Observation of crystal field structure in the conductance of AlAl oxideBi1−xPrx tunnel junctions

Solid State Communications, Vol. 27, pp. 191—196. © Pergamon Press Ltd. 1978. Printed in Great Britain

0038—1098/78/0708—0191 $02.00/0

OBSERVATION OF CRYSTAL FIELD STRUCTURE IN THE CONDUCTANCE OF Al—Al OXIDE—Bii~Pr~ TUNNEL JUNCTIONS* C.S. LAmt and J.D. Leslie Department of Physics, University of Waterloo, Waterloo, Ontario, Canada (Received 19 January 1978 by M.F. Collins) Structure in the conductance of Al—Al oxide—Bi1_~Pr~ tunnel junctions is compared with the theory of Hoizer et al. predicting such structure due to scattering between crystal field split energy levels of the Pr impurity. The experimental results forx = 0.003 and 0.07 are shown to be in excellent agreement with the predictions of Holzer et al., if the crystal field split energy levels of Pr in these Bi—Pr alloys are the same as those measured for bulk BiPr. The structure observed for x = 0.3, while being larger and more complicated than for the more dilute samples, is also shown to be explainable in terms of a modified crystal field split energy level scheme. IN THIS PAPER, we report on an electron tunneling investigation of Bi—Pr superconducting alloys undertaken in order to see if the structures in the tunneling conductance, predicted by Hoizer et al. [1] for superconductors containing impurities with crystal field split energy levels, really exist. We have chosen to study the Bi—Pr system, because it is easier to fabricate tunneling junctions with this material than with La based alloys [2]. Also the crystal field levels of Pr in crystalline BiPr have been determined by Birgeneau et aL [3] through the use of neutron scattering. Of course, Bi is not superconducting in crystalline form, and to obtain a superconducting form it has to be quench-condensed onto a substrate at liquid helium temperatures to form the so-called “amorphous” Bi, with a transition temperature of 6.1 K. Now at first glance, it might appear surprising to attempt to see crystalline electric field effects in “amorphous” Bi. However, Sarkar etal. [4] have reported that amorphous rare-earth-iron alloys in Mossbauer absorption measurements display an electric field gradient, and that its magnitude is well defined and about the same as in crystals. Millhouse and Furrer [5] have shown from neutron scatteringexperiments that a well-defined “crystal field” exists even in liquid rareearth metals. These studies suggest that it should be possible to see crystal field effects in very disordered films. The tunnelingjunctions used in these experiments were in the form of Al—Al oxide—Bi1_~Pr,~., where the *

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Based m part on the Ph.D. thesis of C.S. Lan, University of Waterloo. 1977 (unpublished). t Now at the Department of Physics and Metallurgy, Carnegie—Mellon University, Pittsburgh, PA 15213, U.S.A.

Bi—Pr alloy film was quench condensed onto an Al oxide barrier on an Al film that was being held at helium temperature. The evaporator-cryostat and the junction fabrication technique used in this experiment were similar to those described earlier in the literature [6]. Samples with three different concentrations of Pr in Bi were studied. The A samples were formed from Bi—Pr alloy pellets containing 0.3 at.% Pr in Bi, and had a transition temperature of 5.90 K. The B samples were formed from Bi—Pr alloy pellets containing 7.0 at.% Pr in Bi, and had a transition temperature of 4.45 K. One C sample was formed from Bi—Pr alloy pellets containing 30 at.% Pr in Bi. The C sample had a transition ternperature of 2.25 K. The width of the transition region, i.e. the temperature range over which the film resistance went from 10% to 90% of its final normal state value, increaded with Pr concentration, and was 0.1 K, 0.14 K and 0.6 K for the A, B, and C samples, respectively. Figure 1 shows the relative conductance g(V) of an A type sample in the voltage region greater than 1 rnV. The relative conductance g(V) is obtained by computing the ratio (dV/dfjN/(d V/dI)8 at a number of closely spaced voltage points. The (d V/dI)8 data were taken at 1.35 K and the (dV/dJ)N data were taken at 8.0 K. Although, not shown here, the (dV/dJ)s curve shows a resistance minimum at 1.0 mV corresponding to the energy gap. In Fig. 1, the rapid rise ing(V) as Vis decreased below 3 mV is associated with the high voltage side of this peak in the relative conductance due to the energy gap. The (d V/dJ)N data show the presence of a zero bias anomaly, m that the resistance vanes from 675 ~ at OmV to 605 ~2at 15 mY. Apart from this .

