HIGHER DEGREE EXCHANGE AND ANISOTROPIC MAGNETIZATION IN PARAMAGNETIC TbzY1-zSb

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Submitted on 1 Jan 1971

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HIGHER DEGREE EXCHANGE AND ANISOTROPIC MAGNETIZATION IN

PARAMAGNETIC TbzY1-zSb

B. Cooper, I. Jacobs, C. Graham, O. Vogt

To cite this version:

B. Cooper, I. Jacobs, C. Graham, O. Vogt. HIGHER DEGREE EXCHANGE AND ANISOTROPIC MAGNETIZATION IN PARAMAGNETIC TbzY1-zSb. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-359-C1-361. �10.1051/jphyscol:19711123�. �jpa-00213940�

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TERRES RARES ET ALLIAGES

HIGHER DEGREE EXCHANGE AND ANISOTROPIC MAGNETIZATION

J N PARAMAGNETIC Tb,Y, -, Sb

B. R. COOPER, I. S. JACOBS and C . D. GRAHAM (*)

General Electric Research and Development Center Schenectady, N. Y. 12301, U. S. A.

and 0. VOGT

Laboratorium fur Festkorperphysik, ETH, Zurich, Switzerland

R6umB.

-

L'analyse de l'aimantation anisotropique des composes paramagnetiques de type TbzY I - ~ S ~ ( z

<

0,40), en champs continus atteignant 100 kOe, a demontre l'existence d'un Cchange significatif de degre supkieur. Les valeurs de z des kchantillons, dont on a mesure l'aimantation, sont les suivantes : 0,102, 0,205, 0,299, 0,377 et 0,402. On a obtenu les coefficients linkaires et cubiques du champ effectif d'echange. Ces coefficients varient lineairement en fonction de la concentration du Tb. Le coefficient lineaire est isotrope, comme prkvu par la thkorie. De plus, sa valeur est en accord avec la mesure preliminaire de la susceptibilite. Le coefficient cubique apparait isotrope et satisfait la contrainte imposQ par la symktrie cubique.

Abstract. - From an examination and analysis of the high moment anisotropic magnetization up to 100 kOe (D. C . field) in paramagnetic TbzY I-zSb (z 5 ^0.40),the existence of significant higher degree exchange is demonstrated. Magne- tization was measured on samples with z = 0.102, 0.205, 0.299, 0.377, and 0.402. Quantitative values are obtained for the linear and cubic coefficients of the effective exchange field. Each of these coefficients scales linearly with Tb concentration. The linear term coefficient is isotropic in accord with theory and agrees well with the earlier estimate from low moment behavior. The cubic term coefficient satisfies the constraint of cubic symmetry and seems to be isotropic.

Crystal-field effects may compete with, or even domi- nate, exchange effects in determining the nature, indeed even the occurrence of magnetic ordering in rare earth materials [I]-[3]. This is most striking when the crystal- field-only ground state is a singlet (with zero moment for zero effective magnetic field). Magnetization occurs in the presence of an He,, (external field plus exchange field) by admixture of excited state wavefunctions polarizing the ground state. There is no ordering until the exchange reaches some critical value [I]-[3]. The low field magnetization below this threshold is linear with field (giving the Van Vleck susceptibility at low temperature), and for a cubic material is isotropic. At temperature low compared to the crystal-field splitting to the first excited state, the high field magnetization is markedly anisotropic. For TmSb (NaC1-structure) such behavior has been observed and quantitati- vely understood with crystal-field effects and zero exchange [4]. This provides a base for examining the exchange in related rare earth compounds.

The system TbzYl -,Sb is isomorphous to TmSb.

The Tb3+ ion in its octahedral site with a predomi- nantly fourth-order crystal-field has a singlet ground state

r1

and an energy level scheme identical, except for a scaling factor, to that of Tm3+. Prior work [5]

has shown that an exchange field linear in M (He,, ⁼H

+

AM)

with A proportional to concentration (z) well describes the low moment behavior. ( M is the magnetization per Tb ion.)

