Solid State Communications, Vo1.64,No.9, pp.1201-1202, 1987. Printed in Great Britain. ... the ground state, the excited levels being ap- preciably separated ...
Solid State Communications, Printed in Great Britain.
Vo1.64,No.9,
pp.1201-1202,
1987.
0038-1098187 $3.00 + .OO Pergamon Journals Ltd.
Magnetic specific heat of Dy* in DyBa2Cu307_8 compared to the 2-d, S-3 Ising adel prediction M.W. Dirken and L.J. de Jongh Kamerlingh Onnes Laboratory, Leiden University, P.O. Box 9506, 2300 RA Leiden, The Netherlands
(Received
7th September
1987, by E.F. Bertaut)
The magnetic specific heat contribution due to the Dy 3+_ ions in DyBa2Cu307_A, as measured by Ramirez et al., is compared to the Onsager solution for the specific heat of the S=$ Ising magnet on the square lattice. Good agreement is found showing that the magnetic behaviour is analogous to a 2-d magnetic superexchange insulator.
In two recent communications from this laboratory [1,2] the magnetic behaviour of the Gd atoms in the superconducting orthorhombic and tetragonal phases of the the semiconducting GdBa2Cu307_R has ceramic high-Tc superconductor been studied. It was shown that the Gd s eets apparently are magnetically highly isolated from one another. The behaviour is quite similar to a 2-dimensional (2-d) antiferromagnetic insulator with a strong magnetic anisotropy, probably of dipolar origin, that leads to a 2-d Ising-type magnetic ordering transition at TN = 2.24 K. Although the experimental magnetic susceptibility and specific heat data were compared with theoretical predictions for the 2-d Ising antiferromagnet with spin S=$ on the square lattice tive'i;u;;et ;z;,ris,Etc;;;; ;$ &qF;;& spin of S=7/2. In this respect DyBa2Cu307_6 is a much more attractive candidate since Dy3+ ions tend to have a low-lying doublet as the ground state, the excited levels being appreciably separated from this ground doublet. As a consequence of this energy level configuration, which is due to crystal field effects in combination with spin-orbit cou ling, the magnetic ordering phenomena in Dy 3% compounds can often be treated in terms of an effective spin formalism. Furthermore, the expectation s=h values for the magnetic moment of this doublet are usually quite anisotropic, with typical gvalues of g ~5-15, g, = O-2. When g >> g,, the magnetic interactions between neighbouring Dy can be well described by the Ising spins hamiltonian with spins S=# Jc' = -25
1
Sz Ss ij
We note that although the site-symmetry of in this material is lower than the Dy-ions this need not invalidate the above uniaxial, All that is needed is a low-lying argument. doublet with strongly anisotropic properties and this can also be realized in %~'%'bi8a;c);al symmetry. While experiments on DyBagCu30 in our laboratory were in progress, we rece!;id a preprint of a paper by Ramirez et al. [31, who specific heat data on orthorhombic report
A magnetic ordering anomaly in the DyBagCugO specific %&I; was observed at TN = 0.92 K, the associated entropy being equal indeed to the Rln2 expected for a Kramers doublet. In this note we compare their data to the famous Onsager solution [4] for the specific heat of the 2-d Ising S=g magnetic model on the square lattice, where the magnetic interaction J is restricted to the four nearest neighbours. In Fig. 1 the fit of this theory to the experimental data ot the Bell Labs. group is shown, yielding a good agreement taking for the intralayer interaction the value J/kg = 0.81 K, which is the only adjustable parameter in the fit. There is some rounding apparent in the data quite close to TN, which could be due to crystal imperfections. upward Furthermore, the deviations of the experimental data from the theoretical curve seen for T > 1.5 K can be easily accounted for by the combination of the lattice specific heat, the contribution from the Cu-0 triple layers, and the c ntribution from higher lying doublets s+ ions. In the same Figure the dashed of the Dy curve gives the prediction for the simple cubic S=$ Ising model 151, also scaled at TN. Clearly, the 3-d model completely fails to fit the data. It should be pointed out that the magnetic properties of the RE layers in the ceramic superconductors provide a valuable probe to study the nature of the superconducting Cu-0 triple layers. In particular, the fact that the specific heat anomaly can be excellently fitted on basis of a 2-d nearest-neighbour-only interaction hamiltonian, shows that the main magnetic interaction between the Dy spins has to be of very short range (as remarked in [1,2] in case ordering within the RE of antiferromagnetic layers the magnetic interactions between Dy and Cu spins are cancelling because of symmetry). Interactions of the RKKY type between Dy spins in the same layer or in adjacent RE layers are very unlikely since these are of long range -3 (r ) so that they would: (i) increase the effective number of interacting magnetic neighbours within the same Dy-layer; (ii) introduce a 3-d character to the magnetic ordering. Both effects would produce serious deviations of the form of the specific heat curve from the Onsager prediction in Fig. 1, viz. the amount entropy involved above Tc would become less, so that the 1201
1202
MAGNETIC
SPECIFIC
HEAT OF Dy3+ IN DyBa2Cu307_6
I 2 t
I(
F
u
!O
T(K)
Fig. 1 Experimental specific heat data from ref. 3 fitted to the prediction for the Ising model with S=# on the 2-d simple quadratic lattice (solid curve). For comparison the theoretical prediction for the Ising model with S=f on the simple cubic lattice is also shown (dotted curve, also fitted to TN). anomaly would become more asymmetric [5,6]. In this respect we disagree with Ramirez et al. [3] who argue in favour of an RKKY interaction between the RE atoms in these materials on basis of a correlation between the observed transition temperatures for RB = Sm,Gd,Dy with the De Gennes factor (gJ_l)* J(J+l). Any such agreement should be accidental, since such a comparison cannot be valid considering that for both Dy and Sm only an effective doublet is involved in the magnetic ordering, instead of the full moment J (this is in fact already pointed out in ref. 3). For magnetic insulators with nearest-neighbour-only superexchange the value For of TN with g2S(S+l). should scale the TN-values are GdBa$u307_o and DyBa2Cu307_6 Considering 2.24 K and 0.92 K, respectively.
