Recent achievements in MgB 2 physics and applications: A large-area SQUID magnetometer and...

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Recent achievements in MgB 2 physics and applications: A large-area SQUID magnetometer and point-contact spectroscopy measurements R.S. Gonnelli a, * , D. Daghero a , A. Calzolari a , G.A. Ummarino a , M. Tortello a , V.A. Stepanov b , N.D. Zhigadlo c , K. Rogacki c , J. Karpinski c , C. Portesi d , E. Monticone d , D. Mijatovic e , D. Veldhuis e , A. Brinkman e a Dipartimento di Fisica, Politecnico di Torino, Torino, Italy b P.N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia c Laboratory for Solid State Physics, ETHZ, CH-8093 Zurich, Switzerland d Istituto Nazionale di Ricerca Metrologica (INRIM), Torino, Italy e Low Temperature Division and MESA+ Research Institute, University of Twente, Enschede, The Netherlands Abstract In the first part of the present paper we discuss the fabrication and the characterization of an MgB 2 -based SQUID magnetometer with a directly coupled large-area pick-up loop, made on an MgB 2 film deposited by an all in situ technique. The coarse structure of the SQUID was defined by optical lithography and Ar-ion milling, while the two nanobridges acting as weak links in the superconducting loop were made by focused ion beam (FIB) milling. The device was characterized at different temperatures and showed Josephson quan- tum interference up to 20 K as well as a noise level already compatible with the recording of an adult magnetocardiogram. In the second part, concerning the fundamental physics of MgB 2 , we present the results of very recent point-contact measurements on Mg 1x Mn x B 2 single crystals with 34.1 P T c P 13.3 K (i.e. 0.37% 6 x 6 1.5%). The experimental conductance curves were fitted with the generalized two-band BTK model and their behaviour in magnetic fields was studied to check if both the order parameters (OPs) of the r and p bands were present in the whole doping range. The dependence of the OPs (evaluated through the fit) on the Andreev critical tem- perature of the junctions is analyzed in the framework of the two-band Eliashberg theory by including the effects of magnetic impurities. The results give an evidence of a dominant effect of the magnetic impurities on the r-band channel. Ó 2006 Elsevier B.V. All rights reserved. PACS: 74.70.Ad; 74.50.+r; 74.45.+c; 85.25.Dq Keywords: Magnesium diboride; SQUID; Weak links; Point contacts 1. Introduction The phenomena related to weak superconductivity have played and still play a central role in the studies of super- conductivity. In the last few years, for example, they have been of particular importance in the experimental study of two-band superconductivity in the MgB 2 system as well as in the fabrication of Josephson junctions or simple pro- totypical devices aimed at exploring possible uses of this compound in superconducting electronics. From the applicative point of view, many of the MgB 2 - based Josephson junctions studied so far are of the weak- link type—being the fabrication of trilayer planar junctions of the SIS type still at the beginning and in need of further technological development [1], especially for the need of ex situ annealing in most of the deposition techniques. 0921-4534/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2006.01.018 * Corresponding author. Fax: +39 011 5647399. E-mail address: [email protected] (R.S. Gonnelli). www.elsevier.com/locate/physc Physica C 435 (2006) 59–65

Transcript of Recent achievements in MgB 2 physics and applications: A large-area SQUID magnetometer and...

www.elsevier.com/locate/physc

Physica C 435 (2006) 59–65

Recent achievements in MgB2 physics and applications:A large-area SQUID magnetometer and point-contact

spectroscopy measurements

R.S. Gonnelli a,*, D. Daghero a, A. Calzolari a, G.A. Ummarino a, M. Tortello a,V.A. Stepanov b, N.D. Zhigadlo c, K. Rogacki c, J. Karpinski c, C. Portesi d, E. Monticone d,

D. Mijatovic e, D. Veldhuis e, A. Brinkman e

a Dipartimento di Fisica, Politecnico di Torino, Torino, Italyb P.N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

c Laboratory for Solid State Physics, ETHZ, CH-8093 Zurich, Switzerlandd Istituto Nazionale di Ricerca Metrologica (INRIM), Torino, Italy

e Low Temperature Division and MESA+ Research Institute, University of Twente, Enschede, The Netherlands

Abstract

In the first part of the present paper we discuss the fabrication and the characterization of an MgB2-based SQUID magnetometer witha directly coupled large-area pick-up loop, made on an MgB2 film deposited by an all in situ technique. The coarse structure of theSQUID was defined by optical lithography and Ar-ion milling, while the two nanobridges acting as weak links in the superconductingloop were made by focused ion beam (FIB) milling. The device was characterized at different temperatures and showed Josephson quan-tum interference up to 20 K as well as a noise level already compatible with the recording of an adult magnetocardiogram.

