Solid State Communications, Vol. 44, No. 5, pp. 649-652, 1982. Printed in Great Britain.
0038-1098/82/410649-04503.00/0 Pergamon Press Ltd.
SUPERCONDUCTING PROPERTIES OF AMORPHOUS TRANSITION METAL ALLOYS J. Flasck, J. Wood, A.S. Edelstein, J.E. Keem and F.P. MisseU Energy Conversion Devices, Inc., 1675 West Maple Road, Troy, MI 48084, U.S.A.
(Received 28 April 1982 by A.R. Miedema) We have co-sputtered amorphous films of several Mo and W-based superconducting alloys. Measurements of To, (dHc2/dT)r c and the normal state resistivity near Tc were made on a number of these alloys. Our results and other data from the literature are studied to examine the correlation between T e and the dressed density of states at the Fermi level. SINCE THE CLASSIC paper of Collver and Hammond [1 ], which examined the systematics of T e in amorphous transition metal alloys, many attempts have been made to explain the properties of this new class of materials [2-4]. In particular the smooth variation of T c across the 4d and 5d series was noted by Collver and Hammond, who suggested that an atomic parameter, which varies smoothly through the d-shell, might explain the behavior of T e. These authors speculated that the Hopfield parameter  r / = N(EF) ( 12 ) (where N(EF) is the density of electronic states at the Fermi level and ( 12 ) is the mean square of the matrix element for electron-phonon scattering) might show this behavior. On the other hand, for transition metal alloys, Varma and Dynes  have shown that (12 )/(602 ) ((6o2) is a mean square phonon frequency) is roughly constant within a class of materials for which the main contribution to N(EF) comes from one type of atomic orbital. Thus the variations in the electron-phonon coupling constant X = N(EF)( 12 )/111(602 ) would be due to changes in N(EF). However, Butler  has calculated the variation of ( 12 ) and N(EF) for 4d transition metals and has found the changes in ( 12 ) to be larger than those in N(EF). Consequently, ( 12 ) should be more important in determining the variation of Tc across the 4d series. These contributions have helped to point out the difficulties involved in interpreting the Collver and Hammond data. Some experimental evidence has been put forward in support of the picture of Varma and Dynes for amorphous transition metal alloys. Johnson et al.  measured the magnetization for a series of bulk glasses of composition (Mol_xRux)aoP2o. The variation of N(EF) with composition was estimated from the temperature independent part of the magnetic susceptibility (magnetization) and was found to decrease with increasing Ru. Since T e also decreased with increasing Ru content, this was taken to suggest that N(EF) was mainly responsible for determining variations in T e. However,
the determination of N(EF) from magnetization measurements is problematic and seems to be more questionable than the use of dHc2/dT data as described below. Similarly, Wiesmann et al.  estimated the electron-phonon enhanced density of states N*(EF) = (1 + X)N(EF) from dHc2/dT for Nb3Sn and Nb3Ge samples which had been disordered by a-particle irradiation. For Nb3Ge, these authors observed a simple proportionality between the estimated density of states and To, while for Nb3Sn the relationship was more complex. This suggests that, for NbaGe, N*(EF) is mainly responsible for changes in T e. In the present paper, we present results on a number of co-sputtered amorphous films of Mo and W-based alloys. These results are studied in relation to other data from the literature to examine the correlation between Te and the electron-phonon dressed density of states at the Fermi level N*(EF). Samples were co-sputtered onto glass substrates from appropriately modified Mo or W targets in an RF diode sputtering system. Base pressures of 10 -6 torr were obtained prior to initiating a flow of Ar at a pressure of 6-7/am. Sample