The z-dependent exchange leaves the system paramagnetic for z

<

0.40, with a rigid upward shift of curves of reciprocal susceptibility,

x-'

(per Tb ion) vs. T with increasing z. Analysis [5] of this behavior yielded the

(*) Present address : School of Metallurgy and Materials Science, U. of Pennsylvania, Philadelphia, Penn.

splitting between TI and the 'first excited,

r4,

triplet state of 11.9 OK, and the linear coefficient

At higher concentration, 0.40

<

^z

<

1, the increased exchange produces an antiferromagnet

via a polarization instability of the ground state wave function.

Pulsed high field measurements [5] of the large anisotropic magnetizations in the paramagnetic regime showed appreciable departure from behavior calculated with a linear molecular field. This suggested important higher degree exchange, i. e. terms with higher powers of the magnetization (per ion) in He,,. Such higher degree exchange, expected when there are large orbital contributions to the magnetic moment, occurs for rare earth compounds [6]. Its possible presence pro- vides a special challenge for research on such compounds. By improving the high moment paramagnetic magnetization measurements, the suggestion of higher degree exchange can be confirmed and made quantitative.

Single crystals of five compositions in the paramagnetic range of the family Tb,Yl -.Sb were prepared [5].

Their nominal compositions were refined, as described below, yielding z = 0.102, 0.205, 0.299, 0.377, and 0.402 with an uncertainty of about $- 1

%.

Magnetization measurements to fields of 24 kOe (electromagnet) for 1.8 O K

<

T

<

300 OK were made with a vibrating sample magnetometer, and to fields of 100 kOe (superconducting solenoid) at 1.6 OK with a very low frequency sample motion magnetometer using an integrating digital voltmeter. At the lowest temperatures, measurements were made in the three principal directions,

<

1 11 $,

<

110

>,

and

<

100

> ^.

Susceptibility data for 50 OK

<

T 4 300 OK fit well t o

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711123

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C 1 - 3 6 0 B. R. COOPER, I. S. JAC( IBS AND C . D. GRAHAM

a Curie-Weiss Law and provided one evaluation of z from the free ion behavior with J = 6, g = 312.

The magnetization data (M in p, per Tb ion) for three compositions are shown in figure 1 along with two calculated curves for each data set. We note that

FIG. 1. - Anisotropic magnetization of TbzY x-*Sb at 1.6 OK for z = 0.205, 0.299, 0.377 compared to theory with

Heff

-

^H

⁺

1Mand Heff = H

+

AM

+

DM3.

M ([100], z) reaches values just under 6 p~ at the highest fields. This behavior is part of a step-wise approach to saturation characteristic of the [loo]

direction [7], i. e. almost complete intermediate polarization of the ground state prior to a level crossing.

From the earlier study 151, the calculated values of M ([loo], z) are almost completely independent of z and of the form of the exchange field. Thus we have a second method of evaluating z, which gave excellent agreement with the

x-'

vs T method.

The calculated curves drawn with dashed lines were obtained from crystal-field theory plus an effective field, He, = H

+

AM. The value of l / z obtained from the low moment analysis [5] was used. The fit is rather poor, confirming the earlier study. In contrast we recall the success with (Tm, Y) Sb. Thus we turn to a more elaborate representation of He,,. The most general expression for the exchange field allowed for f-electrons, which changes sign with a reversal of the external field is a series extending to MI3

Heff = H

+

^AM

+

^{D M ~}

+

^NM'

+

^PM'

+

Which terms are significant depends on microscopic models [6], [8] for the higher degree exchange. Existing calculations are usually for simple model systems.