In the second part, concerning the fundamental physics of MgB2, we present the results of very recent point-contact measurements onMg1�xMnxB2 single crystals with 34.1 P Tc P 13.3 K (i.e. 0.37% 6 x 6 1.5%). The experimental conductance curves were fitted with thegeneralized two-band BTK model and their behaviour in magnetic fields was studied to check if both the order parameters (OPs) of the rand p bands were present in the whole doping range. The dependence of the OPs (evaluated through the fit) on the Andreev critical tem-perature of the junctions is analyzed in the framework of the two-band Eliashberg theory by including the effects of magnetic impurities.The results give an evidence of a dominant effect of the magnetic impurities on the r-band channel.� 2006 Elsevier B.V. All rights reserved.

PACS: 74.70.Ad; 74.50.+r; 74.45.+c; 85.25.Dq

Keywords: Magnesium diboride; SQUID; Weak links; Point contacts

1. Introduction

The phenomena related to weak superconductivity haveplayed and still play a central role in the studies of super-conductivity. In the last few years, for example, they havebeen of particular importance in the experimental study

0921-4534/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.physc.2006.01.018

* Corresponding author. Fax: +39 011 5647399.E-mail address: [email protected] (R.S. Gonnelli).

of two-band superconductivity in the MgB2 system as wellas in the fabrication of Josephson junctions or simple pro-totypical devices aimed at exploring possible uses of thiscompound in superconducting electronics.

From the applicative point of view, many of the MgB2-based Josephson junctions studied so far are of the weak-link type—being the fabrication of trilayer planar junctionsof the SIS type still at the beginning and in need of furthertechnological development [1], especially for the need ofex situ annealing in most of the deposition techniques.

60 R.S. Gonnelli et al. / Physica C 435 (2006) 59–65

Local weakening of superconductivity has been achieved,among others, by creating nanobridges with focused ionbeam (FIB) in narrow strips of MgB2 [2] or by means ofcombined nanoscale FIB and ion-beam damage [3]. More-over, weak-link SNS junctions have been used to fabricatesimple prototypical devices such as SQUIDs [4–6] withinteresting and promising features.

As far as the fundamental research is concerned, weaksuperconductivity and the proximity effect have been lar-gely exploited to investigate the superconducting propertiesof the compound. In particular, Andreev reflection at thenormal metal-superconductor interface has been used todetermine the number, the amplitudes and the symmetryof the order parameters in MgB2—as well as to investigatethe effects of chemical substitutions and induced disorder.Andreev reflection is the key mechanism for the supercon-ducting proximity effect, since it provides the elementarymechanism for converting single electron states from a nor-mal metal to Cooper pairs in the superconducting conden-sate. However, it also provides a powerful tool for thespectroscopic study of superconductors, whenever pointcontacts with small or vanishing potential barrier at thenormal metal/superconductor interface are created. In thecase of MgB2, point-contact spectroscopy has demon-strated to be a powerful investigation technique—at leastas versatile as the more traditional scanning tunnel spec-troscopy—since it allows overcoming the difficulties thatarise from the small size of the available single crystalsand from the anisotropy of the compound.

In this paper, we will first present some of our recentachievements in the application-oriented research onMgB2, i.e. the fabrication and test of a large-area SQUIDmagnetometer on films of good quality and homogeneitydeposited by means of an ‘‘all in situ’’ technique. Thenwe will report on recent results of point-contact spectros-copy in MgB2 single crystals with magnetic impurities(Mn), and we will show how these results shed further lighton the fundamental properties of this compound.

