Hysteretic superconducting resistive transition in Ba0.07K0.93Fe2As2
Taichi Terashima, Kunihiro Kihou, Megumi Tomita, Satoshi Tsuchiya, Naoki Kikugawa, Shigeyuki Ishida, Chul-Ho Lee, Akira Iyo, Hiroshi Eisaki, Shinya Uji
aa r X i v : . [ c ond - m a t . s up r- c on ] M a y Ver. 6
Hysteretic superconducting resistive transition in Ba . K . Fe As Taichi Terashima,
1, 2
Kunihiro Kihou,
2, 3
Megumi Tomita, Satoshi Tsuchiya, Naoki Kikugawa, Shigeyuki Ishida,
2, 3
Chul-Ho Lee,
2, 3
Akira Iyo,
2, 3
Hiroshi Eisaki,
2, 3 and Shinya Uji
1, 2 National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan JST, Transformative Research Project on Iron Pnictides (TRIP), Chiyoda, Tokyo 102-0075, Japan National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan (Dated: June 23, 2018)We have observed hysteresis in superconducting resistive transition curves of Ba . K . Fe As ( T c ∼ ab plane by 20 ◦ or more. The temperature and angle dependences of the upper criticalfield indicate a strong paramagnetic effect for in-plane fields. We suggest that the hysteresis canbe attributed to a first-order superconducting transition due to the paramagnetic effect. Magnetictorque data are also shown. PACS numbers: 74.70.Xa, 74.25.Dw, 74.25.Op
I. INTRODUCTION
Magnetic fields destroy spin-singlet superconductivityvia two different mechanisms: orbital and spin param-agnetic effects. The former leads to the formation of amixed state and, in the absence of the latter, a second-order transition to the normal state at the orbital crit-ical field B ∗ c (0) = Φ / πξ , where Φ and ξ are theflux quantum and superconducting coherence length, re-spectively. The latter lowers the normal state energydue to spin polarization and, in the absence of the for-mer, may cause a first-order transition to the normalstate at the paramagnetic critical field B po = ∆ / √ µ B ,where ∆ and µ B are the superconducting energy gapand Bohr magneton, respectively. The Maki parameter α = √ B ∗ c (0) /B po describes the relative importance ofthe two effects. The three parameters may be estimatedfrom experimental data using the weak-coupling BCS re-lations: B ∗ c (0) = 0 . | B ′ c | T c , B po (in Tesla) =1.84 T c ,and α = 0 . | B ′ c | , where B ′ c = d B c / d T | T c .It was predicted that when α > It was subsequently proposed thatin such cases a novel superconducting state, now calledthe FFLO state, in which an order parameter oscillates inreal space due to a finite center-of-mass momentum q = 0of Cooper paris, may occur between the BCS and normalstates. Although those predictions were already madein mid 1960’s, strong experimental evidence for them hasappeared only recently, for two types of compounds: aheavy-fermion superconductor CeCoIn and organicsuperconductors.
Iron-pnictide superconductors, first discovered byKamihara et al ., are also good candidates for the obser-vation of the first-order transition or the FFLO state. They have large upper critical fields B c , and clear para-magnetic limiting of B c ( T ) curves has indeed been re-ported for some of them. Importantly they are multi-band superconductors. In multi-band superconductors,high-field behavior due to the spin paramagnetic effect would contain much richer physics than that in single-band superconductors, as illustrated by the followingquestions. The Maki parameter may be estimated foreach band from band parameters. If α > q vector is given by q = gµ B H/ ¯ hv F in the simplest case,and hence q varies from band to band. How is a compro-mise reached in reality ?We report here electrical resistance and magnetictorque measurements on Ba . K . Fe As . It is amulti-band superconductor, where the Fermi surface con-sists of three large hole cylinders at the zone center andsmall hole cylinders near the corners. The size of thesuperconducting energy gap varies considerably from FScylinder to cylinder.
We observe hysteresis in resis-tive transition curves at low temperatures for in-planefields and suggest that it is due to a first-order supercon-ducting transition.
