Anisotropy Fields in Hexagonal Ferrimagnetic Oxides by FerrimagneticResonanceD. J. De Bitetto Citation: Journal of Applied Physics 35, 3482 (1964); doi: 10.1063/1.1713254 View online: http://dx.doi.org/10.1063/1.1713254 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/35/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetization Processes and Reversal in Ferrimagnetic Oxides with HighAnisotropy Field J. Appl. Phys. 39, 879 (1968); 10.1063/1.2163658 Domain Structure of Hexagonal Ferrimagnetic Oxides with High Anisotropy Field J. Appl. Phys. 37, 3826 (1966); 10.1063/1.1707934 Nonlinear Effects of Crystalline Anisotropy on Ferrimagnetic Resonance J. Appl. Phys. 31, 2059 (1960); 10.1063/1.1735497 Anisotropy Properties of Hexagonal Ferrimagnetic Oxides J. Appl. Phys. 31, S137 (1960); 10.1063/1.1984636 Microwave Resonance in Hexagonal Ferrimagnetic Single Crystals J. Appl. Phys. 30, S175 (1959); 10.1063/1.2185873

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JOURNAL OF APPLIED PHYSICS VOLUME 35. NUMBER 12 DECEMBER 1964

Anisotropy Fields in Hexagonal Ferrimagnetic Oxides by Ferrimagnetic Resonance*

D. J. DE BITETTO

Philips Laboratories, Irvington-on-Hudson, New York

(Received 16 December 1963; in final form 22 June 1964)

Room-temperature microwave ferrimagnetic resonance measurements of the large uniaxial magneto­crystalline anisotropy fields (Han) of two compositional series of hexagonal ferrimagnetic oxides are re­ported. Han was found to increase rapidly in the AI-substitution series (SrO· xAIzO,· (6-x)Fe20,) from 19.3 to 53.4 kOe as x was increased from 0 to 1.7. In the TiCo series (BaO·x[TiCoO,} (6-x)Fe;O,) , 1I an was found to decrease from 17.5 to 6.6 kOe as x was increased from 0 to 0.78. Experimental plots are given for the varia­tion of Han with x. The linewidths of these oriented polycrystalline compounds were all about 2 kOe. The g value was consistently found to be about 1.9.

Variation with x of the respective saturation magnetizations, anisotropy constants and anisotropy fields are discussed; relations are presented. '

1. INTRODUCTION

T HE substitution of certain ions in place of some Fe+3 ions in the highly anisotropic ferrimagnetic

material called Ferroxdure1 (BaO· 6Fe203) has been found to produce substantial and interesting changes in its magnetic properties. The resulting substitution compounds are permanent ferrimagnetic materials with a hexagonal crystal structure of the magnetoplumbite type.2 Because of their high magnetocrystalline anisot­ropy energy (which results in a high apparent magnetic anisotropy field Han along the crystallographic c axis), these materials are potentially useful at millimeter wavelengths. For example, the values of Han for Fer­roxdure is about 17 kOe, resulting in a ferrimagnetic resonant frequency of about 50 Gclsec with no exter­nally applied magnetic field. In this study, it was found possible to obtain values of Han throughout the range of 7 to 53 kOe by a suitable choice of composition in two chosen compositional series. Since these materials have approximately the free spin g value, this corre­sponds to placing the zero-applied-field resonance line at any frequency in the 23- to 145-Gc/sec range.

Several members of the two compositional series SrO . xAlz03· (6-x)Fe203 and BaO· x (TiCo03) • (6-x)Fe203 were prepared as oriented polycrystalline ceramics by the magnetics group under the direction of F. G. Brockman. Their preparation procedure, similar to that of Stuijts et al.,s together with their static magnetic measurements are described elsewhere.4

The above compounds were studied at room tempera­ture by microwave ferrimagnetic resonance (FMR) techniques.5 The purpose of the investigation was to

* This work was supported in part by the U. S. Army Signal Corps.

