We present the first results of directional point-contact measurements in
Mg_{1-x}Mn_{x}B_2 single crystals, with x up to 0.015 and bulk T_c down to 13.3
K. The order parameters Delta_{sigma} and Delta_{pi} were obtained by fitting
the conductance curves with the two-band Blonder-Tinkham-Klapwijk (BTK) model.
Both Delta_{pi} and Delta_{sigma} decrease with the critical temperature of the
junctions T_c^A, but remain clearly distinct up to the highest Mn content. Once
analyzed within the Eliashberg theory, the results indicate that spin-flip
scattering is dominant in the sigma band, as also confirmed by first-principle
band structure calculations.Comment: 4 pages, 5 eps figures. New theoretical results added, text and some
  figures changed. References adde

A. Calzolari

A. A. Abrikosov

D. Daghero

F. Bernardini

G. A. Ummarino

J. Karpinski

K. Rogacki

M. Tortello

N. D. Zhigadlo

R. S. Gonnelli

S. Massidda

V. A. Stepanov

English

arXiv

We present the first results of directional point-contact measurements in Mg1xMnxB2 single crystals, with x up to 0.015 and bulk Tc down to 13.3 K. The order parameters and were obtained by fitting the conductance curves with the two-band Blonder-Tinkham-Klapwijk model. Both and decrease with the critical temperature of the junctions TAc , but remain clearly distinct up to the highest Mn content. Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the band, as also confirmed by first-principles band-structure calculation

Gonnelli, Renato

Daghero, Dario

Ummarino, Giovanni

Calzolari, Andrea

Tortello, Mauro

Stepanov, V.A

Zhigadlo, N.D

Rogacki, K

Karpinski, J.

Bernardini, F.

Massidda, S.

PORTO Publications Open Repository TOrino

Effect of magnetic impurities in a two-band superconductor: A point-contact study of Mn-substituted MgB2 single crystals

Crossref

Effect of Magnetic Impurities in a Two-Band Superconductor: A Point-Contact Study of Mn-Substituted
                    
                      
                        MgB

We present the first results of directional point-contact measurements in Mg1xMnxB2 single crystals,
with x up to 0.015 and bulk Tc down to 13.3 K. The order parameters  and  were obtained by fitting
the conductance curves with the two-band Blonder-Tinkham-Klapwijk model. Both  and  decrease
with the critical temperature of the junctions TAc , but remain clearly distinct up to the highest Mn content.
Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the
 band, as also confirmed by first-principles band-structure calculations

GONNELLI, Renato

DAGHERO, Dario

CALZOLARI, ANDREA

TORTELLO, MAURO

UMMARINO, Giovanni

Stepanov, V. A

Zhigadlo, N. D

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

We present the first results of directional point-contact measurements in Mg(1-x)Mn(x)B(2) single crystals, with x up to 0.015 and bulk T(c) down to 13.3 K. The order parameters Delta(sigma) and Delta(pi) were obtained by fitting the conductance curves with the two-band Blonder-Tinkham-Klapwijk model. Both Delta(pi) and Delta(sigma) decrease with the critical temperature of the junctions T(c)(A), but remain clearly distinct up to the highest Mn content. Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the sigma band, as also confirmed by first-principles band-structure calculations

