a sample of Ferroxdure which starting from the remanentstate at room temperature has been heated to a temperatureplotted as abscissa and cooled to room temperature again.

-200 -100 o /00 200 300 400

Owing to the very high coercive, force at elevatedtemperatures, i.e. the high' resistance to demagne- .tization, the' remanent magnetization' of a rod of.Ferroxdure generally returns to its original valueafter heating to temperatures up to 400 oe. Fig. 7show? the remanent induction of a rod with dernag-netization factor N=0.008[N'=0,1] which was mag-netized at room temperature, then heated to th~ tem-perature plotted as abscissa and measured at roomtempérature. During and after the heat treatment itwas not exposed to a magnetic field except its owndemagnetizing field. Thus the remanence can bevaried reversibly by a factor 4. (see fig. 6 and 7)by varying the temperatme bet~~een between 20 oe' ..and 400°C. This effect can be utilized in temperaturemeasuring and regulating' devices, .provided thedemagnetizing factor is not too' large.

Demagnetization curve. and' value , 'of (BH)max

Fig. 8 shows the B-H curve for .a material with'fairly large values of the coercive forces jHc andBHc· In fig. 9 the remanent indJ_!ction is plottedas a function of a dernagnetising field which, is,-, .applied and, removed before measurement. It isseen that demagnetizing fields up -to floH = 0.16Wb/m2 [H = 1600 oersted] do not lower the re-manence by more than 1%. As a consequence Fer:roxdure magnets can be magnetized 'outside themagnetic circuit ip. which they are to be used, not-withstanding the fact that they are thus exposed tostronger .demagnetizing fields. '

, .'

'I~.,

202 PHILIPS, TECHNICAL REVIEW VOL. 13, No., 7

The. (BH)max values for Ferroxdure lie in therange of6400-7200 JJm3[0.8 X 106-0.9 X 106 gauss Oe].These ~alues are not large in comparison with,e.g. those for "Ticonal" G with (BH)max values upto 45800 11m3 [5.7 X 106 gauss' Oe]. However,as was already mentioned in part I, the (BH)maxvalue should not be used without some reserve asa criterion for the volûme of permanent magnetmaterial necessary to obtain a given .field strengthin an air gap of given' volume. This is due to tbefact that the demagnetizing field caused by anair gap (and thus also the stray field) depends on 'the magnetic permeability of the permanent magnetmaterial, the demagnetizing field being stronger thehigher the permeability. As the relative permeabilityof Ferroxdure is only about 1, as against a val:ue of

-H-2000 o_ 2000 4000 6000 oersted '

.lP I/,

/"/

.' . ~

/ ~

.5JVI

V I1V/ I/ /

./ V0 j 0

11

2 / -II -~ - -"'~Hrr,105#,0 105 2-101 :rKff , 4-105

-02 10 " 8

gauss'

0000

Q 5000

, -~

0,2 ~ M ~~70015 \-f!~H

Fig. B, .Magnetization curve (B-H c~rve) for Ferroxd~re.

. aboU:i 4 for "Ticonal", Ferroxdure compares morefavourably with "Ticonal" G than is apparent fromthe comparison of the (BH);nax v~iues. The work-ing point of the material shown in fig. 8 (corre-sponding to (BH)~a;'_ = 6650 'J Jm3 [0.83X 106

gauss, oersted]) is iJ = 0.0925 Wb/m2 [925 gauss],f.CtJH = ":"'0:09;WbJm2 [H = -900 Oe].

Owing to the -rather low remanent inductiontogether with the very high coercive' force ofFerroxdure; the design of a magnetic circuit withthis material will be quite different from tbat fortraditional materials, The permanent magnet in aFerroxdurè circuit has to be disc-shaped (see fig. 2

, .

70DDS-1000 -2000 -1000 0 oersted

'b9

,2 r,I

I10 I 0

·1 .-

,-H-:rIOS -2-105 -105 OA

,I m.- - - - or

auss

,0

Q 1000

-0M

Fig. 9. Remanent inductio~ Br" of a sample or"Ferroxdurewhich, starting from the remanent state, has been sub-jected to a demagnetizing field II during sqme'time.

of part I), while in circuit~ using traditionalmaterials generallyamore rod-shaped magnet hasto he used, For certain loudspeaker circuits thisproved to be no disadvantage, since the loudspeaker, cone itself has a certain later ai extension.

