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Upper and lower critical magnetic fields of
superconducting NdFeAsO1–xFx single crystals studied
by Hall-probe magnetization and specific heat
Z. Pribulova, Thierry Klein, J. Kacmarcik, C. Marcenat, M. Konczykowski, S.
L. Bud’Ko, M. Tillman, P. C. Canfield
To cite this version:
Z. Pribulova, Thierry Klein, J. Kacmarcik, C. Marcenat, M. Konczykowski, et al.. Upper and lower
critical magnetic fields of superconducting NdFeAsO1–xFx single crystals studied by Hall-probe
mag-netization and specific heat. Physical Review B: Condensed Matter and Materials Physics (1998-2015),
American Physical Society, 2009, 79, pp.020508(R). �10.1103/PhysRevB.79.020508�. �hal-00957171�
Upper and lower critical magnetic fields of superconducting NdFeAsO
1−xF
xsingle crystals
studied by Hall-probe magnetization and specific heat
Z. Pribulova,1,2T. Klein,1,3J. Kacmarcik,2,4C. Marcenat,4M. Konczykowski,5S. L. Bud’ko,6M. Tillman,6and
P. C. Canfield6
1Institut Néel, CNRS, BP 166, 38042 Grenoble Cedex 9, France
2Centre of Low Temperature Physics, IEP, SAS and FS, UPJŠ, Watsonova 47, 043 53 Košice, Slovakia 3Institut Universitaire de France and Université Joseph Fourier, BP 53, 38041 Grenoble Cedex 9, France 4Institut Nanosciences et Cryogénie, SPSMS-LATEQS, CEA, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
5Laboratoire des Solides Irradiés, Ecole Polytechnique, 91128 Palaiseau, France
6Department of Physics and Astronomy, Ames Laboratory, Iowa State University, Ames, Iowa 50011, USA
共Received 15 December 2008; published 27 January 2009兲
The upper and lower critical fields have been deduced from specific heat and Hall-probe magnetization measurements in nonoptimally doped Nd共O,F兲FeAs single crystals 共Tc⬃ 32– 35 K兲. The anisotropy of the penetration depth共⌫兲 is temperature independent and on the order of 4.0⫾ 1.5. Similarly specific-heat data
lead to an anisotropy of the coherence length ⌫⬃ 5.5⫾ 1.5 close to Tc. Our results suggest the presence of rather large thermal fluctuations and the existence of a vortex liquid phase over a broad temperature range 共⬃5 K large at 2 T兲.
DOI:10.1103/PhysRevB.79.020508 PACS number共s兲: 74.25.Ha, 74.25.Fy, 74.25.Nf, 74.25.Op
The recent discovery of superconductivity at unusually high temperature 共up to 56 K兲 in rare-earth iron oxypnictides1,2has been the focus of a tremendous number
of theoretical and experimental works in the past few months. The possible coexistence of superconductivity with a complex magnetic structure3makes this system particularly
fascinating and a nonconventional pairing mechanism 共asso-ciated with multigap superconductivity in electron and hole pockets兲 has been suggested by different groups.4In this
con-text, it is very important to have a precise determination of the temperature dependence of the critical fields and corre-sponding anisotropies.
We will focus on the superconducting properties of the NdFeAs共O,F兲 compound.5
The aim of this Rapid Communi-cation is to present combined Hall-probe magnetization and specific-heat 共Cp兲 measurements performed on Nd-doped
single crystals. A superconducting anomaly was clearly vis-ible in Cp around 35 K and, as previously observed in
high-Tc oxides, this anomaly is symmetric and broad and
rapidly collapses as the magnetic field is increased. On the other hand, the lower critical field presents a classical tem-perature dependence for both Ha 储c and Ha 储ab 关with Hcc1共0兲 ⬃ 120⫾ 30 G and Hc1
ab
⬃ 40⫾ 10 G兴 and the aniso-tropy of the penetration depth remains on the order of 4 on the entire temperature range. A similar anisotropy is obtained for the upper critical field from the Cpmeasurements.
