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DYNAMIC AND STATIC METHODS OF
DETERMINING MAGNETOSTRICTION
CONSTANTS IN FERRIMAGNETS WITH
ORBITALLY DEGENERATE IONS : A
COMPARATIVE STUDY
R. Rivoire, R. Krishnan
To cite this version:
JOURNAL DE PHYSIQUE Colloque C1, suppliment au no 4 , Tome 38, Aoril 1977, page C1-199
DYNAMIC AND STATIC METHODS
OF DETERMINING MAGNETOSTRICTION CONSTANTS
IN FERRIMAGNETS WITH ORBITALLY DEGENERATE IONS
:
A COMPARATIVE STUDY
R. RIVOIRE and R. KRISHNAN
Laboratoire de Magnttisme, C . N. R. S., 1, Place Aristide Briand, 92190 Meudon-Bellevue, France
Rbum6. - On compare les mkthodes dynamiques et statiques de mesure des constantes de magnetostriction 1.hkl. Cette etude comparative devient importante dans les cas oh I'on considere un ion paramagnetique avec un moment orbital non nu]. En effet on sait que dans ce cas I'aniso- tropie magnetique K I depend de la mtthode de mesure.
Dans cet article, on decrit les etudes effectuks par dilatomktrie et par resonance sur exactement les rne^mes irhantillons.
Les compositions etudiks sont : NiFetO4 avec des ions Niz+ dans les sites tetraedriques et
Y 3FesO12 : Zn
+
Ru3+ . I - Ru4+. La premitre composition apparait comme un cas limite pour des techniques de rbonance car la courbe de resonance est deformke par la contrainte uniaxiale ;I'kart entre les rCsultats des deux mtthodes est eleve.
La methode par rksonance et la methode statique fournissent le mCme signe pour l l h r l , mais la
premiere surestime la valeur absolue d'un facteur 2. Dans le cas du grenat la surestimation sur
l h k l est d'environ 30 % ; en ce qui concerne Kt les deux techniques fournissent des risultats identi-
ques.
En conclusion, la mkthode de resonance est toujours consider& comme valable et interessante. Alors que pour K I les niveaux d'energie les plus bas sont en cause, pour l h k l les etats excites de
plus haut niveaux, qui semblent sensibles aux contraintes uniaxiales, apportent aussi une contribu- tion.
Abstract. - Dynamic and static methods of measuring magnetostriction constants l h k l are
compared. This comparative study becomes relevant for the cases where a paramagnetic ion with non zero orbital moment is involved. Indeed magnetic anisotropy K I in suche cases is known to depend on the method of measurement. Here we report on a study of the very same sample by dila- tometer and resonance techniques. The samples are NiFe204 with tetrahedral Ni2+ and Y 3Fe50 I 2 ;
Zn -5 Ru3'- -4- Ru4+. The formcr is seen to be a limiting case for resonance technique as the reso- nance curve is deformed by the uniaxial stress and the discrepancy between the two methods is very high. Resonance and static methods give the same sign for L h k l but the former overestimates it
by a factor of 2. For the garnet compound the overestimation for l h h - I is about 30 % but as regards
K 1 the two techniques yield similar results.
In conclusion, the resonance method is considered still an attractive and valid one. While for K 1 , the lowest lying energy levels are involved, for l h k l the higher excited states wuld also contri-
bute and which seem to be sensitive to the uniaxial stresses.
