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>
HAL Id: jpa-00214005
https://hal.archives-ouvertes.fr/jpa-00214005
Submitted on 1 Jan 1971
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
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 magnetization 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 FMR 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 advantages. 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, K u , 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(Htes
-6H+HK)x
x (# r e s - SH + HK + 4 uM) , (1)
where co is the microwave frequency, y — gfiBlh, ^ 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 anisotropy, 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 exchangeconductivity effect [9, 10, 11], it depends on co, M,
the exchange constant A, resistivity p, relaxation constant 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./cm 3 , p = 9.7 uQ/cm [12],
A = 2 x 1 0 - 6 erg/cm [13],
X = 4.2 x 107 rad/sec [14], Ks = 0.03 erg/cm2 [14].
The resonance field values Htes 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
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 HKis 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 gyromagnetic 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 extensive and detailed study is needed to 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.
References
[I] USAMI(S.), ITOH (K.), GONDO(Y.), KONNO(H.), [ll] FRAIT (Z.), PAULINY-T~THOVA
(L.), VESELA(M.),
FUNATOGOWA
(Z.), Bull. Fac. Eng., Yokohama
Czech. J. Phys. B, 1970, to be published.
Natl. Univ., 1963, 13, 97.
1121 BOZORTH
(R.M.), Ferromagnetism @. Van Nostrand, Inc.), New York, 1951, Chap. 4.
[2] RODBELL
@. S.), J. Appl. Phys., 1959, 30, 187 S.
(D. M. S.), Pmc. Phys. Soc., 1953, A66, [13] FRAIT(Z.), ONDRIS(M.), Phys. Stat. Sol., 1962,
[3] BAGGULLEY
765.
2, K185.
[4] STANDLEY
(K. J.) and STEVENS
(K. W. H.), Proc. [14] FRAIT(Z.), FRAITOVA
(D.), KOTRBOVA
(M.), HAUPTPhys. Soc., 1956, B69, 993.
MAN (Z.), Czech. J. Phys., 1366, B16, 837.
[S] BARLOW
(G. S.), STANDLEY
(K. J.), Proc. Phys. Soc., [15] AUBERT
(G.), J. Appl. Phys., 1968, 39, 504.
1956, B69, 1052.
(land
?
FORRER
.) (R.), Ann. Phys., 1929, 12,
[6] MEYER(A. J. P.), ASCH(G.), J. Appl. Phys., 1961, [16] WEISS
279.
3
2. 330
--..S.
171 ASCH(G.), C. R. Acad. Sci. Paris, 1959, 249, 1483. [17] DANAN(H.), HERR(A.) and MEYER(A. J. P.), J.
Appl. Phys., 1968, 39, 669.
[8] FISCHER(G.), C. R. Acad. Sci. Paris, 1966, B262,
[18] GRAHAM
(C. D., Jr), J. Appl. Phys., 1960, 31, 150 S.
1654.
(B. S.), J. Phys.
[g] FRAIT<z.), M~CFADEN
(H.), Phys. Rev., 1965, 139, [19] SATO(H.) and CHANDRASEKHAR
Chem. Sol., 1957, 1, 228.
A1173.
(E.), Phys. Rev., 1966,
[lo] AMENT(W. S.), RADO(G. T.), Phys. Rev., 1955, [20] KLEIN(H. P.) and KNELLER
144, 372.
97, 1558.