Theory of the transition temperature and the magnetization in Pr3Tl under change of volume

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Theory of the transition temperature and the magnetization in Pr3Tl under change of volume

D. Yang, P.-A. Lindgård

To cite this version:

D. Yang, P.-A. Lindgård. Theory of the transition temperature and the magnetization in Pr3Tl under change of volume. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-134-C5-135.

�10.1051/jphyscol:1979549�. �jpa-00218966�

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JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-134

Theory of the transition temperature and the magnetization in Pr

3

Tl under change of volume

D. Yang and P.-A. Lindgard

Ris0 National Laboratory, DK-4000 Roskilde, Denmark

Résumé. — Nous avons fait un calcul de T^c et de l'aimantation au moyen du développement en 1/z des fonctions de Green. On trouve un bon accord avec l'expérience en utilisant les paramètres obtenus des courbes de dispersion.

Une dépendance simple et linéaire de A et J(q) en fonction du volume explique les effets de la pression et de la dilution par le La. Ces deux paramètres augmentent fortement sous pression.

Abstract. — We have calculated T^Q and the magnetization using a 1/z expansion of the standard-basis operator theory. A good agreement is obtained using parameters deduced from dispersion relations. A simple linearized volume dependence of both A and J{q) is found to account for the effect of pressure and dilution. Both parameters are found to increase strongly with increasing pressure.

The first neutron scattering study of the magnetic exciton dynamics in the singlet ground state ferro- magnet Pr3Tl was done by Birgeneau et al. [1].

Bucher et al. [2] have shown that Pr3Tl is a nearly ideal crystal field split system (singlet r1 ground state and a T4 triplet at A ) in which the exchange interaction 7(0) just exceeds the critical value. It is therefore of particular interest to vary the 7(0) or A by changing the volume in order to test the theory for the excitons and the predicted transition temperature, Tc. The crystal field and exchange parameters, A and J(q), in Pr3Tl change under pressure. Alloying with La expands the lattice and has essentially the following two effects : 1) dilutes the exchange interaction, 2) acts as a negative pressure. Buyers et al. [3] reported that there was a considerable discrepancy between the exchange interaction deduced from TQ and from the exciton spectrum using the standard basis operator theory in the random phase approximation (RPA).

By including correlation effects in the free energy we shall demonstrate that an overall agreement for Tc

and the saturation moment can be obtained both as a function of pressure and dilution with La of Pr3Tl.

Let us consider the free energy F = F⁽⁰⁾ + F^{( 1 )} where

F(0> = 7(0) M2 - kTIn £ e~E»lkT (1)

n

is the meanfield free energy calculated using the single ion energies E„. The correction term is

^

(1)

= kT± X In | l - ^J(q) ^(to,)! jd*

a/i= + -,zz (2) where

c+~ = 1 and czz = 2 and

0"(to,) = I < p | 5 « | ' - > < i - | S ' | / » > x

x ("p - nr)l(Er - Ep - /co,) are the single ion Greens functions. The magnetization

< S* > is found by minimizing F and J,, from the divergence of the susceptibility. The saturation moment is

M ( T = 0 ) = MM F- X krp +

Srrp P<0

where £rp — Er — Ep, mrp the corresponding matrix element, co; is a pole of the RPA Greens function and a dot represents a derivation with respect to the molecular field. The first term is the RPA result.

Te is found from

_L

^{= y}

m i

^kT

T

^J{q)

**,,[*-- <?m -^1**

(4)

L

⁺

kT-<f»m^

⁹

J

^{)

where XMF(^) 'S t n e m ean field susceptibility. The graphical solution of this equation is shown on figure 1 together with the mean field solution used

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979549

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THEORY OF THE TRANSITION TEMPERATURE AND THE MAGNETIZATION IN Pr,Tl C5-135

Fig. 1 . - The grafical solution for T, (singlet-triplet model) as a function of 4 a: J(O)/A for the mean field (MFT) theory and the present Greens function theory (GFT) using the Ifz expansion.

The 0 indicates T, for A = 77 K. Notice the necessary J(0) deduced from the GFT curve is much smaller.

previously. The difference is clearly quite substantial.

Because of the fluctuations a smaller J(0) can sustain ordering.

Recent neutron scattering measurements [3] of the exciton dispersion of (Pr,-,La,),Tl with c = 0, 0.07 and 0.12 shows a considerable reduction of the dispersion due to the dilution. For simplicity let us assume the volume or concentration dependence of the parameters J(q) and A is of the form

A least squares fit to the dispersion curves (polycrystalline average) gives the exchange parameters to the neighbouring ions

and A , = 80

+

¹^Kand the concentration factors

The RPA theory requires a ratio A/J(O) < 8013 r 27 for ordering. It is evident that the exchange interaction changes much more rapidly than expected for the simple dilution effect (Rex = 0). Also Rex

-

^R,,

within the uncertainty. This is contrary to the assump- tion by Guertin [4]. The volume change AV(c) between c = 0 and c = 1 is 2.7

%.

Assuming this to be linear in c we conclude from the above analyses that the pressure dependence of the critical ratio should be small because both J(0) and A change nearly iden- tically. The calculated (using the full level scheme) M(0) = 0.5 pB is in reasonable agreement with the .0.28 x

$

^pBobtained in a polycrystalline sample [5].

The measured

and

can be accounted for by equation (4) using A(O)/J(O,O) = 51.45 and R,, - Rex = 0.01 $- 0.003.

Independent (preliminary) neutron studies of Pr,Tl indicate an increase in the dispersion with increasing pressure. This supports our conclusion that both A and J(O) have a strong and similar volume dependence and that the available experimental data is compatible with this picture. Further measurements may illucidate the physical mechanism contributing to the exchange and crystal field parameters.

References

[I] BIRGENEAU, R. J., ALS-NIELSEN, J. and BUCHER, E., Phys. [4] GUERTIN, R. P., CROW, 3. E., MISSELL, F. P. and FONER, S., Rev. Lett. 27 (1971) 1530. Phys. Rev. B 17 (1978) 2183.

121 BUCHER, E., MAITA, J. P. and COOPER, A. S., Phys. Rev. B 6 [5] KJEMS, J., NIELSEN, M., BUYERS, W. J. L. and CROW, J. E.,

(1972) 2709. (1979) (this proceedings), J. Physique Colhq. 40 ((1979)

[3] ALS-NIELSEN, J., KJEMS, J., BUYERS, W. J. L. and BIRGE- C5

NEAU, R. J., J. P h y ~ . C 10 (1977) 2673.