Electric resistivity

The results of measurements of the resistivityof Ferroxdure as a function of temperature, arereproduced in fig. 10 12). The electric resistivity ofFerroxdure can be seen to be very large, larger than106 Qm [108 Qcm] at room temperature. This canbe understood from the fact that BaFe12019 containsonly trivalent iron ions 11).

Ferroxdure will therefore prove to be a very

J!]QQ -20 'T!"K) 1.570010

ID a5} ,3 -.

"I

f"-1

1\I\..0

"\~.

1 I\..11\

logel.nanJ

5

2 4

3

2 '

-2

Fig. 10. The logarithm, of the' resistivity e for Ferroxdureof the approximate composition BaFe12019 as a function ofabs?lute temperature. Plotted is log (! vs lOOO/T.

U) J. H. de Boer and E. J:W. Verwey, Proc. Rhys.Soc. 49, extra part, 59, 1937. '

12) The measurements were carried out by J. Sm i t of thislaboratory. ,#'

JANUARY 1952 . 20~FERROXDURE .(PHYSICAL BACKGROUND)\

- '

suitable material for high frequency applications,especially in combination with Ferroxcube, e.g.in ,cases where it is desired to subject thismaterial, to a polarizing field. One applicationof a polarizing field is that a low or negativetemperature coefficient of the permeability may thus

'.

. ~" ~, ..

be obtained (see A and also reference 2) of part I).The compound BaFe1S02;, which contains both

ferric and ferrous ions, shows a' much higher cdn-ductivity than BaFe12019•

A summary of the properties of Ferroxdure isgiven in table IV.

Table IV. Some ap~roxi~ate data on Ferroxdure at room temperature. The compositionof the essential phase is BaFe12019' The material, being a sintered ceramic, is brittleand ~an be ground.

Èlectric resistivity >109 .om [lOB .ocm]

D it {X-ray valueenSl .y actual value

Saturation magnetic moment per unit mass 8.75 X 10-5 Wb m/kg [70 gauss cm3/g]

5300 kg/m3 [5.3 g/~m3]approx. 4·800 kg/cm3 [approx. 4..8 g/cm3]

Remanent induction approx. 0.205 Wb/m2 [approx. 2050 gauss]

approx. 0.145 Wb/m2 [approx. 14·50 Oe]

0.24 Wb/m2 [approx. 2400 Oe]

(BH)mnx approx. 6800J/m3 [approx. 0.85 X 109 gauss Oe]

B-coercive force ItonHc [BHc]

Working point B ~ 0.1 Wb/m2 [B ~ 1000 gauss]#oH ~ -0.085 Wb/m2 [H ~ -850 Oe]

-0.2 % per °CTemperature coefficient of remanent in-

duction

approx. -0.15 % per °CTemperature coefficient of induction in

working point

Curie temperature 4.50 °C

General

Ill. SATURATION MAGNETIZATION AND CRYSTAL STRUCTURE

The saturation magnetization is of great interestfrom a practical as well as from a more fundamentalpoint of view. Indeed, it has already been mentionedthat an important quantity like the remanent mag-netization is closely related to the saturation mag-. netization. As regards the theoretical aspects, froma study of the saturation magnetization it will bepos~ible to get an insight into the mechanism whichis responsible for the magnetic behaviour of theoxides which are dealt with. It will be found thatthis mechanism is completely analogous to that whichprevails in the Ferroxcuhe materials, which weretreated in detail in A (cf. I, 1») (non-compensatedantiferromagnetism). Because, of this analogybetween Ferroxdure and Ferroxcube we shall startwith recalling some facts about the latter materials._ Ferroxcube materials are ferromagnetic oxideswhich chemically belong to the group of cubicferrites, the crystal structure of which is the so-called spinel structure. In this structure there are 1

two .non-equivalent crystallographic positions avail-', able" for the metal ions, the so-called octahedral 1)and tetrahedral sites, which form' the octahedral . 2)~nd tetrahedral sublattices respectively. The inter-

i .."-'-..,

action between two magnetic ions is dependent onthe kind of sites they oécupy. So even if a ferritewith only one kind of magnetic ions (situated onboth sublattices) is considered, one has to distinguishbetween three different interactions, which we shallcall briefly: tetrahedral - tetrahedral, tetrahedral-octahedral and octahedral - octahedral interactions,meaning the interaction between a magnetic mo-ment on a tetrahedral site with another one ona tetrahedral site etc. N éel was the first to pointout the importance of these three interactionsand he generalized the existing "molecular field"theory of ferromagnetism for the case of thesedifferent interactions 1). From the experimentaldata regarding the values of the saturation mag-netization at zero absolute temperature 2) andregarding the temperature dependence of the para-magnetic susceptibility above the Curie pointX = J/#oH = #r-1 [X = J/H = (ll-l)/4:n;] Néeldeduced that a strong tendency exists for anti-

