Effects of Fe substitution on the transport properties of the superconductor MgB
2 Bhasker Gahtori, Ratan Lal, and S. K. AgarwalSuperconductivity and Cryogenics Division, National Physical Laboratory, Dr. K. S. Krishnan Road, New Delhi 110012, India
Y. K. Kuo,*K. M. Sivakumar, and J. K. Hsu
Department of Physics, National Dong Hwa University, Hualien 974, Taiwan
J. Y. Lin
Institute of Physics, National Chiao Tung University, Hsinchu 30050, Taiwan
Ashok Rao
Department of Physics, Manipal Institute of Technology, Manipal 576104, Karnataka, India
S. K. Chen and J. L. MacManus-Driscoll
Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, United Kingdom 共Received 3 August 2006; revised manuscript received 13 February 2007; published 16 May 2007兲
A systematic study has been made on the effect of Fe substitution by means of resistivity, thermal conduc-tivity, and Seebeck coefficient of the Mg1−xFexB2superconductor involving 0%, 0.3%, 0.6%, 1.2%, and 3.0% Fe content. The superconducting transition has been found to be very sharp共⬃0.2 K兲 for a pristine sample and substitution of Fe results in the decrease of TCwith the increase in the transition width. Thermal conductivity
is found to decrease with Fe content in general, such that the shoulder present in the pristine sample tends to fade away with increasing Fe. An analysis has been made on the normal state resistivity in terms of a two-band model, and of the thermal conductivity in terms of the Wiedemann-Franz law and the lattice thermal conduc-tivity, and the information obtained on the basis of this analysis has been discussed. Besides, the electronic density of states共DOS兲 near the Fermi level remains nearly unaffected upon Fe substitution, as evidenced by the Seebeck coefficient measurements. When compared with Mn, Fe behaves like a nonmagnetic element with a modest variation in TCand on the other hand, the TCdepression is much stronger when compared with other elements like Al, Cu, etc. Therefore, the observed variation in TCfor the presently investigated concentrations
of Fe is attributed to the specific nature of the given substituent element共Fe兲 in altering the phonon frequency and/or electron-phonon coupling strength rather than spin-flip scattering or change in DOS or disorder.
DOI:10.1103/PhysRevB.75.184513 PACS number共s兲: 74.70.Ad, 74.25.Fy, 74.62.Dh
I. INTRODUCTION
Recently reported superconductivity in magnesium di-boride 共MgB2兲 at ⬃40 K, highest for an intermetallic compound,1 has resulted in intensive investigations both theoretically and experimentally to exploit the possible su-perconductivity at higher than 40 K for practical applica-tions, and to understand the underlying mechanisms of the normal and superconducting states of this system.2–5 The structure of MgB2 is a simple hexagonal AlB2 type with honeycomb-type boron layers and interpenetrating Mg layers.3 It has been well established that it is a multiband, namely and, and conventional s-wave phonon mediated BCS-type superconductor.3The two bands and the respective superconducting gaps are associated with different parts of its Fermi surface.4 It is believed that the -band is of hole type and is mainly responsible for the superconductivity in MgB2whereas the-band is an electron type with compara-tively negligible contribution.4In spite of the fact that MgB
2 is one of the simplest binary compounds with a simple crys-tal structure, some of its physical, chemical, and electrical properties are very intriguing and not yet fully understood even after numerous investigations.5
Chemical substitution, like in other superconductors, serves as a useful tool to modify the structure and other
physical properties of MgB2to study the underlying mecha-nism of superconductivity and improve some of its important parameters for practical applications. To explain the varia-tions observed in TCupon different substitutions, so far
vari-ous mechanisms, such as pair breaking effect, reduction in density of states共DOS兲, decrease in phonon frequency, and band narrowing or expansion due to increase and/or decrease in the lattice constants and/or disorder have been proposed.6–10 For example, the reduction in T
C with Al
sub-stitution for B has been attributed to the decrease in DOS at
EFdue to the electron doping in the-band.11,12Moreover, a
sharp drop in TC has been reported for the substitution of
magnetic element such as Mn, while a different mechanism, spin-flip scattering and/or pair breaking effect has been pro-posed to the observed TC variation.13,14 On the other hand,
another magnetic element Fe had shown much slower varia-tions in TCin comparison with Mn共Refs.8,15, and16兲 and
such a diverse variation between Fe and Mn has been attrib-uted to the nonmagnetic nature of Fe in Mg lattice.17 The major setback with such substitutional studies is the limita-tion in the solubility of the third element at the Mg and/or at the B site,18 except for aluminum 共Al兲 and carbon 共C兲,11,19 which can be readily substituted at Mg and B sites, respec-tively. Nevertheless, other elements show successful
tution at Mg/ B sites only if their concentration is below 5%.6,7,15
Among the transition metal substitutes attempt-ed,6–8,10,20–22 Fe substitution in MgB
2 behaves in a unique way and is of particular importance from the application viewpoint.2 In terms of applications, metal cladding on MgB2or for any superconducting wire is the most important part vis-à-vis the critical current density. A recent report has revealed that Fe can be a potential candidate as a practical cladding metal or as a diffusion barrier for MgB2 wire fabrication.2 Recent NMR investigations on Fe substituted MgB2 have revealed that the density of states close to the Fermi level remains nearly unaffected upon its substitution up to 3%.23It is well known that Seebeck coefficient is very sensitive to the changes in the DOS around the Fermi level, particularly doping induced changes in the electronic struc-ture of MgB2 can be effectively investigated.11,21,22 There-fore, a further systematic investigation on the effect of Fe substitution in the transport properties of MgB2is in the right perspective. In the present work we have carried out electri-cal resistivity, thermal conductivity, and Seebeck coefficient measurements on Mg1−xFexB2共x=0% to 3%兲 samples from 10 to 300 K to elucidate some of the above-mentioned as-pects along with the theoretical analysis of the obtained data.