1 J. J. Went, G. W. Rathenau, E. W. Gorter, and G. W. van Oosterhout, Philips Tech. Rev. 13, 194 (1952).

2 V. Adelskold, Arkiv Kemi, Min.-Geol. 12A, 1 (1938). 3 A. L. Stuijts, G. W. Rathenau, and G. H. Weber, Philips Tech.

Rev. 16, 141 (1954). • D. J. De Bitetto, F. K. du Pre, and F. G. Brockman, Final

Report for USARDL, Contract No. DA 36-039 SC-85279. • Part of the work reported herein was done in a coordinated

program with the magnetics group to study the static magnetic and microwave properties of these components. For a preliminary report of this work, see J. Appl. Phys. 29, 1127 (1958), as well as Ref. 4.

study the dependence of the Han, g value, and the linewidth (b.H) upon composition. Some considerations regarding their saturation magnetizations (M), anisot­ropy constants (K), and anisotropy fields (Han) are also presented.

II. EXPERIMENTAL

A. Procedure

The details of the FMR experimental arrangement are described elsewhere.4 The apparatus is essentially a microwave transmission line which passes through a region of variable uniform de magnetic field and pro­ceeds to its termination at a crystal detector. The magnetic samples to be investigated are inserted into the line at the point of the applied magnetic field. Resonance absorption was observed by recording the microwave power transmitted to the detector at various de magnetic fields. The microwave power source was one of a series of commercially available klystrons which together covered the frequency range~ 20~75 Gc/sec. The tube was used either directlv or used to drive a second-harmonic generator so th;t microwave power was obtained at any frequency in the range 20-150 Gc/sec.

The waveguide size and associated equipment used at each frequency was such that the microwave radia­tion was always propagated in the fundamental TEo! mode; the frequency used for each material was such that applied magnetic fields no greater than 10 kOe were required to obtain resonance. The sample ma­terials were ground into one of two shapes: an E-plane slab (in which Han lies in the plane of the slab) or an H-plane slab (in which Han is perpendicular to the plane of the slab). In either case, the slab was centrally mounted on the broad wall of a special section of wave­guide (having a removable top wall for accessibility) such that Han was oriented perpendicular to the rf H fiel? The externally applied de magnetic field (Hap) was dlrected parallel to Han and was sufficient to keep the specimen magnetically saturated. The longest di­mension of the specimen was oriented in the direction of propagation of the microwaves, and the length was

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always comparable to or longer than the wavelength of the radiation used. The width of the H-plane speci­mens was of the order of 1/15 of the wavelength being used to insure that the sample be in a uniform rf field. The width of the E-plane specimens was about i of the height of the appropriate waveguide size. The thickness of all slabs was chosen such that further re­ductions in thickness did not produce further changes in linewidth or line shape. It was assumed that this procedure eliminated distortion of the line shape as well as falsification of fJI due to incomplete microwave penetration. Depending upon the frequency used, the thicknesses ranged from 250 to 25 /J.. The total volume of the specimen was adjusted by changes in length so that the maximum microwave power that was absorbed (i.e., at resonance) by the specimen was less than half the input power.

Resonance absorption measurements were made at constant frequency by observing the transmitted micro­wave power as the applied m.agnetic field Hap was swept from 0 to 10 kOe. The voltage from the microwave detector, proportional to the transmitted microwave power, was fed to one axis of an X-Y dc recorder. The other axis was driven by the output voltage from a linear Hall-effect probe placed in the magnetic field. The transmitted power exhibits a minimum at the Hap required for resonance in accordance with the Kittel resonance relationS

where f is the frequency at resonance, N x, N 1/, and IV. are the demagnetization factors of the specimen (con­sidered as an ellipsoid) where z is the direction of Han and Hap, M is the saturation magnetization of the material (at its x-ray density), and 'Y = ge/2mc, where g is the gyromagnetic ratio (or spectroscopic splitting factor),7 Using Eq. (1), both 'Y and Han were obtained for each sample by measuring the Hap required for resonance at a number of different frequencies. The demagnetizing coefficients were estimated using Os­born's formulas. s The saturation magnetizations used were: (1) average values reported in the literature for the Sr series; (2) room-temperature values for the Ba series measured statically by our magnetics group and corrected to x-ray density.4 Linewidths (fJI) were ob-

8 C. Kittel, Phys. Rev. 73, 155 (1948). 7 In the derivation of Eq. (1) it was assumed that the size of

the specimen is much less than the wavelength. This, however, was seldom true in our experiments since we often used specimens that were longer than the wavelength in the direction of propaga­tion. Although this results in a slow variation of the phase of the precession along the length of the specimen, it seems clear never­theless that one can still apply Eq. (1) as long as the demagnetizing coefficient in the direction of propagation, computed on the basis that the sample is only a half wavelength long, is still «1.

