Magnetization-dependent $T_c$ shift in FSF trilayers with a strong ferromagnet

a r X i v :c o n d -m a t /0512623v 1 [c o n d -m a t .s u p r -c o n ] 23 D e c 2005

Magnetization-dependent T c shift in F/S/F trilayers with a strong ferromagnet

Ion C.Moraru,W.P.Pratt,Jr.,Norman O.Birge ?

Department of Physics and Astronomy,Michigan State University,East Lansing,Michigan 48824-2320,USA

(Dated:February 6,2008)

We have measured the superconducting transition temperature T c of Ni/Nb/Ni trilayers when the magnetizations of the two outer Ni layers are parallel (P)and antiparallel (AP).The largest di?erence in T c occurs when the Nb thickness is just above the critical thickness at which superconductivity disappears completely.We have observed a di?erence in T c between the P and AP states as large as 41mK -a signi?cant increase over earlier results in samples with higher T c and with a CuNi alloy in place of the Ni.Our result also demonstrates that strong elemental ferromagnets are promising candidates for future investigations of ferromagnet/superconductor heterostructures.

PACS numbers:74.45.+c,85.75.-d,85.25.-j,73.43.Qt

Heterostructures composed of ferromagnetic (F)and superconducting (S)materials have attracted much theo-retical and experimental attention due to the rich physics produced by the interplay between competing symme-tries of the order parameters [1].In an S/F bilayer the exchange ?eld of the ferromagnet modulates the super-conducting order parameter as it decays inside the fer-romagnet over a very short distance.Kontos et al.[2]used tunneling spectroscopy to observe the damped os-cillations of the order parameter by measuring the den-sity of states (DOS)for di?erent thickness ferromagnets.Ryazanov et al.[3]observed π-state Josephson coupling in an S/F/S trilayer ?rst by varying temperature,then later by varying the thickness of the ferromagnet [4].Ear-lier,several groups [5,6,7]had observed oscillations in the critical temperature T c of S/F bilayers as a function of the ferromagnet thickness d F .Under ideal conditions T c oscillations arise from interference between the trans-mitted superconducting wave function through the S/F interface and the wave re?ected from the opposite surface of the ferromagnet,although in some cases alternative explanations have been proposed [8].In many experi-ments,weakly ferromagnetic alloys were used in order to reduce the size of the exchange splitting in the conduc-tion band,E ex ,and thus increase the penetration length ξF for Cooper pairs,where ξF = v F /2E ex in the clean limit and v F is the Fermi velocity of the ferromagnet [9].An alternative way to probe the in?uence of a ferro-magnet on a superconductor is to look for T c variations in an F/S/F trilayer structure based on the mutual ori-entation of the two ferromagnet magnetizations [10,11].This e?ect was observed [12]and later reproduced [13]in a Cu 1?x Ni x /Nb/Cu 1?x Ni x system,where a weak fer-romagnet was used because it is ”less devastating to su-perconductivity.”The largest di?erence in T c observed between the antiparallel (AP)and parallel (P)states of the F-layer mutual magnetizations was only 6mK when T c was 2.8K.Unlike other experiments [2,3,4,5,6,7]that require the ferromagnet thickness to be comparable to ξF ,however,a positive feature of this experiment is that the T c di?erence is predicted to persist even for thick

F layers [10,11].Thus it proves advantageous in study-ing systems with strong elemental ferromagnets,which have extremely short values of ξF .

Experimental studies of F/S systems with strong fer-romagnets are of interest because they provide new chal-lenges to theory,which does not yet address the full com-plexity of the ferromagnetic state with its di?erent DOS and v F of the majority and minority spin bands.Fur-thermore,pure elemental ferromagnets are in the clean limit,ξF

Sets of Ni(7)/Nb(d s )/Ni(7)/Fe 50Mn 50(8)/Nb(2)multi-layers (all thicknesses are in nm)were directly deposited onto Si substrates by magnetically-enhanced triode dc sputtering in a high vacuum chamber with a base pres-sure in the low 10?8Torr and an Ar pressure of 2.0·10?3Torr.The Ni thickness of 7nm was chosen to be much longer than ξF ,which we estimate to be 0.8nm using 2E ex =0.23eV and v F =0.28·106m/s for the major-ity band [17].The purpose of the FeMn is to pin the magnetization direction of the top Ni layer by exchange bias [18].The non-superconducting Nb capping layer protects the FeMn from oxidation.After deposition,the samples were heated to 180?C under vacuum,just above the blocking temperature of FeMn,and cooled in an ap-