II. EXPERIMENT
Polycrystalline samples of Mg1−xFexB2 with x varying from 0 to 3% have been synthesized by the solid state reac-tion route. Synthesis details and structural characterizareac-tion of these samples have already been described elsewhere.23 Nominal substitution level of Fe is limited up to 3%, beyond which appearance of a significant amount of impurity phases is noticed. Both the lattice constants, a and c were found to decrease with increasing Fe content. The atomic radii values of Fe and Mg and the linear variation in lattice constants up to 1.2% of Fe 共cf. Fig. 2 of Ref. 23兲 clearly indicate the
successful substitution of Fe at Mg site as per the Vegard’s relationship. Beyond 1.2% Fe, deviation from the linear variation has been noticed, which is most likely due to the solubility limit of Fe in the MgB2 lattice and the gradual formation of impurity phases. However, since the concentra-tion of Fe is only 3.0% in the impurity phase system, from the viewpoints of electrical and thermal conductions we may formally treat the Fe sites of the impurity phase, if any, also as scatterer sites for the carriers of the host MgB2system. In fact, according to Ref.23, the 3.0% Fe sample is found to have almost the same density of states at the Fermi level as other samples. This implies that the possible secondary phase in the 3.0% Fe sample does not affect the electronic nature of the carriers of the system. When it is so, the secondary phase 共involving Fe, etc.兲 may be treated as a source for the scat-tering of the conduction electrons or lattice vibrations. More detailed clarification about the impurity phases and solubility of Fe can be seen in Ref.23. Electrical resistivity共T兲 mea-surements have been carried out by the standard four-probe method. Seebeck coefficient S共T兲 and thermal conductivity 共T兲 measurements have been performed simultaneously by a heat pulse technique in a helium closed-cycle refrigerator
from 10– 300 K. Detailed description about the experimental techniques can be found elsewhere.24
III. RESULTS AND DISCUSSION A. Electrical resistivity
The temperature-dependent electrical resistivity 共T兲 of the Mg1−xFexB2alloys共x=0.00–0.03兲 is shown in Fig.1共a兲. From these measurements we obtain the superconducting transition temperature in a way described by Osofsky et al.25 These values of TC, presented in TableI and plotted in the
inset of Fig.1共a兲, are found to be consistent with the mag-netization measurements.23 While the transition has been very sharp共less than 0.2 K兲 for the pristine sample, signifi-cant transition broadening ⌬TC could be noticed with
in-creasing Fe content共⌬TC⬃2 K for x=3% sample兲. From the
inset of Fig. 1共a兲, it can be seen that the TC depression is
rather linear up to x = 1.2% with a rate dTC/ dx⬃3 K/%,
beyond which deviation from linearity with x was observed. An important effect of this type of TCvariation with x in the
Fe substituted samples 共and also in the Al substituted samples of Ref.11兲 is that the Abrikosov-Gorkov pair
break-ing theory of TC degradation,26 which requires sharper TC
degradation with increasing x, may not be applicable in the
FIG. 1.共a兲 The temperature-dependent electrical resistivity共T兲 of Mg1−xFexB2alloys for x = 0.00– 0.03. The solid lines are fit for the experimental data with Eq.共3兲. Inset, superconducting transition temperature TC 共open circles兲 and residual resistivity 共RR兲 共filled
squares兲 as a function of Fe concentration. 共b兲 The slope d/dT 共50–300 K兲.
present case. It is worth mentioning that the residual resis-tivity 共RR兲 0 obtained from the measurements appears to increase with increasing Fe substitution关see TableIand inset of Fig.1共a兲兴. Similar to that of the TCvariation, the
depen-dence of RR deviates from linearity at x = 1.2%. Actually the similar linear dependences of TCand RR is expected in
stan-dard models, since dTC/ dx and d0/ dx are determined by the same parameter, the normal state scattering rate, for both magnetic and nonmagnetic impurities.