NdFeAs共O,F兲 samples have been synthesized at high pressure in a cubic multianvil apparatus. More details of the synthesis are given elsewhere.6 Both Hall-probe
magnetiza-tion and Cpmeasurements have been performed on the same
plateletlike single crystals extracted from the polycrystalline batch 关with dimensions of ⬃100⫻ 100⫻ 30 m3 共sample 1兲, ⬃120⫻ 80⫻ 30 m3 共sample 2兲, and ⬃170⫻ 100 ⫻ 50 m3 共sample 3兲兴.
The local magnetization of the platelet has been measured by placing the sample on the top of an array of miniature Hall probes of dimensions 4 ⫻ 4 or 8 ⫻ 8 m2. The ac
trans-mittivity 共Tac
⬘
, related to the local susceptibility兲 has beenmeasured by applying a small共⬃1 G兲 ac field and recording the corresponding response of the probe as a function of the temperature关see Fig.1共a兲兴. Tac
⬘
is obtained by subtracting theresponse in the normal state from the data and is rescaled to −1 at T = 4.2 K 共due to the small but nonzero distance be-tween the probe and the sample surface, about 10% of the external field is still picked up by the probe in the supercon-ducting state兲. As shown in Fig.1共a兲, the transmittivity mea-sured in the center of the sample first presents a small para-magnetic increase starting at ⬃37 K followed by a sharp diamagnetic jump at T⬃ 34 K 共sample 1兲. This paramag-netic bump 共also observed in zero-field-cooled dc measure-ments兲 reflects a nonhomogeneous distribution of the field7
between 34 and 37 K. However, the presence of a clear anomaly in the specific heat emphasizes the overall good quality of the platelets. A similar bump has been observed in sample 2 between 34.5 and 37.5 K and in sample 3 between 36.5 and 37.5 K. Note also that previous global magnetiza-tion measurements8 yield to an onset of the diamagnetic
re-sponse of the polycrystalline batch around T⬃ 51 K, in agreement with a resistivity Tc on the order of 50 K for
optimally doped samples.5 We did not find any sign of
su-perconductivity around 51 K in our platelets, indicating that the diamagnetic response observed above 40 K in global measurements is due to a distribution of Tc values 共i.e., F
content兲 within the polycrystalline batch.
Specific-heat measurements have been performed on the same crystallites 共samples 1 and 2兲 using an ac technique. This high-sensitivity technique 共typically 1 part in 104兲 is
very well adapted to measuring Cp of very small samples.
Heat was supplied to the sample at a frequency= 10 Hz by a light-emitting diode via an optical fiber. The temperature oscillations have been recorded with a thermocouple which has been calibrated from measurements on ultrapure silicon. The superconducting contribution to the specific heat 共⌬Cp兲
has been obtained by subtracting the curve at 0Ha= 7 T
共for Ha 储c兲 from the curves obtained for lower fields as well
as a 共Ha/T兲2 contribution to account for the presence of a
magnetic background. As shown in Fig. 1共b兲 共sample 1兲, there is no sharp discontinuity at Tcand the anomaly has the
shape of a rounded peak with a height on the order of a few 10−3 of the total specific heat. The other striking behavior is
the influence of the magnetic field. As previously observed in cuprates,9 the smearing of the anomaly with field is unex-pectedly strong with an almost field-independent onset. The maximum of Cp is pushed downward in temperature by the
field with a characteristic average slope on the order of −2 T / K for Ha 储c and −7 T / K for Ha 储ab 共compared to
−1.5 and −9 T / K, respectively, in optimally doped YBaCuO; note that the shift is possibly nonlinear for small magnetic field and see solid line in Fig. 2 and discussion below兲. As in cuprates, the shape of the anomaly precludes any precise determination of Hc2. However, assuming that Hc2 is close to the maximum of Cp 共Hmax兲 and taking the
corresponding linear temperature dependence, we hence get
Hc2共0兲 ⬃ 0.7⫻ dHmax/dT⫻ Tc⬃ 40 and ⬃170 T for Ha 储c