FIG.1:Critical temperature vs.Nb thickness for Ni(7)/Nb(d s)/Ni(7)/Fe50Mn50(8)/Nb(2)samples(all thick-nesses are in nm).Di?erent symbols represent di?erent sput-tering runs.The solid line represents the theoretical?t.Inset: Schematic cross-section of the samples.

plied?eld of200Oe in the plane of the multilayer.This procedure pins the top Ni layer while leaving the bottom Ni layer free to rotate in a small applied magnetic?eld. Four-probe resistance measurements with the current in the plane of the multilayer were performed to deter-mine T c.Samples had lateral dimensions4.3mm x1.6 mm.The T c of each sample was de?ned to be the temper-ature at which the resistance dropped to half its normal state value.Fig.1shows the results for T c measure-ments for samples from several sputtering runs,where d s was varied between16-52nm.T c shows a strong depen-dence on the superconductor thickness close to a critical thickness,d cr s,where the sensitivity to ferromagnetism is enhanced.There is no superconductivity above36mK for d s

The magnetic con?guration of our structures was veri-?ed on simultaneously sputtered samples of larger lateral size,in a SQUID magnetometer.Fig.2shows a plot of magnetization vs.applied?eld H for a sample with d s= 18nm taken at100K.The narrow hysteresis loop near H =0shows the switching behavior of the free Ni layer with a coercive?eld H c=35Oe.The wider loop shows switch-ing of the pinned layer and is shifted to nonzero H due to the exchange bias between the top Ni layer and the FeMn. Applied?elds of±100Oe switch the spin-valve between the P and AP con?gurations.The nearly zero net mag-netization observed at-100Oe indicates very good AP alignment between the pinned and free Ni layers,while the nearly saturated magnetization observed at+100Oe indicates good P alignment.Similarly good alignment of the P and AP states can be achieved at low temperature. The inset to Fig.2shows a minor hysteresis loop

with FIG.2:Magnetization vs.applied?eld for a d s=18nm sample measured at T=100K.At±50Oe the free bottom Ni layer switches while the pinned top Ni layer switches at -500Oe.Inset:minor loop measured at T=2.29K showing the switching of the free Ni layer.

H c≈50Oe taken at2.29K,which corresponds to the

middle of the superconducting transition for this sample. We obtain the same behavior for temperatures above and below the transition temperature.

Measurements of T P c and T AP

c

were performed by al-ternating the applied?eld between+100and-100Oe,as the temperature was slowly decreased through the tran-sition region.The largest shift in critical temperature,

?T c≡T AP

c

?T P

c

,should occur in samples with the Nb thickness close to d cr s.Fig.3shows a plot of R vs.T for a sample with d s=17nm,measured in a dilution refrigerator.Two distinct transitions are observed for P and AP alignment,with a separation in temperature ?T c≈28mK.A second sample with d s=17nm showed a?T c≈41mK,but with a slightly broader transition centered at0.34K.Samples with d s=18nm and T c be-tween2and3K exhibit values of?T c of only a few mK, similar to the CuNi/Nb/CuNi samples measured previ-ously[12,13].

The inset to Fig.3shows a plot of R vs.H for the ?rst d s=17nm sample at a temperature in the middle of the transition(0.51K).The data clearly show well-established P and AP states at±100Oe,respectively, with a di?erence in resistance of1.5?.Above the tran-sition the resistance does not change perceptibly when switching from P to AP alignment.An interesting fea-ture of the R vs.H curve is the behavior of the resistance as the?eld is swept down from+150Oe towards-50Oe and as the?eld is swept up from-150Oe towards+50Oe. In both cases the resistance increases to a value higher than that of the P state after the?eld passes through zero.We believe this behavior involves the breaking of

FIG.3:Resistance vs.temperature for the P and AP states of a d s=17nm sample measured in±100Oe.Two distinct transitions are observed,with?T c=28mK.Inset:Resis-tance vs.applied?eld at T=0.51K(dotted line in main graph).

the free ferromagnetic layer into domains when H≈H c. The domain-wall fringe?elds penetrate the superconduc-tor,thus suppressing T c slightly and producing a higher resistance.Note that this e?ect is opposite to that ob-served by other

groups

[19,

20],

where inhomogeneous

magnetization led to enhanced superconductivity in F/S bilayers.In those experiments,the domain size must be smaller than the superconducting coherence length so that the Cooper pairs sample multiple domains[21],and the magnetic?eld penetrating into the superconductor must be small.