2. Applications of MgB2: a large-area SQUID

magnetometer

The successful fabrication of superconducting quantuminterference devices based on magnesium diboride has beenalready reported by several groups [4–6]. The high transi-tion temperature of MgB2 as well as its simple structureand metallic character and the relatively easy depositionof good-quality films are advantages in the realization ofSQUIDs and magnetometers, opening the possibility ofthe development of superconductive electronic devicesoperated by compact and low-cost single-stage cryocoolers.Recently, the fabrication and characterization of an MgB2

magnetometer that operates up to a temperature close to39 K has been reported [7]. In this case, the magnetometerwas made by starting from high-quality epitaxial MgB2

films obtained by hybrid physical chemical vapor deposi-tion (HPCVD) [8] and by realizing two nanobridges whose

size was much smaller than that of the grains in the film.The problem of most techniques for the production ofMgB2 films—including HPCVD—is that they do not allowthe deposition of homogeneous films over large areas(of the order of some square centimeters). On the otherhand, the large-area homogeneity is an essential require-ment for the fabrication of large pick-up coils that areneeded in order to optimize the sensitivity of SQUIDmagnetometers. In this regard, we have recently grownlarge-area homogeneous films by co-evaporation and wehave used them to fabricate an MgB2 magnetometer witha large directly-coupled pick-up loop, whose characteristicswill be discussed in the following.

The MgB2 thin films used in the present work weredeposited on silicon nitride (Si3N4) substrates by an allin situ technique [9]. It consists in the co-evaporation ofB and Mg by means of an electron gun and a resistive hea-ter, respectively, while the substrate is kept at a constantand relatively low temperature (280–290 �C). The evapora-tion rate of Mg was taken as twice the rate of evaporationof B, so as to enrich the precursor film in Mg. This film wasthen annealed in the same deposition chamber at 500 �Cfor 5–10 min in an inert atmosphere (1 mbar of Ar). Thefilms obtained in this way have a shiny gold-like surfaceand cover homogeneously the whole surface of the sub-strate (usually 2 · 2 cm2). The rms roughness determinedby AFM analysis on images of 5 lm · 5 lm is usuallyrather small (620 nm) with a minimum value of about8 nm, and the grain size is of the order of 200 nm [10].The films with the lower surface roughness show vertically-and horizontally-packed plate-like grains from which apartial c-axis orientation can be inferred. This is also con-firmed by the results of X-ray analysis, where mainly the(00 n) reflections are observed. The resistivity vs. tempera-ture curves, measured with the standard four-contact tech-nique, show critical temperatures Tc ranging from 30 to36 K with rather narrow transitions (0.5 K < DTc < 1 K).The residual resistivity is of the order of 10–15 lX cm,while the RRR ratio ranges between 1.1 and 1.3. The val-ues of the critical current density Jc, evaluated at differenttemperatures for different microbridges (10 lm long and10 lm wide) patterned on an area of about 1 cm2 of thesame film by standard photolithography and Ar ion-beammilling are very uniform over the film surface and reachvalues of the order of 5–6 · 106 A/cm2 at low temperature[10].

The first step in the realization of the magnetometerconsisted in the definition of its coarse structures by stan-dard photolithography and their realization by Ar ion-beam milling. The MgB2 film was previously covered bya 25 nm-thick gold layer to avoid degradation during thestructuring process. Fig. 1 shows the design of the magne-tometer as well as a zoom in the region of the internal loopof the SQUID. The side of the external directly-coupledpick-up loop (square washer) is lp = 1 cm and the widthof the strips is wp = 2 mm, while the internal loop of theSQUID has an area of 51 lm · 5 lm. We then used FIB

Fig. 1. The layout of the magnetometer with the SQUID. The geometrical parameters cited in the text are explicitly indicated.

R.S. Gonnelli et al. / Physica C 435 (2006) 59–65 61

milling (Ga+ ions) for the fabrication of two nanobridgesin the 5 lm-wide striplines of the SQUID. The height,width and length of the nanobridges were 100 nm,240 nm (FWHM) and 150 nm, respectively, as determinedfrom the known film thickness, beam profile and FIB etch-ing parameters.