1. Introduction.
-
Magnetostriction along with ani- sotropy is a fundamental parameter of a magnetic compound and is important from both fundamental and applications points of view. The magnetostriction constants like A,,, and A,,,
of a magnetic crystal are normally determined by static methods like dilatometer o r strain gauge techniques o r by dynamic method involving ferromagnetic resonance under stress. While the former is a direct method the latter is based on the study of magnetoelastic energy contributions to the total anisotropy of the sample under a stress.It is well known that when certain magnetic ions with relaxation phenomenon are involved, the time taken for a thermodynamical equilibrium distribution of electrons amongst the different available levels becomes an important parameter and could influence the results
in dynamical methods of measurements. Such a problem is known already in the measurements of magnetic anisotropy of certain rare earth garnets by static and dynamic methods [I]. It is the purpose of this paper to attempt a t a comparative study of the measu- rements of magnetostriction constants A,,, by dilato- meter and resonance methods. Such a study is very desirable as on the one hand the resonance technique is attractive as it calls for only small size samples and is being employed more and more by workers and on the other no systematic study has been so far reported where the same specimen has been measured
by both static and dynamic methods as we report here. For such a study one has to choose a metal ion with non zero orbital moment and we have hence considered Ru3+, Ru4+ ~n ' Y,Fe,O,, and Ni2+ in the tetrahedral
C1-200 R. RIVOIRE AND R. KRISHNAN
sites of NiFe204. The above compounds have been already investigated by us and others [2-51.
2. Experimental. - As the two methods we are employing here have been already described in the litterature we shall mention here only briefly the experi- mental conditions which are relevent for the discussion of the results [6-81.
In the static method the spherical sample was oriented such that the change in length 6111 was always measured along [011] with the static field either parallel or perpendicular to this axis, the field lying in the [I 101 plane, the angle it makes with [OOl] being 0. Under this configuration we have
For the resonance method, the stress was applied along [I101 and the resonance fields measured in the (1 10) plane, and we computed, 1,
,,
and A,,,
from the change in the field for resonance (6H) brought by the uniaxial stress along the symmetry axes. To calculate the stress the effective area was taken as k r R 2 where k is a constant less than unity that we discuss later and R is the radius of the sample. In all cases we limited ourselves to the conditions where the change in the resonance field was of the order of 10%
of the line- width and it was proportional to the stress.3. Results and discussions. - Table la and Ib show the results obtained by the two techniques at 295 and 77 K for NiFe204 both in the annealed and the quenched states. In resonance experiments it is customary to take the effective surface as knR2 where k = 213. It is beyond the scope of this paper to go
into details of this particular problem. We only wish to remark that k is actually an adjustable parameter such that the resonance results agree with those of static. As we disposed static measurement results on NiFe204 in the annealed state [8] we took k = 0.8 in order that our results by resonance method show the best agreement. Once this value of k is chosen it is to be maintained since it cannot be modified either by changing the ionic distribution or by small dopings like Ru in YIG. In any case the absolute value of k will not influence our results. In table Ia and b the difference (A,,,)
,,,,,,,,,
- (A,,,),,,,,,,,
is attributed to the presence of Ni2' in the tetrahedral sites as has been discussed in earlier publication [4]. It is seen that the contribution from Ni2' is generally overes- timated (except for A,,, at 295 K) b y resonance method by about a factor of 2. In this connection it should be mentioned that for quenched sample a t 77 K the resonance curve was deformed by the appli- cation of the uniaxial stress though the linear depen- dence of 6H on the uniaxial stress was still maintained. This would indicate the limit of the validity of this technique. Nevertheless it is noteworthy that the two methods give the same sign A,,,.For the case of YIG : Ru
+
Zn crystals neither deformation of resonance curve nor non linearity of 6H with stress were observed.Table I1 shows the results at 295 K for YlG :
Ru
+
Zn. Resonance techniques were inadequate at 77 K due to large anisotropies involved.Two different compositions were measured. In these samples Z n 2 + are introduced to induce Ru4+ in the crystal by the mechanism Zn2 +
+
Ru4+ = 2 Fe3'.