L. Néel, Ann. Physique 3,137,1948.In tbis part when speaking of the saturation magnetizationwe always mean the saturation magnetization at zeroabsolute temperature. ,

204 PHILIPS TECHNICAL REVIEW VOL. 13, No. 7

parallel alignment óf magnetic moments on neigh-bouring non-equivalent sites and a much weakertendency for antiparallel alignment of magneticmoments on neighbouring e q u i.v a l.en.t sites. Inorder to explain roughly the value of the saturationmagnetization of most of the single ferrites, forwhich the conditions are. most simple, it is suffi-cient to take into account the predominant nega-tive tetrahedral-octahedral interaction only., Wethus obtain in this simple case for the value of thesaturation moment Ms expressed in Bohr magne-tons per m~lecule the formula: '.

,M; = (Ms}tetr- (Ms)oct,

where (Ms}tetr and (Ms)oct are the sum, of all mag-netic moments in one "molecule'.', situated on tetra-hedral and octahedral sites respectively., Fromthis the saturation magnetic moment per unitmass in Wh m/kg fgauss cm3/gram], 0'0' is foundaccording to the formula:

0'0 = !-loMs f-lnNA [0'0 = Ms f-lnN' A] ,. Wm Wm

in which NA is Avogadro's number, !-lB is thevalue of the B 0 h r magneton, viz. 9.27 X 10-24

Am2 19.27X 10-21erg/gauss] and Wmis the molecularweight 3).

We see from the foregoing that Néel's theoryis of a formal character in so far as it presupposesthe existence of the interactions between the mag-netic moments 'on the various lattice sites and ad-justs the sign and magnitude of the interactionsso as to he in accordance with the experiments.However, the mere existence of such interactionscan not he understood in a more or less "elementary"way, as these interactions must be fundamentallydifferent from the (positive) interaction betweenthe magnetic moments in a ferromagnetic metal.As is well known, the interaction in these metals,the so-called exchange interaction, is of a shortrange nature, 'i.e, it is negligible between magneticmoments which are not on neighbouring sites.However, in the ferrites with spinel structure, themagnetic ions are always more or less separatedby large oxygen ions and thus are much too far apartto permit of an appreciable direct exchange inter-action. Besides this, the exchange interaction is alsoimpeded' by the shielding effect Of the oxygen ions.

\

~) NA = 6.025 X 1026 molecules per kg molecule, N'A =6.025 X 1023 molecules per gram molecule. The factorIlo mayalso be suppressed, in which case Uo is expressedin Am2fkg. The two possibilities correspond to the twopossible ways of defining I). magnetic moment, viz., bya "volumemoment" m" (energy= m"II) or by an "areamoment" mA (energy••= mAB).

Néel already pointed out that a rather Intricatemechanism, proposed by Kramers 4), might beresponsible for the above-m~ntioned interactionshetween two magnetic ions separated by a non-magnetic anion. In this mechanism, called super-exchange, the anions play an essential role. Amore quantitative theory based. on these ideaswas given by Anderson 6).

(1)

.-<'~

1/~ -

71/I

/ I

0

0'

Ip,-1

4000ftgaussoersted

3000

20002·10'

1000

-400 500 600 800 ~<t70013

Fig.1.The reciprocal of the paramagnetic susceptibility 1h ofBaFe12019 as a function of temperature. It should be noticedthat in a normal ferromagnetic ahove the Cur i,e point thiscurveshouldbe a straightlineaccording to the Cur ie -Wei sslaw. If a straight line would be drawn tangentially to thelh vs. T curve in the Curiepoint (l/X = 0) it is seen thatI/X is smaller and thus X is larger than if a Cur i e -Wei s slawwouldhold. Thismaybemade plausibleby the assumptionthat at the Cur i e point only the weakest interactionslose their ordering influence whereas the stronger inter-actions still cause a local ordering of the magnetic moments,which is destroyed only at higher temperature. Thus withincreasing temperature the number of "free" magneticmoments increases, by which increase the susceptibility fallsoff more slowly than in a normal ferromagnetic above theCurie point.