Each nanobridge of the SQUID showed a non-hyster-etic RSJ Josephson characteristic with a critical current Ic

of about 1.3 mA at 4.2 K. The quality factor of the junc-tions IcRN was of the order of 0.7 mV, comparable withthose obtained in similar weak-link structures [4,6,11].The Josephson current of the junctions was observed upto about 20 K. At the same temperature also the voltagemodulation of the magnetometer in an external magneticfield disappears, which is a proof of the correct functioningof the SQUID. Fig. 2 shows this voltage modulation as afunction of the normalized flux of the applied magneticfield, measured at 14 K for different values of the bias cur-rent. The variation of the applied magnetic field, dBU0

, thatproduces a U0 step in the SQUID, changes with tempera-ture since the effective area of the loop depends on the mag-netic field penetration depth k(T). As a consequence, by

1 2 3 4 5 60

10

20

30

40

50

0.0 0.2 0.4 0.6 0.8 1.0

0.2

0.3

0.4

0.5

0.6

Ae

ff(m

m2)

T/TcV(μ

V)

Φext

/Φ0

Fig. 2. The voltage modulation of the magnetometer as a function of theapplied external magnetic flux, recorded at constant temperature (14 K)and different currents. Inset: temperature dependence of the experimentalvalues of Aeff (symbols) extracted from the measured dBU0

(see text fordetails) compared to the fit (dashed line) with the function Aeff =(Aeff(0) + 1.16 · 106 k2(T)) with the k(T) dependence given by the two-band model.

studying the behaviour of the SQUID as a function ofthe temperature one can also obtain information on somephysical properties of the superconducting film the deviceis based on, i.e. the low-temperature penetration depthk(0). To do this, we first evaluated the effective area fromeach experimental value of dBU0

, obtaining the experimen-tal Aeff(T) curve. Then, we calculated the expression of Aeff

of the SQUID magnetometer as a function of the temper-ature, and used this expression to fit the experimentalcurve.

Let us see this procedure in detail. The effective sensingarea Aeff of a square-washer magnetometer is usuallyexpressed by

Aeff ¼Lc

Lp þ Lc

Ap þ Asq; ð1Þ

where Lc is the coupling inductance between the magne-tometer and the SQUID, Lp is the inductance of the pickupcircuit, Ap is its area and Asq is the area of the SQUID.Since in our geometry the conditions Asq� Ap andLc� Lp are fulfilled, the effective area Aeff can be approx-imated by [12–14]

Aeff �Lc

Lp

Ap ¼lðl0gðkÞ þ 2:5� 10�6k2=wdÞ

1:25l0ðlp � 2wpÞAp; ð2Þ

where l is the slit length, d is the film thickness, w the widthof the superconducting strip of the SQUID circuit and, aspreviously pointed out, lp is the side length of the pickupcoil and wp its width. In the previous formula g(k) repre-sents the ratio K(k)/K 0(k) of the complete elliptic integralsof the first kind having k = s/(s + 2w) as argument, wheres is the slit width. All the geometrical parameters involvedin Eq. (2) are shown in Fig. 1. From the physical point ofview the two terms in the numerator of Eq. (2) representthe geometrical coupling inductance between the pickuploop and the SQUID, and the kinetic inductance betweenthem which, in turn, depends on the penetration depth k.Since k is a function of temperature, a strong temperaturedependency appears in the behaviour of Aeff, particularly atT close to Tc. By introducing all the geometrical parame-ters in Eq. (2), one obtains

Aeff ¼ ð0:19� 10�6 þ 1:16� 106k2ðT ÞÞ m2. ð3Þ

2 10 100 2000.5

1

10

SB1/

2(p

T·H

z-1/2)

Frequency (Hz)

Fig. 3. The noise spectrum of the magnetometer measured in a flux-lockedloop at 14 K.

62 R.S. Gonnelli et al. / Physica C 435 (2006) 59–65

The contribution of the second term is significant for k lar-ger than 90 nm, condition that is verified ‘‘a posteriori’’ inour MgB2 thin films. It is now possible to calculate Aeff(0)and k(0), by iteratively fitting the Aeff(T) experimental dataextracted from dBU0

. To do this, it is necessary to use a spe-cific model for the T dependency of k. Here, we used thetwo-band model for transport in the c-axis direction andin the limit of large impurity scattering [15]. The result ofthe iterated calculation is shown in the inset of Fig. 2 asa function of the ratio T/Tc and converges to the valuesAeff(0) = 0.22 mm2 and k(0) = 170 nm. The k(0) value isin agreement with other data reported in the literatureand with the theoretical expectations for the dirty case[15]. The film certainly contains a remarkable level ofimpurities, as it is shown by the relatively low critical tem-perature and by the significant role played by interbandscattering on its properties [16]. On the other hand, thegood fit by using the two-band model for transport outof the ab plane indicates that the transport is not mainlyalong this plane, as a consequence of the misorientationof the grains in the film.