Vol. 64, No. 9
that g=2 and S=7/2 for the Gd commpound, S=s for the Dy compound, the factor g*S(S+l) is in the same ratio as the TN values when g = 5.9 for DyBaZCu307_6which is a reasonable g -value for the doublet ground state in an insulating Dy compound. In conclusion, these results would agree with a 2-d insulating magnetic model for the RE-sheets, the main magnetic interactions being a superexchange interaction between nearest-neighbouring RE-ions via two oxygen bridges as proposed in [1,2], where it was also shown that dipolar interactions probably account for about 20% of the total magnetic interaction for the Gd compound. Considering that the dipolar energy scales with g*S*, and assuming the same antiferromagnetic ordering along the c-axis as for the Gd-compound, the dipolar field would amount to 0.054 tesla for DyBa2Cug0 _ , which is less than 10% of the intralayer exe 71?ange field of 0.60 tesla calculated from J/k - 0.81 K. The absence of an apprecBable magnetic between coupling RE layers as neighbouring demonstrated in refs. [1,2] and in this work is significant. rather Although dipolar interactions between adjacent RE layers are negligible 11,219 and interlayer superexchange interactions involve too many intervening atoms to be apprethe question is why the (super)conciable, ducting Cu-0 triple layers apparently do not mediate a magnetic coupline between the RE layers between which they are sandwiched. After all, the same oxygen atoms that provide the intralayer RE superexchange are also taking part in the (super)conducting processes in the Cu-0 triple layer. Thus, although the RE-oxygen bonds are able to provide the weak RE superexchange interaction, they only lead to a very small amount of conduction electron density at the RE sites [1,7,8]. In this respect we note that the RE-0 distances are in agreement with what is expected on basis of the RE3+ and 02- ionic radii. In fact, the absence of a magnetic coupling between the RE layers is an indirect proof of the extreme 2-dimensional character of the conduction processes in these materials, since both features should have the same origin. This work is part of the research program of the Werkgroep Fundamenteel Materialen Onderzoek (Leiden Materials Science Group) and is sponsored by the "Stichting voor Fundamenteel Onderzoek der Materie" (Foundation for FundaResearch of Matter), with mental financial voor support from the "Nederlandse Organisatie Zuiver-Wetenschappelijk Onderzoek" (Netherlands for Organization the Advancement of Pure Research). We acknowledge the stimulating collaboration with our colleagues in physics and chemistry at Leiden working on the high-Tc superconductors project.
REFERENCES 1)
2)
3) 4)
H.H.A. Smit, M.W. Dirken, R.C. Thiel and L.J. de Jongh, Solid State Commun., in the press. J. van den Berg, C.J. van der Beek, P.H. Kes, J.A. Mydosh, G.J. Nieuwenhuys and L.J. de Jongh, Solid State Commun., in the press. A.P. Ramirez, L.F. Schneemeyer and J.V. Waszczak, preprint. L. Onsager, Phys. Rev. -65 (1944) 117.
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See e.g. L.J. de .Jongh, J. Appl. Phys. 49 (1978) 1305. See e-.g. M.E. Fisher, Rep. Progr. Phys. -30 (1967) part LI, p. 671. G.J. Kramer, H.B. Brom, J. van den Berg, D..J.W. Ydo, P.H. Kes and State Solid Commun., in the press. J.T. Markert, T.W. Noh, S.E. Russek and R.M. Cotts, Solid State Commun. -63 (1987) 847.