Anderson's theory explains the negative signof the interaction. The theory shows that for givendistances between the anion 0 and the first magneticion Me(1) and between the anion and the secondmagnetic ion Me(2)the interaction is the Iarger thenearer the angle Me(1)'O-Me(2) is to 180°. The inter-,action will be smallest if the angle Me(1)'O-Me(2)is 90°. As regards the dependence of the super-exchange interaction op. the distances Me(l>'O,O-Me(2),it can be said that it will decrease rapidlywith increasing distances. If :the dependence ondistance is taken into account by neglecting inter-actions involving Me-O distances larger than 3 Aone can estimate the strength of the interaction

\ between two magnetic ions from the given angles anddistances. Thus a useful rule of thumb is obtained.

4) H. A. Kramers, Physica I, 182-192, 1934.5) P. W. Anderson, Phys. Rev. 79, 70S, 1950.

JANUARY 1952

<.

FERROXDURE (ANTIFERROMAGNETISM) 205.

The preponderance' of the interactions of mag-netic moments on non-equivalent lattice sites inthe fezrites ca~ according to this rule he ascribedto the fact that the angle Metetr-O-Meoct is of theorder of '120°, whereas the ,angles Metetr-O-Metetrand',Meoct-O-Meoct are of the order of 80° and 90°respectively..... ' From-this it is suggested that also for compoundsmore complex than the ferrites, it should he possibleto determine very roughly the various interactionswithout an intricate analysis of the experimentaldata, once the crystal structure (and thus the variousangles and distances) of the compound is known anduse is made of the above-formulated rule of thumb.In this way l,t is possible to make an estimate ofthe saturation magnetization.

The value of the saturation magnetization aswell as the temperature dependence of the magneticsusceptibility (fig. 1) of the two oxides to he treatedin this part of the paper lend strong supportto the assumption that also in these materialsthere exists a negative super exchange interactionbetween the magnetic ions.

Crystal structure of BaFe12019

It was already mentioned that the main compo-,• -nent of the permanent magnet material which is

available at the moment under the name of Ferrox-dure is a ferromagnetic phase with hexágonalsymmetry, the formula of which is BaO.6Fe203 orBaFe12019' It was shown by Adelsköld 6) thatthis compound is isomorphous to the mineral mag-netoplumbite, which has a composition near toPb (Fe, Mn)12019'The crystalstructure ofthis mineralwas determined by the same author and is shown infig.2a (see page 207). The structure given here isslightly idealized, i.e. small deviations of the para-meters (coordinates of the ions in the unit cell)or'the iron and oxygen ions from the simple valuesused in this figure have been neglected. The figureshows that the oxygen ions form a hexagonal close-packed lattice, some sites of which are occupiedby the Ba-ions. The same 'argument is 'valid ifthe Ba-ions are replaced by strontium or lead ions.These three ions have ionic radii which do not; differ, appreciably ft;9m .the radius of an oxygen ion. This, is shown in the following table.

The ferric ions are found in the interstices of, the oxygen lattice, like the metal ions in the spinel; structure, A closer inspection of the crystal struc-tut~ shows that there are five non-equivalent lattice

~) V. Adelsköld, Arkiv för Kemi,Mineralogioch Geologi, 12A, No. 29, 1, 1938.

I Table J. Ionic radii accordingto V.M.Goldschmidt.

ion radius in A

02- ,1.32Ba2+ 1.43Sr2+ 1.27Pb2+ 1.32

sites for the ferric ions. In order to be able to calcu-late the strength of the various interactions fromexperimental data, one would have to generalizethé molecular fielC:l-theory of ferromagnetism forthe case of five suhlattices, which would be muchtoo complicated. However, if the crystal structureis known, we can apply our rule of thumb for thestrengths of the interactions, In order to facilitatecomparison with the spinel structure, which thanksto former publications may he more familiar toour readers, the spinel lattice has been drawn alsoin a slightly idealized form in fig. 2b, with a ver-tical orientation of the [lll] direction.

A comparison shows that in these idealized struc-tures a large part of the ionic configuration in theBaFe12019 lattice is identical with that of thespinellattice, as was already pointed out by Adels-köld. In the layers between these spinel "blocks"the oxygen lattice contains a Ba2+ ion. .In thesame layer as the Ba2+ ion a ferric ion (@) appearssurrounded in an unusual way-by a trigonal bipyra-mid of five oxygen ions.

The ferric ions on octahedrally surrounded sites'belong to three different crystallographic positions(e, @) and ®) so that together with the te-trahedral position (0) there are five non-equivalentcrystallographic positions as shown in th~efig. 2a.

