Anisotropic Superconducting Properties of
Optimally Doped BaFe(AsP) under Pressure
Magnetic measurements on optimally doped single crystals of BaFe(AsP) () with magnetic fields applied along different crystallographic axes were performed under pressure, enabling the pressure evolution of coherence lengths and the anisotropy factor to be followed. Despite a decrease in the superconducting critical temperature, our studies reveal that the superconducting properties become more anisotropic under pressure. With appropriate scaling, we directly compare these properties with the values obtained for BaFe(AsP) as a function of phosphorus content.
pacs:74.70.Xa, 62.50.-p, 74.25.Op
The discovery of superconductivity in iron based compounds has triggered intense experimental and theoretical investigations Ishida_review (). One of the most heavily studied families is the so called 122 iron-arsenides (MFeAs, where M=Ca, Sr, Ba and Eu), where the ground state can be tuned from a spin density wave (SDW) to superconductivity by charge doping Rotter08 (); Sasmal08 () or pressure Alireza09 (); Terashima09 (). For example, superconductivity in BaFeAs can be induced by hole-doping Rotter08 (), electron-doping Ning09 (), isoelectronic substitution Kasahara10 (), and external physical pressure Alireza09 ().
The availability of high quality BaFe(AsP) single crystals has enabled detailed investigations of the charge and spin dynamics spanning the entire phase diagram. The SDW state is suppressed for and superconductivity is observed for where a maximum superconducting critical temperature, , of 31 K is seen at Kasahara10 (); Chong10 (). Quantum oscillation experiments revealed the existence of big Fermi surface sheets at the ‘overdoped’ side () Shishido10 (). In contrast, small Fermi pockets were detected in the parent compound of MFeAs Harrison09 (); Sebastian08 (). In addition, an enhancement of the quasiparticle effective mass, , was observed by quantum oscillations at the overdoped side on approaching the SDW state Shishido10 (). On the other hand, nuclear magnetic resonance (NMR) measurements on the same part of the phase diagram reported a drastic enhancement of two-dimensional antiferromagnetic fluctuations on approaching the SDW state Nakai10 (). Taking these experiments together as well as various anomalous transport properties Kasahara10 (), it is evidenced that the BaFe(AsP) system features an antiferromagnetic quantum critical point at .
Apart from the interesting normal state properties mentioned above, the superconducting properties for also exhibit anomalous behavior. In particular, careful analysis of the temperature dependence of thermal conductivity Hashimoto10 (), magnetic penetration depth Hashimoto10 () and NMR spin-lattice relaxation rate Nakai10b () suggests the presence of line nodes in the superconducting gap.
The layered structure of the 122 systems naturally raises the question regarding the anisotropy of physical properties. The ability to apply magnetic field along both the ab-plane and the c-axis offers an excellent opportunity to study the anisotropy of superconducting properties under pressure. Here we report magnetic measurements for single crystals with under hydrostatic pressure.
High pressure experiments were performed using a Moissanite anvil cell on high-quality single crystals grown in Kyoto. The anvil cell is cylindrical with a diameter of 18 mm and a length of 40 mm, and can be rotated with respect to the magnetic field axis for anisotropy studies. Single crystals used for this study were grown from mixtures of FeAs, Fe, P(powders) and Ba (flakes) placed in an alumina crucible, sealed in an evacuated quartz tube and kept at for 12 hours, followed by a slow cooling to at the rate of /hr Kasahara10b (). X-ray diffraction studies established the lattice constants to be and , and the coordinate of pnictogen atoms in the unit cell is , giving the phosphorus fraction of . In addition, energy-dispersive X-ray spectroscopy established the variation in from sample to sample to be less than 2%. High sensitivity Faraday inductive measurements were performed by placing a 10-turn microcoil inside the gasket hole of the anvil cell Goh08 (); Alireza03 (); Haase09 () (see the inset to Figure 1a). The superconducting transition was detected by two methods: (i) the shift in the resonant frequency of the LCR circuit consisting of a microcoil attached to an NMR probe (resonator mode), and (ii) a conventional mutual inductance method where a 140-turn modulation coil was also added inside the pressure cell. Glycerin was used as the pressure transmitting fluid and Ruby fluorescence spectroscopy was employed to determine the pressure achieved.