Our analysis follows the empirical procedure of per- forming a least-mean-square fit to the experimental

data set ([h, k, l], z ) with an increasing number of terms in the series for He,, starting with the lowest degree. While this order of adding terms of higher degree may not be unique, it has the attraction of simplicity coupled with the common tendency for terms of higher degree to decrease [6], [8]. The coefficients are neither constrained with respect to orientation nor to concentration. As a measure of the convergence of the fitting, we examine the root-mean-square deviation, between calculated and experimental data. In most cases the fit (by this measure, or by other statistical methods) continues to improve up to the inclusion of terms of the seventh degree. At this stage, AH has dropped to about 0.5 kOe which is the uncertainty in the measured H.

In figure 2 we present the composition and orientation dependence of the linear

(A)

and cubic (D) exchange field coefficients. Each is plotted as a function of the highest degree term of He,, in the fitting.

TbZ Y 1-z Sb

vs. COMPOSITION vs. ORIENTATION

FIG. 2. - Composition and orientation dependence of the linear (3,) and cubic (D) exchange field coefficients.

We find in figure 2a that ACllll/z settles down quickly as soon as higher degree terms are included.

Its values are roughly constant with respect to z, as found in the low moment analysis [5]. In figure 2b, the orientation dependences for z = 0.205 and 0.377 are found to be negligible. Thus A/z is isotropic as required by symmetry. We note that a composite average value

;l/z

⁼- 6.88 kOe/p, is within 2

%

of the earlier estimate [5].

In figure 2c, the behavior of D c l , , l / ~ is seen to be convergent and also independent of z, but the relative scatter of the data is greater. With regard to orientation dependence, cubic symmetry imposes the constraint [5],D,,ool=4D,11,1-3D,lt11.Theresults(Fig.2~

of two z-values show no distinct trend, from which we conclude that D,,,,,, is roughly isotropic, thereby meeting - the constraint as well. A composite average is Dlz = - 0.21 k~e/~(p;).

From the convergence behavior with terms of still

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HIGHER DEGREE EXCHANGE AND ANISOTROPIC MAGNETIZATION IN PARAMAGNETIC C 1 - 361

higher degree, there was an indication that their contributions are meaningful. However, the experimental uncertainties prevent a quantitative evaluation.

The solid-line curves of figure 1 are calculated with the linear plus cubic exchange field using the average parameters, x/z and

w.

The fit is reasonably good, and in marked improvement over the other set of curves. The remaining deviations are attributable t o

1) the role of possible higher degree terms, 2) the approximations of a homogeneous molecular field, and 3) the experimental uncertainties in magnetization measurements at the highest fields.

The conclusions are as presented in the abstract.

We are grateful t o Miss E. Kreiger for her aid with the numerical calculations and to H. F. Burne for his aid with the measurements.

References

[I] TRAMMELL (G. T.), J. Appl. Phys., 1960, 31,'362S ; [ S ] COOPER (B. R.) and VOGT (O.), Phys. Rev. B, 1970,

Phys. Rev., 1963, 131, 932. 1, 1218.

123 BLEANEY (B.), PYOC. Roy. Soc. (London), 1963, A 276, [6] BIRGENAU (R. J.), HUTCHINGS (M. T.), BAKER (J. M.)

19. and RILEY (J. D.), J. Appl. Phys., 1969, 40, 1070.

131 For a review see COOPER (B. R.), J. Appl. Phys., [7] COOPER (B. R.), Phys. Letters, 1966, 22, 244.

1969, 40, 1344, and also COOPER (B. R.) and ^[8]ELLIOTT (R. J.) and THORPE (M. F.), J. Appl. Phys., VOGT (O.), Proceedings of this conference. 1968,39,802.

[4] VOGT (0.) and COOPER (B. R.), J. Appl. Phys., 1968, 39, 1202 ; COOPER (B. R.) and VOGT (O.), Phys.

Rev. B., 1970, 1, 1211.

HIGHER DEGREE EXCHANGE AND ANISOTROPIC MAGNETIZATION IN PARAMAGNETIC TbzY1-zSb

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