THE g-FACTOR AND SURFACE MAGNETIZATION OF PURE IRON ALONG [100] AND [111] DIRECTIONS

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THE g-FACTOR AND SURFACE MAGNETIZATION OF PURE IRON ALONG [100] AND [111]

DIRECTIONS

Z. Frait, R. Gemperle

To cite this version:

Z. Frait, R. Gemperle. THE g-FACTOR AND SURFACE MAGNETIZATION OF PURE IRON ALONG [100] AND [111] DIRECTIONS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-541- C1-542. �10.1051/jphyscol:19711182�. �jpa-00214005�

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JOURNAL DE PHYSIQUE Colloque C 1, supplement au n° 2-3, Tome 32, Fevrier-Mars 1971, page C 1 - 541

THE g-FACTOR AND SURFACE MAGNETIZATION OF PURE IRON ALONG [100] AND [111] DIRECTIONS

by Z. FRAIT and R. GEMPERLE

Institute of Physics, Czechoslovak Academy of Sciences, Prague

Résumé. — En vue de la détermination exacte du facteur g du fer nous avons étudié la résonance ferromagnétique entre 12 et 70 GHz sur des monocristaux en forme de whiskers dans les directions [100] et [111], à la température ambiante.

Le facteur g est le même pour les deux directions (2,089 ± 0,007), et indépendant de la fréquence. La valeur de l'intensité de l'aimantation est déduite des mesures de l'antirésonance à 70 GHz, les résultats montrent une petite anisotropie

(Mioo = 1 697,3 u. e. m./cm^ ; M m = 1 700,0 u. e. m./cm').

Abstract. — In order to obtain exact values of the spectroscopic splitting factor in pure iron along the [100] and [111]

crystallographic directions, measurements of ferromagnetic resonance in whisker type single crystals have been performed in the frequency range 12 4- 70 GHz, at room temperature. The results show that the ^-factor is independent on frequency in the given range and yield the value g = 2.089 ± 0.007 for both directions. A slight anisotropy of the surface magne- tization has been found (Mioo = 1 697.3 e. m. u./cm3; M m = 1700.0 e. m. u./cm3) using the antiresonance measurement at 70 GHz.

I. Introduction. — The values; of the spectroscopic splitting factor (^-factor) in pure iron measured untill now [1 + 8] vary from 2.03 to 2.16, i. e. in a range much borader than the reported limits of experimental accuracy (usually + 0.02). The measurements were mostly performed on polycrystals, the only measurement in single crystals at room temperature has been reported by Usami et al. [1] on thin films (g = 2.03).

Rodbell [2] found in whiskers g = 2.05 at 315 °C.

In order to obtain more exact data we have performed F M R measurements on pure (99.99 %) iron single crystals, at room temperature, using microwave frequencies from 12 to 70 GHz. As we were looking for a possible anisotropy of the g-factor, two types of single crystals in the whisker form were used, with long axis pointing along the [100] or [111] direction.

The experiments on such samples offer several advan- tages. The small linewidth [2] yields high accuracy of resonance measurements, the natural surface of good samples has perfect quality, the samples have low demagnetizing field values and are easily saturated.

II. Measurements and their evaluation. — The main disadvantage of evaluating measurements on single crystals is the necessity of exact knowledge of magnetocrystalline anisotropy constants. However, the method of evaluation used by us permits to avoid this difficulty ; moreover, it excludes the influence of inaccuracy in static demagnetizing field determination and, as far as possible, of other secondary effects.

Our basic assumption is the independence of the g-factor, surface magnetization and anisotropy constants on frequency in the range considered. This was verified on bulk crystals in a previous experiment [9], further justification will be mentioned later on.

The FMR experiments were performed at 28 °C on five microwave spectrometers (in the X, Ku, K, Ka and V bands). We used an auxiliary hf modulation of the static magnetic field, narrow-band amplification and lock-in detection, measuring the derivative of the real component of surface impedance (in arbitrary units) as a function of the applied static field. The microwave

frequency was measured accurately to 2 x 10~4, a NMR gaussmeter was used for magnetic field measurement. The accuracy of the resonance field determination is limited from + 10 Oe at 12.5 GHz (linewidth approx. 100 Oe) to + 20 Oe at 70 GHz (linewidth approx. 250 Oe). The length of our samples was about 2 mm and width of the order of 10 um, they were magnetized along their long axis.

For the evaluation of the results we have used KittePs resonance condition in the form

co² = y²(H^tes -6H+H^K)x

x ( #^{r e s} - SH + H^K + 4 uM) , (1) where co is the microwave frequency, y — gfi^Blh, ^^B i^s the Bohr magneton and h the Planck constant, Hni is the value of the applied static field at the maximum of the real component of surface impedance,

HK = Ha + Hd,

H^ is the effective field of the magnetocrystalline ani- sotropy, Hd is the effective demagnetizing field of the sample and M the surface magnetization. The resonance field correction 8H includes the influence of relaxation, surface spin pinning and the exchange- conductivity effect [9, 10, 11], it depends on co, M, the exchange constant A, resistivity p, relaxation cons- tant X and the surface anisotropy constant Ks. Since 8H depends on co, it has to be calculated a priori;

here it was determined by means of a computer from the theoretical formulas for the surface impedance derived previously [9], using following parameters : M = 1 700 e. m. u./cm3, p = 9.7 uQ/cm [12],

A = 2 x 1 0- 6 erg/cm [13],

X = 4.2 x 10⁷ rad/sec [14], K^s = 0.03 erg/cm² [14].

