SUPERCONDUCTIVITY IN METALLIC GLASSES W. Johnson
To cite this version:
W. Johnson. SUPERCONDUCTIVITY IN METALLIC GLASSES. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-731-C8-741. 10.1051/jphyscol:19808183. jpa-00220286
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HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE CoZZoque C8, suppZBment au n08, Tome 41, aoCt 1980, page ~8-731
SUPERCONDUCTIVITY IN METALLIC GLASSES
W.L. Johnson
W. M. Keck Laboratory of Engineering Materials, CaZifornia Institute of TechnoZogy, Pasadem, California 91125, U.S.A.
I. INTRODUCTION
The earliest studies of amorphous superconduc- tors were carried out twenty-five years ago on thin where D(0) = electron density pf states at fi lms of simple metals prepared by vapor deposition the Fermi level on a cryogenic substrate(''*). ~er~mann(~),and 2 = average squared electron-ion the author(4) have surveyed some of the properties matrix element of such materials in recent reviews. In the past ten years, studies of amorphous superconductors M = ionic mass 2 have been extended to transition and
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Experimental evidence obtained from superconductive In crystalline metals, the influence of long tunneling indeed supports this con~lusion(~~~~~~~).range order on electronic band structure results in The author(4) has attempted to explain the large deviations of the electronic density of states systematics of superconductivity in simple amor- D(E) from the free electron model. These deviations phous metals by assuming that the strong disorder in turn influence electron-phonon scattering, and leads to a nearly spherical Fermi surface. A electron screening. The absence of long rangeorder simple jellium model was used to determine the in amorphous metals tends to eliminate these band variation of X with a few simple parameters such as structure effects and leads to a free electron-li ke valence Z, atomic volume va, and ionic mass M. In Fermi surface. As a result, the jellium model the jellium model, the ionic plasma frequency gives a much better description of amorphous as compared to crystalline simple metals which are not Q P = (*)'(where N = density of ions) is a we1 1 described by the jellium model(4). The micro- natural scale for phonon frequencies. A plot of scopic origin and systematics of superconductivity the dimensionless ratio [kBTc/#S2 1 for amorphous P are correspondingly easier to understand in amor- simple metals as a function of average valence Z phous metals . is shown in Fig. 1 and suggests remarkably system- atic relationship. Roughly speaking, this ratio is 6. Transition Metals a measure of the exponential factor on the right The superconducting properties of amorphous hand side of eqn. (1) ,. and thus a measure of A. transition metals are governed mainly by the Using Z, va, and b1 as input parameters in the partially occupied d-states. In contrast with the jellium model, together with the Heine-Abarenkov case of simple metals, one cannot use the free pseudopotential form factors for simple metals, a electron approach to understand these materials. simple model calculation of h was carried out (4) The d-electrons are perhaps best described as being It was found that X is determined mainly byvalence. tightly bound. Friedel(18), Cyrot-Lackmann (19) , These results are illustrated in Fig. 2. and others have discussed the tight-binding approx- imation TBA as it applied to liquid transition metals. Recently, Varma and ~ynes'~') have ana- - lyzed superconductivity in crystalline transition Amorphous Simple I metals using an extension of the TBA method to Metals Pb.9 Cu.~ - 1.2- *I: : include the nonorthogonal ity of atomic d-orbi tals ,J P?75B!25 - 1.0 - centered on neighboring atoms. They find that the II Te9Te.l d-band contribution D~(E,~)to D(E~)is the most 0.8 - GO*:*. .S%Cu., important microscopic parameter which determines X. / '?ES?z 2 2 0.6 - II Their argument shows that the ratio [/
.//*cd,9~e., 0.2 - Applying the Varma-Dynes analysis to the case ,'I f Mg., Z~II (melt-quenched) of amorphous transition metals requires information 0 ---:I L 0 2 4 regarding the behavior of Dd(c). Several experi- Valence Z mental techniques have been used to obtain such information. These include measurements of mag- Fig. 1. Variation with valence of the supercon- netic susceptibility, low temperature specific ducting transition temperature of simple heat, x-ray and ultraviolet photoemission spectra, amorphous metals. The values of Tc are and also indirect deduction of D(E~)from upper normalized to the characteristic bare critical field, Hc2(T), measurements. Magnetic phonon temperature ChS2 /K ] of each P susceptibility measurements on metal 1ic glasses of material. the series (Mol-xRux)80P20 have been reported(21 1, The temperature independent contribution to the susceptibility, G, was found to be large and to decrease with x as sb~wnin Fig. 3. If one Fig. 2. Values of the electron- phonon coupling constant A calcu- lated using a simple jelliummdel with Z, M, and v, as input para- meters. See ref. 4 for details.