compositions were determined from Auger or energy dispersive X-ray spectroscopy and should be accurate to within 5%. The amorphous nature of the samples was verified by X-ray diffraction. In most cases, no crystalline peaks were observed. For some samples, Bragg peaks were observed and these are indicated in Table 1. Resistance measurements were of the four-point probe type. Sample film thicknesses were determined by means of a Dektak mechanical stylus and are listed in Table 1. Since mechanical masks were used to define the sample geometry, there were some shadowing effects and, therefore, uncertainties in the cross-sectional area. Thus, our absolute values of the resistivity in some cases have uncertainties up to 15-20%. In Table 1 we list values of the resistivity at 25 K, designated as P0. The superconducting critical temperature T c was measured resistivity and temperatures were obtained from a
SUPERCONDUCTING PROPERTIES OF AMORPHOUS TRANSITION METAL ALLOYS
Vol. 44, No. 5
Table 1. Properties of superconducting alloys Composition
-- dHc2/dT (T/K)
Mo63Rus Si3z Mo54RUllSi35 Mo48Ru23Si21 C8 Moa6RH26Si19C9 M061Rh26Si13 Mo65Rh 18Nil7 Mo63Rh13Siz4
7.3 7.7 6.4 6.5 7.3 7.2 7.2 7.3 7.4 6.3 7.9 7.3 7.3 7.7 5.5 5.4 5.9 5.4 4.6 4.5 4.6 4.8 4.9 7.4 7.6 7.7 7.6 5.2 5.1 5.0
4.2 4.6 4.0 3.4 2.5 1.6 2.9 2.4 3.3 3.7 2.7 2.7 2.4 2.8 3.3 3.7 . 2.0 -
1.9 1.8 2.3 -
0.5 0.6 1. l 0.8 2.1 1.8 1.1 2.2 2.0 1.1 1.6 1.8 2.0 1.0 0.5 1.1 1.4 0.8 0.8 0.7 0.7 0.8 0.4 1.1 1.2 1.2 0.9 0.13 0.25 0.5
Mo59Rh25S116 Mo 74Rh6 Si2o Mo4o Rh27 Re22 Sil1 Mo/vRhsRe54Si~l Mo28Rh12Re44Si16 Mo44Rh27Re14Sils Mo46RlhsRe26Si10* Mo79NiloSial Mov2Ni9Si19
Mo 74Ni20Si6 MoToNi2sSis
Mo43Ti9Si46C2 Mos4Ti19Si2sC 2 MossTi24SilgCz + Mos3 TilaSia3 Mo47Ti4oSi13]" Mo64Ge 36 Mo69Ge31 Mo74Ge26 Mo94Ge 6 W82Si loC8 W94C6 W92C85 * Re peaks,
t Ti peaks.
2.2 2.2 2.1 2.1 2.1 2.1 2.2 2.1 2.2 . -1.0 2.0 2.2 2.2 2.3
6.0 . . 5.2 3.3 2.8 1.8 3.5
2.8 2.8 3.3 2.7 2.4
. 2.8 4.3 -
; W peaks.
carbon-glass thermometer in good contact with the sample. T c values are accurate to better than 0.1 K. Magnetic fields up to 90 kG were provided by a superconducting solenoid. The critical field slopes near Tc, (dHcJdT)T c, are uncertain to less than 5%. Results for all samples studied are given in Table 1. It is interesting to note how little variation is seen in our values o f the critical field slope. For the materials of Table 1, we note that the T e values fall in the range 4 . 5 - 7 . 9 K for these samples with metalloid content in the range of 6 - 4 8 N . According to the GLAG theory [ 1 0 - 1 3 ] , the resistivity, P0, and critical field slope, (dHc2/dT)To, are related to the dressed density of states for two spin directions N*(EF) by the relation,
2.7 3.1 2.3
where/3 is an enhancement factor (of order one) for strong coupling superconductors. Bergmann  used this relation to study the electron density of states at the Fermi surface in amorphous strong-coupling superconductors. Good agreement with the measured field slopes was obtained when X was taken from tunnelling measurements and N(EF) was calculated from the free electron model. In the present case we consider transition metal alloys, where both s- and d-electrons contribute to superconductivity. In principle the quantities Po and N*(EF) must be averaged in some appropriate manner to account for the s- and d-contributions . Nevertheless, Shull et al.  showed for amorphous Lal_~Gax foils that N*(Er), obtained from specific heat measurements, was in excellent agreement with values calculated from the slope o f the upper critical field. Koch et al.  show that agreement is also obtained for amorphous La76Au24 and other transition metal
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SUPERCONDUCTING PROPERTIES OF AMORPHOUS TRANSITION METAL ALLOYS