The resonance field values H^tes were measured at eleven frequencies in the range from 12.5 to 70 GHz.

Using the computed corrections 8H the values of y and HK were found from least-squares fit of equation (1) to the experimental data. The deviations of the measured values of HTes from the values calculated

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711182

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C 1 - 542 2. FRAIT AND R. GEMPERLE from equation (1) (using the least-squares method) are

distributed at random, with no systematic frequency dependence. Thus there is no evidence of the frequency dependent g-factor, in the limit of the present accuracy.

The least-squares procedures has been carried out for eleven values of 4 n M from 21 300 e. m. u. to 21 500 e. m. u. in order to obtain the functions y = y(4 nM), HK = HK(4 nM). As HK is very slightly dependent on 4 n M the appropriate values of 4 n M and y were computed from the antiresonance field values Ha,, (measured at 70 GHz) and the antiresonance condition

where 6Ha,, was computed in the same manner as 6H.

111. Results. - Twenty samples with the long axis parallel to the [loo] direction and ten [ I l l ] samples were selected from various batches of whiskers, both fresh and old (up to two years) whiskers were measured.

The mean value of g-factor has been found equal for both crystallographic directions investigated,

(see Fig. 1). The value closest to ours was measured by Meyer and Asch (2.09) [7]. The present value compares well with the results of measurements of the gyro- magnetic factor g' ; from the results of several authors [7] one obtains by means of Kittel-Van Vleck formula g,,,, = 2.078 _f 0.01. We cannot explain the spread of g-values measured for individual samples (see Fig. I), which is several times higher than the accuracy of measurement. One cannot exclude, that the g-factor is slightly dependent on small amount of impurities or small residual stresses in the samples, such possible effect could explain the difference in g found by different authors [ l i- 81. However, much more exten- sive and detailed study is needed t o substantiate such hypothesis.

For the surface magnetization different values have been found for the [loo] and [ I l l ] direction,

FIG. 1. - Plot of the number of samples (n) vs g-factor values of individua1 samples for all samples measured (full line) and

for [I001 direction only (dashed line).

the accuracy for the experimental determination of this parameter is mainly given by the accuracy of antiresonance field measurement (+ 15 Oe) and is approx.

+

1.3 e. m. u./cm3. The difference between the two axes is approx. of one order of magnitude higher than found by Aubert in nickel 1151. The mean value of M itself is lower than the value determined by Weiss and Forrer, M = 1 714 e. m. u./cm3 [16]. Using the recent saturation magnetization value at absolute zero (Danan et al. [17]) and the value of the ratio of room temperature value to absolute zero value (determined by Graham [18]) one obtains the value 1708 e. m. u./cm3, in better agreement with our results. A secondary result of the present experiment is the value for the first two anisotropy constants, Kl = 4.86 f 0.3 x lo5 erg/cm3,

in agreement with static measurements 118, 19, 201.

[I] USAMI (S.), ITOH (K.), GONDO (Y.), KONNO (H.), FUNATOGOWA (Z.), Bull. Fac. Eng., Yokohama Natl. Univ., 1963, 13, 97.

[2] RODBELL @. S.), J. Appl. Phys., 1959, 30, 187 S.

[3] BAGGULLEY (D. M. S.), Pmc. Phys. Soc., 1953, A66, 765.

References

[4] STANDLEY (K. J.) and STEVENS (K. W. H.), Proc.

Phys. Soc., 1956, B69, 993.

[S] BARLOW (G. S.), STANDLEY (K. J.), Proc. Phys. Soc., 1956, B69, 1052.

[6] MEYER (A. J. P.), ASCH (G.), J. Appl. Phys., 1961, 32. 330 S.

-- -.. -

171 ASCH (G.), C. R. Acad. Sci. Paris, 1959, 249, 1483.

[8] FISCHER (G.), C. R. Acad. Sci. Paris, 1966, B262, 1654.

[g] FRAIT<z.), M~CFADEN (H.), Phys. Rev., 1965, 139, A1173.

[lo] AMENT (W. S.), RADO (G. T.), Phys. Rev., 1955, 97, 1558.

[ll] FRAIT (Z.), PAULINY-T~THOVA (L.), VESELA (M.), Czech. J . Phys. B, 1970, to be published.

1121 BOZORTH (R. M.), Ferromagnetism @. Van Nos- trand, Inc.), New York, 1951, Chap. 4.

[13] FRAIT (Z.), ONDRIS (M.), Phys. Stat. Sol., 1962, 2, K185.

[14] FRAIT (Z.), FRAITOVA (D.), KOTRBOVA (M.), HAUPT-

MAN (Z.), Czech. J. Phys., 1366, B16, 837.

[15] AUBERT (G.), J. Appl. Phys., 1968, 39, 504.

[16] WEISS (l?.) and FORRER (R.), Ann. Phys., 1929, 12, 279.

[17] DANAN (H.), HERR (A.) and MEYER (A. J. P.), J.

Appl. Phys., 1968, 39, 669.

[18] GRAHAM (C. D., Jr), J. Appl. Phys., 1960, 31, 150 S.

[19] SATO (H.) and CHANDRASEKHAR (B. S.), J. Phys.

Chem. Sol., 1957, 1, 228.

[20] KLEIN (H. P.) and KNELLER (E.), Phys. Rev., 1966, 144, 372.