With the aid of our rule of thumb based onAnderson's theory we can now assign a direction(up or down, at 0 OK) to the magnetic moments ofthe various ions provided that we arbitrarily fix thedirection of the moment of the ion in the @ lattice(e.g. up). Now both adjacent moments in the.lattice will point down. The @ -oxygen-. inter-action is namely large, because the angle@ -oxygen- 0 is large (of the order of 140°),whereas the competing \'I) -oxygen- • interaction,which would tend" to orient the (i) -momentsmutually antiparallel, will He 'small because theangle @I-oxygen- ~ is 'near 90° (of the orderof 80°). Continuing according to this principle 'weobtain the directions of the moments as givenin, fig. 2a. ., Thus for the complete unit cell16 moments point-.irig up' and 8 pointing down are found i.e, ~ resultaat'spo~taneous magnetiza tion of 16 - 8 =,8 moments.

."»Ó,

[

206 PlIILIPS TECHNICAL REVIEW VOL. 13, No. 7

As each ferric ion has a moment öf 5 Bohr magnet-ons, for the saturation magnetic moment Ms a valueof 40 Bohr magnetons per unit .cell is obtained;which according to formula (1) is equivalent to0'0 = 12.5 X 10-5 wp m/kg [100.5 gauss-cmê/g] 7). Infig. 3 the measured values of the saturation mooment are plotted against temperature 8). Byextra-polating this curve towards 0 "K we arrive ata value of ""'.13.75 X 10-3 Wb m/kg [""nO gauss-cm3/grJ for the saturation moment at zero tempera-ture, which, given the crude assumptions involvedin our rule ofthumb and the uncértaintyin the extra-polation, is in satisfactory agreement with theory 9)..Wb·m cgsmkg-' . g/cm3

10·10:" 80

crt ter7,5-I(J 60

5·10 40I

2.5'105 20

70004

Fig. 3. Saturation magnetic moment a as a function oftemperature.

The Iow value of the remanent magnetization ofFerroxdure can now be understood from a morefundamental point of view as being due to thefact that in this material the magnetic hehaviouris determined by the tendency for ant i par a 11e Ialignment of the ionic magnetic moments, whichwill always give rise to a rather low saturation mag-netization and thus to a Iow remanent magneti-zation.

Crystal structure of BaFe~ Fe~027

. The second oxide .that will be considered hereand which also is magnetically hard has a crystalstructure very' similar to that ?f BaF.'e12019.

,\

"

7) In applying formula (1) it should he taken into accountthat one unit cell of BaFe12010contains two "molecules".

S) Sinee the materials under consideration show an extremelylarge magnetic anisotropy, a very high field strength isnecessary to measure the saturation magnetization ina direction of difficult magnetization. Therefore smallsingle crystals were taken, which were measured in thedirection. of easy magnetization. The measurements were

/ performed with an apparatus deseribed in reference 1)of part Il. The error is of the order of two percent.

9) In making the extrapolation one should take into accountthat aecording to Ne r n st' s theorem the slope of themagnetization vs, temperature curve has to become zeronear 0 oK.

\

..

The chemical, composrnon of this oxide isBaO.2FeO.8Fe203 or BaFe~IFe~~I027' As may beseen from fig. ,2c the structure of .this compound,which was determined by P. B. Braun of thisIaboratoryl''}, can also he described as consistingof spinel "blocks" separated by layers containingBa-ions. Thcse layers are identical withthose in thestructure of BaFe12019. The difference between thetwo structures is that in BaFe~IFei~I027 the spinel"blocks" are higher than in BaF~12019 (cf. :!tg. 2a);because two "molecules" of FeIIFe~II04 (magnetite)are introduced into each block.

The arrangement perpendicular to the hexagonal-axis is thereby slightly altered as compared withthe arrangement of the analogous ions in'BaFe12019.The position of the. ferrous ions cannot be deter-mined by X-rays, but in order to obey the eleètro-static valency rule 11) they shoul~ be located some-where midway between the layers containing ba-rium. Assuming a preference for an octahedralposition like in magnetite, they should be situatedin ® or ® sublattiees, both of which have momentspointing up.. Each Fe2+ ion having a moment of 4 Bohrmagnetons the spontaneous magnetization of thisoxide obtained with the aid of our rule of thumbis (20-12) 5+ 4 X 4 = 56 Bohr magnetons, or:0'0 = 12.4 X 10-5 Wbm/kg [99.6 gauss em3/g].

This value should be compared with theexperimental value 0'0 = 10.6 X 10-5 Wb m/kg[85 gauss cm3/g].