R. S. GONNELLI

D. DAGHERO

G. A. UMMARINO

A. CALZOLARI

M. TORTELLO

V. A. STEPANOV

N. D. ZHIGADLO

K. ROGACKI

J. KARPINSKI

S. MASSIDDA

BERNARDINI, FABIO

Archivio istituzionale della ricerca - Università di Cagliari

Effect of Magnetic Impurities in a Two-Band Superconductor:A Point-Contact Study of Mn-Substituted MgB2 Single CrystalsR. S. Gonnelli,1 D. Daghero,1 G. A. Ummarino,1 A. Calzolari,1 M. Tortello,1 V. A. Stepanov,2 N. D. Zhigadlo,3K. Rogacki,3,* J. Karpinski,3 F. Bernardini,4 and S. Massidda41Dipartimento di Fisica and CNISM, Politecnico di Torino, 10129 Torino, Italy2P.N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia3Laboratory for Solid State Physics, ETHZ, CH-8093 Zurich, Switzerland4Dipartimento di Fisica, Universita` di Cagliari, 09042 Monserrato (CA), Italy(Received 12 October 2005; published 19 July 2006)We present the first results of directional point-contact measurements in Mg1xMnxB2 single crystals,with x up to 0.015 and bulk Tc down to 13.3 K. The order parameters  and  were obtained by fittingthe conductance curves with the two-band Blonder-Tinkham-Klapwijk model. Both  and  decreasewith the critical temperature of the junctions TAc , but remain clearly distinct up to the highest Mn content.Once analyzed within the Eliashberg theory, the results indicate that spin-flip scattering is dominant in the band, as also confirmed by first-principles band-structure calculations.DOI: 10.1103/PhysRevLett.97.037001 PACS numbers: 74.50.+r, 74.45.+c, 74.70.AdThe two-band character of superconductivity in MgB2[1,2] has been almost completely understood and explainedby now, but the effects of disorder and chemical doping arestill in need of some experimental clarification. Severalsubstitutions have been tried [3] but none of the few suc-cessful have been able to enhance the Tc of the compound.However, their study has proven useful to clarify the role ofthe different scattering channels and to try to control themselectively. Substitutions with magnetic impurities (Mn,Fe) represent a class of its own because of the spin-flippair-breaking scattering that is expected to dramaticallysuppress superconductivity—even though the way it doesit in a two-band superconductor has never been studiedexperimentally. Up until now, only two successful Mnsubstitutions in the Mg site have been reported: one inpolycrystalline samples [4] and one in single crystals [5].Here, we present the first results of point-contact spectros-copy (PCS) in the Mn-substituted MgB2 single crystalsgrown at ETHZ, which allowed us to study the effects ofmagnetic impurities on the order parameters (OPs) of atwo-band superconductor. The trend of the OP amplitudes and  as a function of the critical temperature of thecontacts, TAc , can be explained within the Eliashberg theoryas being mainly due to a doping-induced increase in thepair-breaking scattering within the  bands, with smallercontributions from the - or the - channels. Thisresult, apparently in contrast with the Mn position in thelattice, is however confirmed by first-principles calcula-tions of the local effect of a Mn impurity on the bandstructure of MgB2.The high-quality Mg1xMnxB2 single crystals used forour measurements were grown by using the high-pressuretechnique set up for pure MgB2, and by replacing part ofthe Mg precursor with metallic Mn [5]. The Mn content xof each crystal was measured by energy dispersive x-rayanalysis (EDX) through a careful evaluation of the Mn=Mgratio; the crystals are single phase and homogeneouswithin x (x  0:0010). As shown elsewhere [5], thedependence of the lattice constants on the Mn contentindicates that Mn replaces Mg in the lattice. Themagnetic-field dependence of the Curie part C of themagnetic moment clearly indicates that Mn ions are diva-lent (i.e., Mn2) and in the low-spin state (S  1=2), asalso confirmed by our first-principles band-structure cal-culations. The crystals we used were carefully selectedamong those with the sharpest superconducting