Iii Results and Discussion
Figure 1 presents the temperature dependence of the resonant frequency at different magnetic fields for ab-plane (Figure 1a) and c-axis (Figure 1b), for pressurized to 21.5 kbar. The transition to the superconducting state, manifested by an increase in the resonant frequency, is clearly observed. The superconducting critical temperature, , at zero field and ambient pressure determined by this technique (not shown) is 30.5 K, which is in good agreement with the measured by the mutual inductance method (see the inset of Figure 3) and resistivity measurements reported elsewhere Kasahara10 (). This value of confirms that is at the optimal doping of the BaFe(AsP) system. The superconducting transition, which is still very sharp at 21.5 kbar, demonstrates the high quality of the crystals and pressure transmitting fluid used in this study.
The superconducting transition with magnetic field applied shows a very distinct behavior for different field orientations. As evidenced in Figure 1, is depressed at a faster rate for c-axis. The values extracted at high fields are presented in Figure 2 for ambient pressure, 9.4 kbar and 21.5 kbar. With increasing pressure, the rate of change of with field remains more or less constant for ab-plane whereas for c-axis, this rate increases strongly. Interestingly, high pressure resistivity studies on the optimally electron-doped Ba(FeCo)As Colombier10 () and hole-doped BaKFeAs Torikachvili08 () with revealed only a small variation in the rate of change of . Thus, the BaFe(AsP) system at optimal doping is rather special and we now extract anisotropic superconducting and normal state properties under pressure.
Apart from a slight curvature very near which has also been observed by other groups (see e.g. Butch10 ()), the variation of over our accessible field range is very linear. Equivalently, the initial slope of the – curves is approximately constant over the field range of 13 T. For ambient pressure data, T/K and T/K for field along the ab-plane and c-axis, respectively. According to the Werthamer-Helfand-Hohenberg (WHH) prescription WHH (), , giving T and T. We note that a similar WHH treatment by Chong et al. Chong10 () based on resistivity data on BaFe(AsP) gives similar T but higher T. In addition, Hashimoto et al. Hashimoto10 () reported T based on specific heat and torque magnetometry measurements on BaFe(AsP).
|1 bar||9.4 kbar||21.5 kbar|
The anisotropy factor is defined as , which for the same reduces to the ratio of the initial slopes . As tabulated in Table 1, the pressure dependence of is remarkable: relative to ambient pressure, increases by more than a factor of 2 at 21.5 kbar despite a decreasing . Since glycerin is hydrostatic at this pressure range, if we assume the anisotropy of superconducting properties is directly coupled to the anisotropy of the crystal lattice, it is tempting to conclude that the crystal lattice is more compressible along the direction. However, neutron diffraction experiments performed on BaFeAs up to 60 kbar detected only minor changes in the lattice constants over the entire pressure range Kimber09 (). Furthermore, the neutron result showed that the c-axis is slightly more compressible than the direction. For the heavy fermion superconductor CeCoIn, the anisotropy factor determined from the initial slopes decreases under pressure Knebel10 (). This is accompanied by an initial increase in , which peaks at 13 kbar. Furthermore, even more drastic behavior is seen in CeCuSi: the anisotropy factor crosses under pressure while increases strongly from 0.68 K at ambient pressure () to 1.62 K at 24.2 kbar () Sheikin00 ().
The Ginzburg-Landau coherence length along the two principal axes can be calculated from the set of equations Tinkhambook ()
where Wb is the flux quantum. High pressure neutron diffraction Kimber09 () found that the c-axis lattice constant decreases linearly by merely 2% over 60 kbar. However, our analysis shows that already drops by 27% at 9.4 kbar. This suggests that the coupling between the superconducting layers is significantly weakened upon applying a small amount of pressure. In contrast, increases nearly linearly over the pressure range of our experiment.