8 J. A. Oshorn, Phys. Rev. 67, 351 (1945).

tained by measuring the width of the resonance lines at half of their depth, For comparison, some single-crystal resonance lines were also measured.9 Clearly, the line­width of the polycrystalline form (rv 2000 Oe) cannot be considered an intrinsic property of the material, being about 40 times that of the single crystal. We have not investigated the cause of the broadening of the line. The anisotropy in the basal plane is far too small to explain it. Moreover, it seems safe to assume that it is not due only to imperfect alignment of the (oriented) crystallites, such measurements of the remanence4 in a direction perpendicular to the preferred one show that differences in orientation of different crystallites in the best samples are only of the order to 5°. It does not seem likely that such small misalignments could give rise to the broad lines observed in such samples.10

For the possible application of resonance isolators, the off-resonance microwave absorption losses of these materials are of considerable importance. Accordingly, several compositions in the two above-mentioned series were investigated for their "forward losses," i.e., trans­mission loss measurements were made on magnetized long thin slabs positioned off center in a rectangular waveguide at the position of minimum absorption. In this procedure, it was assumed that most of the sample occupied a position of circular rf polarization opposite in sense to that required for resonance. Although the slabs in general were quite long (rv5 em) and somewhat thick (75 to 250/J.), the forward losses never exceeded 0.6 dB. It was therefore concluded that these materials should in general be satisfactory resonance isolator elements.4

B. Results

The results of the room-temperature microwave meas­urements are listed as Han and !:lH in Tables I and II. The deduced values of Han (which were usually larger than the measured quantity Hap) have an accuracy of about 2%; H up was determined with an absolute accuracy of 1% by a rotating coil gaussmeter and there was an additional 1% uncertainty in the position of the resonance line; the frequency was determined with an absolute accuracy of 0.3% by commercial microwave wavemeters. The variations of Han between specimens of the same composition were less than 2%. The accu­racy of the !:lH determinations was again of the order of 2% for a given specimen, but variations of this quantity between specimens were sometimes as large

9 Actually, two compositions in single-crystal form were also investigated. Although each showed the same anisotropy field as its corresponding polycrystalline compound, their resonance line­width (.-.500e) is about 1/40 that of the polycrystalline materials. Also, their measured g value ( ...... 1.96) appeared to be ...... 2% higher than that of the polycrystalline materials.

10 It might be mentioned that the linewidth decreased somewhat with prolonged firing of the samples, which also resulted in a noticeable increase in crystalline size. Since this decrease in line­width (::;;30%) was considered too small to be of interest, no detailed investigation was made of this effect.

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3484 D. J. DE BITETTO

TABLE I. Measured values of anisotropy field Hail (kOe) and FMR linewidth I::.H (kOe) for SrO·xAhOa· (6-X)Fe20a.

x 0 0.1 0.2 0.5 1.0 1.35 1.42 1.50 1.70

Han 19.3 20.1 20.7 23.4 31.0 40.6 42.1 44.3 5.3.4 MI 1.6 1.8 2.0 2.5 3.3 2.5 2.3 2.3 9.7

TABLE II. Measured values of anisotropy field Han (kOe) and FMR Iinewidth MJ (kOe) for BaO·x[TiCoOaJ· (6-x)Fe203'

o 17.5 1.6

0.25

14.8 1.85

0.48

11.5 2.5

0.68

8.75 1.7

0.78

6.55 2.0

as 20%. 'Y/27r was found to be about the same for all compositions investigated, the mean value being 'Y /2-rr = 2.68 (corresponding to g= 1.91). The accuracy of the determination of 'Y depends, among other things, on the precision and magnitude of the difference in the resonant frequencies attainable for a given composition. For the differences used in this work, and with the above-mentioned inaccuracies in the Hap values, the maximum inaccuracies in 'Y were about 7%. Actually, the agreement in 'Y from one composition to another was usually within 3%.

