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Submitted on 1 Jan 1978
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NUCLEAR SPIN RELAXATION AND
TRANSITION-METAL IMPURITIES IN
SUPERCONDUCTING ALUMINIUM
K. Parvin, D. Maclaughlin
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-876
NUCLEAR SPIN RELAXATION AND TRANSITION-METAL IMPURITIES IN SUPERCONDUCTING ALUMINIUM + K. P a r v i n and D.E. MacLaughlin
Department of Physics, University of California, Riverside, California 92521, U.S.A. * Natuurkundig Laboratorium, Valokenierstraat 65, Amsterdam, Pays-Bas
Résumé.- Nous avons effectué des mesures du temps de relaxation nucléaire T de la matrice sur des alliages ARMn et AStV normaux et supraconducteurs. Les résultats semblent indiquer qu'un élargisse-ment suppléélargisse-mentaire des excitations supraconductrices se produit avec à peu près la même amplitude pour les deux systèmes. Des théories d'affaiblissement des paires ou de fluctuation de spins dans un état lié résonnant ne rendent compte ni de l'ordre de grandeur des résultats ni de 1'indépendance de l'élargissement avec la nature de l'impureté.
Abstract.- Host nuclear spin-lattice relaxation times T have been measured in the normal and super-conducting states of dilute A£Mn and AAV alloys. The data appear to indicate the presence of an ad-dional broadening of superconducting excitations of nearly the same magnitude for the two alloy systems. Neither the magnitude nor the sample independence of the results are accounted for by pair-weakening or spin-fluctuation theories of resonant bound impurity states.
1. INTRODUCTION.- Effects of 3d transition metal im-purities on nontransition superconducting host me-tals have been extensively studied in the framework of the Friedel-Anderson model /1,2/. Localized mo-ments may or may not appear at impurity sites, de-pending on the values of parameters introduced- in this model. In the nonmagnetic case the rate of de-pression of the superconducting transition tempe-rature T is appreciably greater than for nonreso-nant nonmagnetic impurities. The pair-weakening nature of this depression / ] / results in a law of corresponding states which predicts that, apart from impurity averaging of energy-gap anisotropy /3/, a universal dependence of superconducting properties on reduced temperature T/T should be found. For thermodynamic quantities such as the specific heat /4/ this universal dependence has been verified ex-perimentally. Preliminary measurements of nuclear spin-lattice relaxation times T in dilute AftMn alloys, however, did not yield such a law /5/.
We report here measurements of T in careful-ly prepared A&Mn and AJtV alloys. These confirm the preliminary results, and in addition indicate that the behaviour of the A&V system is also anomalous. Since V 'ions are considerably further from the con-dition for magnetism than Mn ions in AJt, the ten-dency for spin-fluctuation behaviour in AJIMn /6/ seems not to affect the anomaly appreciably.
2. EXPERIMENT.- Samples were prepared by melting the
' Research supported by the U.S. National Science Foundation
constituents in a graphite crucible at about 1000 C in the presence of 200 torr of ultrapure argon gas. The melt was stirred by a graphite rod for about one hour and then rapidly quenched into ice water. The ingots were annealed in 10- 5 torr vacuum at 500°C
and quenched into ice water to encourage homogeneity. Two pieces were cut from the ingot for residual re-sistivity ratio measurements;these agreed with each other and with previous measurements to within 10 %
111. Samples for NMR measurements were filed, pas-sed through a 45-y sieve, and thermally treated as before. Values of T determined using standard techniques were consistent with the results of Babic et al. /6/. 2 7A£ spin-lattice relaxation ra-tes were measured at zero applied field in the nor-mal and superconducting states by the field-cycling technique of Hebel and Slichter /8/.
3. DISCUSSION.- The temperature dependence of T in the superconducting state is due to the energy de-pendence of the superconducting density of excited
states 19/. The minimum value T. . found just below i m m
T is controlled mainly by the energy breadth of the states at the gap edge ; increasing the breadth de-creases T . If the 3d impurities were entirely
i min ' nonmagnetic, their only effect would be to reduce
the excited-state breadth due to energy-gap aniso-tropy /3/, and thereby decrease T . /9,10/. In the theory of Clem /3/ the breadth is given in the dir-ty limit by a parameter a = 0.64 I <a2>/£ , where I
is the impurity mean free path, <a2> is the
mean-square anisotropy of the pure host, and £ is the
superconducting coherence length. This theory maybe generalized to include other contributions to a /11/. Figure 1 shows our experimental results to- gether with fits to theory treating
a
and the zero-Fig. 1 : Dependence of 2 7nuclear spin-lattice ~ ~
relaxation time T on inverse reduced temperature Tc/T. The inset
SLOWS
values of the broadening pa- rametera
obtained from fits to the TI data (closed circles) and estimated from resistivity measurements (open circles)temperature energy gap A(0) as adjustable parameters. The inset compares these values of a to estimates from the residual resistivity : the measured-values of a are an order of magnitude larger than expected. Since weak energy-gap averaging is unlikely in these systems 151, we conclude tentatively that the impu- rities anomalously broaden the excited states. The broadening is found not to depend sensitively on impurity concentration. Preliminary.measurements on ARMg alloys confirms the result of Masuda-/lo/ that
-
anisotropy averaging substantially accounts for re- laxation in nonresonant nomnagnetic alloys.
A Hartree-Fock calculation of Machida and Nakanishi 1121 indicates that the resonant impurity states should broaden excitations by an amount of the same order as that expected from anisotropy ave- raging, which is insufficient to explain our results. It can be shown /11/ that in this theory the broa- dening depends on impurity species only through the rate of depression of Tc. In the limit appropriate to AR-based alloys a recent perturbation treatment
of Sakurai 1131 renormalizes the Hartree-Fock para- meters but preserves the form of the lower-order theory ; the T I anomaly is therefore not explained by this approach. It should be noted that the resi- dual resistivities for V, Cr, and Mn are nearly the same in AR. The anomalous broadening may be related to the impurity cross-section for resonant scatte- ring.
ACKNOWLEDGMENTS.- We are grateful for numerous use- ful discussions with E. Simgnek and P.K. Tse.
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