BCS theory gives the (zero temperature) coherence length , where is the Fermi velocity, is the Fermi wavevector, is the effective mass and ( in the BCS s-wave treatment) is the energy gap at zero temperature Tinkhambook (). This allows us to extract several normal state properties. Assuming that and are only weakly dependent on pressure, we estimate the relative change of simply from the values of and . In Table 1 we list the values of bar) at pressure for two different principal axes and . increases with increasing pressure, implying a progressive reduction in the charge coupling along the c-axis. Interestingly, decreases as pressure is applied, suggesting that pressure tunes the system away from a quantum critical point. This is analogous to the evolution of and in BaFe(AsP) observed by the de Haas-van Alphen (dHvA) effect Shishido10 () and NMR Nakai10b (), respectively, where a striking enhancement of both quantities has been observed on approaching the critical concentration . We note that in CeRhIn, pressure kbar brings the system away from an antiferromagnetic quantum critical point Knebel10 (). A similar analysis of the critical field data in CeRhIn showed a reduction of the effective mass above kbar, the pressure at which is the maximum Knebel10 ().
Bandstructure calculations for BaFe(AsP) indicate that the warping of the hole sheet becomes more pronounced with increasing Shishido10 (). This suggests a more three dimensional Fermi surface with increasing . If the Fermi surface also becomes more three dimensional under pressure, possibly due to a more compressible -axis relative to the direction (as observed by neutron diffraction on BaFeAs Kimber09 ()), the present observation of increasing anisotropy in superconducting properties is intriguing. One possible explanation is that the superconducting gap displays a significant dependence, becomes more anisotropic under pressure, and is smaller on the part of the Fermi surface where the Fermi velocity has a larger component Kogan02 (); Kogan03 (); Graser10 (). Indeed, recent angle-resolved photoemission studies on the optimally hole-doped BaKFeAs found a significant dependence of the magnitude of the superconducting gap for a three dimensional hole sheet Zhang10 (); Xu10 ().
Figure 3b shows the pressure dependence of . Corroborating measurements were performed by the mutual inductance method. The initial variation of under pressure is approximately linear with the rate of K/kbar. This rate is comparable to the initial suppression rate of about K/kbar for the optimally hole-doped BaKFeAs Torikachvili08 (), but slower than that for the optimally electron-doped Ba(FeCo)As (roughly K/bar)Colombier10 (). At 37 kbar, the transition is slightly broadened, possibly due to the inhomogeneity of the pressure transmitting fluid at this pressure. The fact that is depressed rather slowly and is still so high at 37 kbar is remarkable. This is to be contrasted to Alireza et al.’s observation Alireza09 () on BaFeAs, where above 40 kbar is depressed rapidly with pressure, but remains rather constant above 50 kbar.
The birth of superconductivity in the BaFe(AsP) system has been understood in terms of chemical pressure exerted by phosphorus substitution. Comparing the initial slope of as a function of pressure Colombier09 () against that for BaFe(AsP) at low phosphorus content Kasahara10 (), we estimate that 1% phosphorus content corresponds to 2.4 kbar. Using this linear scaling relation, the can be added to Figure 3b for a direct comparison. For BaFe(AsP) at , further increment of the phosphorus content depresses . Since charge carriers are not introduced via phosphorus substitution, this reduction of has been attributed to the suppression of antiferromagnetic fluctuations Nakai10 (), which provide glue for Cooper pairings. With physical pressure applied in our studies, which also does not introduce charge carriers, it is tempting to argue that a suppression of antiferromagnetic fluctuations is responsible for the reduction of . The evolution of discussed earlier hints at the possibility of this mechanism. NMR studies under pressure along this direction, which form the subject of future works, will be important to clarify this situation.
The dHvA experiment on BaFe(AsP) Shishido10 () allows the calculation of from the dHvA frequency via the Onsager relation Shoenbergbook (). Since for the dHvA experiment the magnetic field is applied along the c-axis, the in-plane coherence length, , can be extracted using the BCS theory discussed above. The value of the numerical constant for depends on the nodal structure of the gap as well as the dimensionality of the system Tinkhambook (); Won94 (). For our analysis, we take . Figure 3a shows the -dependence of plotted on the same graph as and under pressure, using the same pressure-phosphorus content scaling relation. Interestingly, taking into account only the Fermi velocity of the band, an electron band at the Brillouin zone corner, a smooth overall variation of and is observed. For a multiband system, the transition to the superconducting state is governed by the band with the shortest coherence length. Given that the band with the larger effective mass and the larger gap gives the shortest coherence length, this comparative study strongly suggests that the band might also have a larger gap, in addition to the large effective mass already observed Shishido10 ().