III. DISCUSSION AND INTERPRETATION

A. SrO·xAb03' (6-x)Fe 203 Series

0.4

0.2

, , , 'x ,

• BERTAUT .t 01. (Bal L> MONES a BANKS (Bal x VAN UITERT a SWANEKAMP (Bal )II BOZaRTH a KRAMER (Pb) o BROCKMAN a STENECK (Ba) o II til II (Sr)

A

, MQl= (I_~)~, x MIa) 2 ,

FIG. 2. Variation of saturation magnetization with composition in MeO·xAhO,· (6-x)Fe20,.

It is evident that Han rises rapidly with increasing aluminum. Also represented in the figure are two functions arrived at by the following considerations:

The magnteocrystalline anisotropy energy density (E) in hexagonal crystals with uniaxial anisotropy is knownll to obey the relation

E=K sin28,

where 8 is the angle that the magnetization makes with the preferred or easy axis of the crystal (the crystallo­graphic c axis) and K is the anisotropy constant. From this relation, one obtains the well-known relation for the equivalent anisotropy fieldll which acts along the c

The points in Fig. 1 show the experimental values of axis, i.e., H ~n from Table I plotted against aluminum content.

H"n=2K/M. (2)

60

50

r.:J40 .. ... :!

i I

,g 30

C. c:

" :J:

20

10

Ha~X) = Ha~{~~;J~1

~

I /

I

6 H (X) = H (0)' .,.--....;6;,,-~X_ ..... an an 3§-X +(~) 2. 55J

O~~k-~ __ ~ __ ~ __ ~ __ -L __ ~ __ -L __ ~

o .2 .4 .6 .8 1.0 1.2 1.4 1.6 1.8

X in SrO,XAl203'(6-X)Fe203

FIG. 1. Variation of anisotropy field with composition in SrO·xAh03· (6-X)Fe20a.

To understand the variation of Han with composition, we can consider separately the dependeI;lce of K and M on x, and then combine these according to Eq. (2).

We shall first consider the M(x) relation. The points in Fig. 2 are the experimental results reported by various workers in the field4 ,12-16 obtained from the more general substitutional series MeO· xA120 3 • (6- x) Fe203, where Me is either Sr, Ba, or Pb, the crystal structure being the same for all. The reported saturation M values were normalized to their respective M(O) values as measured by the same worker and at the respective temperature of his measurements. Hence, the nor­malized points in the figure represent results obtained at various temperatures ranging from 4 OK to room temperature. The normalizing procedure reduced the otherwise scattered points to surprisingly good general

II J. Smit and H. P. J. Wijn, Ferrites (John Wiley & Sons, Inc., New York, 1959).

12 C. GuiJlaud and G. Villers, Compt. Rend. 242, 2817 (1956). 1a F. Bertaut, A. Deschamps, and R. Pauthenet, Compt. Rend.

246, 2594 (1958); F. Bertaut, A. Deschamps, R. Pauthenet, and S. Pickart, Colloq. Intern. Magn. Grenoble 1958, p. 346.

14 L. G. Van Uitert, J. App!. Phys. 28, 317 (1957); L. G. Van Uitert and F. W. Swanekamp, ilnd. 28, 482 (1957).

16 A. H. Mones and E. Banks, J. Phys. Chern. Solids 4, 217 (1958).

16 R. M. Bozorth and V. Kramer, Colloq. Intern. Magn., Grenoble 1958, p. 333.

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agreement, as is evident in the figure. The requirements for such agreement, other than the assumption that the distribution of the Al into the magnetic structure be the same for the Sr, Ba, and Pb series, is that the thermomagnetization M(T) curves for all compositions in these series be a family of curves having M(T) functions that differ only by a proportionality constant. The simplest case is that of linear M(T) curves, and it appears that the AI-substitution compounds under discussion rather closely fit this category, at least for these moderate values of X.1 ,4,15,17

The solid line in Fig. 2 gives the best smooth fit to all the normalized experimental points. Note that M(x) goes to zero at about x= 3. The average of the reported experimental absolute values of M(O) is 19.8 Bohr magnetons per molecule, the values ranging between 18.6 and 20.6.