One of us has recently studied the magnetic aniso- tropy K, in these compounds and has confirmed the presence of Ru4+ along with Ru3+ [9] in the crystals. The effective area for these garnets was taken as 213 nR2 in agreement with the value published currently by usMagrzetostriction constants i.,,, and I.,
,
,
for slowly cooled and quenched NiFe204 crystal.a) Resonance technique ; b) Dilatometer technique
Slowly cooled (A) Quenched from
1 050 OC (B) Contribution from
DYNAMIC A N D STATIC METHODS OF DETERMINING MAGNETOSTRICTION CONSTANTS C1-201
TABLE I1
Magnetostriction constants by resonance and dilatometer techniques for YIG : Ru
+
Zn crystals at 295 KSample wt
%
i,,,, x lo6 A , , , x lo6 AR-
AD
21,
No. Ru ZnO Resonance Dilatometer Resonance Dilatometer
-
- - - - -1 1.0 0.6 36 27 8.7 6.8 - + 3 0 0 / ; :
2 0.23 0.18 7.3 7.7
+
0.5-
0.2+
0.35
0.15 0 and other workers also. While for smaller Ru contentthe two methods give similar results within the limits of experimental error for higher Ru concentration, the resonance method yield I.,,, higher by about 30
%.
It is interesting to note that the difference here is isotropic whereas in the case of quenched NiFe,O, the difference was much pronounced along [OOl].With the results at hand we wanted to know the situation for K, too since the relaxation problems if they exist then they ought to influence the anisotropy as well. Unfortunately we could not do a systematic study but we measured only YIG : Ru
+
Zn 1. It was rather surprising to find that both the resonance and torsion balance methods yielded K, values which agreed to within 10%.
This leads us t o think that relaxation effects could influence magnetostriction measurements though they apparently do not perturbK , measurements. In this connection it might be
remarked that the microscopic origin of K,, lies in the lowest lying revels of an ion whereas excited states lying much above the ground state ( - 10 000 cm-') seem to influence the magnetostriction. A similar argu- ment was used to show that agreement between theo- retical and experimental values could be improved for the case of Ni2+ in the tetrahedral site [lo]. In this paper the authors have obtained smaller values of
A,2,, as compared to ours for a quenched NiFe20,.
The one ion contribution from tetrahedral Ni2+ to magnetoelastic energy is extremely high with
u , N 21 000 cm-' and u2
-
13000 cm-' whereu, and u2 have the usual definition [ll]. So slight
differences in tetrahedral NiZC concentrations by diffe- rence in the quenching methods could cause large changes in
A,,,.
We have, by studying the same sample by static and
dynamic methods shown that the latter could yield relatively higher values for the magnetostriction constants. However even under limiting conditions like in quenched NiFe,O, the dynamic method gives the correct sign for
A,,,,.
This is note worthy because the state of art in the theoretical prediction to day isnot on the magnitude of A,,, but on the sign. So the
resonance method is still attractive for complex compositions where one has to deal with small crys- tals. Though this present work has shown for the first time the merits and demerits of the resonance techni- que some more systematic study is needed to get a better understanding of the microscopic origin of these results. The work on some 3d, 5d and 4f metal ions is in progress which could hopefully give some ideas on the behaviour and particularities of the different nature of the orbitals involved.
The authors wish to thank A. Malmanche for pre- cise X-ray orientation of the samples.
References
[I] TEALE, R. W., PEARSON, R. G . and HIGHT, M. I., J. Appl.
Phys. Supp/. 32 (1961) 1503.
[2] KRISHNAN, R., CAGAN, V. and RIVOIRE, M., A . I. P. Conf.
Proc. 5 (1971) 704.
[3] HANSEN, P., Phys. Rev. B 7 (1973) 246. [4] DE LACHEISSERIE, E., J. Phys. 37 (1976) 379.
(51 KRISHNAN, K. and RIVO~RE, M., Phys. Star. Sol. (a) 7 (1971)
K 39.
[6] SMITH, A. B. and JONES, R. V., J. AppL Phys. 34 (1963) 1283 ;
KRISHANN, R. and CAGAN, V., Proc. Znt. Conf. Ferrifes
(1970) 57.
[71 VAUTIER, R. and DE LACHEISSERIE, E., Revue Phys. Appl. 1
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[8] Do LACHEISSERIE, E., Doctorat Thesis Paris 1967. [9] KRISHNAN, R., OUDET, X., PORTE, M. and MARAIS, A.,
Inr. Conf. Mag. (1976) Paper 7C 3.
[lo] LIOLIOU~SIS, K. T. and POINTON, A. J., Znt. Conf. on Ferrites