transitionsand best structural properties, so that secondary phases orother impurities can be excluded. They had different Mncontents x between 0.0037 and 0.0150, corresponding tobulk critical temperatures Tc (from dc magnetization) be-tween 33.9 and 13.3 K, with Tc10%–90% increasingwith doping from 0.65 K to 5.4 K. The point contacts weremade by putting a small drop of Ag paint ([ ’ 50 m) onthe flat side surface of the crystal [6] so as to inject thecurrent mainly parallel to the ab planes, which in pureMgB2 is the best configuration to measure both the - and-band gaps [2,6]. In most cases, we studied the tempera-ture and magnetic-field dependencies of the conductancecurves (dI=dV versus V), so as to determine the criticaltemperature of the junction (TAc ) and to understand whetherone or two OPs were present [6,7]. The conductance curveswere then normalized to the normal state and fitted with thetwo-band Blonder-Tinkham-Klapwijk (BTK) model [8], asdescribed elsewhere [6]. The fitting function contains theOPs ;, the coefficients Z; (related to the potentialbarrier and to the Fermi-velocity mismatch at the inter-face), and the lifetime broadening coefficients ; asadjustable parameters, plus the weight w of the -bandcontribution to the conductance. Whenever possible, weselected contacts with rather high resistance (RN * 30 ),and with no dips [9] in the conductance curves, so as tofulfill the requirements for ballistic conduction [10].Figure 1 reports some normalized conductance curves(symbols) in crystals with different Mn content. From nowPRL 97, 037001 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending21 JULY 20060031-9007=06=97(3)=037001(4) 037001-1 © 2006 The American Physical Societyon, we will label the curves with the corresponding value ofTAc instead of x or the bulk Tc, since PCS is a local, surface-sensitive probe. TAc can be smaller than the bulk Tc if thebulk transition is broad (as for the most-doped crystals) orif proximity effect occurs at the S=N interface (when  a, being a the true contact size).Lines in Fig. 1 represent the two-band BTK fit of theexperimental curves. In conventional superconductors,spin-flip scattering makes the gap become ill defined [11]or even creates bands of states within the original energygap [12,13]. Strong-coupling calculations for MgB2 [14]have shown that magnetic impurities can give rise to sub-gap states in both the partial - and -band density ofstates (DOS), that are not taken into account by the BTKmodel. However, the subgap features in the DOS are by farsmaller than the peaks connected to the OPs  and [14]. At finite temperature they are further smeared out, sothat it would be very difficult to observe them experimen-tally. The same can be expected in the Andreev-reflectioncurves. In fact, all the experimental conductance curves arerather broadened and have smaller amplitude (see Fig. 1)than in pure MgB2 [6], so that even if subgap structuresexist, they are practically unobservable. Hence, the BTKmodel can be used as a reasonable, first-order approxima-tion to a more specific model for Andreev reflection in asuperconductor with magnetic impurities, which is lackingat the present moment.Even if the fit of the curves in Fig. 1 indicates theexistence of two OPs, it is clear that some curves—espe-cially at the highest doping levels—show little or nostructures associated to . To check in a more convincingway if two OPs persist up to the highest Mn content, westudied the magnetic-field dependence of the dI=dV curvesin the whole range of TAc .Figure 2(a) shows the magnetic-field dependence of theconductance curve of a contact with TAc  31 K (circles)with the relevant two-band BTK fit (lines). The zero-fieldcurve shows both the peaks corresponding to  and thesmooth shoulders related to . The magnetic field makesthe small-gap features reduce in amplitude, progressivelyunveiling the underlying large-gap features. An outwardshift of the peaks is observed at some B  B, when