and Ha 储ab, respectively. The corresponding anisotropy of
the coherence length ⌫=c/ab= ⌫Hc2 is hence on the order
of Hc2 ab
共0兲 / Hc2 c
共0兲 ⬃ 4. The uncertainty on the Hc2 values is
rather large but ⌫can also be estimated from the total shape -1 -0.5 0 T ' ac C p / T (arb .unit s) 1T 0T 0.5T 2T 1T 0T (a) 0T //c 0.2T //c 0.5T //c 1T //c 3T //c 5T //c 1T //ab 3T //ab 7T //ab 25 30 35 40 0 (b) T (K) C p / T (arb .unit s) 0 4 8 0 100 200 B rem (G ) µ 0Ha(G) 32K (0°) 25K (0°) 4K (7°) 4K (55°)
FIG. 1. 共Color online兲 共a兲 Temperature dependence of the ac transmittivity and specific heat in a non-optimally doped Nd共F , O兲FeAs platelet 共sample 1兲 for the indicated field values 共Ha 储c兲. In the inset: Remanent field 共Brem兲 as a function of the
applied field 0Ha共see text for details兲 for the indicated tempera-tures and field orientation. The solid lines are共Ha− Hp兲2fits to the data. 共b兲 Temperature dependence of the specific heat in a non-optimally doped Nd共F , O兲FeAs platelet 共sample 1兲 for Ha 储c共closed black symbols兲 and Ha 储ab 共open red symbols兲 for the indicated field values. The inset shows sample 1 mounted on the thermo-couple cross, for which the width of the legs is⬇50 m, as well as for sample 3共bottom left corner兲.
0 1 2 3 4 5 6 7 8 31 31.5 32 32.5 33
µ
0H
c2(T
)
T(K) 7.5 T/K 2.3 T/K (a) 0 1 2 3 24 26 28 30 32 34 H c2( from Cp) Hirr(from T')µ
0H
(T
)
T (K)Vortex
Liquid ?
(b)FIG. 2. 共a兲 Temperature dependence of the upper critical field 关maximum of the specific-heat anomaly; see Fig. 1共a兲兴 for Ha 储c 共circles兲 and Ha 储ab 共squares兲. 共b兲 Comparison between Hc2
共de-duced from Cp, closed symbols兲 and the onset of the diamagnetic response Hirr共open symbols兲 for Ha 储csuggesting the existence of a broad vortex liquid phase.
PRIBULOVA et al. PHYSICAL REVIEW B 79, 020508共R兲 共2009兲
of the anomaly, writing ⌬C共⌫⫻ Ha 储ab兲 ⬃ ⌬C共Ha 储c兲,
con-sistently leading to ⌫⬃ 5.5⫾ 1.5. This value is also in good
agreement with the one previously reported by Welp et al.10 and with recent band-structure calculations.11
The influence of Ha on the Cp anomaly and its overall
shape is strikingly different from the one observed in classi-cal superconductors or even in the 共K , Ba兲BiO3 system 共Tc
⬃ 32 K兲 共Ref.12兲 or MgB2共Tc⬃ 39 K兲 共Ref.13兲 of similar Tcvalues. It is tempting to attribute these deviations to fluc-tuation effects. To reinforce this idea, it is worth noting that the onset of the diamagnetic response well coincides with the inflection point of the Cp anomaly for Ha= 0 but is pushed
toward substantially lower temperature in field共⬃5 K lower than the Cpshift for0Ha= 2 T兲. As Tac
⬘
is sensitive topin-ning, this result suggests that the irreversibility line is well separated from the superconducting transition for Ha⫽0共see
inset of Fig.2共b兲 for Ha 储c; a similar result—not shown—is
obtained for Ha 储ab兲, supporting the idea of an extended
vor-tex liquid phase. The importance of thermal fluctuations can be quantified by the Ginzburg number14 Gi=共kBTc/⑀0c兲2/8,
where ⑀0 关=共⌽0/4ab兲2兴 is the line tension of the vortex
matter. Large values 共see below兲 combined with small
values hence lead here to ⑀0c⬃ 200 K 共i.e., similar to
cu-prates兲 compared to ⬃1000 K in 共K , Ba兲BiO3 and even
⬃104 in MgB
2. Although smaller than in cuprates due to
smaller Tcvalues, thermal fluctuations are hence expected to
play a role in this system possibly leading to the melting of the vortex solid 共Gi⬃ 3 ⫻ 10−3– 10−2兲. A similar conclusion
was drawn by Welp et al.10Note that, as expected for vortex
melting, the irreversibility line clearly presents a positive curvature 关Hirr⬀共1 − T / Tc兲␣ with ␣⬃ 1.5; for a review see
Ref. 14兴. Similarly, thermal fluctuations may also induce an upward curvature in the Hc2line15but even though our data
suggest the existence of such a curvature共see also Ref. 10兲, we cannot unambiguously conclude given the uncertainties and limited temperature range of the Cp data.