VALENCE Z
assumes that the Paul i paramagnetic contribution have used XPS and UPS measurements to gain insight associated with D(E~)dominates x0, then this can into the variation of D(E) for E < cF. Typical be interpreted to indicate a smooth decrease of results are shown in Fig. 4 for the alloy D(cF) with increasing x as shown in the figure. (f.100~6R~0~4)80B20.The data suggest that a general Also shown in the figure is the variation of Tc loss of structure in D(E) Occurs on going from the with x for these metallic glasses and the varia- crystalline to the amorphous state. ' It also sug- tion of Tc vrith x for amorphous Mol-xRux thin gests that D(E) is characterized by a broad maxi- films pre ared by cryoquenching by, Coll ver and mum with the peak occurring somewhat below the Hamm~nd(~~.These results suggest a direct re1a- Fermi level of the alloy. In other words, Dd(~) tionship between D(E) and Tc. Recent low tempera- appears to vary rather smoothly with d-band ture specific heat meas~rements(~)on the same occupation exhibiting a maximum for a roughly half series of metallic glasses have confirmed the de- filled d-shell. The variatfon of Tc observed by crease of D(E) with x, The absolute values of Col 1ver and ~amnond'~)for cryoqueiched films of D(E) obtained from the coefficient of the linear transition metals and alloys ofaneighboring metals contribution to c are in remarkably good agree- of the 4d series is shown in Fig. 5. The variation P ment with D(E) values estimated from xo (4) . of Tc through a simi 1 ar broad maximum js consistent Schroeder et a1(22) and Amamou and the author(23) with the Varma-Dynes analysis if the density of JOURNAL DE PHYSIQUE
Fig. 3. (top) The temperature inde- pendent contribution xo to the magnetic susceptibility and corre- sponding density of states 2 D(0) = 2 pB x0 estimated by assum- ing xo is dominated by Pauli para- magnetism. (bottom) The variation of Tc for the same alloys along with that observed by Collver and Hammond for ~~lol-xRuxthin films.
states Dd(&) has the above characteristics. In electrons. This is due to the highly disordered contrast, the Matthias curve for crystalline tran- atomic arrangement. In the case of simple metals, sition metals is shown in the same figure. In the the atomic potential is comparatively weak. The crystalline case, a rapid variation of Dd(cF) with Ziman theory of liquid metals(11) is premised on d-band occupation is predicted by band structure the assumption of weak scattering and as such calculations(24y25) and confirmed by specific heat neglects multiple scattering effects. Using the measurements (9y20y26). Those crystalline metals simplest solution to the Boltzmann equation, one and alloys for which cF falls near a sharp maximum can estimate the electronic mean free path for in D(E) have high Tc values as expected in the amorphous simple metals directly from measurements Varma-Dynes model. The crystalline to amorphous of p(T). At cryogenic temperatures, p(T -+ 0) transition washes out the d-band structure and thus ranges from 25-100 pQcm for typical simple metals. leads to a smoother variation of both Dd(g) and From consequently Tc(4).