the-band structures become dominant and determine theshape of the curve. Unlike in pure MgB2, here B is intenseenough (if compared to Bc2, strongly reduced by Mnimpurities) to partly depress , while the -band partialconductance seems not to vanish at B. This makes it1.01.1wπ=0.80TcA=32.8 KRN= 36 ΩMn  0.40 %RN= 67 Ω1.01.1wπ=0.70TcA=27.9 KRN= 12 ΩRN= 182 ΩMn  0.65 %1.001.051.10wπ=0.66TcA= 22.5 KRN= 10 ΩMn  1.07 %1.001.05wπ=0.70TcA=18.0 KMn  1.20 %-20 -10 0 10 201.001.05wπ=0.66TcA= 11.8 KMn  1.50 %NormalizedconductanceVoltage (mV)FIG. 1. Normalized conductance curves (symbols) of differentab-plane junctions in Mg1xMnxB2 single crystals at T 4:2 K. The curves are labeled with the corresponding TAc values.The Mn content and the normal-state junction resistance areshown as well. Lines: best-fit curves given by the two-band BTKmodel. The -band weight w is also indicated. In the absenceof specific theoretical predictions, we took 0:66 	 w 	 0:8 asfor ab-plane contacts in pure MgB2 [2,6].-30 -20 -10 0 10 20 301.001.011.021.031.041.051.06-20 -10 0 10 201.001.011.021.031.041.051.06(a)AN 352/4bulk Tc = 33.9 KTcA = 31.0 KNormalized conductanceVoltage (mV) B (T)   0   0.5    1.0   1.5   2.0   3.0(b) B (T)   0   0.2   0.5    1.0   1.5   2.0bulk Tc = 19.2 KTcA = 18 KAN 389/6bNormalized conductanceVoltage (mV)FIG. 2. Experimental conductance curves at T  4:2 K of twocontacts with TAc  31 K (a) and TAc  18 K (b), in a magneticfield B k c (circles) and the relevant two-band BTK fit (lines).Vertical lines indicate the position of the conductance peaks. Thebest-fitting parameters in zero field are:   2:5 meV,  5:2 meV;   2:3 meV,   6:0 meV; Z  0:55, Z 0:82, w  0:7 for panel (a);   1:56 meV,  2:8 meV;   2:01 meV,   3:8 meV; Z  0:43, Z 0:50, w  0:7 for panel (b). The two-band BTK fit workswell up to Bc2 [ ’ 3:5 T in (a) and ’ 2:5 T in (b)].PRL 97, 037001 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending21 JULY 2006037001-2impossible to separate the partial - and -band conduc-tances as we did in pure MgB2 [6,7], but the shift of theconductance peaks is anyway a clear proof of the existenceof two OPs. The same happens in contacts with much lowerTAc values. For example, Fig. 2(b) reports the magnetic-field dependence of the normalized conductance curve of acontact with TAc  18 K. Here the zero-field conductancedoes not show clear structures related to  but an outwardshift of the conductance maxima is observed anyway atB  B ’ 1 T. For contacts with TAc < 17 K, the low-temperature, zero-field conductance curves can be verywell fitted with the two-band BTK model (see the bottomcurve in Fig. 1), but the critical field is so small and thecurves are so broadened that their magnetic-field depen-dence is not conclusive, at least within our experimentalresolution. Moreover, some conductance curves in thisregion admit a standard (i.e., single-band) BTK fit aswell, which gives an OP amplitude  that is the ‘‘average’’of the values given by the two-band fit. However, thesingle-band fit often fails in reproducing both the positionof the peaks and the width of the Andreev-reflection struc-tures in the conductance, as shown in Fig. 3 for a contactwith the lowest TAc . This suggests that two OPs are likely tobe present also in the most-doped samples.The complete dependence of the OPs on TAc is reportedin Fig. 4. Vertical error bars include both the uncertainty onthe OP in each fit and the spread of OP values over differentcontacts with the same TAc (within the experimental uncer-tainty on TAc represented by horizontal error bars). ForTAc < 17 K only the results of the two-band BTK fit areshown, based on the preceding discussion and on theregular trend of the OPs for TAc  18 K. In fact, the pres-ence of a single OP in the low-TAc region would imply asudden change in the slope of the curves around TAc 17 K that is not justified by any observed discontinuity inthe physical properties of the compound [5]. The persis-tence of two distinct OPs up to the highest