The first penetration field Hp has been deduced by
mea-suring the remanent field共Brem兲 in the sample after applying
an external field Haand sweeping the field back to zero. For Ha⬍ Hp no vortices penetrate the sample and the remanent
field remains equal to zero. Ha is progressively increased
until a finite remanent field is obtained as vortices remain pinned in the sample for Ha⬎ Hp 关Brem increasing as 共Ha
− Hp兲2; see solid line in the inset of Fig.1共a兲兴. Theoretically
speaking, Hp is expected to depend on the position of the
probe, being larger in the center of the sample as vortices first remain pinned close to sample edges. However, experi-mentally, a nonzero Bremvalue could be detected almost
si-multaneously on all the probes due to the nonzero distance between the sample and the probe. Note that we did not observe any significant change in the Brem共Ha兲 curve up to Ha⬃ 3Hp as the magnetic field was tilted away from the c
axis 共with an angleH
aⱕ 60° – 70°兲. Even though the angle
between the internal field 共H兲 and the c axis is reduced by
the demagnetization effects, this surprising behavior suggests that the induction共B兲 in the sample remains perpendicular to the platelets up to large Hvalues关see inset of Fig.1共a兲for
sample 1 atHa= 7° and 55°兴. Brem finally decreases with
for Haⱖ 3Hp 共and/or forHaⱖ 70°兲, indicating that the
vor-tices finally align on the applied field for large Ha 共and/or
Ha兲 values.
In samples with rectangular cross sections, flux lines par-tially penetrate into the sample through the sharp corners even for Ha⬍ Hp 共Refs. 16 and17兲 but remain “pinned” at
the sample equator. The magnetization at Ha= Hp is then
larger than Hc1 and the standard “elliptical” correction for Hc1 关=Hp/共1 − N兲, where N is the demagnetization factor兴
cannot be used anymore. Following Ref.16, in the presence of geometrical barriers, Hp is related to Hc1 through Hc1
⬇ Hp/tanh共
冑
␣d /2w兲, where ␣ varies from 0.36 in strips to0.67 in disks 共2w and d being the sample width and thick-ness, respectively兲. Taking an average␣value of⬃0.5,18we
hence got19 Hcc1共0兲 ⬃ 110⫾ 20 G in sample 1, Hc1 c
共0兲 ⬃ 100⫾ 20 G in sample 2, and Hc1
c共0兲 ⬃ 140⫾ 30 G in
sample 3. To obtain Hp in the ab plane, sample 3 has been
rotated by 90° putting the probe on the small side of the sample 关i.e., applying Ha along the long direction of the
sample so that Hp ab共0兲 ⬃ H c1 ab兴. We hence obtained H c1 ab ⬃ 40⫾ 10 G 共in sample 3兲.
The temperature dependence of Hc1 for both Ha 储c
共samples 1 and 3; the data for sample 1 have been rescaled by a factor of 1.5兲 and Ha 储ab共sample 3兲 is displayed in Fig.