The critical temperature of F/S/F trilayers in the P and AP states has been calculated theoretically by sev-eral groups[10,11,22,23,24].Since many experiments employ ferromagnetic alloys,the usual approach involves solving the Usadel equations in the dirty limit for both the superconductor and the ferromagnet.(The dirty limit applies to S when l S<ξBCS= v Sγ/π2k B T c0,and to F when l F<ξF,where l S and l F are the electron mean free paths in S and F,and T c0is the transition tempera-ture of the bulk superconductor.)In our case,however, the ferromagnetic metal is both pure and strong,thus in the clean limit l F>ξF.Hence we use the theory of[11] as modi?ed in section3.2of[25]to make it more appro-priate for the clean limit.This theory does not,however, incorporate a full description of the majority and mi-nority spin bands of a strong ferromagnet,with di?erent DOS,v F,and transmission coe?cients.The expression for the normalized critical temperature of the trilayer is ln t c+ReΨ 1t c(d s/ξS)2 ?Ψ 1

ξS

N F v FξS

2N S D S(d cr s)

1

(d cr s/ξs)

=0.24(3)

Estimates of the product N F v F vary substantially in the literature.From[27]and[17],we obtain respectively N F=1.77·1048J?1m?3and v F=0.28·106m/s. Fierz et al.[28],however,quoteρF l F=0.7?2.3f?m2 for Ni,which when combined with the Einstein relation 1/ρF l F=N F v F e2/3imply values3-10times smaller for N F v https://www.sodocs.net/doc/2c5038718.html,bining these values with N S=5.31·1047 J?1m?3[29]and using our measured D S(d cr s)=2.8·10?4m2/s,we obtain T F=0.05?0.6.The bulk resis-tivity of our sputtered Ni?lms at4.2K isρF=33n?m, which leads to values of l F between7and70nm,given the range inρF l F quoted above.Since the Ni used in our trilayers is thin,l F is probably limited by surface scat-tering,so we use the lower estimate l F=7nm,hence ξF/l F≈0.1.In fact,the?t to T c(d s)is quite insensitive to the values of T F andξF/l F.We usedξF/l F=0.1and T F=0.3to obtain the curve shown in Fig.1,which?ts the data remarkably well.

A more stringent test of the theory is the prediction of ?T c,which depends sensitively on both T F andξF/l F.

FIG.4:Symbols:?T c vs.T c for our11thinnest samples. The line represents a?t usingξF/l F=0.7and T F=1.0, values larger than our best estimates.

Thickness deviations from nominal values produce scat-

ter in plots of T c or?T c vs.d s,therefore Fig.4shows a plot of?T c versus T c.If we calculate?T c using our best estimate ofξF/l F and the upper limit of T F given above, the maximum value of?T c is only a few mK when T c is well below1K–hardly visible on Fig.4.If we relax the constraints we have placed on the parameters,and instead try to produce the best?t to the?T c(d s)data, we?nd that a reasonable?t can be obtained whenξF/l F is allowed to be much larger than our original estimate. Fig.4shows a?t usingξF/l F=0.7and T F=1.0.Sim-ilar curves can be produced by simultaneously varying ξF/l F and T F while keeping their product nearly con-stant.Fitting the?T c data requires lettingξF/l F exceed our estimate substantially.Our l F estimate may be too large,because the resistivity is dominated by the longer of the majority or minority band l F,whereas the F/S proximity e?ect depends on the shorter of the two[8].A shorter l F is also implied by the observation of complete damping of T c oscillations in Nb/Ni bilayers for d F>4 nm[16].Nevertheless,producing a reasonable?t to our ?T c data entails either increasingξF/l F beyond the clean limit,or increasing T F beyond our original estimate.

In conclusion,we have observed a large di?erence in T c between the P and AP magnetic states of Ni/Nb/Ni trilayers,with T P c

c

.Recently,Ruzanov et al.

[30]reported a T c di?erence between the P and AP states of a Ni0.8Fe0.2/Nb/Ni0.8Fe0.2trilayer,but with

T P c>T AP

c

.Understanding these opposing behaviors in F/S systems with strong ferromagnets will require fur-ther experiments,as well as theoretical models able to account for the complexity of real ferromagnets[31]. We are grateful to R.Loloee and J.Bass for fruitful discussions.This work was supported by NSF grants DMR9809688,0405238,0202476and by the Keck Mi-crofabrication Facility.

?Electronic address:birge@https://www.sodocs.net/doc/2c5038718.html,

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