Resistivity in MgB2can be considered as the outcome of the scattering processes of carriers of and bands with defects共point defects, sheetlike faults, dislocations, etc.兲, im-purities共Fe, etc.兲 and phonons. In fact, according to Lue et
al.23 there is no magnetic moment on Fe in the Mg
1−xFexB2 samples. Thus we do not expect the presence of any electron-spin scattering process in the system. The resistivityb due
to the combined scattering of the carriers of the and bands with defects, impurities, and phonons is given by
b共T兲 =def,b+imp,b+ph,b共T兲. 共1兲 Here def,b andimp,b are temperature-independent resistivi-ties due to the scattering of b-band electrons by defects and impurities, respectively. The quantityph,b in Eq.共1兲 is the resistivity due to scattering of b-band electrons by phonons. ph,bis temperature dependent and is, in general, given by the Bloch-Gruneisen expression27 ph,b= Ab共m − 1兲D共T/D兲m
冕
0 D/T zm 共ez− 1兲共1 − e−z兲dz. 共2兲 Here Abdepends on the band parameters via Ab=A0F,b p,b2 . A0is independent of band specifications, and of m andD共Debye
temperature兲. F,b is the Fermi velocity and p,b is the plasma frequency both corresponding to the band b. We have obtained this dependence of Ab onF,b andp,bby
consid-ering Eq.共7.63兲 of Ziman.28According to Ref.29the values of F,b and p,b for MgB2 are F,= 2.4⫻105m / s, F, = 5.63⫻105m / s,
p,= 2.27 eV, and p,= 6.19 eV. The
overall resistivity共T兲 of the system due to the contribution of the and bands is given by30
1 共T兲= 1 共T兲+ 1 共T兲. 共3兲
From this equation the residual resistivity is given by
0= 0,0, 共0,+0,兲, 共4兲 where24 0,b= ␥b 0pb 2 . 共5兲
Here ␥b is the sum of the scattering rates of the b-band
carriers with the impurity and defects. 0= 8.85 ⫻10−12F / m is the free space permittivity. Using the above expressions along with the values of F,b andp,b we have
fitted the experimental data with Eq.共3兲 in terms of the
pa-rameters ␥, ␥, A0, m, and D for various samples of
Mg1−xFexB2. The values of these fitting parameters are tabu-lated in TableI. An excellent fitting of Eq.共3兲 to the
experi-mental data has been achieved with these parameters. From Table I we see that␥⬍␥ for all the considered samples. This is what we expect from the work of Mazin et
al.30From the values of␥
and␥for x = 0.0 we estimate the contributions of the andcarriers to the residual resistiv-ity. We obtain,def,= 44.3⍀ cm and def,= 25.6⍀ cm. For x⬎0,0,bis the direct sum of the values of the resistiv-ities due to defects共def,b兲 and impurities 共imp,b兲. That is to say
0,b=def,b+imp,b. 共6兲 Another information that we can draw on the basis of TableIis that the temperature dependence of共T兲, as signi-fied by the values of m andD, varies nonmonotonically with
increasing x. This is because the uncertainties in the fitting of the values of m andDare much less than the difference in
the values of m or D for different x. For example,
100关m共x=0.0兲−m共x=0.003兲兴/m共x=0.0兲=15.9% is much larger than the 2.0% uncertainty in the fitting of m. It may be noted here that the uncertainty in the fitting of theDvalues
is less than 0.5%. Since the values ofDvary by less than
12% for the considered values of x, and since the highest temperature for which measurements are done 共300 K兲 is much less thanD共x兲, we do not expect a significant effect of
Don the temperature variation of共T兲. Then the sensitivity
of the temperature dependence 共T兲 is governed mainly by the parameter m关cf. Eq. 共2兲兴. From TableIwe see that the value of m decreases by about 16% for the 0.3% sample. But with a 0.6% substitution of Fe the value of m increases sharply to 3.63 and then decreases for 1.2% sample. For the
TABLE I. Values of TC, residual resistivity0共x兲 and the parameters␥, ␥, A, m, andDobtained by
fitting Eq.共3兲 with the observed resistivity for samples of Mg1−xFexB2with various x.
X TC 共K兲 共⍀ cm兲0共x兲 共meV兲␥ 共meV兲␥ A0 共107⍀ s−1K−1兲 m 共K兲D 0.00 38.8 16.3 10.2 43.7 1.32 2.95 1076 0.003 37.9 25.1 12.6 77.1 1.70 2.48 1043 0.006 37.0 37.3 16 136.2 1.60 3.63 1021 0.012 34.9 73.1 24.7 385.3 1.67 2.91 1152 0.03 32.9 110.4 33.4 771.8 1.63 3.10 1131
3.0% sample the value of m is equal to that for the unsubsti-tuted sample within 5%. Reported results of Lorenz et al.11 on Al-substituted samples of MgB2are also expected to lead to such nonmonotonic variation of m as obtained here.
