Anisotropy Fields in Hexagonal Ferrimagnetic Oxides by Ferrimagnetic Resonance

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  • 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: View Table of Contents: 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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    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 magneto-crystalline anisotropy fields (Han) of two compositional series of hexagonal ferrimagnetic oxides are re-ported. 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 (BaOx[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 varia-tion 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. '


    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 anisot-ropy 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 Fer-roxdure is about 17 kOe, resulting in a ferrimagnetic resonant frequency of about 50 Gclsec with no exter-nally 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 corre-sponds 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 tempera-ture 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), anisot-ropy constants (K), and anisotropy fields (Han) are also presented.


    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 pro-ceeds 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 radia-tion 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 ma-terials 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 wave-guide (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 di-mension 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 speci-mens 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 re-ductions 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 micro-wave 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 (con-sidered 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 Os-born'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 propaga-tion. Although this results in a slow variation of the phase of the precession along the length of the specimen, it seems clear never-theless 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 line-width 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., trans-mission 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 meas-urements 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 accu-racy 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 line-width (.-.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 line-width (::;;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 SrOxAhOa (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 BaOx[TiCoOaJ (6-x)Fe203'

    o 17.5 1.6


    14.8 1.85


    11.5 2.5


    8.75 1.7


    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 t...


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