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Fig. 2. The relative conductance, g(V) = (d V/dI)N/(dV/dI)s, for sample B1, an Al—Al oxide—Bi0.93Pr0.07 tunnel junction. The (dV/dI)8 and the (dV/dJ)N data were measured at 1.35 K and 8.0 K, respectively. g(V) approaches 0.98 at high voltage rather than 1.00 due to a systematic error involving annealing of the tunnel junction. smooth drop in resistance as the voltage is increased, there is no structure in the normal state tunneling data. The (d V/dI)s data also show the zero bias anomaly, but it is generally assumed that the zero bias anomaly will be

as large in (dV/dJ)8 as in (dV/dI)N, and hence cancel out in the relative conductance [7]. The dashed line in Fig. 1 shows the behaviour of pure “amorphous” Bi. The conductance dip of approx-

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Fig. 3. The relative conductance, g(V) = (dV/dJ)N/(dV/dJ)s, for sample C, an Al—Al oxide—Bi0.7Pr0., tunnel junction. The (dV/dJ)8 and the (dV/dI)N data were measured at 1.35 and 10.0 K, respectively. g(V) approaches 0.57 at high voltage rather than 1.00 due to a systematic error involving annealing of the tunnel junction. irnately 2% extending from 8 to 13 mV is phonon structure which can be analyzed using McMillan’s inversion procedure [8] to obtain the electron-coupled phonon spectrum of the superconductor. In sample A1, this phonon induced structure has been smeared out, and is not readily discernible. The largest structure observable is a 0.5% conductance dip extending from 6.5 to 7.2 mV, centered at 6.9 mY. Figure 2 shows the relative conductance g(V) for sample B1 The normal state data (dV/dI)N were measured at 8.0 K, and apart from showing a zero bias anomaly which caused the junction resistance to vary smoothly from 4300~2at OmV to 3800~7at 15 mY, there were no sharp structures in (dV/dI)N. The superconducting state data (d V/dI)~were measured at 1.35 K, and showed a resistance minimum at 0.9 mY corresponding to the energy gap. The zero bias anomaly could be seen once again in the (d V/dI)~data as a smooth decrease in resistance as the voltage is increased. Once again sharp structure is observed only in the (d V/dI)8 data, which indicates that this structure is associated with the superconductivity of the li—Pr alloy. The relative conductance of sample B1 shows a structurebetween V = 6.5 mY and V = 7.3 mY. The structure is a conductance dip of 0.8% magnitude with its center at 7.0 mV. The relative conductance for sample B1 with a 7, of 4.45 K is very similar to that for sample A1 with a 7 of 5.90K. The conductance dip for sample B1 is located at the same voltage as for sample A1, although it is somewhat larger in magnitude, i.e. 0.8% for sample B1 compared to 0.5% for sampleA1. The fact .

that the relative conductance for sample B, is shown levelling off at 0.98 rather than 1.00 at high energy is due to a systematic experimental error. It is caused by the junction resistance changing its value due to annealing of the sample as the junction is cycled from 1.35 K for the measurement of the superconducting data to 8.0 K for the measurement of the normal state data. On returning to the low temperature, the general shape of the (d V/dI)~was identical, but the overall resistance values had shifted slightly. Since we are interested only in the location of the structure in g(V) and not in the exact values of conductance, this shift is not important in this study. Birgeneau et aL [3] have performed inelastic neutron scattering experiments on BiPr. The symmetry of this bulk crystalline form, containing 50 at.% Pr, is that of the NaCI (Bl) type of structure. They found that the energy level of the Pr’~ion was split by the crystal electric field into four levels r1, I’,, F4, and I’s. The ground state I’i is a singlet while the first excited state F4 is a triplet at 5.8 ±0.6 meY above the ground state energy. A doublet F, is located 4.1 meV above F4, and a triplet F5 is located 7.7 meV above [‘3. The four peaks that they observed at 4.1, 5.8, 7.6 and 11.7 meV were identifled as the F4—F3, [‘1 F4, r,—r’5, and the F4—I’5 transitions, respectively. Our li—Pr alloy films are admittedly different from the bulk samples studied by Birgeneau et aL However, if we assume that the crystal field splitting scheme for BiPr obtained by Birgeneau et aL applies to our Bi—Pr alloy films, then the calculation of Holzer et aL predicts

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that we should see structure in the tunneling conductance at V = ~ + 6 mY, where i~is the energy gap value and 6 is the energy difference between the ground state and the first excited energy level of the Pr’~ion.According to the results of Birgeneau et ci., 6 is the energy difference between the F~level and the [‘4 level, i.e. 6 = 5.8 ±0.6 mY. Since the energy gap for the A and B types of samples is approximately 1 mV, the calculation of Holzer eta!, predicts that the largest crystil field structure in the tunneling conductance should occur at 6.8 ±0.6 mY. As we have shown in Figs. 1 and 2, the

for sample C. To obtain this curve the ratio (d V/dJ)N/ (dV/dI)~was computed at a number of closely spaced voltage points. The (dV/dI)N vs V data that was used in this calculation is not really appropriate because of the shifts in overall resistance of the tunnel junction that are occurring because of the annealing. However, we are more interested in the voltage location of structures in g(V) rather than the exact shape and magnitude of the structure. While the (dV/dI)N vs V curves for samples is rather structureless, as is also the case for (dV/dI)N vs V curves for samples A and B, the (dV/dI)8 curves