x value indicatesthat Mn doping does not significantly increase non-spin-flip interband scattering. Actually, this is also suggested bythe very low Mn concentration (1.5% at most) and by thedecrease of both the OPs with TAc [while interband scat-tering would increase  [15] ]. Changes in the DOSs atthe Fermi level [15] and in the phonon spectra 2F;!are certainly negligible here, because Mn is isovalent withMg [5] and the Mn content is very small. The latter reasonalso allows neglecting the effect of  and  intraband non-spin-flip scattering. This leads to conclude that the mainpossible cause of the experimental trend of Fig. 4 is anincrease in the spin-flip scattering in the -, -, or -channels.This simple picture can be made quantitative by solvingthe Eliashberg equations (EE) in the presence of randomlydistributed magnetic impurities, treated within the Bornapproximation [16]. According to the reasoning above, weused the same phonon spectra, DOS values, and Coulombpseudopotential as in pure MgB2 [2,6], and neglected allthe non-spin-flip scattering rates. We thus took as the onlyadjustable parameters the spin-flip scattering rates withinthe bands ( and ) and between bands (). Weimmediately found that  is necessary to fit the TAc andOP values and that it must be greater than both  and—otherwise  decreases too fast on decreasing TAc .As for , this agrees with the predictions of Ref. [14].For simplicity, we analyzed separately the two cases:(a)  > ,   0 and (b)  > ,   0.First of all, we fixed       0 at TAc 39:4 K (i.e., x  0). Second, we found the values of theparameters that give the experimental values of  and at TAc  18:0 K [cases (a) and (b)], by solving theimaginary-axis EE and analytically continuing the solutionto the real axis. Once determined the values of  and-20 -10 0 10 201.001.021.041.061.08 2-gap fit 1-gap fitAN 364/2bulk Tc = 13.3 KTcA = 9.6 KNormalized conductanceVoltage (mV)0 2 41.041.06 2-gap fit 1-gap fitNorm. conductanceVoltage (mV)FIG. 3. Symbols: zero-field, low-temperature (T  4:2 K)conductance curve of a contact with TAc  9:6 K made on themost-doped crystals (x  0:015). Solid line: best fit given by thetwo-band BTK model. Dashed line: best fit given by the standard(single-band) BTK model. Arrows indicate the smooth structuresrelated to the two order parameters, which are magnified in theinset for clarity.10 15 20 25 30 35 40012345678 ∆π (experimental)Energy gap(s) (meV)Andreev critical temperature, TcA (K) Eliashberg (Γσσ and Γσπ )∆σ (experimental) Eliashberg (Γσσ and Γππ )FIG. 4. Symbols: amplitudes of the order parameters as afunction of the critical temperature of the junctions, TAc . Lines:theoretical curves obtained by solving the Eliashberg equationsin the presence of magnetic scattering in the - and -channels [case (a), solid lines] or in the - and - channels[case (b), dashed lines].PRL 97, 037001 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending21 JULY 2006037001-3 in these two points, we searched for the simplestTAc  and TAc  curves connecting them and allow-ing the fit of the experimental values of TAc and of the OPsin the whole doping range, with no restrictions on . Wefound out that these curves are a parabola (for ) and astraight line (for ). In both cases,  follows analmost parabolic trend as a function of TAc , as shown inFig. 5. The resulting theoretical curves that best fit the OPsare reported in Fig. 4 as solid lines [case (a)] and dashedlines [case (b)]. The agreement between experimental dataand theoretical calculations [especially in case (a)] is strik-ing in the whole range of TAc . That our simple but reason-able model works so well suggests that, up to x  0:015,Mg1xMnxB2 can be treated as a perturbation of MgB2,with only the addition of  intraband magnetic scatteringand smaller contributions from either the  intraband orthe interband magnetic scattering.The intense Mn pair-breaking scattering in the -channel has been recently predicted as being due to thehybridization