The crystal structure of the series of compounds under investigation is the magnetoplumbite structure, the unit cell of which contains two molecules.2 The unit cell, in which no aluminum has been substituted, is known to contain 24 Fe+3 moments, of which 16 point in one direction and 8 in the opposite direction along the c axis.! A linear relation for M(x) was derived during our earlier work!8 and was based on the assumption that the substituted Al exclusively replaces some of the Fe+3

ions in the favorably oriented group of 16 moments per unit cell.19 This assumption appears to be valid on the basis of x-ray data13 for these moderate values of x(x<3). However, the resulting linear M(x) relation represented by the dashed line in Fig. 2 is seen to be satisfactory only for x< 1.0.20-24 In order to predict M(x) [and hence H an(X)] more accurately over a larger range of x, it was necessary to use an empirical relation for M(x) obtained by a curve fitting procedure to the points of Fig. 2. This relation is:

M(x)/M(O) = t[2-x+ (X/3)2·55], (3)

and actually the solid curve in Fig. 2 is drawn according to this relation.

Among several possible assumptions for the K(x) relation, the one that was found to best fit the experi-

17 R. Pauthenet and G. Rimet, Compt. Rend. 249, 1875 (1959). 18 F. K. du Pre, D. J. De Bitetto, and F. G. Brockman, J. App!.

Phys. 29, 1127 (1958). 19 E. W. Gorter, Proc. lEE, Pt. B 104, 255 (1957). 20 Since the nonlinear M(x) relationship is inconsistent with the

x-ray prescription for AI substitution, thi!> suggests that the Al may cause a modification of the original orientational relationship of the five magnetic sublattices. Indeed, it is known that on the basis of Anderson's theory of superexchange interactions between spins,2l a strong interaction exists that competes with the dominant one.22

If the addition of AI causes the competing collinear magnetic structure to become the dominant one, then the experimental M (x) results and the x-ray results can readily be understood. A modification of the original collinear structure to a canted ar­rangement23 or to a ferrimagnetic spiral arrangementM could also explain the results.

21 P. W. Anderson, Phys. Rev. 79, 705 (1950). lll! E. W. Gorter, thesis, University of Leyden (June 1954). 23 Y. Yalet and C. Kittel, Phys. Rev. 87, 290 (1952). 24 T. A. Kaplan, Phys. Rev. 119, 1460 (1960); D. Lyons, T.

Kaplan, K. Dwight, and N. Menyuk, ibid. 126, 540 (1962).

'" e 3.0 <J

~ ~

II) 4) 2,0

2

'" 1.0

0.5 1.0 1.5 2.0 X in $rO,xAt20 3 · (6-X)Fe203

FIG. 3. Variation of anisotropy constant with composition in SrO·xAbO.· (6-X)Fe20a.

mental results is one which assumes K proportional to the total number of moments per cell, i.e.,

K(x)/K(O) = (24-4x)/24. (4)

This assumption implies that the magnetocrystalline coupling has about the same strength for all of the five crystallographic sites. This relation is plotted as the solid line in Fig. 3, along with points deduced by means of Eq. (2) from the experimental Han values listed in TabJe I and the empirical relation for M[Eq. (3)]. It is evident that the relation fits the experimental points quite well, tending to verify the above assumption for K(x).

If we combine Eq. (4) with the empirical relation of Eq. (3), we obtain

Han(x)=Han(O)· (6-x)/3[2-x+(x/3)2.55], (5)

which is plotted as the solid line in Fig. 1. The agree­ment with the experimental points is quite good, being within 3% over the entire range of x investigated. For comparison, a dashed line relation is also plotted in the figure, and represents the relation derived during our earlier work18 using the linear M(x) relation together with Eq. (4) for K(x). It is seen that it is a good fit to the experimental points only for x'::; 1.0.

B. BaO·x[TiCoOa]·(6-x)Fe203 Series

The points in Fig. 4 show the experimental values of Han from Table II plotted against TiCo content (x). It is evident that Han decreases rapidly with increasing TiCo. Also plotted in the figure is a relation for Han (x) arrived at by combining M(x) and K(x) as described below.

Figure 5 shows normalized room-temperature experi­mental values of saturation magnetization M(x)/M(O) plotted against x as obtained by Brockman.4 Also plotted are two points reported by Gorter et al,2s obtained at liquid-nitrogen temperature, and two points reported by Smit and Wijnll measured at liquid-hydro­gen temperature in high magnetic fields. The dashed line linear variation given by Gorter25 is based on the

26 H. Casimir et id., J. Phys. Radium 20, 360 (1959).

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3486 D. J. DE BITETTO

18 -;;; ..., ? 16 .. o , 14

E

" - 12 c o

I10

o ...J W 8-IL

~ sl

~ 41 2 2L « I

°0~~~OL~2--~~0~~4--~~0~.6~~~0~.8~~~l.O~~~1.2

X in BaO'x [TiC003}{S-xlFe203

FIG. 4. Variation of anisotroEY field with composition in BaO·x[TiCo03J· (6-x)Fe203.

assumption that both Ti and Co ions substitute prefer­entially for some Fe ions in only the A sites (the 16 favorably oriented moments), which obviously fits his data quite well. However, this assumption does not closely fit either the data of Brockman or that of Smit and Wijn.