structure that we observe in the tunneling conductance of our A and B types of samples occurs at 6.9 to 7.0 mV. We thus see that the experimentally observed structure in the tunneling conductance of these Al—Al oxide— Bi1_~Pr~tunnel junctions is in excellent agreement with the calculation of Holzer et aL based on the crystal field effect, as long as we assume that the crystal field splitting between the ground state and the first excited state for our Bi—Pr alloys is the same as that measured by Birgeneau et ci. for crystalline BiPr. The (dV/dI)8 vs V curve for sample Cwas measured at 1.35 K shortly after the junction had been completed by the evaporation of the Bi—Pr alloy film. The (d V/dI)8 vs V data indicated the presence of sizeable structure at a number of voltages in the 0—12 mY range. After carefully measuring the junction resistance as a function of voltage to record the magnitude and location of this structure, the sample was warmed to 8 K during the process of measuring the film resistance vs temperature curve to establish the transition temperature of the Bi—Pr alloy film. On recooling the sample to 1.2 K, two effects were noted. First, the structure in the (d V/dJ)s vs V curve had changed. Secondly, the resistance of the tunnel junction had become significantly lower, i.e. at a bias of 15 mY the junction resistance had changed from 1100 to 900 ~2.We attribute both of these on changes to antheannealing process which hadoftaken place warming sample to 8 K. Annealing quench-condensed alloys at very low temperature is a well-known effect [6]. Also the change of tunnel junction resistance with annealing of an amorphous layer in the junction has been observed previously [9].

for sample C contains very sharp structure. Therefore we have used the (dV/dI)N vs V data obtained at 10 K for sample C without any adjustments to compute g(V). This accounts for the fact that g(V) approaches a value between 0.55 and 0.60 at high bias, rather than 1.0 which would have been obtained if the correct (dV/dJ)N vs V data could have been obtained. We have shown g(V) in Fig. 3, in order to put the derivative data for sample C in the same format at that used for samples A and B. The (dV/dJ)s vs V data used to compute Fig. 3 is that which was obtained at 1.35 K shortly after the junction had been completed by the evaporation of the Bi—Pr alloy film. Figure 3 shows large sharp conductance dips at 2.45, 3.6, 4.4, 5.25, and 6.3 mY and smaller conductance dips at 7.8 and 10.8 mV. While this structure obtained with sample C is much larger and more complicated than that obtained with samples A and B, we would like to show that it could have the same origin in terms of crystal field effects on the tunneling conductance. Sample C has such a small energy gap, i.e. certainly less than 0.4 meY, that for the purpose of this analysis we can treat sample C as gapless. This means that the energies at which the conductance dips occur in Fig. 3 correspond to the actual energies 3lon. of Astransitions can be seenbetween from crystal field levels of the Pr transition energies observed Fig. 3, there are many more than in the case of samples A and B, where we see only the transition energy of 5.8 meY, corresponding to the transition from the ground state to the first excited state, i.e. F, to F 4. There are two possible explanations of the structure in Fig. 3 in terms of a crystal field effect model. If we restrict ourselves to considering that transitions out of the ground state are the only possibility, as is the case in the theory of Holzer et ci., then we are forced to condude that the Pr is sitting in a number of different crystal environments, and thus has a number of different crystal field levels from those measured by Birgeneau et al. Thus the results of Fig. 3 would have to be interpreted in terms of crystal field levels at 2.45, 3.6, 4.4, 5.25, 6.3,7.8, and 10.8meV. Such a possibility must be

Sample C was warmed to 10K and the (d V/dI)N vs V curve was measured. It was found that the junction resistance had undergone a further lowering as a result of this annealing, in that the junction resistance at 15 mV had decreased from 900 to 610 ~7.The overall shape of the (dV/dI)N vs V curve for sample C was similar to that obtained for samples A and B, however, the magnitude of the zero bias anomaly was approximately a factor of 7 smaller than that obtained for samples A and B, Figure 3 shows the relative conductance curveg(V)

