STATISTICAL CONTRIBUTION OF THE TETRAHEDRAL IRON TO THE EXCHANGE INTERACTION IN MIXED YTTERBIUM GALLIUM GARNETS

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STATISTICAL CONTRIBUTION OF THE TETRAHEDRAL IRON TO THE EXCHANGE INTERACTION IN MIXED YTTERBIUM GALLIUM

GARNETS

A. Grill, M. Schieber

To cite this version:

A. Grill, M. Schieber. STATISTICAL CONTRIBUTION OF THE TETRAHEDRAL IRON TO THE EXCHANGE INTERACTION IN MIXED YTTERBIUM GALLIUM GARNETS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-195-C1-196. �10.1051/jphyscol:1971159�. �jpa-00214486�

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JOURNAL DE PHYSIQUE Colloque C I , suppliment aau ^rto2-3, Tome 32, Fiurier-Murf 1971, page C 1

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¹⁹⁵

STATISTICAL CONTRIBUTION

OF THE TETRAHEDRAL IRON TO THE EXCHANGE INTERACTION IN MIXED YTTERBIUM GALLIUM GARNETS

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A. GRILL and M. SCHIEBER

Department of Physics, Hebrew University, Jerusalem, lsrael

Rksume. - La susceptibilitk magnetique des cristaux de type grenat, Yb3Ga,Fe5-zO~z avec x variant entre 0 et 4 a ete mesure dans des champs magnetiques jusqu'a ^10,5kOe. On a determine le point Curie ferrimagnetique par etude de la variation de la permeabilite avec la temperature. On a trouve que I'aimantation ⁰⁰ de tous les grenats mesurCs, extrapolee en champ nu1 et a 0 OK correspond au modele statistique de Novik. L'aimantation ^aoest donnee par ^rro- 15 nd O d - ¹⁰na or - 5 ^GC quand na

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^NJ2^;^{n d}⁼^Nd/3sont les occupations relatives des ions magnetiques dans les deux sous-reseaux : Na et Nd representant le nornbre d'ions Fe dans les sous-reseapx a et d. ^{L T ~}= 1 -2(1 --nd)6 ; ud = 1 - 2(1 -na)4 ; ac = 1-2(1-nd)6 pour des petites valeurs de x mais ac = 1 - 2 ( l - r ~ d ) ~ pour x > 1,s. L'exemplaire avec x

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⁴est paramagnetique jusqu'a 4,2 OK.

Abstract. - The magnetic susceptibility ^,yof single crystals of Yb,GaZFes-zO~~ with x varying between ⁰and 4 has been measured in magnetic fields up to 10.5 kOe. The ferrimagnetic Curie point has been determined separately by measuring the variation of permeability with temperature. It has been found that the magnetization ⁰⁰of all measured garnets extrapolated to zero field and zero temperature follow Novik's statistical models. The magnetization uo is given by ⁰⁰ ⁼15 nd crd - 10 nn - 5 rr, where na

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^Na/2^;^{n d}⁼^Nd/3are the relative occupancy of the magnetic ions for the different sites ; Nnand NO represent thenumbers ofiron ions in thesitesa and d; 0 , = 1 - 2(1 - 1 ~ 6 ) ~ ; ud = 1 -2(1- na)4;

uc

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¹^-²⁽¹^-^nd)Gfor small values of x but ^{uc =}1 - 2(1--11d)~ for x > 1.5.

The sample with x = 4 is paramagnetic down to 4.20 ^OK.

Introduction. - The site distribution of various diamagnetic ions such as Ga3+ or A13+ in ferrimagnetic iron garnets has been thoroughly investigated by Geller et al. [I]. The theoretical spontaneous magnetization of the substituted iron garnets at 4.2 ^O^Khas been calculated [I, 21 by a simple model which sub- tracts the magnetization of the substituted from that of the nonsubstituted compound, allowing the deri- vation of a certain site distribution of the various ions in the garnet structure. A different model has been proposed by Novik [3] which takes into account the statistics of interaction between the magnetic ions in the a (octahedral), d (tetrahedral) and c (dode- cahedral) sublattices of the ferrirnagnetic iron garnets.

Designating the spontaneous magnetization of the three sublattices by a,, a,, a, and the relative occu- pation of the sublattices by the magnetic ions by n,, n,, n,, the spontaneous magnetization is given at 0 ^{O K}by

aO = 1 5 n d o d - 1 0 n a o , - 5 n c a , (1) where :

n, = N,/2 ; nd = N d / 3 (2) and

o, = 1 - 2(1

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^{nJ6 ;}^a,⁼1 - 2(1 - n,)4 ;

a, = 1 - 2(1

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^iz,)' (3)

N, and N, represent the number of nonsubstituted iron ions in the sites a and d and z is the number of interacting magnetic neighbours of a central rare earth c ion.

