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FERROMAGNETIC RELAXATION MODEL OF MAGNETIC ORDERING IN Y(Fe0.022Co0.978)2 AT
LOW TEMPERATURES
M. Corson, G. Hoy, B. Kolk
To cite this version:
M. Corson, G. Hoy, B. Kolk. FERROMAGNETIC RELAXATION MODEL OF MAGNETIC OR-
DERING IN Y(Fe0.022Co0.978)2 AT LOW TEMPERATURES. Journal de Physique Colloques, 1979,
40 (C2), pp.C2-159-C2-160. �10.1051/jphyscol:1979256�. �jpa-00218654�
FERROMAGNETIC RELAXATION MODEL OF MAGNETIC ORDERING IN Y ( F e
Q > 0 2 2C o
Q > 9 7 8)
2AT LOW TEMPERATURES
M.R. Corson, G.R. Hoy and B. Kolk
Physios Department* Boston University, Boston Massachusetts, 02215, U.S.A.
Abstract.- Mossbauer measurements were performed on the pseudobinary cubic Laves phase compound Y(Feo.o22Co0.978)2 from 300 K down to 0.18 K. Our spectra recorded between 300 K and 8 K show a simple quadrupole doublet with (e2qQ)/2 = -0.42 mm/s, whereas below 4.2 K a nuclear Zeeman plus qua- drupole pattern begins to emerge. We have applied a stochastic, ferromagnetic relaxation model to interpret these results. The total spectrum consists of two subspectra from magnetically inequiva- lent sites. We obtain Curie temperatures for the two sites of 3.2 ± 0.2 K and 4.3 i 0.1 L Above 3 K, the relaxation rates show T9 temperature dependences. The maximum effective magnetic field of 115 kG suggests an iron magnetic moment of one Bohr magneton. Inhomogeneous field broadening is also obser- ved.
1. Introduction.- Much work has been done on the ma- gnetic properties of the cubic Laves phase compounds RB2, where R is yttrium or a rare earth, and B is a
transition metal. The pseudobinary system
Y(Fe Co, )„ has been studied for many values of x x i-x 2
over a wide temperature range, using both Mossbauer spectroscopy IM and bulk magnetization measurements /2/. Previous studies of Y(Fe COj_ )2 show that the magnetic moment of an iron atom deviates from that predicted by the rigid band model of Piercy and Taylor /3/ for x < 0.1. In addition, it is known that a single iron-atom impurity in YCo2 possesses a magnetic moment IM. These facts suggest that a transition from an itinerant to a localized elec- tron model occurs in this system for small values of x.
2. Experimental.- The polycrystalline Y(Fe0.o22 Co0.97a)2 absorber, which was kindly supplied by the Netherlands group /l/, was mounted inside the mixing chamber of our He-3/He-4 dilution refrigera- tor. Mossbauer measurements were performed from 300 K down to 0.18 K. The resulting spectra (see Fig. 1) show a simple quadrupole splitting from 300 K down to 8 K. Below 4.2 K, the spectrum begins to broaden, and between 3 K and 2 K the hyperfine pattern is unresolved. Below 2 K, a clearly defined Zeeman plus quadrupole pattern emerges, although with significant line broadening. We believe that
the observed line broadening is primarily due to relaxation processes.
As was found for ZrFe2 / 4 / , our total spectrum consists of two subspectra. One subspectrum is from iron nuclei at which the axially symmetric electric field gradient (EFG) major axis is parallel to the
jllT) easy axis of magnetization (identified here by 0°), and has a relative weight of one. The other
subspectrum is from iron atoms where this angle is 70.53° (here called 70°), with a relative weight of three.
12 Fig. 1 Representative data for an Y(Feo.o22Coo.978)2 absorber are shown as crosses. The solid curves are obtained from ferromagnetic relaxation theory using the parameters given in the text.