An illustration of the striking sensibility of the magneticbehaviour to changes in tbe crystal structure and an additionalconfirmation of the usefulness of our rule of thumb can begiven by considering yet another compound.A potassium compound exists with the formula

K20.UFe20a or KFen017, which has a crystal structure verysimilar to that of BaFe12010'This compound, however, isnon-ferromagnetie, ~ven at very low temperatures.The crystalstructure, givenin fig.2d, was proved by A del s -

köld to be the same as that of Na20. llAl20a or Na Aln017(the so-called" p-alumina"), the structure of which was deter-mined by Bee ver sand Ros S 12).The lattice is identical withthat of BaFe1201Dexcept for the arrangement in the layercontaining the large ion i.e. the Ba resp. K ion. In KFen017the @ position is unoccupied and the three oxygen ionspresent in the BaFe12010structure have been replaced hereby one oxygen ion situated midway between the ferfic ions

-,in the @ positions. TIlls slight difference, in structure ex-plains the large difference in magnetic behaviour. In fact, in

10) The results of this determination will be published ingreater detail elsewhere.

11) In a stable ionic structure the valency of each anion isexactly or nearly equal, with opposite sign, to the sumof the electrostatic bonds to it from the adjacent cations.

12) C. A. Bee ver sand M. A. S. Ros s, Z. Kristallogr. 97..57, 1937.

JANUARY 1952 FERROXDURE (ANTIFERROMAGNETISM)

Fig. 2. a) Crystal structure of BaFe120l9"b) Spinel structure, with a vertical orientation of the [UI] direction.c) Crystal structure of BaFe~IFe~~I027 (only half of the unit cell, which possesses a mirror plane, is shown).d) Crystal structure of KFen01,.

The large unhatched spheres are the oxygen ions, the large hatched ones are the Ba or K ions. The small spheres are theFe ions: these are hatched in different ways in order to indicate the different crystallographic positions. All the structures areslightly idealized. In parts of the structures a, c, d the positions of the ions are identical to those in the spinel structure b.Such parts are indicated by long brackets. The arrows indicate the direction of the magnetic moment of the ions, thedirection for one arbitrary ion in each structure being supposed to point upwards.

£.

,-,, \I I'_,

,-, \\ I<:.»

mirrorplane

70037

l

,,-'I \\ ,, ....

207

b

:I. "" . .".~:, ,," '208 PHILIPS 'TECHNICAL -REVIEW VOL. 13, No. 7

BaFe1201Dthe predominant @-oxygen- @j) interactionscaused the moments in the @ lattices .to be parallel;in KFel1017 b~cause the @) lattice is empty only the, ® -oxygen-@ interaction has to be 'considered, and as theangle is 180°, this interaction win be strong. The result isthat the layer containing the K-ion will be a mirror planefor the directions of the magnetic moments, and theresultant moment of each half unit cell will he cancelled bythat of the other half unit cell.The result is an antiferromagnetic behaviour, in accordance

with experiment. The antiferromagnetic çu r ie temperaturemay be expeeted to be,very near to the Cur i e temperatureof BaFe12019"Experimental indications supporting thisconclusion have been found.

Summary of parts I, Il, m. The m;terial manufactured atpresent under the name of Ferroxdure is an oxidic ceramicmaterial of the" approximate composition BaFe12010. It isa magnetically hard material which does not contain anycobalt or nickel and which thus offers gr~at economic ad-

vantages. It is characterized by possessing an extremelyhigh value of the coercive force and rather low remanenceand saturation magnetization. The extremely high value ofthe coercive force is due to a large crystal anisotropy. Thecombination of the two properties, large coercive force andlow saturation magnetization means that the material hasa large, resistance to demagnetization and thus is very wellsuited for applications where a large resistance to demagneti-zatión is of importance. In the second place these propertiesopen new ways for the design of permanent magnets. The(BH)max value of Ferroxdure is rather low. Its specific elec-tric resistivity is high so that, it is very well suited forhigh frequency applications.The low value of the saturation magnetization and of the

remanent magnetization can be understood to be due to thefact that the mechanism which determines the magnetic he-haviour of Ferröxdure is non-compensated antiferromagne-tism. The strength of the various interactions between themagnetic ions can he estimated theoretically if the crystalstructure is known in detail and if use is made of a rule ofthumb, based on And ers 0 n 's theory of superexchangeinteraction. • In this way the value of the saturationmagnetization of Ferroxdure can be estimated and it isshown that the theoretical value thus obtained does'not differmuch from the value obtained from experiment.

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