C. Effects of Disorder on Superconductivity
In amorphous metals, essentially every atom can act as a scattering center for conduction and free electron values for the Femi velocity, C8-735
- I- Sputter Cleaned Amorphous (MqsRu.,)80B20 - X-ray Photoemission Spectrum
I 24 Electron Energy (eV) -
Fig. 4. Tk x-ray photoemission spectrum of (Mo0~6Ru0~4)80B20shows the width and shape of the d-band. UPS spectra are given in ref. 22. vFYone obtains an electron mean free path Re which ranges from several times the interatomic distance d up to roughly 10 d. The Ziman model is expected where t is the reduced tempertature t = 2.; tobreak down when Re = d. Mott has termed this the r;: )! electron diffusion(27) or strong scattering regime while the penetration depth is given by (29) and predicts that this regime is approached when Resistivities of this order are in % -% p? 300 yQcm. Ad(t) = 0.615 AL(0) h P t (5) fact observed in amorphous transition metals where where AL(0) is the London penetration depth. For = It should be 0 eqn. (3) gives values of a, d. amorphous metals ~~(0)is in the range 30-10'OA noted that still larger values of p (i.e. while Ad(0) is of the order of 1 vm. The Ginzburg- 3000 v~cm)are expected to result in Anderson p Landau parameter K = (A/<) is of order 10-100(30,311. (28) localization of electronic states . As a consequence of the above facts, amor- The small value of Re typically found for phous superconductors have a large upper critical amorphous metals (27y28)has important consequences field H~~(T)(~~'~~),small lower critical field for superconductivity. The purity parameter HC, (T)(~~),and exhibit large critical fluctua- A = (cO/te) where to is the zero temperature P coherence length in the clean limit (to= '3(29) tion~'~~).The upper critical field behavior is ITA- is exceptionally large, A a 10-100, for amorphous particularly interesting and has recently been P metals. Thus, amorphous metals are a case of studied over an extended range of t for amorphous superconductivity in the extreme dirty limit (29) . transition metal alloys by Tenhover, Tsuei , and In this limit the coherence length becomes the author(31). Examples of these data are shown JOURNAL DE PHYSIQUE
(GROUP NUMBER)
Fig. 5. The variation of Tc with average group number for thin amorphous films of 4d transition metals and alloys. For comparison, the variation of Tc in corresponding crystalline metals and alloys is shown. in Fig. 6. The theoretical calculation of Hc2(T) for the alloys in Fig. 6. On this basis, it is in the dirty limit has been carried out by several suggested that this behavior is related to strong- authors(33y34y35). Corrections to the basic theory electron scattering effects and the tendency toward for spin orbit scattering(35), paramagnetic 1imi t- electron localization. Such effects would also be i ng (36) strong-coup~in~(~~),an anisotropy expected for the case of ultrathin films (39) . effectsi38) have been successful in explaining The topological and chemical disorder in most data on known superconductors. Exceptioos.to amorphous transition metal a1 loys should result in this included recent results on ultra thin films(39), large fluctuations in the atomic environment. In and the data in Fig. 6. The figure shows the the TBA model of the d-band, one would expect large L theoretical curves for A(t) = (Hc2(T)/Hc2(0)) where fluctuations in the two center overlap integral (17) L Hc2(0) is obtained by linear extrapolation. By letting the spin-orbi t coupling parameter As, -t a, one obtains the highest appropriate theoretical prediction for fi(t). The theory is clearly inade- quate to explain the persistent linearity of K(t) where and F2 are the position vectors of at low t. Combining the data of Fig. 6 with all neighboring atoms, Va the atomic potential, and other available data on amorphous re,veals that the ad an atomic d-orbital. Roughly J depends on discrepancy with theory systematically increases (31 1x1 = 1F2-F1 1 = a as with increasing normal state resistivity p . Values of p of the order of 200 @cm are observed Reduced Temperature ( T/ T, )
L Fig. 6. The reduced upper critical field h(t) = Hc2(T)/Hc2(0) vs. t for several transition-metal-base metallic glasses. Dashed lines are theoretical curves. where qo is the Slater coefficient for decay of Chemical disorder (e.g. fluctuations in Flo-Mo, the d-orbital. The d-band width is of order Mo-Ru, and Ru-Ru coordination) wi 11 produce addi- tional diagonal disorder. One might expect to approach the Anderson localization criteria for the d-band of a transition metal glass. where z is the first neighbor coordination number. The above discussion ignores s-d (p-d) hybrid- Frem the atomic pair correlation function of metal- ization which can be parametrized by a parameter If Jsd + 0, then the d-electrons would be I ic glasses(41 ) (e. g. (M0.5~u0.5)80~20 we estimate Jsd. decoupled from the ssp-electrons and could exhibit the mean value of !L to be Z = 3A while fluctuations localization for sufficiently high disorder. For in !L are of order At = 1.0i. Taking ~(1)= lev, finite Jsd. the localization would tend to be and qo = 1i-I (40) gives Jo s 10-30 eV. Thus the suppressed by the greater spatial extent of s,p relative fluctuations in J(!L) are typically oribtals. This interesting problem has important consequences for superconductivity since the qOA% (9) d-electron time and spatial correlation effects ($)=(+) I%l!L=i = ~COSB> play an important role in the microscopic theory of the inhomogeneous superconducting state. The factor