The noise properties of the device were measured in aflux-locked loop and are shown in Fig. 3. The effectivemagnetic field noise results in S1=2

B ’ 1:1pT=ffiffiffiffiffiffi

Hzp

. Thisvalue is still rather high, despite the large pick-up area ofthe magnetometer, considering that for HTS magnetome-ters noise levels of the order of tenths of fT per square rootof Hz are achievable. Nevertheless, in principle this devicewould be already suitable for recording an adult magneto-cardiogram (MCG).

3. Fundamentals of MgB2: point-contact spectroscopy in

Mn-doped single crystals

The effects of disorder and chemical doping in the two-band superconductivity of MgB2 have been recently stud-ied by several groups (see, for example, Ref. [17–19]) butare still in need of some experimental clarification in order

to understand the role of the different scattering channelsand to try to control them selectively. In particular, thesubstitution of magnetic impurities in the Mg sites havebeen discussed only in few papers up to now, probablydue to the difficulties in obtaining the correct stoichiometry[20–22]. In this section, we present the results of recentpoint-contact spectroscopy measurements in Mn-substi-tuted MgB2 single crystals that allowed us to perform thefirst experimental study of the effects of magnetic impuri-ties on the order parameters of a two-band super-conductor.

We carried out point-contact measurements on high-quality Mg1�xMnxB2 single crystals grown at ETHZ (Zur-ich) by using the same high-pressure technique setup forpure MgB2, and by simply replacing part of the Mg precur-sor with metallic Mn [22]. The Mn content of each crystalwas measured by EDX, while measurements of the mag-netic moment clearly indicate that the Mn ions, whichreplace the Mg ones as evidenced by X-ray spectroscopy,are divalent (i.e. Mn2+) and in the low-spin state (S =1/2). In our experiments, we used only carefully selectedcrystals having the sharpest superconducting transitions(determined by dc magnetization measurements) and thebest structural properties. Their Mn contents x werebetween 0.0037 and 0.0150, corresponding to bulk criticaltemperatures Tc between 33.9 and 13.3 K and DTc(10–90%) between 0.65 and 5.4 K, respectively. To obtain junc-tions with reproducible characteristics we used the so called‘‘soft’’ point-contact technique, which consists in putting asmall drop of silver paint (Ø ’ 50 lm) on the flat side sur-face of the crystal and thus injecting the current mainlyparallel to the ab planes [23]. The conductance curves ofthe contacts (dI/dV vs. V) were studied at different temper-atures and in the presence of magnetic fields of differentintensity, in order to determine the critical temperature ofthe junction (the ‘‘Andreev critical temperature’’, T A

c ),and to understand whether one or two order parameterswere present. The dI/dV curves of the contacts which ful-filled the requirements for ballistic conduction were thennormalized and fitted with the two-band BTK model [24],as shown elsewhere [23]. The weight wp of the p-band con-tribution to the total conductance was taken between 0.66and 0.8 as for ab plane contacts in the pure compound[23,25].

Fig. 4 shows some normalized conductance curves (sym-bols) in crystals with different Mn content, in zero and non-zero magnetic field, with the relevant two-band BTK fit(lines).

Since point-contact spectroscopy is a local, surface-sen-sitive technique, the gaps measured in a given contactshould be compared to the critical temperature T A

c of thesame contact. This is what we will do in the following.The two-band BTK fit of the conductance curves ofFig. 4 in zero field indicates the existence of two orderparameters in the Mg1�xMnxB2 system, but, especially atthe highest doping levels, little or no structures associatedto the larger gap are present in the curves. To check

1.02

1.05

B=1 T

B=0AN 352/4Tc

A = 31 K

1.00

1.02

1.04

B=1 T

B=0AN 355/7T

c

A = 25.5 K

Nor

mal

ized

con

duct

ance

-30 -20 -10 0 10 20 300.99

1.02

1.05

B=1 T

B=0AN 389/6bTc

A = 18.0 K

Voltage (mV)

Fig. 4. From top to bottom, dI/dV vs. V curves of three contacts incrystals with increasing Mn content and correspondingly reduced T A

c . Inall the cases, the application of a suitable magnetic field (around 1 T)depresses the p-band contribution to the total conductance thus evidenc-ing the underlying r-band structures.