In order to gauge such a nonmonotonic variation of m with the Fe content we consider the m dependence of共T兲. Following Eqs.共2兲 and 共3兲 we obtain the following form of
the slope d/ dT as s =共d/ dT兲=共T/D兲m−1mm+2共T→0兲. The
first term共T/D兲m−1decreases sharply with m as共T/D兲1
for T→0, in contrast to the second factor mm+2 which in-creases with m. However, the variation of mm+2is relatively
much slower. For example, taking T = 10 K, D= 103K,
共T/D兲m−1decreases by a factor of 104while the factor mm+2
increases only by 256 for m increasing from 2 to 4. This implies that for low T共T→0兲 the variation of the slope s is dominated by the factor 共T/D兲m−1. Since 共T/D兲m−1
de-creases with increasing m, s will also decrease with m. In Fig. 1共b兲 it is the slope of the x = 0.3% Fe sample that is significantly different near T = 50 K. So, we expect that at least this sample will follow the same higher value of 共d/ dT兲 for low T 共T→0兲 also. The value of s is therefore, expected to be the highest for the x = 0.3% Fe sample. In view of the above-mentioned variation of s with m we may say that the x = 0.3% Fe sample will correspond to the lowest value of m共cf. TableI兲.
B. Thermal conductivity
The temperature-dependent thermal conductivity 共T兲 data of the various Fe-substituted MgB2 samples are pre-sented in Fig.2. The absence of any hump in below TC
共inset of Fig.2兲 agrees well with the reported共T兲 data.21,27
It would be appropriate to mention here that the data in Fig.
2has been shifted by different amounts for the sake of clear qualitative depiction. For x = 0, the thermal conductivity共T兲 shows a shoulder near 110 K. Other groups have also ob-served a shoulder in for the pristine sample.21,27With in-creasing x the shoulder near T⬃110 K becomes weaker and eventually fades away for the 3.0% sample. This is in con-trast to the appearance of a shoulder for all x in Cr-substituted MgB2.21 In the Fe-substituted samples, the ther-mal conductivity decreases with x for Tⱕ260 K. At 300 K, is highest for the 0.3% sample and lowest for the 1.2% sample. As far as the quantitative values ofare con-cerned it may be noted that the room temperature value 共⬃190 mW/cm K兲 is nearly invariant of the Fe content.
We may write the total thermal conductivity of Mg1−xFexB2 as composed of two parts—the first共el兲 is the electronic contribution due to conduction electrons and the second共ph兲 is the lattice contribution due to the phonons. That is to say,
=el+ph. 共7兲
The electronic contributionelmay be expressed in terms of the dc resistivity 共T兲, Eq. 共3兲, by using the
Wiedemann-Franz law31
el=
L0T
共T兲. 共8兲
L0 being the Lorenz number.
From Eqs.共7兲 and 共8兲 we have found that at any given
temperature the lattice contribution to the experimental ther-mal conductivity follows the relation
ph共x
⬘
,T兲 ⬍ph共x⬙
,T兲 for x⬘
⬍ x⬙
. 共9兲 Here x⬘
, x⬙
= 0.0, 0.003, 0.006, 0.012, and 0.03.Since 共T兲 involves contributions from both and bands of MgB2, el also involves contributions from these two bands. The phonon contributionph, however, has noth-ing to do with the electronic bands and and is entirely contributed by the lattice. In general, we may express the lattice thermal conductivityph by32
ph共T兲 = t3
冕
0D/T z4
共ez− 1兲共1 − e−z兲K共t,z兲dz. 共10兲 Here t = T / TCis reduced transition temperature, and K共t,z兲 is
the sum of the scattering rates of phonons due to different scattering sources. From the inset of Fig.2we see that there is no hump inbelow TC. Thus, according to Ref.32we do
not consider the scattering of phonons by electrons in K共t,z兲. There are then four main sources of phonon scattering events which we feel are important in deciding the values ofphin MgB2. They are共1兲 grain boundaries in the sample, 共2兲 point defects, 共3兲 strain fields of sheetlike faults, and 共4兲 strain fields of dislocations. We thus write32
K共t,z兲 = K0+ Kpdt4z4+ Ksft2z2+ Kdistz. 共11兲 Here K0is the boundary scattering rate, Kpdis the scattering rate of phonons from the point defects, Ksfis the scattering
FIG. 2. The temperature-dependent thermal conductivity for Mg1−xFexB2 alloys 共x=0.00–0.03兲. The solid lines are fit for the experimental data with Eq.共7兲. The inset 共10–50 K兲 is to clarify that there is no hump in below TC⬃39 K. The data is shifted by
rate from sheetlike faults, and Kdisis the scattering rate from dislocations.