of the  bands of MgB2 with the d orbitals ofMn [17]. To prove that scattering in this channel is muchgreater than in the - and - ones, we performedpreliminary calculations of the electronic structure near aMn impurity in a 2 2 4 MgB2 superlattice. The resultsshow that around the Fermi level (EF) there is a spin-downdz2 band, responsible for the Mn magnetic moment, verysensitive to the details of structural parameters [17]. The and  bands behave quite differently near the Mn impurity:while the  electron spectral density is depleted around EF(due to the -d interaction), the  bands have a largeamplitude. Furthermore, the  bands show a sizeable ( 15 meV) exchange splitting near EF, larger than the super-conducting gap—which is consistent with the observedcomplete suppression of superconductivity at about 2% ofMn [5]. On the other hand, the impurity-induced mixing of and  states around Mn (providing a qualitative indica-tion of interband scattering) is present but not very impor-tant. These results can explain the quick drop of Tc, withthe persistence of the two distinct gaps, and a largerscattering within the  band [18].In conclusion, we have presented the results of the firstexperimental study of the effects of magnetic impurities onthe order parameters  and  of a two-band supercon-ductor. We have shown that, in Mg1xMnxB2,  and decrease regularly with the critical temperature but remainclearly distinct down to the lowest TAc . Within theEliashberg theory, this is due to an increase in spin-flipscattering in the  bands on increasing the Mn content,with possible smaller contributions from the - or the- channels. This somehow unexpected conclusion isalso supported by first-principles calculations of the bandstructure of MgB2 in the vicinity of a Mn impurity.This work was done within the PRIN ProjectNo. 2004022024 and the INTAS Project No. 01-0617.V. A. S. acknowledges support by RFBR (Project No. 06-02-16490).*On leave from: Institute of Low Temperature andStructure Research, Polish Academy of Sciences, 50-950Wroclaw, Poland.[1] A. Y. Liu, I. I. Mazin, and J. Kortus, Phys. Rev. Lett. 87,087005 (2001); H. J. Choi et al., Nature (London) 418,758 (2002).[2] A. Brinkman et al., Phys. Rev. B 65, 180517(R) (2002);A. A. Golubov et al., Phys. Rev. B 66, 054524 (2002).[3] J. R. Cava, H. W. Zandbergen, and K. Inumaru, Physica(Amsterdam) 385C, 8 (2003).[4] S. Xu, Y. Moritomo, K. Kato, and A. Nakimura, J. Phys.Soc. Jpn. 70, 1889 (2001).[5] K. Rogacki et al., Phys. Rev. B 73, 174520 (2006).[6] R. S. Gonnelli et al., Phys. Rev. Lett. 89, 247004 (2002).[7] R. S. Gonnelli et al., Phys. Rev. B 69, 100504(R) (2004).[8] G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Phys.Rev. B 25, 4515 (1982).[9] Goutam Sheet, S. Mukhopadhyay, and P. Raychaudhuri,Phys. Rev. B 69, 134507 (2004).[10] A. M. Duif, A. G. M. Jansen, and P. Wyder, J. Phys.Condens. Matter 1, 3157 (1989).[11] A. A. Abrikosov and L. P. Gor’kov, Sov. Phys. JETP 12,1243 (1961).[12] H. Shiba, Prog. Theor. Phys. 40, 435 (1968).[13] E. Schachinger and J. P. Carbotte, Phys. Rev. B 29, 165(1984).[14] C. P. Moca and C. Horea, Phys. Rev. B 66, 052501 (2002).[15] J. Kortus et al., Phys. Rev. Lett. 94, 027002 (2005).[16] O. V. Dolgov et al., Phys. Rev. B 72, 024504 (2005).[17] P. Jiji Thomas Joseph and Prabhakar P. Singh, cond-mat/0512675.[18] F. Bernardini et al. (to be published).10 15 20 25 30 35 400.00.51.01.52.02.53.03.54.0{Γ σσ,Γ σπ,Γ ππ(meV)Critical temperature TcA (K)case (b){case (a) ΓσσΓππΓσσΓσπFIG. 5. Spin-flip scattering parameters used to fit the data ofFig. 4 as a function of TAc . Solid symbols: case (a),  (squares)and  (circles). Open symbols: case (b),  (squares) and (triangles). Lines are guides to the eye.PRL 97, 037001 (2006) P H Y S I C A L R E V I E W L E T T E R S week ending21 JULY 2006037001-4

Effect of Magnetic Impurities in a Two-Band Superconductor: A Point-Contact Study of Mn-Substituted MgB2 Single Crystals

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