10 15 20 25 30 35 400

1

2

3

4

5

6

7

8

BCS

Δσ

Δπ

Ene

rgy

gap(

s) (

meV

)

Andreev critical temperature, Tc

A (K)

0.0 0.3 0.6 0.9 1.2 1.5

10

20

30

40

TcA

(K)

Mn content (%)

Fig. 5. The dependence of the r- and p-band order parameters as afunction of the critical temperature T A

c of the contact. In the inset, thedependence of the critical temperature of the contact on the Mn content isshown.

R.S. Gonnelli et al. / Physica C 435 (2006) 59–65 63

whether two-band superconductivity really persists up tothe highest Mn content, we studied the magnetic-fielddependence of the conductance curves in the whole rangeof critical temperatures. Looking at the curves shown inFig. 4, it is possible to see that, on applying the magneticfield, the small-gap features begin to reduce in amplitude,progressively unveiling the underlying large-gap peaks –just like in the case of undoped MgB2 [23]. We observean outward shift of the peaks at some field B = B* (inFig. 4 always around 1 T), when the r-band structuresbecome dominant and determine the shape of the conduc-tance curve. Unlike in pure MgB2, here B* is intenseenough, compared to the strongly suppressed critical field,to partly depress Dr, while the p-band partial conductanceseems not to vanish at B*. Thus, it is not possible to sepa-rate the partial contributions of the r and p bands to thetotal conductance as we did in pure MgB2 [23]. Neverthe-less, the observed shift of the conductance peaks is a clearproof of the existence of two gaps. This shift is clearly pres-ent up to x = 0.012 when T A

c ¼ 18 K as shown in Fig. 4.Even before fitting the conductance curves, it is quite evi-dent from Fig. 4 that both the small p-band gap (roughlyindicated by the conductance peaks at B = 0) and the lar-ger r-band one (roughly indicated by the conductance

peaks at B = 1 T) monotonically decrease at the increaseof the Mn doping level—although remaining well sepa-rated up to the lowest T A

c . The BTK fit of the curves inthe presence of magnetic field fully confirms this observa-tion, thus quantifying the values of the order parametersin a way completely consistent with the results obtainedin zero field.

As far as the reliability of a BTK fit in the presence ofparamagnetic impurities is concerned, it is worthwhile toobserve that all the experimental conductance curves arerather broadened (both by the ‘‘internal’’ magnetic fieldand by the temperature) and have smaller amplitude (seeFig. 4) than in pure MgB2 [23]. As a consequence, even ifthe sub-gap structures in the DOS predicted by strong-cou-pling calculations for MgB2 in the presence of magneticimpurities [26] exist, they are practically unobservable here.Anyway, the BTK model is intended here as a first-orderapproximation to a more specific model for Andreev reflec-tion in the presence of magnetic impurities on the super-conducting side of the contact, still to be developed.

At a doping level higher than 1.2%, the critical temper-ature of the contacts T A

c is lower than 17 K (see the inset ofFig. 5). The zero-field dI/dV curves of these contacts are sobroadened and the critical fields are so small that the anal-ysis of their magnetic-field dependence does not allow con-cluding anything about the presence of one or two gaps.However, these curves can be very well fitted by the two-band BTK model, and even if a standard single-bandBTK fit is sometimes possible, it is often unable to repro-duce both the position of the peaks and the width of theAndreev-reflection structures in the conductance [27]. Thissuggests that two gaps are likely to be present even in themost doped samples.

Fig. 5 shows the full dependence of the gaps on thelocal critical temperature T A

c . Each point is the result of

10 15 20 25 30 35 400.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Γ σσ,Γ

ππ(m

eV)

Tc

A (K)

Γσσ

Γππ

Fig. 6. The dependence of Crr and Cpp as a function of the criticaltemperature T A

c of the contact. With these values, the Eliashberg equationsgive the order parameters reported in Fig. 5 as solid lines.

64 R.S. Gonnelli et al. / Physica C 435 (2006) 59–65

an average of the gap values obtained at that T Ac , while the

error bars include both the uncertainty on the gaps in eachfit and the spread of their values over different contacts. Wepresent only the results of the two-band BTK fit even atT A

c < 17 K since they better agree with the regular trendof the gaps for T A

c P 18 K. A transition to a single-gapregime around 17 K would require an abrupt change inthe slope of the curves at this T A

c , and no discontinuity inthe physical properties of the compound at this dopinglevel is observed that could justify this behaviour [22].