In summary, we have studied the effect of pressure on the superconducting properties of optimally doped BaFe(AsP) with . We find that is suppressed rather slowly under pressure, and remains as high as 19.4 K at 37 kbar. The coupling between superconducting layers becomes progressively weakened under pressure and the anisotropy in the superconducting properties increases with applied pressure, which might be due to an increase in the anisotropy of the superconducting gap. The effective mass associated with the in-plane charge dynamics reduces at higher pressures. With appropriate scaling, the pressure dependence of the superconducting properties agrees nicely with the -dependence of the same properties for BaFe(AsP). The band is likely to play a prominent role in determining the superconducting and thermodynamic properties of this system.
Acknowledgements.The authors acknowledge K. Shimizu, A. Miyake, N. Naka, H. Hirabayashi for assistance with ruby fluorescence and M. Sutherland, G. G. Lonzarich, D. E. Khmelnitskii and P. L. Alireza for discussions. This work was supported by Grants-in-Aid for Scientific Research on Innovative Areas “Heavy Electron” (No. 20102006) from MEXT, for the GCOE Program“The Next Generation of Physics, Spun from Universality and Emergence” from MEXT, and for Scientific Research from JSPS as well as Trinity College (Cambridge). S.K.G. acknowledges the Great Britain Sasakawa Foundation for travel grant and Kyoto University for hospitality.
- (1) K. Ishida, Y. Nakai and H. Hosono, J. Phys. Soc. Jpn. 78, 062001 (2009).
- (2) M. Rotter, M. Tegel and D. Johrendt, Phys. Rev. Lett. 101, 107006 (2008).
- (3) K. Sasmal, B. Lv, B. Lorenz, A. M. Guloy, F. Chen, Y-Y. Xue and C-W. Chu, Phys. Rev. Lett. 101, 107007 (2008).
- (4) P. L. Alireza, Y. T. C. Ko, J. Gillett, C. M. Petrone, J. M. Cole, S. E. Sebastian and G. G. Lonzarich, J. Phys.: Condens. Matter 21, 012208 (2009).
- (5) T. Terashima, M. Kimata, H. Satsukawa, A. Harada, K. Hazama, S. Uji, H. S. Suzuki, T. Matsumoto and K. Murata, J. Phys. Soc. Jpn. 78, 083701 (2009).
- (6) F. Ning, K. Ahilan, T. Imai, A. S. Sefat, R. Jin, M. A. McGuire, B. C. Sales and D. Mandrus , J. Phys. Soc. Jpn. 78, 013711 (2009).
- (7) S. Kasahara, T. Shibauchi, K. Hashimoto, K. Ikada, S. Tonegawa, R. Okazaki, H. Shishido, H. Ikeda, H. Takeya, K. Hirata, T. Terashima and Y. Matsuda, Phys. Rev. B 81, 184519 (2010).
- (8) S. V. Chong, S. Hashimoto and K. Kadowaki, Solid State Communications 150, 1178 (2010).
- (9) H. Shishido, A. F. Bangura, A. I. Coldea, S. Tonegawa, K. Hashimoto, S. Kasahara, P. M. C. Rourke, H. Ikeda, T. Terashima, R. Settai, Y. Onuki, D. Vignolles, C. Proust, B. Vignolle, A. McCollam, Y. Matsuda, T. Shibauchi, and A. Carrington, Phys. Rev. Lett. 104, 057008 (2010).
- (10) N. Harrison, R. D. McDonald, C. H. Mielke, E. D. Bauer, F. Ronning and J. D. Thompson, J. Phys.: Condens. Matter 21, 322202 (2009).
- (11) S. E. Sebastian, J. Gillett, N. Harrison, P. H. C. Lau, D. J. Singh, C. H. Mielke, and G. G. Lonzarich, J. Phys.: Condens. Matter 20, 422203 (2008).
- (12) Y. Nakai, T. Iye, S. Kitagawa, K. Ishida, H. Ikeda, S. Kasahara, H. Shishido, T. Shibauchi, Y. Matsuda and T. Terashima, arXiv:1005.2853 (2010).