In order to maintain a consistency of our analysis we have used those values ofDin Eq.共10兲 which we have obtained
fromanalysis共TableI兲. The fitting parameters K0, Kpd, Ksf, and Kdisare given in TableII. These parameters do not fol-low a monotonic variation with x. The main reason for this is that the residual resistivity0is not linear in x, and that the temperature dependence of 共T兲 is also nonmonotonic 共cf. values of m in TableI兲. Despite this we find from Table II
that the parameters K0 and Kpd vary with x in a manner to oppose each others’ effect. Then, for xⱕ0.012, the decrease of Ksf and Kdis with increasing x may be understood as a process for the relation of Eq. 共9兲. In view of Eq. 共9兲 the
overall coupling of the phonons with defects and/or Fe de-creases with increasing x. From the viewpoint of TableII, up to x⬇0.012 the shoulder appears due to the dominance of the reduction of the effects of the boundary scattering共K0兲 and dislocations 共Kdis兲 over the effect of the point defects 共Kpd兲. For the 3.0% Fe content, on the other hand, the shoul-der appears due to the dominance of the effect of the point defects over the defects.
Although, the parameters of TableII do not show a sys-tematic variation with x, according to Eq. 共10兲 their
com-bined effect, or equivalently the comcom-bined effect of defects and Fe, becomes weaker for phonons with increasing x. This situation is different from that of the interaction of phonons with electrons as evidenced from the variations of parameters
A0and m in TableI. The variations of A0 with x means that the electron-phonon interaction is strongest for the x = 0.003 sample, decreasing a little with further substitution.
C. Seebeck coefficient
The temperature-dependent Seebeck coefficient S共T兲 of the Mg1−xFexB2 alloys with various x is shown in Fig. 3. Each curve is offset by 1V / K for clarity. For the presently investigated Mg1−xFexB2 samples, the common features ob-served in Seebeck coefficient, such as the positive sign, the small magnitude at 300 K, the linear variation between TCto
⬃150 K 共solid lines and arrows in the figure兲, and the ten-dency to saturate at higher temperatures are in well ac-cordance with the behavior widely reported for MgB2.11,21,22,33,34 The transition temperatures determined from the Seebeck coefficient measurements are generally consistent with the electrical resistivity measurements for
these Mg1−xFexB2 alloys. The notable observation of the present results of Seebeck coefficient measurements is that the variations in S共T兲 in the normal state are nearly compo-sition independent, which is significantly in contrast to the general behavior observed by other substituents in MgB2.11,21,22,34 Fe is a trivalent element and effectively an electron dopant. Besides, one can expect a slight band broad-ening due to the increase in the lattice compression as the lattice parameters of Mg1−xFexB2 alloys decrease monotoni-cally with the Fe concentration. Electron doping and the band broadening generally lead to a systematic decrease in DOS around EFin MgB2. Further, recently reported Seebeck coefficient measurements on Al substituted MgB2 have cor-related the changes in EF to the observed systematic
varia-tions in the slope of S共T兲 between TCto 200 K,11where the
value of EF is related to the slope of temperature-dependent
Seebeck coefficient through the classical formula
S T= 2k B 2 3eEF , 共12兲
assuming a one-band model with an energy-independent re-laxation time. Some of the other transition elements like Co and Cr have shown significantly large and systematic varia-tions in the magnitude of normal-state Seebeck coefficient upon their substitution and such variations have been attrib-uted to the reduction in DOS.21,22As a nonmagnetic trivalent element, one would expect that Fe should show a similar effect as Al substitution, which in turn must reduce the DOS in holelike-band by electron doping and the electronic to-pological transition of the Fermi surface from two to three
TABLE II. Values of the parameters K0, Kpd, Ksf, and Kdisof Eq. 共10兲. x K0 共cm K/mW兲 Kpd 共cm K/mW兲 Ksf 共cm K/mW兲 Kdis 共cm K/mW兲 0.00 3.55 0.35 319 28.4 0.003 0.94 1.22 85 7.6 0.006 0.63 2.26 57 5.0 0.012 0.64 1.40 57 5.1 0.03 0.79 0.79 71 7.9
FIG. 3. The temperature-dependent Seebeck coefficient curves for Mg1−xFexB2alloys共x=0.00–0.03兲. Inset, the slopes of Seebeck coefficient dS / dT共open circles兲 in the linear region and the values of room-temperature Seebeck coefficient S共300 K兲 共filled squares兲 as a function of Fe concentration. No systematic variations in dS / dT and S共300 K兲 with respect to Fe concentration could be noticed.
dimensional.35 Such changes in the electronic structure can change the magnitude and as well the sign of S dramatically. However, as shown in the inset of Fig.3, no systematic cor-relation between the magnitude of S共300 K兲 and dS/dT with respect to Fe concentration could be noticed. This is in good agreement with the earlier theoretical prediction that the DOS remains unaffected for small concentrations of dopants, and rapid reduction of DOS occurs when TCdecreases below
⬃25 K in MgB2.19 It is worth mentioning that previous NMR investigation on Fe substituted MgB2samples revealed a nearly unaffected DOS and the observed variations in TC
has been attributed to the decrease in phonon frequency and/or reduced electron-phonon coupling strength as a result of disorder.23The present Seebeck coefficient measurements also indicate no significant changes in DOS for Fe substitu-tion levels up to 3%, which is in strong support to the NMR investigations.