The existence of two distinct order parameters up to thehighest x values is an indication that the quasiparticle scat-tering between r and p bands (interband) is not signifi-cantly increased by the Mn doping. Due to the very lowMn concentration, this is an expected result as far as thenon-spin-flip part of the interband scattering is concerned.However, some theoretical calculations indicate that alsothe spin-flip interband scattering should be negligible fora random distribution of impurities [26]. As a first approx-imation, the effects on the gap values of the changes in thephonon spectra a2Fr,p(x) and in the DOS at the Fermilevel can be neglected due to the very low Mn concentra-tion and the absence of electron doping (Mn is isovalentwith Mg), respectively [22]. Hence, the only physical pro-cess that can explain the experimental decrease of the gapsshown in Fig. 5 is the pair-breaking spin-flip scatteringwithin the bands. In addition to this, the particular depen-dence of the gaps on T A

c exhibiting the highest slope for ther-band gap Dr suggests an increase of spin-flip scatteringin both the r and p bands on increasing the Mn content,but with a dominant role of the former.

We can discuss these results in a more quantitative wayby trying to fit the Dr,p vs. T A

c dependence through thesolution of the Eliashberg equations (EE) in the presenceof randomly distributed magnetic impurities and randomlyoriented magnetic moments. Following the previous con-siderations, we used for the calculations the same parame-ters as in pure MgB2 [23], we neglected all the non-spin-flipscattering (inter- and intraband) and assumed the spin-flipscattering to be much more effective within the bands thanbetween them. As a matter of fact, it is possible to showthat the introduction of a relevant spin-flip interband scat-tering rate would lead to a depression of the gaps much fas-ter than that experimentally observed. Thus, the onlyadjustable parameters for us are the spin-flip intraband

scattering rates Crr and Cpp. We then solved the imagi-nary-axis Eliashberg equations and performed the analyti-cal continuation of the solution to the real axis by lookingat the simplest CppðT A

c Þ and CrrðT Ac Þ functions that are able

to give the experimental values of T Ac and of the gaps in the

whole doping range. We found out that these curves followa parabolic behaviour as a function of T A

c , as shown inFig. 6. The resulting theoretical Dr,p vs. T A

c curves arereported in Fig. 5 as solid lines. They show an almost per-fect agreement with the experimental data in the wholerange of T A

c . These results suggest that the effects of mag-netic Mn ions up to x = 0.015 in Mg1�xMnxB2 can be

accounted for by only adding intraband magnetic scatter-ing in the model, with a dominant role in the r-band[27]. On the contrary, Mn substitutions seem not toincrease significantly the interband scattering, both spin-flip and non-spin-flip. These results shed light for the firsttime on the effect of magnetic impurities on the orderparameters of a two-band superconductor.

4. Conclusions

We have presented the recent results of our research onMgB2, concerning applicative and fundamental aspects,both related to weak superconductivity and proximityeffect. From the point of view of applications, we havereported on the fabrication and test of a SQUID magne-tometer with a directly-coupled pick-up loop, made bystarting from MgB2 films of good quality and high homo-geneity over areas of some square centimeters. The Joseph-son junctions of the SQUID are of the SNS type and weremade by FIB. This device already presents interesting fea-tures for applications, such as a high operating temperatureand a reasonably good effective magnetic noise.

As far as the fundamental physics of MgB2 is concerned,we have presented the results of the first experimental studyof the effects of magnetic impurities on the order parame-ters Dr and Dp of a two-band superconductor by meansof Andreev-reflection spectroscopy. This study is insertedin a more general project of investigation of the effects ofvarious substitutions in MgB2, motivated by the need ofclarifying the role of inter- and intraband scattering rates.We have shown that the main effect of magnetic impuritiesis to almost linearly decrease the order parameters Dr andDp (that remain well distinct up to the highest doping) aswell as the critical temperature. Within the Eliashberg the-ory, this behaviour can be perfectly explained as being onlydue to an increase in spin-flip scattering within the r and pbands on increasing the Mn content, with a major contri-

R.S. Gonnelli et al. / Physica C 435 (2006) 59–65 65

bution in the r-band and little or no increase in interbandscattering.

Acknowledgements

This work was done within the PRIN Project No.2004022024 and the INTAS Project No. 01-0617. V.A.S.acknowledges support by RFBR (Project No. 06-0216490).

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