Solid StateCommunications, Vol. 7, PP.59—61, 1969. PergamonPress. Printedin GreatBritain

SPINCORRELATIONSIN PARAMAGNETIC SUPERCONDUCTORS*

R.P.Guertintand R.D.Parks

Departmentof PhysicsandAstronomyUniversity of Rochester,Rochester,New York, U.S.A.

(Received27 August1968)

Anomalousbehaviorobservedin the dependenceof the super-conductingtransitiontemperatureof Th,_~Er~on Er concentrationis relatedto the onsetof spin—spincorrelationsamongthe Erimpurities.

THE ADDITION of magneticimpurities to a theoryand is independentof the natureof thesuperconductorcausesa severedepressionof ordering. If the orderingis ferromagnetictherethe transitiontemperature.A first Born approx- can be a secondeffect, viz., a conductionelec-imation calculationin theexchangescattering tron polarization,which, in itself, leadsto aof theconductionelectronsgives the zero field more severereductionin T~than predictedbyphaseboundaryasI the AG theory. The latterhas beenreportedonly

for the InLa3_,,Gd2,system.~ In both theT~ ~{1 1 j (~)=0 , (1) La1 _~Gd~and InLa3_~Gd~systemsdepartures

in — +2 +217 T~~ T0 — from the AG theoryare observedat temperatures

where 1, and T00 arethe superconducting considerablyhigherthan the temperatureoftransitiontemperatureswith andwithout magnetic magneticordering TM, asdeterminedby magneticimpuritiesrespectively,cu (z) is the digamma susceptibility measurementsmadein the normalfunction,and the exchangescatteringtime ~ state.2,6-8 (TM is takento be the temperatureatis inverselyproportionalto the spin impurity which a peakoccurs in the magneticsuscept-concentrationn. The aboveexpression,which ibility >,~). Following thespirit of the recentwasderivedby Abrikosov and Gor’kov (AG)’ is work of Bennemann

4’9and Garland,9we mightvalid only if the magneticimpurities are ~ attributethe anomalousbehaviorto the presencecorrelated. of spin—spincorrelationsamongthe magneticim-

purities, which are expectedto occur at temper-A departurefrom the AG theoryfor large ,~ atureswell above TM. Sucheffects havealso

has beenreportedfor a numberof magnetically beensuggestedas the explanationfor anomalousdopedsuperconductingsystems.2’3As pointed behaviorobservedin the Sn

3La,_~Gd~system.’O~l1

out by Bennemann4the onsetof magneticorder- The purposeof this note is to presentnew results

ing can leadto severaleffects. Oneis the re- on the Th1 _~Er~systemwhich are particularly

duction in spin-flip scatteringwhich leadsto an relevantto the abovediscussion.increasein 2~overthat predictedby the AG

Measurementsweremadeof T~and ~ (in thenormal state)of Th, ~ Er2, alloys in theconcen-

* Work supportedin part by the Air ForceOfficeof Scientific Research. tration range 0.01 ~ x ~ 0.50, with a standard

a.c.mutual inductancetechnique. Theexperimentst address:Tufts University,Medford, werecarriedout in a combination ~andMassachusetts. 59 adiabaticdemagnetizationcryostat.Susceptibility

60 SPIN CORRELATIONSIN PARAMAGNETIC SUPERCONDUCTORS Vol. 7, No. 1

•\I5I~ \Tc

2~

o I 2 3

~“~~cr(Ae)

FiG. 1. Plot of the superconductingtransitiontemperatures1’,, and magneticorderingtemperaturesTM for the Th, - ~Er~ alloy systemnormalizedto the Abrikosov—Gor’kovcritical concentration.Thepoints with error barsdenotethe temperaturesat which the magneticsusceptibilitydepartsthe Curielaw. The TM vs.n/n~~plOtis a linearextrapolationof datatakenin the concentrationrange19.3—50 a/o Er.

_____________________________________ sharpmaximawith temperatureand therefore0 indicatethat thetransitionto the magnetically

8 /o~ orderedstateis abruptand well-defined. This18.5% Er behavioris qualitatively dissimilar to that

reportedfor theInLa3_~Gd2,6and La,~Gd~8

systems,which exhibit broadsusceptibilitymaxima(aswell asgigantic susceptibilities)suggestingthat the magnetictransitionis ill-definedand gradualwith temperature.The dis-parity in behaviorbetweenTh

1 _2,Er2, and theLa—Gd systemscanbe attributedprobablyto theratherlargevalueof n~in the former system

0 I 2 3 ~ ~ a/o comparedto ,z~..~1a/o for theI/I (K’) La—Gd systems).The absenceof well-defined

FIG. 2. The magneticsusceptibilityx vs. magneticphasetransitionsin very dilutemagneticinversetemperaturefor two Th, _2,Er~alloys, systemshasbeenwell documented(e.g., refer-The arrowsdenotethe temperatureT at ences5 and 12).which ~ departsfrom a Curie law begavior.The solid lines are the expectedCurie Shownin Fig. 1 is the line of susceptibilitysusceptibility includingdemagnetizing

maxima(which representsthe linearextrapolationcorrections. of datatakenin the concentrationrange

19.3—50 a/o Er) togetherwith the 7, vs. nmeasurementsmadein the normal state curve for Th1 2, Er2,. Note that thecurves inter-(for n> n~’,where n0,. is the(critical) concen- sectwell below the temperatureat whichtration requiredto suppress~l, to zero) show anomalousbehaviorappearsin the 1, curve.

Vol. 7, No. 1 SPIN CORRELATIONS IN PARAMAGNETIC SUPERCONDUCTORS 61

A closerexaminationof the x vs. T datareveals reducedspin—flip scatteringof the electrons.that x departsfrom the Curie law at a temper- The pictureis lesscleat in the InLa3_~Gd~andature TD well abovethe temperatureof the La,_~Gd~systems,becauseof the widesusceptibilitypeak, TM. Presumably,

7’D is distribution of internal fields and absenceofroughly the temperatureat which spin—spin well-definedmagneticorderingtemperatures,correlationsbetweenthe magneticimpurities bothof which maybe consequencesof the smallstart to becomeimportant. The evaluationof TD impurity concentrations(flcr -~1 a/o).from the susceptibilitydatais illustrated inFig. 2. Shownalso in Fig. 1 is the line The results in Fig. 1 demonstratethat the

vs. n/n~,which is seento intersectthe superconductingstatein a metal with magneticT

0 vs. n/n~~curve at approximatelythe point impurities is particularly sensitiveto interactionswherethe T~,curve departsfrom the AG theory. amongthe impurity spins; and that studiesof theThis we takeasevidencefor the effect of spin superconductingstateprovide ausefulmeansofcorrelations(in the paramagneticstate)on super- studyingspin correlationsandmagneticorderingconductivity. The enhancementof T~over the phenomenain metals.

valuepredictedby the AG theory reflectsthe

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Un comportementirrégulier remarquédans la d~pendancede latemperaturede transitionsuperconductricede Th, ~ Er~pour uneconcentrationEr dependdu debut descorrelationsderotationsparmi les impuretésd’Er.