:alloys. Very recently, Tenhover et al.  mention that good agreement is also found for (Moo.sRuo.s)aoP2o, (Moo.6Ruo.4)aoB2o and (Moo.6Ruo.4)s2Bls. We calculated N*(EF) with/3 -- 1 (appropriate for weak or intermediate coupling materials; see below) for those compositions of Table 1 for which field measurements had been made. Following Johnson et al.  and Wiesmann et al. , we seek a correlation between N*(EF) and T c. Initially we examine materials of composition (Mol_yTr)l_xSi x where T is a 4d or 5d transition metal. These data are shown in Fig. 1. Here we have also plotted T c vs. N*(EF) for (Moo.6Ruo.4)l_xBx, (Moo.6Ruo.4)l_xSix, and (Mox_xRu~)soP2o , calculated from the data of Johnson et al. [8, 17]. For these data, we note a tendency for T~ to decrease with increasing N*(EF) when the metalloid is Si, whereas the opposite occurs when the metalloid is B. On the other hand, the increase in T c occurs for fixed N*(EF) when the metalloid is P. Our data extend the range for which T c decreases with increasing N*(EF) when the metalloid is Si. The dashed line of Fig. 1 represents this behavior. Although data for Mo46Ru26Si19C 9 and Mo94Ge 6 fall close to the dashed line, there are too few data points to conclude that all group IV metalloids show this behavior.
the density of states while for (Moo.6Ruo.4)l_xSi x the opposite is true. In both cases, the highest Tc results for the lowest values o f x . All of the data under consideration are consistent with the smooth variation of T e across the transition metal series as observed by Collver and Hammond. So the present results indicate that in addition to the density of states, there are other important factors determining T c for these materials. In summary, the phonon dressed density of states is inadequate for characterizing Te in these materials. The tendencies which we have observed in our discussion of Fig. 1 indicate the importance of the metalloid for superconductivity. Previous authors [4, 6] have largely ignored the role of the metalloid and hybridization. The present discussion indicates that they may play an important role in determining Tc in amorphous transition metal superconductors. Finally, it would be useful to have further theoretical and experimental investigations of the applicability of equation (1) to amorphous transition metals.
Acknowledgements - We wish to acknowledge useful discussions with S. Frota-Pess6a and J.T. Chen. We thank J. Tyler for structural and compositional analyses. This research benefited from the overall support of energy conversion at ECD by the Atlantic Richfield Company. REFERENCES 1.
AL • A&~
3. o\\ •
_ _ _ _L___ ]
N*( 104~d-m3 ) Fig. 1. T c vs. N*(EF) for some amorphous transition metal alloys. D, (Mo l_xRux)soP2o ; z~, (Moo.6Ruo.4)l_xBx [I 7]; o, (Moo.6Ruo.4)l_xSi x [1 7]; 4, ,,, (MOl_y Ty)l_xSi x (this work).
4. 5. 6. 7. 8. 9.
Thus, our data and those of Johnson et al., when plotted as we have done in Fig. 1, indicate a correlation between Tc and N*(EF). However, this correlation depends upon the metalloid in the alloy and is different for each metalloid. Since these materials are intermediate coupling superconductors [18-20], a similar correlation probably exists between Te and N(Ev). (See Figs. 10 and 11 of .) A similar situation exists for the dependence of the density of states on metalloid content. For (Moo.6Ruo.4)l-xBx, increasing x results in a decrease in
10. 11. 12. 13. 14. 15.
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SUPERCONDUCTING PROPERTIES OF AMORPHOUS TRANSITION METAL ALLOYS M. Tenhover, W.L. Johnson & C.C. Tsuei, Solid State Commun. 38, 53 (1981). W.L. Johnson & A.R. Williams,Phys. Rev. B20, 1640 (1979). C.C. Tsuei, W i . Johnson, R.B. Laibowitz & J.M.
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Viggiano, Solid State Commun. 24, 615 (1977). W.L.Johnson, C.C. Tsuei, S.I. Raider & R.B. Laibowitz, J. Appl. Phys. 50, 4240 (1979). H. Sadat-Akhavi, J.T. Chen, F.P. Missell & J.E. Keem, Bull. Amer. Phys. Soc. 27,381 (1982).