In a polycrystalline sample, similar to Hall effect, the measured S is the net value of the two bands,and.36,37 Out ofandbands, from the positive value of S it is clear that the holelike-band dominates the thermoelectric trans-port in these Mg1−xFexB2 alloys. To maintain a nearly un-changed DOS we require a compensating effect and/or charge transferring between andbands upon Fe substi-tution. The observed random variations in the room-temperature Seebeck coefficient as well as the slope in the present study clearly reveal that more than one mechanism may be competing with each other in altering the DOS.
D. Discussion
Among the dopants, Mn shows rapid reduction in TCfor a
given concentration and as expected, as a magnetic element, Mn can have dramatic effect on TCdue to the pair breaking
effect through spin-flip scattering.13,14,17Although, Fe substi-tution shows weaker decrease in TC as compared with Mn,
the decrease in TCis more pronounced than the other dopants
like Al, Sc, C, etc., where the depression of TC has been
attributed to the reduction of DOS through the band filling effect.7,10,12,19–22The previous theoretical study has predicted the nonmagnetic nature of Fe in MgB2 lattice and subse-quently NMR investigation has confirmed the entirely non-magnetic nature of Fe and as well as the absence of any traceable magnetic impurities or impurity phases共both can act as a strong source for spin-flip scattering兲, and nearly unchanged DOS.17,23The extrinsic disorder, disorder induced by neutron irradiation shows significant variations in TC,
nevertheless decrease in DOS has also been observed.38,39 On the other hand, according to Putti and Chen et al.27,40in undoped samples, the superconducting transition temperature is insensitive to the intrinsic disorder to a considerable ex-tent, whereas it affects the normal state transport properties significantly. It is interesting to note that only negligible variations in TC 共⬃1 K兲 have been reported for changes in
residual resistivity ratio共RRR兲 from 3 to 8, which is much larger when compared with the RRR variations noticed among the present Fe concentrations共⬃2–4兲. It is common to note that the presence of MgO impurity phases, which can be one of the major sources of disorder and may lead to
increase in RRR, nevertheless have only negligible effect on
TC.
Upon substitution of other elements, except Mn, the TC
shows much smaller variations for dopant concentra-tions equivalent to the present Fe concentration ranges.7,11,20–22,34,41 Particularly, the T
C depression rate is
more pronounced than the other well-known substituent such as Al with the similar variations in the lattice constant upon its substitution. As mentioned earlier, Al and Fe are trivalent, nonmagnetic in MgB2 lattice, and lattice constant decreases upon their substitution. The induced disorder as a result of their substitution at Mg lattice共substitutional disorder兲, may not have any dramatic difference in the extent of disorder between them and hence the substitutional disorder should show nearly identical effect on the superconducting transi-tion temperatures. Further, no traceable magnetic impurities were noticed by NMR measurements,23and hence the effect of small amounts of FeB impurity phase for higher Fe con-tents can be treated similar to the inevitable MgO impurity phase, which is also nonmagnetic and can be one of the sources of disorder. As mentioned earlier, the superconduct-ing transition temperature is insensitive to disorder to a con-siderable extent. Therefore, in the present case, the substitu-tional disorder共which we treat as intrinsic兲 as a result of Fe substitution, if any, may affect only the normal state proper-ties rather than the superconducting properproper-ties.
These findings, nonmagnetic nature of Fe in MgB2, mod-est TC depression rate when compared with Mn, much
pro-nounced TCdepression rate when compared with other
ele-ments like Al, and nearly unaffected DOS place the Fe substitution in a very unique situation and bring up the im-portance of the phonon contributions to the variation of TC
for MgB2. For a BCS phonon-mediated superconductor, it is well known that the TC is proportional to the phonon
fre-quency , following the McMillian formula. The unusual high critical temperature for MgB2 is partially attributed to the high frequency of the E2g phonon mode 共 = 64– 82 meV兲.4,19The present Fe substitution is expected to specifically modify the phonon spectrum, in order to alter the phonon frequency and/or electron-phonon coupling strength. However, absence of such an effect in the isoelectronic共like Al兲 and other dopants is an open question. Most probably, such a scenario depends on the specific nature of the given substituent element.