3. As shown, Hcc1 clearly flattens off at low temperatures 共down to 1.6 K for sample 1兲, indicating that the gap is fully open in our NdAsFe共O,Fe兲 single crystals. This result is in striking contrast with Hp measurements in Ref. 21, which
suggested that Hc1 varies linearly at low temperature in
LaFeAs共O,F兲, hence suggesting the existence of gapless
su-3 4 5 6 7 0 0.2 0.4 0.6 0.8 1 0 50 100 150 200 T/T c µ 0 H c1 (G )
FIG. 3. Temperature dependence of the lower critical field Hc1
along the c direction共solid squares for sample 3 and solid lozenges for sample 1, rescaled by a factor of 1.5兲 and ab plane for sample 3 共solid circles兲. The solid lines are the standard behaviors expected from the BCS theory. The corresponding temperature dependence of the anisotropy共⌫= 1.3⫻ ⌫Hc1兲 is also reported 共open squares兲. The error bars correspond to the uncertainties on the determination of Hp; the whole curve might be shifted ⫾1.5 due to the uncertainty of the demagnetization factor. In all cases, ⌫remains flat in T. The
⌫ values deduced from Cp 共present work: open circles; Ref.10: open lozenge兲 and transport 共Ref.27; open triangles兲 measurements are also displayed.
perconductivity. On the other hand, a very similar tempera-ture dependence 关and Hc1共0兲 values兴 was recently obtained
by Okazaki et al.22 in Pr-doped samples.
The lower critical field is related to the penetration depth through Hc1
c
= ⌽0 2/共4
ab2 兲关Ln共兲 + c共兲兴, where = ab/ab
共 being the coherence length兲 and c共兲 is a -dependent function tending toward ⬃0.5 for large values. Taking
Hcc2共0兲 ⬃ 40 T, one gets ab共0兲 ⬃ 270⫾ 40 nm.23 Those
values are consistent with those previously obtained in ox-ypnictides. Indeed, slightly lower ab values 共⬃200 nm兲
have been reported in both Sm- and Nd-doped samples with higher Tc 共⬃50 K, from either torque,20 muon relaxation,24
or plasma frequency25 measurements兲, whereas
⬃ 360– 390 nm have been obtained in La-doped samples with lower Tcvalues 关⬃23 K 共Refs.21and26兲兴.
For H储ab, Hc1 ab = ⌽0 2/共4 abc兲关Ln共ⴱ兲 + c共ⴱ兲兴, with ⴱ = c/ab, and Hc2 ab = ⌽0 2/ 共2cab兲 ⬃ 170 T, leading to c
⬃ 1200⫾ 200 nm and a corresponding anisotropy 共⌫兲 on
the order of 4.0 共⫾1.5兲, almost temperature independent down to 1.6 K 共see Fig. 3, sample 3, ⌫= ⌫Hc1
⫻兵1 + Ln共⌫兲 / 关Ln共兲 + 0.5兴其 ⬃ 1.3⫻ ⌫Hc1兲. Note that our data
are in striking contrast with those deduced from torque mea-surements in Sm-doped samples20 which led to strongly
in-creasing ⌫values, exceeding 30 at low temperature. On the
other hand, our ⌫ consistently tends toward ⌫ for T → Tc
deduced either from Cp共present work and Ref.10兲 or
trans-port data.27 The difference between the anisotropies mea-sured at low 共⌫兲 and high 共⌫兲 fields remains within our
error bars and we hence cannot comment on a possible simi-larity with MgB2in which the coexistence of two gaps leads
to a strong field and temperature dependence of the anisotropy.28
In conclusion, specific heat and Hall-probe magnetization data suggest that ⌫⬃ ⌫⬃ 5 ⫾ 2 in NdFeAs共F,O兲 single
crystals. Whereas the irreversibility rapidly shifts toward lower temperature for increasing Ha, the Cp anomaly
col-lapses and shows only a minor shift, suggesting the presence of strong thermal fluctuations possibly leading to the melting of the vortex solid.
We would like to thank K. van der Beek for very fruitful discussions and preliminary magneto-optic images. Work at the Ames Laboratory was supported by the Department of Energy, Basic Energy Sciences under Contract No. DE-AC02-07CH11358. Z.P. thanks the Slovak Research and De-velopment Agency共Contract No. LPP-0101-06兲. J.K. thanks the 6th Framework Programme MCA Transfer of Knowledge project ExtreM 共Project No. MTKD-CT-2005-03002兲.
