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Pressure dependence of the critical fluctuations in the singlet-ground-state system, Pr3Tl
J. Kjems, M. Nielsen, W. Buyers, J. Crow
To cite this version:
J. Kjems, M. Nielsen, W. Buyers, J. Crow. Pressure dependence of the critical fluctuations in the singlet-ground-state system, Pr3Tl. Journal de Physique Colloques, 1979, 40 (C5), pp.C5-132-C5-133.
�10.1051/jphyscol:1979548�. �jpa-00218965�
JOURNAL DE PHYSIQUE Colloque C5, supplément au n° 5, Tome 40, Mai 1979, page C5-132
Pressure dependence of the critical fluctuations in the singlet-ground-state system, Pr 3 Tl
J. K. Kjems (*), M. Nielsen (*), W. J. L. Buyers (**) and J. E. Crow (***)
(*) Riso National Laboratory, DK-4000 Roskilde, Denmark
(**) Atomic Energy of Canada Limited, Chalk River, Ontario, Canada (***) Temple University, Philadelphia, Pa. 19122, U.S.A.
Résumé. — Les fluctuations critiques et l'aimantation dans un échantillon polycristallin de Pr
3Tl ont été mesurées par la diffusion neutronique en fonction de la pression. Au-dessus de T
cla diffusion quasi-élastique peut être représentée par une théorie dans laquelle les électrons de conduction diminuent fortement le temps de vie des excitons, mais cette théorie s'avère inadéquate pour décrire les modes excitoniques qui sont bien définis expé- rimentalement pour de faibles valeurs de q.
Abstract. — The pressure dependence of the magnetization and of the critical Fluctuations in a polycrystalline sample of Pr
3Tl have been studied by neutron scattering. Above T
Qthe quasielastic intensity is better reproduced by a theory in which the excitons are strongly damped by the conduction electrons than by the theory for small or zero damping, but the theory is inconsistent with the observation of well-defined excitons at low q.
The singlet-ground-state system, Pr
3Tl, has turned out to be particularly interesting because of the near critical condition for magnetic ordering. The first excited state of the Pr
+ 3 3H
4multiplet is a triplet at A = 77 K, and the exchange interaction, J(q = 0), is just strong enough to cause the onset of ferro- magnetic ordering at ! T
c= i l . 8 K . Recent high pressure studies by Guertin et al. have shown that 7",.
is lowered as much as 1.5 K/kbar [1].
Here we report on a neutron scattering study of the critical fluctuations in a polycrystalline sample of Pr
3Tl in the temperature range 4 K to 30 K and for pressures between 0 and 4 kbar. At 0 kbar Als-Niel- sen et al. [2] found that the intensity of the quasi- elastic component (CPI) of S(q, co) diverges as T -> T
cand q -> 0 but that the excitons appear to remain at finite frequencies. Qualitatively their results agree with RPA calculations for localized 4f electrons in which damping effects are assumed negligible [3], but there are quantitative discrepancies. This led Becker et al. [4] to suggest that damping of the modes by the coupling to the conduction electrons can greatly change the spectrum at low q and co. Both theoretical treatments give simple expressions for the central peak intensity integrated over energy (CPI).
The theory without damping gives
I* Mo
CPI = S(q, co) dco =
=
nuju(0) u(0)
(1 -u
iaJ(q))' (1 -u{0)J(q)Y
U )When the damping by the conduction electrons is included, Becker et al. find
CPI = % ^ _. , (2) 1 - u(0)J(q)
where w(0) is the single-ion susceptibility apart from factors of g/x
B; w
eland u
iaare the contributions to u(0) from elastic (Curie-Weiss) and inelastic (Van Vleck) transitions, respectively. In Eq. (2) all of the 4f spectral weight has been transferred to the central component because the integration is taken over the overdamped exciton as well as over the Curie-Weiss terms. However, Huber [6], using the same formalism as Becker et al. to introduce the conduction electron damping, shows that the spectral weight of Eq. (1) and ref. [3] is, in fact, correct when there is a separation between the high-frequency and low-frequency parts of the response. The CPI of Eq. (1), which contains the factor
u
el~ T-
1vy{-AIT),
vanishes rapidly as T
e-> 0, unlike the CPI of Eq. (2).
The present measurements were carried out at the Riso DR3 reactor on a cold source spectrometer (k
0= 1.553 A
- 1) working in the two axis mode.
The polycrystalline Pr
3Tl sample was mounted inside a high pressure cell made from aluminum alloy, A126SWP, following the design by Daniels [5], with
4He as the pressure medium.
The scattering due to the critical fluctuations, which was observed near the forward beam in the
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979548
PRESSURE DEPENDENCE OF CRITICAL FLUCTUATIONS IN SINGLET-GROUND-STATE SYSTEM C5-133
0 10 20 30
TEMPERATURE (K)
0 5 10 15 20 25
TEMPERATURE
(Kl
Fig. I. - Integrated quasielastic intensity (CPI) for a poly- Fig. 2. - Integrated intensity of the (1 11) powder line versus crystalline sample of Pr,TI. The solid lines are calculations, corrected temperature at 3 different hydrostatic pressures. The solid lines for the vertical resolution of 0.16 A-', for small damping [3] [6], are least squares fits which were used to determine T, and the Eq. (1) of the text. The broken lines are the corresponding curves saturation magnetization.
for large damping 141, only used in the paramagnetic phase. Both theories are normalized at To at 0 pressure.
polycrystal, was superposed on an angle-dependent background from the pressure cell. Excellent repro- ducibility was, however, achieved by fixing the spectrometer setting for each pressure and scanning the temperature. The results for Q = 0.03 8- are
shown in figure 1 for 0 and 4 kbar respectively. Tc was determined from the integrated intensity of the (111) powder line and the results for three different pressures are shown in figure 2. The solid lines are least squares fits which were used to extract Tc as well as the saturation magnetization. We find that dTc/dp = - 1 K/kbar, somewhat lower than the value reported by Guertin et al. and the saturation moment is found to be 40 % larger than the values determined from their magnetization curves.
In figure 1 we see that the theories where the damping is zero [3] or small [6] predict a too rapid decrease of intensity as T, is lowered whereas the theory [4] where the conduction electron damping is assumed large is in better although not overwhelming accord with the present data. The latter theory, however, predicts an overdamped exciton branch at low q in contrast to the finite-frequency branch observed experimentally [2].
Note added in proof : The calculated curves lack a factor of T, by mistake. When included the agreement experimental data and the large damping tabulation is considerably improved.
References
[I] GUERTIN, R. P., CROW, J. E., MISSELL, F. P. and FONER, S., [4] BECKER, K. W., FULDE, P. and KELLER, J., Z. Phys. B 28 (1977)
Phys. Rev. B 17 (1978) 2183. 9.
[2] ALS-NIELSEN, J., KIEMS, J. K., BUYERS, W. J. L. and BIRGE- [5] See e.g. SKALYO, J., MINKIEWICZ, V. J., SHIRANE, G. and
NEAU,