- (13) K. Hashimoto, M. Yamashita, S. Kasahara, Y. Senshu, N. Nakata, S. Tonegawa, K. Ikada, A. Serafin, A. Carrington, T. Terashima, H. Ikeda, T. Shibauchi and Y. Matsuda, Phys. Rev. B 81, 220501(R) (2010).
- (14) Y. Nakai, T. Iye, S. Kitagawa, K. Ishida, S. Kasahara, T. Shibauchi, Y. Matsuda and T. Terashima, Phys. Rev. B 81, 020503(R) (2010).
- (15) S. Kasahara, K. Hashimoto, R. Okazaki, H. Shishido, M. Yamashita, K. Ikada, S. Tonegawa, N. Nakata, Y. Sensyu, H. Takeya, K. Hirata, T. Shibauchi, T. Terashima and Y. Matsuda, Physica C (2010) (in press).
- (16) S. K. Goh, P. L. Alireza, P. D. A. Mann, A.-M. Cumberlidge, C. Bergemann, M. Sutherland and Y. Maeno, Curr. Appl. Phys. 8, 304 (2008).
- (17) J. Haase, S. K. Goh, T. Meissner, P. L. Alireza, and D. Rybicki, Rev. Sci. Instrum. 80, 073905 (2009).
- (18) P. L. Alireza and S. R. Julian, Rev. Sci. Instrum. 74, 4728 (2003).
- (19) E. Colombier, M. S. Torikachvili, N. Ni, A. Thaler, S. L. Bud’ko and P. C. Canfield, Supercond. Sci. Technol. 23, 054003 (2010).
- (20) M. S. Torikachvili, S. L. Bud’ko, N. Ni and P. C. Canfield, Phys. Rev. B 78, 104527 (2008).
- (21) N. P. Butch, S. R. Saha, X. H. Zhang, K. Kirshenbaum, R. L. Greene and J. Paglione, Phys. Rev. B 81, 024518 (2010).
- (22) N. R. Werthamer, E. Helfand and P. C. Hohenberg, Phys. Rev. 147, 295 (1966).
- (23) M. Tinkham, Introduction to Superconductivity 2, Dover Publication Inc. (2004).
- (24) S. A. J. Kimber, A. Kreyssig, Y-Z. Zhang, H. O. Jeschke, R. Valent, F. Yokaichiya, E. Colombier, J. Yan, T. C. Hansen, T. Chatterji, R. J. McQueeney, P. C. Canfield, A. I. Goldman and D. N. Argyriou, Nat. Mater. 8, 471 (2009).
- (25) G. Knebel, D. Aoki, J.-P. Brison, L. Howald, G. Lapertot, J. Panarin, S. Raymond and J. Flouquet, Phys. Status Solidi B 247, 557 (2010).
- (26) I. Sheikin, D. Braithwaite, J.-P. Brison, W. Assmus and J. Flouquet, J. Low Temp. Phys. 118, 113 (2000).
- (27) V. G. Kogan, Phys. Rev. B 66, 020509(R) (2002).
- (28) P. Miranović, K. Machida and V. G. Kogan, J. Phys. Soc. Jpn. 72, 221 (2003).
- (29) S. Graser, A. F. Kemper, T. A. Maier, H.-P. Cheng, P. J. Hirschfeld and D. J. Scalapino, Phys. Rev. B 81, 214503 (2010).
- (30) Y. Zhang, L. X. Yang, F. Chen, B. Zhou, X. F. Wang, X. H. Chen, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, J. P. Hu, B. P. Xie and D. L. Feng, arXiv:1006.3936 (2010).
- (31) Y.-M. Xu, Y.-B. Huang, X.-Y. Cui, R. Elia, R. Milan, M. Shi, G.-F. Chen, P. Zheng, N.-L. Wang, P.-C. Dai, J.-P. Hu, Z. Wang and H. Ding, arXiv:1006.3958 (2010).
- (32) E. Colombier, S. L. Bud’ko, N. Ni and P. C. Canfield, Phys. Rev. B 79, 224518 (2009).
- (33) D. Shoenberg, Magnetic oscillations in metals, Cambridge University Press (1984).
- (34) H. Won and K. Maki, Phys. Rev. B 49, 1397 (1994).