Another substitutional possibility that was men­tioned by Gorter25 that does not agree so well with his data, but does fit Brockman's and Smit and Wijn's data equally well, appears to be a better compromise. This is based on a random distribution of both Ti and Co ions among only the 18 octahedral sites. The result­ing relation governing this event is

M(x)/ M(O)= 1- (7/36)x, (6)

which is plotted as the solid line in Fig. S. Since this relation is a better fit to all the points, it is considered the correct one. The conclusion that Co occupies octahedral sites is in agreement with the similar conclu­sion by Lotgering et al.26 based on the analysis of low-

.6 o .i ~.4

.2

Ti ,Co random among all octahedral sites

" ~,,[] b Ti, Co preferential in A - sites " ""

a BROCKMAN et 01.

e GORTER

A SMIT a WIJN

[]

OL-__ -L __ ~~ __ ~ __ ~ ____ J-__ ~ __ ~

o .2 .4 .6 .8 1.0 1.2 1.4

X in BoO, X [TiCaOs]' (S-Xl FezOs

FIG. 5. Variation of saturation magnetization with composition in BaO·x[TiCo03} (6-x)Fe20 3.

26 F. K. Lotgering, U. Enz, and J. Smit, Philips Res. Rept. (to be published); also, J. Smit, F. K. Lotgering, and U. Enz, J. Appl. Phys. Suppl. 31, 137 (1960).

temperature torque curves In the region of the com­pensation point.

For K(x) we assume that the magnetocrystalline anisotropy energy can be expressed as the difference between two quadratic terms

n= (K t -K2)sin28=K'sin28,

where we associate KI with the anisotropy energy due only to the Fe+3 ions and K2 with that due to the pres­ence of the CO+2 ions. We also assume that each Fe ion gives the same contribution to Kl(X). We similarly assume that each Co ion gives the same contribution to K 2(x), with the reservation that its contribution may differ in magnitude from that of the Fe ion. Hence

Kl(X)=C(24-4x) and K 2(x)=aC(2x),

where C is a constant.

,.;- 3.5 E " "-~3.0 :;;

~:25l 22.0

;: CIJ

81.5r ~ 1.0~ ~05~ 2

<! 0 I O~----~0~.2----~O~.4--·--~0~.6~--~O~.8~--~1.0~--~1.2

X in BoO, X[TiCoOJ'{S-xl Fe203

FIG. 6. Variation of anisotropy constant with composition in BaO·x[TiCo03} (6-x)Fe203.

Hence the effective anisotropy constant K' becomes proportional to 12-x(2+a). Combining this with Eq. (6), we obtain an expression for Han(x) containing the parameter a. This parameter is determined by choosing the value that gives the best fit to the experi­mental points of Fig. 4. The value so obtained is a = 8.2, hence we arrive at

Han(x)/Han(O) = (1-0.8Sx)/1-0.194x). (7)

This relation is plotted in Fig. 4 and predicts a zero H an at X= 1.18, which agrees fairly closely with the room-temperature result27 and 90 0 K result26 inferred from the experimental results of other workers.

Having determined a as above, we now have for K' (x)

K' (x)/ K' (0) = 1-0.8Sx. (8)

This linear relation is plotted in Fig. 6; the points plotted in the figure were determined by combining the experimentally obtained values of Han (from Table II) with values of M determined by Eq. (6). It is obvious that the relation of Eq. (8) agrees with the points quite well, and hence verifies our independent

27 Ref. 11, p. 208.

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A N ISO T R 0 P Y FIE L D SIN HEX AGO N A L FER RIM A G NET leo X IDE S 3487

assumptions regarding K(x). Although the room~ temperature points reported by Smit and Wijn27 do not indicate a linear variation of K' with x, the more recent measurements of Lotgering et al.26 at 90cK indicate a linear variation at x< 1.18 very similar to our Eq. (8). We note that this relation predicts a vanishing K' at X= 1.18, and a planar anisotropy at x> 1.18, in close agreement with the experimental findings of other workers.26 ,27