1Y. Kamihara et al., J. Am. Chem. Soc. 130, 3296共2008兲. 2C. Wang et al., EPL 83, 67006共2008兲.
3See, for instance, C. de la Cruz et al., Nature共London兲 453, 899
共2008兲; A. J. Drew et al., Phys. Rev. Lett. 101, 097010 共2008兲; Z. S. Wang et al., Phys. Rev. B 78, 140501共R兲 共2008兲; S. Kitao et al., J. Phys. Soc. Jpn. 77, 103706共2008兲.
4L. Boeri et al., Phys. Rev. Lett. 101, 026403共2008兲; I. I. Mazin
et al., ibid. 101, 057003共2008兲.
5Z. A. Ren et al., EPL 82, 57002共2008兲. 6M. Tillman et al.共unpublished兲.
7N. Avraham et al., Phys. Rev. B 77, 214525共2008兲. 8R. Prozorov et al., arXiv:0805.2783共unpublished兲.
9A. Carrington et al., Phys. Rev. B 55, R8674共1997兲, and
refer-ences therein.
10U. Welp et al., Phys. Rev. B 78, 140510共R兲 共2008兲.
11D. J. Singh and M. H. Du, Phys. Rev. Lett. 100, 237003共2008兲. 12S. Blanchard et al., Phys. Rev. Lett. 88, 177201共2002兲. 13L. Lyard et al., Phys. Rev. B 66, 180502共R兲 共2002兲. 14G. Blatter et al., Rev. Mod. Phys. 66, 1125共1994兲. 15T. Klein et al., Phys. Rev. Lett. 92, 037005共2004兲. 16E. H. Brandt, Phys. Rev. B 59, 3369共1999兲. 17E. Zeldov et al., Phys. Rev. Lett. 73, 1428共1994兲. 18A detailed analysis on MgB
2samples showed that all measured
samples fell within those two共strips and disks兲 limits; L. Lyard,
T. Klein, J. Marcus, R. Brusetti, C. Marcenat, M. Konc-zykowski, V. Mosser, K. H. Kim, B. W. Kang, H. S. Lee, and S. I. Lee, Phys. Rev. B 70, 180504共R兲 共2004兲.
19Note that for the rather high d / 2w ratio of our platelets a
stan-dard “elliptical” correction would only slightly overestimate Hc1: for samples 1 and 2 d / 2w⬃ 0.3, leading to 1 / 共1 − N兲
⬃ 4.0⫾ 0.2 for strips and 2.8⫾ 0.2 for disks compared to Hc1/Hp⬃ 2.7⫾ 0.4 for geometrical corrections.
20S. Weyeneth et al., arXiv:0806.1024共unpublished兲. 21C. Ren et al., arXiv:0804.1726共unpublished兲. 22R. Okazaki et al., arXiv:0811.3669共unpublished兲. 23Our H
c2 values are significantly higher than those reported in
Ref.10but lower than those previously reported from transport measurements 关see Ying Jia, Peng Cheng, Lei Fang, Huiqian Luo, Huan Yang, Cong Ren, Lei Shan, Changzhi Gu, and Hai-Hu Wen, Appl. Phys. Lett. 93, 032503共2008兲; C. Senatore et al., Phys. Rev. B 78, 054514共2008兲兴; however, a change by a factor 2 of Hc2induces a change in of less than 10%.
24A. J. Drew et al., arXiv:0805.1042, Phys. Rev. Lett.共to be
pub-lished兲; R. Khasanov et al., Phys. Rev. B 78, 092506 共2008兲.
25A. Dubroka et al., Phys. Rev. Lett. 101, 097011共2008兲. 26H. Luetkens et al., Phys. Rev. Lett. 101, 097009共2008兲. 27Y. Jia et al., Supercond. Sci. Technol. 21, 105018共2008兲. 28L. Lyard et al., Phys. Rev. Lett. 92, 057001共2004兲.
PRIBULOVA et al. PHYSICAL REVIEW B 79, 020508共R兲 共2009兲