IV. CONCLUSIONS
We have investigated the superconducting and electronic properties of Fe substituted Mg1−xFexB2 samples with x = 0%, 0.3%, 0.6%, 1.2%, and 3% superconductor by electri-cal resistivity, thermal conductivity, and Seebeck coefficient measurements from 10– 300 K. Superconducting transition temperature共TC兲 decreases rather linearly as a function of Fe
concentration up to x = 1.2%, beyond which the solubility limit of Fe in the MgB2 lattice was noticed. The two-band model provides an excellent description of the resistivity data in terms of the Bloch-Grueneisen model and the cou-pling of the carriers with defects and/or impurity increases with Fe substitution nonmonotonically between 22% and
30%. Thermal conductivity of the pristine material is seen to be the highest and exhibits a shoulder near 110 K which gradually fades out with increasing x. The overall coupling of phonons with defects and/or impurities as signified by the lattice thermal conductivity decreases with increasing Fe content. It has been found that the room-temperature See-beck coefficient as well as the slope of SeeSee-beck coefficient in the linear region共from TCto about 150 K兲 show little change
with respect to the Fe substitution, indicating that the DOS near the Fermi level remains nearly unaffected in these Mg1−xFexB2 alloys, consistent with the previous NMR report.23The conclusions from the present results on the Fe substituted Mg1−xFexB2 alloys, a modest TC depression rate
when compared with Mn, a much pronounced TCdepression
rate when compared with other elements like Al, and nearly unaffected DOS rules out the possibility of spin-flip scatter-ing and/or reduction of the DOS as well as disorder as a cause for the observed variations in TCand place the role of
Fe in the MgB2 lattice as a distinct one. The absence of consistent variation in the electronic and superconducting properties between Fe and other similar substituent elements 共with parallel characteristics like the nonmagnetic and triva-lent element Al兲 substituted MgB2 suggest that the specific electronic nature of the given substituent element共Fe兲 plays an important role in altering the phonon frequency and/or electron-phonon coupling strength.
ACKNOWLEDGMENTS
The authors are thankful to S. K. Joshi, NPL, New Delhi and M. A. H. Ahsan, Department of Physics, JMI, New Delhi for valuable discussions. One of the authors共B.G.兲 is grate-ful to CSIR for financial help under Contract No. CSIR-80共0056兲/05/EMR-II. This research is supported by the Na-tional Science Council of Taiwan under Contract No. NSC-94-2112-M-259-012共Y.K.K.兲.
*Electronic address: [email protected]
1J. Nagamastu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Nature共London兲 410, 63 共2001兲.
2S. Jin, H. Mavoori, C. Bower, and R. B. van Dover, Nature 共Lon-don兲 411, 563 共2001兲.
3I. I. Mazin and V. P. Antropov, Physica C 385, 49共2003兲, cf. Fig. 2.
4J. M. An and W. E. Pickett, Phys. Rev. Lett. 86, 4366共2001兲. 5J. M. Rowell, Supercond. Sci. Technol. 16, R17共2003兲. 6C. H. Cheng, Y. Zhao, X. T. Zhu, J. Nowotny, C. C. Sorrell, T.
Finlayson, and H. Zhang, Physica C 386, 588共2003兲. 7M. Kühberger and G. Gritzner, Physica C 370, 39共2002兲. 8Y. Moritomo and Sh. Xu, arXiv:cond-mat/0104568
共unpub-lished兲.
9D. Di Castro, M. Ortolani, E. Cappelluti, U. Schade, N. D. Zhi-gadlo, and J. Karpinski, Phys. Rev. B 73, 174509共2006兲. 10S. Agrestini, C. Metallo, M. Filippi, G. Campi, C. Sanipoli, S. De
Negri, M. Giovannini, A. Saccone, A. Latini, and A. Bianconi, J. Phys. Chem. Solids 65, 1479共2004兲.
11B. Lorenz, R. L. Meng, Y. Y. Xue, and C. W. Chu, Phys. Rev. B
64, 052513共2001兲.
12O. de la Peña, A. Aguayo, and R. de Coss, Phys. Rev. B 66, 012511共2002兲.
13K. Rogacki, B. Batlogg, J. Karpinski, N. D. Zhigadlo, G. Schuck, S. M. Kazakov, P. Wagli, R. Puzniak, A. Wisniewski, F. Car-bone, A. Brinkman, and D. van der Marel, Phys. Rev. B 73, 174520共2006兲.
14R. S. Gonnelli, D. Daghero, G. A. Ummarino, A. Calzolari, M. Tortello, V. A. Stepanov, N. D. Zhigadlo, K. Rogacki, J. Karpin-ski, F. Bernardini, and S. Massidda, Phys. Rev. Lett. 97, 037001 共2006兲.
15Y. D. Gao, J. Ding, G. V. S. Rao, and B. V. R. Chowdari, J. Appl. Phys. 93, 8656共2003兲.