0 -from HC2
X - sp. heat
Y (mi) mole-K
0 0.12 016 0.20 0.24
X Boron Concentration
x (Atomic Percent Metalloid) Fig. 9. Linear coefficient for low temperature specific heat vs. composition for (Ilo0~6R~0~4)1-~x Fig. 7. liearest neighbor distance d vs.composition metallic glasses. The open circles were deduced for (~lo0.6R~0.4)1-xBx,~(~100.6R~0.4)1-xSi,, and from critical field data and eqn. (11). The (Pd0.5Ni0.5)l-xPx metallic glasses. Distances crosses are taken directly from specific heat data. were determined from the Debye formula. (see ref.42)
Electrical Resistivity vs. Metal loid Content
300
LII!l~~~lllll~l~l~~,,,,lll10 20 30 x (Atomic Percent Metalloid)
Fig. 8. Electrical resistivity vs. composition for (Mo0~6R~0~4)1-xBxand (HO~.~RU,,.~)~-~S~~metallic glasses. role in both the atomic scale structure and elec- A clear feature in the SAS intensity is observed
tronic properties of metallic glasses. This is for scattering vector K % 0.3. This feature is best illustrated by the example of most pronounced for x = 0.18 an can be interpreted (Mo~.~Ru~.~)~-xBx glasses which can be obtained by assuming a phase segregation into domains of 0 over the composition range 0.10 < x < 0.24. Several characteristic size % 10-15A with a typical inter- 0 properties of these alloys have been found tochange domain distance of 20-30A. discontinuously with composition near x = 0.18. Results of neutron irradiation studies on Some examples shown in Figs. 7 and 8 are the aver- (Moo .6~u0.4)82B1 have previously been reported (46) age nearest neighbor distance and the electrical The SAS spectrum of a neutron irradiated sample is resistivity. The former is found to increase with shown by curve E. The sample was irradiated to a x for x < 0.18 and decrease for x > 0.18. The total fluence of 10'' n/cm2 of fast neutrons latter is nearly independent for x for x < 0.18 (1 !lev) over a period of several days. The overall and increases rapidly for x > 0.18 (from % 120 ~Qcm increase in small angle scattering reflects an to 250 ~Qcm). Another example of such behavior is increase of point defects during irradiation. The also shown for the metal-metalloid glasses large increase in the broad maximum near K % 0.3 (Pd0.5Ni0, 5)1-xPx. The metal1 ic glasses suggests enhanced phase separation. This can be (~o~~~Ru~~~)~-~S~~are similar but show no dis- understood since the increased point defect concen- continuities. The critical field gradient tration should enhance diffusion at room tempera- (dHc2/dT)T and electrical resistivity can be used ture (47) . C together to determine the electronic density of It is clear that both the electronic structure states D(eF) using the relation (43) and atomic scale structure of these metal 1ic glasses are strongly influenced by the phase separation discussed above. On the other hand, the supercon- ducting properties of these materials should reflect only the average properties of the material since c. where y is the equivalent linear coefficient in the the scale of phase separation 10-252\ is substan- tially smaller than the coherence length of the electronic heat capacity (in erg and 6 is 0 in units of (~cm). Values of y so obtained are superconductor ~~(0)= 50A. However, it may be plotted for (~100~6R~0~4)1-xBxglasses in Fig. 9. possible to produce a coarser phase separation by thermal aging of the glass. This would result in Specific heat data(44), available for two of the an intrinsically inhomogeneous su~erconducti~d alloys, is included in the figure and agrees material. An example of clear phase separation on extremely we1 1 with the y deduced from Hc2. A a much larger scale has been observed in a novel precipitious drop in y vs. x occurs near x = 0.18 2 family of superconducting metal 1i c glasses with y c 4 (m~/mole-K ) for x < 0.18 and 2 (~b~-~~b~)~-~~u~(~~).Here, phase separation on a y = 2 (mJ/mole-K ) for x > 0.18. We conclude that scale of % 1000 A leads to an inhomogeneous super- D(E~)drops by roughly a factor of 2 over this conducting' material in which both phases percolate narrow composition interval. throughout the sample. All of the above facts suggest some type phase transition or dramatic structural change near IV. SUblNARY x = 0.18. The above observations,are explained by assuming two different amorphous phases with com- This article, as mentioned in the introduction, positions x < 0.18 and x > 0.18. Near x = 0.18, was not intended to be a comprehensive review. The the alloy would contain both phase in comparable questions raised in the article serve to emphasize proportions. The technique of small angle x-ray that the electronic structure of superconducting scattering SAS was used to obtain evidence of the metallic glasses is far from being well understood. proposed phase separation (45). Typical small angle Rore generally, the electronic and atomic scale scattering spectra are shown in Fig. 10. Curves structure of metallic glasses may be considerably A,B,C, and D show spectra for as quenched foils more complex than previous1 y recognized. Emphasis with x = 0.12, 0.14, 0.18, and 0.20 respectively. has been given to several current problems in the JOURNAL DE PHYSIQUE
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