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considered because sample C does contain a lot of Pr, but there is no indication of the start of such behaviour in sample B which has about one quarter of the Pr concentration of sample C. It should be noted that the paper of Cochrane eta!. [101 contains a calculation for Pr in concentrated amorphous alloys and indicates that the level splitting gives the nine Pr levels as being arranged in the following manner: one low lying quasidoublet followed by five singlets followed by a quasidoublet [seetheir Fig. 7(b)]. Even though the transition probabilities have not been worked out, such a structure would give a much more complicated tunneling spectrum for amorphous Bi0.70Pr0.,0 (sample C). The other possible interpretation arises if we allow the possibility of transitions from one crystal field level to another, which do not involve the ground state. Obviously, we still need to assume some change in the crystal field levels from those measured by Birgeneau et ci., otherwise we would only see structure at 5.8, 4.1, 7.7 meV or sums of these quantities. However, we will see that only a small change in the Birgeneau et aL level scheme is needed to explain most of the transition energies see in Fig. 3. In Fig. 3 it can be seen that there is a large conductance dip centered around 5.8 mV, but it appears to be split into two peaks, with one at 5.3 mV and the other at 6.3 mV. If we take this as evidence that the first excited level [‘4 has been split into two levels 1 meV apart, i.e. F~at 5.3 meV and F~’at 6.3 meV above the ground level F~,but assume that the other levels [‘3 and [‘5 maintain their original energies with respect to the ground state, i.e. 9.9 and 17.6 meV, respectively, then we can explain almost all the structures in Fig. 3 in terms of transitions between the energy levels of this slightly altered energy level scheme. Thus the 5.3 and 6.3 mV structures correspond to F~to [‘~ and F~to F transitions, respectively. The 3.6 and 4.4 mY structures correspond to F to [‘3 and [‘~ to [‘3 transitions, respectively. The 7.8 mV structure corresponds to a [‘3 to I’, transition and the lO8mY structure corresponds to the second harmonic of the F~to F~transition. The only structure that is difficult to explain on this basis is the rather strong conductance dip at 2.45 mY. Possibly it could be some type of interference effect between a r1 to F~’and a F to [‘3 transition, which would yield the

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correct energy difference, however the structure is quite strong to be a second order effect. Alternatively, this 2.45 mY transition could be a F~to F’~’transition, where F’ could be the third state of the [‘4 triplet which has been shifted to 2.45 meY above the ground state from its initial position of 5.8 meY. Obviously from the tunneling results alone we cannot choose which of the two possible explanations of the tunneling results on sample Cis the correct one. The first explanation requires the crystal field split levels of this high Pr concentration Bi—Pr alloy to be very different from those of bulk BiPr, but all the transitions are taken as occurring from the ground state to the various excited states. The second explanation involves a crystal field split level scheme very close to that for bulk BiPr but requires transitions between energy levels that one would not expect to be appreciably populated thermally. Because of the instability of sample C, it was not possible to do a detailed study of how the structure changed with temperature. However, a (dV/dI)8 vs V measurement taken after the annealing at 8K indicated that the conductance dips at 5.3 and 6.3 mY were merging together again into a single conductance dip at 5.9 mY, the conductance dips at 3.6 and 4.4 mY were becoming a single conductance dip at 3.8 mY and the conductance dip at 2.45 mY was becoming smaller and moving up in energy to 2.8 mV. The shorting of the junction with annealing past 10K prevented further study of the change of the structure with annealing. While there are still a number of questions about the details of the fitting of the structure that we observe in these Al—Al oxide—Bi,_~Pr~ tunnel junctions, the one thing that is definite is that the origin of this structure must be connected with the crystal field effect. The structure is observed only with the Bii_~Pr~ alloys in the superconducting state. The structure that is observed is too sharp to be phonon structure in such disordered alloys, and is occurring at too high an energy above the energy gap to allow any trivial explanation in terms of a number of different energy gaps in the sample or a proximity sandwich. The only mechanism that predicts sharp conductance dips in the energy range observed is the crystal field split impurity level model of Holzer eta!. Also our tunneling conductances are very BCS-like as required by their theory.

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HOLZER P., KELLER J. & FULDE P.,J. Low Temp. Phys. 14,247(1974).

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FULDE P. & PESCHEL I.,Adv. Phys. 21, 1(1972). BIRGENEAU R.I., BUCHER E., PASSELL L., PRICE D.L. & TURBERFIELD K.C., J. AppL Phys. 41,900

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SARKAR D., SEGNAN R., CORNELL E.K., CALLEN E., HARRIS R., PLISCHKE M. & ZUCKERMAN M.J., Phys. Rev. Lett. 32, 542 (1974).

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MILLHOUSE A.H. & FURRER A.,Phys. Rev. Lett. 35, 1231 (1975).

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LESLIE J.D., CHEN J.T. & CHEN T.T., Can. J. Phys. 48,2783 (1970).

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CHEN J.T., CHEN T.T., LESLIE J.D. & SMITH H.J.T., Phys. Lett. 25A, 679 (1967). MCMILLAN W.L. & ROWELL J.M., Phys. Rev. Lett. 14, 108 (1965).

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CHEN T.T., Unpublished Ph.D. thesis, University of Waterloo (1969).

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COCHRANE R.W., HARRIS R., PLISCHKE M., ZOBIN D. & ZUCKERMAN M.J. J. Phys. F5, 763 (1975).