Results and discussions. - Single crystals of Yb,Ga,Fe,-,O,, with 0 < x < 4 have been grown as described elsewhere [4]. A large amount of work has been invested in order to characterize the single crystals of substituted YbIG. In order to establish

(*) Supported by the National Bureau of Standards Washing- ton D.C.

a well defined value of x, it has been found necessary to synthesize polycrystalline samples with known values of x and determining accurately the unit cell dimension and the Curie temperature and comparing them with that of single crystal values. The Curie temperature is measured by a method described elsewhere [4]. The results are shown in figure 1. Due

FIG. 1. - Unit cell (solid line) and Curie temperature (bro- ken line) vs. composition of Yb3GazFe~-zO~z :

+

polycrys-

taline ; 0 single crystal.

t o the high anisotropy of the substituted YbIG the value of the spontaneous magnetization of the polycrystalline samples could be taken neither as the cali-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971159

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C 1 - 196 A. GRILL AND M. SCHIEBER bration value of x of the single crystals, nor as a

comparison value for the theoretical calculated magnetizations.

The magnetization of the single crystals has been measured along the easy [ l l l ] direction between 4.2 and 300 O K in fields up to 10.5 kOe in a null coil pendulum magnetometer [5] and the results analysed with a CDC 7090 computer program. A few of the samples with x < 1.50 have been measured also in the harder [100] direction. The results are shown in figure 2. It can be seen that the anisotropy K decreases

Frc. 2. - Anisotropy vs. temperature of Y bZGarFe5-zO~ z I : x = O . 7 5 ; 2 : x - 1.00;3:x=1.20.

with both x and temperature. The decrease of K with T is in agreement with Pearson's results [6] for pure YbIG. The variation of the spontaneous magnetization as a function of composition is shown in figure 3.

The experimental points are shown along the following four calculated curves ; 1. a, = I N, a,

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N, a, I

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3 o, using NCel's method [I], where o,, a,, a, are the magnetizations of the individual ions in the different sublattices ; 2. Gileo's model [7] ; 3. Novik's model [3] with z = 6 ; 4. Novik's model with z = 2.

The crystal with x = 0.8 and 1.0 have a compensa- tion temperature of 900K and 400K respectively.

Figure 3 shows that for low values of x, i. e. x < 1.5 the spontaneous magnetization agrees well with Novik's theory with z = 6 and the points are not too far away from Geller's curve. The two crystals with x = 1.8 and 2.7 d o not fit to curve 3 of figure 3 but rather to curve 4 corresponding to z = 2.

Our experimental results seem to indicate that the

FIG. 3. - Spontaneous magnetization vs. composition of Yb3GazFes-z0 : Curve 1 - calculated from Neel's model ; Curve 2 -calculated from Gilleo's model [7] ; Curve 3-4 -

calculated from Novik's model [3] ;curve 3-2 = 6, curve 4 z = 2

number of interacting magnetic ions is not constant but instead varies with composition. At high values of x, i. e. at a large diamagnetic dilution of the magnetic sublattices only the two nearest iron neighbours of the Yb site contribute to the magnetic interaction, whereas a t low values of x also the next nearest iron neighbours participate in the magnetic inter- action. A possible explanation is the assumption that at least half of the two nearest neighbours of the Yb3+ ions have to be magnetic in order that the four next nearest magnetic neighbouts should participate in the magnetic interaction. This half value corresponds to x < 1.5 and therefore for x < 1.5, z in relation [3] for a, is six whereas for x> 1.5, z is two. Canting of Yb3+ or Fe3+ is investigated and will be reported separately.

Acknowledgments - The authors wish to thank Mrs L. Goldenberg for the valuable technical assis- tance with the magnetic measurements.

References

[I] GELLER (S.), WILLIAMS (H. J.), ESPINOZA (G. P.) and [5] BOZORTH (R. M.), WILLIAMS (H. J.) and WALSCH SHERWOOD (R. C.), The Bell System Tech. J., ( E . D.), Phys. Rev., 1956, 103, 572.

1964, XLIII, 565. [6] PEARSON (R. F.), J.A.P., 1962, 33, 1236.

[21 GELLER (S.), J.A.P., 1966, 37, 1408. [7] GILLEO (M. A.), J. Phys. Chem. Solids, Pergamon [3] NOVIK (I.), Phys. Rev., 1968, 171, 550. Press, 1960, 13, 33.

[4] SCHIEBER (M.), GRILL (A.) and SHIDLOVSKY (I.), J.

Crystal Growth, 1968, 3, 467.