ACKNOWLEDGMENTS

Much of this work was done in collaboration with F. K. du Pre, to whom the author is grateful for an

introduction to this field of study, for his continuing interest and encouragement, and for many valuable discussions. The author is also grateful to D. W. Kraft for his valuable association in the latter phases of the experimental work and for helpful comments on the manuscript. Indebtedness is also acknowledged to F. G. Brockman and W. G. Steneck, Jr., of the mag­netics group for the preparation of all sample materials and for static magnetic measurements. Thanks goes to Mrs. Jeanne Taylor of the x-ray group for determin­ing the unit cell dimensions of the members of the BaO·x[TiCoOa} (6-x)Fe20a series. Able technical as­sistance was provided by F. W. Rock.

JOURNAL OF APPLIED PHYSICS VOLUME 35. NUMBER 12 DECEMBER 1964

Superconducting Tubes and Filaments*

G. ARRHENIUS, R. FITZGERALD, D. C. HAMILTON, B. A. HOLM, AND B. T. MATTHJAst

lnstitute for the Study of Af atter, University oj California, La J oila, California

AND

E. CORENZWIT, T. H. GEBALLE, AND G. W. HULL, JR.

Bell Telephone Laboratories, Inc., Murray Hill, New Jersey

(Received 23 June 1964)

A study is reported of the superconductivity and microstructure which occur when small quantities of La are quenched with Rh in the arc furnace. A strikingly regular prismatic honeycomb of a superconducting compound is found when the La concentration is ~ 0.5 at. %. For smaller concentrations a continuous net­work of the superconducting phase is no longer observed which correlates with the lowering and broadening of the superconducting transition region. Evidence is given that for such low concentrations superconducting tunneling occurs through the elemental Rh phase itself thus pointing to the superconductivity of Rh at lower temperatures.

I T is well known, that under some circumstances, small amounts of a second phase can make a sample

appear completely superconducting because shielding currents flow in such a way as to make the sample com­pletely diamagnetic. Particularly striking examples were found recently in almost all systems prepared by melting small amounts of some rare earth metals with Rh and Irl in an arc furnace. For instance, as little as 0.05 at.% Y in Ir led to the development of complete diamag­netism in the bulk sample; i.e., the entire volume of the bulk melt is shielded by supercurrents when exposed to rf radiation at temperatures well above the transition temperature of Ir. Substantial evidence, which indicates that the superconducting shielding currents are carried by an intermediate-phase compound, can be briefly summarized as follows: For dimensional reasons, neither Y nor La will dissolve appreciably in Rh or Ir because

* Part of this work was carried out under a grant from the U. S. Air Force Office of Scientific Research.

t Also with Bell Telephone Laboratories, Inc., Murray Hill, New Jersey.

1 T. H. Geballe, B. T. Matthias, V. B. Compton, E. Corenzwit, G. 'W. Hull, Jr., and L. D. Longinotti, Phys. Rev. (to be pub­lished). See also Rev. Mod. Phys. 36, 155 (1964).

of the disparity in atomic radii. Therefore, the appear­ance of superconductivity with total shielding of the bulk material must be due to small amounts of an intermediate, superconducting phase, distributed in some rather critical geometric fashion. The size of the heat capacity2 anomaly in the Y-Ir system at the transition drops as one proceeds toward more Ir-rich melts. It can easily be seen that this is not a solid solu­tion, since the superconducting-volume fraction of fine powder prepared from the sample drops in a similar manner. The superconductivity observed in the sys­tems discussed is thought to be due to the ABo compounds.3

Almost as long as superconductivity has been known, the concept of superconducting filaments has been used to explain the kind of behavior described here, although the actual arrangement has never been observed. In

2 We are indebted to J. P. Maita for measuring the heat capaci­ties of the Y-Ir samples.

3 That AB. compounds of the transition elements are likely to be superconducting can be seen from the data in Ref. 1, and also from the results for BaAu. of G. Arrhenius, Ch. J. Raub, D. C. Hamilton, and B. T. Matthias, Phys. Rev. Letters 11, 313 (1963).

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