16S. X. Dou, S. Soltanian, Y. Zhao, E. Getin, Z. Chen, O. Shcherba-kova, and J. Horvat, Supercond. Sci. Technol. 18, 710共2005兲. 17P. J. T. Joseph and P. P. Singh, Solid State Commun. 141, 390
共2007兲.
18R. J. Cava, H. W. Zandbergen, and K. Inumaru, Physica C 385, 8 共2003兲, and references therein.
19J. Kortus, O. V. Dolgov, R. K. Kremer, and A. A. Golubov, Phys. Rev. Lett. 94, 027002共2005兲, and references therein.
20A. Tampieri, G. Celotti, S. Sprio, D. Rinaldi, G. Barucca, and R. Caciuffo, Solid State Commun. 121, 497共2002兲.
21M. E. Yakinci, Y. Balci, and M. A. Aksan, Physica C 408-410, 684共2004兲.
22M. A. Aksan, M. E. Yakinci, and A. Güldeste, J. Alloys Compd.
424, 33共2006兲.
23C. S. Lue, T. H. Su, B. X. Xie, S. K. Chen, J. L. MacManus-Driscoll, Y. K. Kuo, and H. D. Yang, Phys. Rev. B 73, 214505 共2006兲.
24C. S. Lue, Y.-K. Kuo, S.-N. Hong, S. Y. Peng, and C. Cheng, Phys. Rev. B 71, 064202共2005兲.
25M. S. Osofsky, R. J. Soulen, Jr., S. A. Wolf, J. M. Broto, H. Rakoto, J. C. Ousset, G. Coffe, S. Askenazy, P. Pari, I. Bozovic, J. N. Eckstein, and G. F. Virshup, Phys. Rev. Lett. 71, 2315 共1993兲.
26A. A. Abrikosov and L. P. Gorkov, Sov. Phys. JETP 12, 1243 共1961兲.
27M. Putti, V. Braccini, E. Galleani, F. Napoli, I. Pallecchi, A. S. Siri, P. Manfrinetti, and A. Palenzona, Supercond. Sci. Technol.
16, 188共2003兲.
28J. M. Ziman, Principle of the Theory of Solids共Cambridge Uni-versity Press, Cambridge, 1972兲, pp. 224 and 225.
29A. Brinkman, A. A. Golubov, H. Rogalla, O. V. Dolgov, J. Kor-tus, Y. Kong, O. Jepsen, and O. K. Andersen, Phys. Rev. B 65, 180517共R兲 共2002兲.
30I. I. Mazin, O. K. Andersen, O. Jepsen, O. V. Dolgov, J. Kortus, A. A. Golubov, A. B. Kuz’menko, and D. van der Marel, Phys. Rev. Lett. 89, 107002共2002兲.
31E. Bauer, Ch Paul, St Berger, S. Majumdar, H. Michor, M. Gio-vannini, A. Saccone, and A. Bianconi, J. Phys.: Condens. Matter
13, L487共2001兲.
32L. Tewordt and Th. Wölkhausen, Solid State Commun. 70, 839 共1989兲.
33T. Muranaka, J. Akimitsu, and M. Sera, Phys. Rev. B 64, 020505共R兲 共2001兲.
34J. S. Ahn, E. S. Choi, W. Kang, D. J. Singh, M. Han, and E. J. Choi, Phys. Rev. B 65, 214534共2002兲.
35S. Agrestini, C. Metallo, M. Filippi, L. Simonelli, G. Campi, C. Sanipoli, E. Liarokapis, S. De Negri, M. Giovanni, A. Saccone, A. Latini, and A. Bianconi, Phys. Rev. B 70, 134514共2004兲. 36T. Masui and S. Tajima, Physica C 385, 91共2003兲.
37A. Poddar, B. Bandyopadhyay, P. Mandal, D. Bhattacharya, P. Choudhury, U. Sinha, and B. Ghosh, Physica C 390, 191 共2003兲.
38R. H. T. Wilke, S. L. Bud’ko, P. C. Canfield, J. Farmer, and S. T. Hannahs, arXiv:cond-mat/0507185, Phys. Rev. B 共to be pub-lished兲.
39A. P. Gerashenko, K. N. Mikhalev, S. V. Verkhovskii, A. E. Kar-kin, and B. N. Goshchitskii, Phys. Rev. B 65, 132506共2002兲. 40X. H. Chen, Y. S. Wang, Y. Y. Xue, R. L. Meng, Y. Q. Wang, and
C. W. Chu, Phys. Rev. B 65, 024502共2001兲.
41Kiran Singh, Rajneesh Mohan, Nupinder Kaur, N. K. Gaur, Man-glesh Dixit, Vilas Shelke, and R. K. Singh, Physica C 450, 124 共2006兲.