JOURNAL DE PHYSIQUE Colloque Cl, supplément au n° 3, Tome 40, mars 1979, page C2-159
Résumé.- Des observations par effet Mossbauer ont été réalisées sur des composés phase Laves pseudo- binaire et cubique Y(Fe0.022C00.97s)2 àe 300 K à 0,18 K. Le spectre enregistré entre 300 K et 8 K
est un doublet quadrupolaire avec (e2qQ)/2 = -0,42 mm/s; au-dessous de 4.2 K c'est un sextuplet Zeeman plus un doublet quadrupolaire. Nous nous sommes servis d'un modèle de relaxation stochastique et ferromagnétique pour interpréter ces résultats. Le spectre total se compose de 2 sous-spectres provenant de 2 sites qui ne sont pas équivalents du point de vue magnétique. Nous obtenons les tem- pératures Curie pour les 2 sites, soit 3,2 ± 0,2 K et 4,3 ± 0,1 K. Au-dessus de 3 K, les vitesses de relaxation dépendent de la température par une loi en T9. Le champ magnétique effectif de 115 kG^
suggère un moment magnétique ferrique d'un magnéton de Bohr. Un champ non homogène est aussi observé.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979256
c2- 160 JOURNAL DE PHYSIQUE
3. Theory.- Blume /5/ has developed a "non-adiabatic"
stochastic theory of line shape in the effective field approximation, and we have applied this theo- ry to analyze our experimental data. The effective field nuclear Hamiltonian for our case is :
2
= g~?.g(e)f(t) + II(e2q~)/g 1: -1(1+1>7 where I is the nuclear spin, 9is the angle between the effective magnetic field and the EFG symmetry axis, and the function f(t) is a stationary, Markof- fian chain which takes on the values 2 1. The effec- tive magnetic field thus jumps between "up" and"down" along the easy axis of magnetization. This model can be used to study ferromagnetic relaxation, because the probability of finding theeffective ma- gnetic field "up" does not have to equal that of finding it "down". The non-adiabatic theory is nee- ded in our case because the angle 0 for one of the subspectra is not 0'.
4. Results.- Some representative theoretical and experimental results are shown in figure 1. The quadrupole interaction and the isomer shift were assumed identical for both subspectra, as has been found in similar compounds /4/, and are : (e2q~)/2 = -0.42 mm/s, 6 = 0.01 mm/s (at 4.2 K, relative to an iron metal absorber at room temperature). The magni- tude of the fluctuating magnetic field,
!HI
-+ = 115 kG, was found to be the same for both subspectra. All these values (except for the effect of the second order Doppler shift) were held fixed for all tempe- ratures. The full effective magnetic field of 115 kG suggests that the magnetic moment of the iron atom is about one Bohr magneton.The degree of magnetic order (the average va- lue of f(t))for each subspectrum is plotted in fi- gure 2.
TEMPERATURE (K)
This magnetic ordering shows behavior characteristic of magnetization curves having critical temperatures of 3.2
+
0.2 K (0') and 4.3 2 0.1 K (70"). The total probabilities per microsecond, W, of an effective field flip for each subspectrum, as a function of temperature, are found to be :~(0') = (250 2 100) + (0.05 2 0.01)~' w(70°)= (350 2 80) + (0.005
+.
0 . 0 0 1 ) ~ ~Above 3 K, the dominant T' term indicates that Raman processes are responsible for the relaxation.
5. Conclusions.- We report in this paper one of bhe first applications of a non-adiabatic, stochastic model of magnetic ordering to explain complicated Miissbauer spectra. Our approach was motivated by the desire to fit our spectra with a more coherent theo- ry than the often applied distribution o-f fields model. This relaxation theory represents well the overall features of our spectra as a function of temperature. Our values for the reduced magnetic or- der, shown in figure 2, follow characteristic magne- tization curves, and our relaxation rates, W, have reasonable temperature dependences. These facts sup- port the conclusions that relaxation is occuring in our system, and that the derived parameters are rea- sonably accurate. However, as seen in figure l, at low temperatures the theoretical fit is not extre- mely good. In addition, the reduced magnetic order does not approach one and the relaxation rates W do not approach zero at low temperatures. Therefore, we must conclude that there is some residual effect due
to inhomogeneous fields
111.
References
/I/ Luijpen, M.G., Gubbens, P.C.M., Van der Kraan, A.M., Buschow, K.H.J., Physica 86-88B (1977) 141 and references therein.
/2/ Steiner, W., Ortbauer, H., Phys. Status Solidi (A)
2
(1974) 451, and references therein.131 Piercy, A.R., Taylor, K.N.R., J. Phys. C (Proc.
Phys. SOC.)
l
(1968) 1112./4/ Wertheim, G.K., Jaccarino, V., Wernick, J.H., Phys. Rev.
135
(1964) A151./5/ Blume, M., Phys. Rev.
174
(1968) 351.Fig. 2 : The reduced magnetic order parameters for the two sites are plotted as a function of tempera- ture. These values are obtained by fitting our ex- perimental data using ferromagnetic relaxation theory.