II. EXPERIMENTS
High-quality Ba . K . Fe As single crystals wereprepared by a self-flux method. The Ba-to-K ratio wasdetermined from energy-dispersive X-ray analysis (aver-age of measurements on three pieces at 10 points pereach piece). The variation in the Ba content was within ∼ ± R mea-surements were performed in a dilution refrigerator andsuperconducting magnet. A low-frequency ac current(typically f = 13 Hz and I = 100 µ A, corresponding tothe current density in the order of 1 A/cm ) was appliedin the ab plane and perpendicular to the applied field B . The field angle θ is measured from the c axis: θ =90 ◦ for B k ab . Among five measured samples from thesame growth batch, the resistive hysteresis was clearlyobserved in two, only just observed in one, and not ob-served in the last two. The clearly hysteretic samples,called H1 and H2 hereafter, have the residual resistivityratio at T = 12 K and T c of (H1) 62 and 8.2 K and of(H2) 74 and 7.4 K. The slight difference in T c is probablydue to difference in the composition. The two samplesshowing no hysteresis have similar resistivity ratios: 65and 75, respectively. However, the transition widths of R ( B ) curves are very different between the two groups.The 10% to 90% widths for B k ab at T < B c ’s ofthe domains. On the other hand, transition curves of thesamples showing no hysteresis are much broader and fea-tureless. It seems that the intrinsic hysteresis is blurredby larger compositional inhomogeneity. Magnetic torquemeasurements were performed on small pieces cut fromsamples H1 and H2 using piezoresistive microcantilevers. III. RESULTS AND DISCUSSION
Figure 1(a) shows superconducting resistive transitionsin sample H1 at selected temperatures (except for the topcurve). At T = 0.03 K, the hysteresis is visible between B ∼ ∼ ∼ T c and hencelow- B c regions in the sample. Five times difference inthe field sweep rate (0.5 vs 0.1 T/min) leads to no es-sential difference in the R ( B ) curves (compare the twolowest curves). Four times difference in the measuringcurrent (0.05 vs 0.2 mA) leads to no essential differenceexcept for a slight non-Ohmic dependence (inset). Theseobservations seem to exclude possible extrinsic origins ofthe hysteresis such as history-dependent inhomogeneouscurrent path or induced current during field ramping,which would largely be affected by the current density orsweep rate. As the temperature is raised, the hysteresisis still visible at 0.83 K but not at 1.2 K. Figure 1(b)shows R ( B ) curves for different field orientations. As thefield is tilted from the ab plane, the hysteresis is visibleat θ = 80 ◦ but not at 70 ◦ .Resistance measurements on sample H2 give consis-tent results. The resistive hysteresis is observed approx-imately up to T = 1 K (Fig. 2) and for field orientationswithin ∼ ◦ of the ab plane (data not shown). Althoughthe transition width is narrower than that in sample H1,transition consists of several steps as indicated by clearpeaks in the derivative d R /d B curves (Fig. 2, bottomcurve). As noted above, this can be interpreted as an in-dication that the sample consists of domains with slightlydifferent compositions.Figure 3(a) shows the temperature dependences of B c R ( m Ω ) K Fe As sample H1 R N N R ( m Ω ) K Fe As sample H1T = 0.04 K solid line90¡ (B // ab) broken line87¡80¡70¡0¡ (B // c) (a)(b) FIG. 1. (color online). (a) The top curve shows a zero-fieldsuperconducting transition in sample H1 as a function of tem-perature (top axis). The others show resistive transitions infields parallel to the ab plane at selected temperatures asa function of field (bottom axis). The curves are verticallyshifted for clarity. Hysteresis is visible at T = 0.03 and 0.83K but not at 1.2 K. The two lowest curves were obtained withfive times different field sweep rates. A 50% criterion for thedetermination of B c is explained for the upper T = 0.03 Kcurve. The inset shows the current dependence of the transi-tion curves. (b) Resistive transition curves for selected fieldangles. The hysteresis is visible at θ = 90, 87, and 80 ◦ butnot at 70 ◦ in sample H1. Linear fitting to three data points closestto T c gives the initial slopes of B ′ c = -5.3 and -1.1 T/Kfor B k ab and B k c , respectively, corresponding to α = 2.8 and 0.59. The coherence lengths are calculated tobe ξ ab = 7.2 nm and ξ c = 1.5 nm. The Maki parame-ter α for B k ab is so large that theories developed forsingle-band superconductors would predict a first-ordersuperconducting transition or the FFLO state. Further,the clear flattening at low temperatures of the B c ( T )curve for B k ab indicates a strong paramagnetic limit-ing, and B c (0) = 12.7 T is close to a simple estimate R ( m Ω ) d R / d B ( m Ω / T ) T = 1.1 KBa K Fe As sample H2B // ab0.80 K0.03 K FIG. 2. (color online). (a) Superconducting resistive transi-tions in sample H2 at selected temperatures. The curves arevertically shifted for clarity. Hysteresis is visible at T = 0.03and 0.80 K but not at 1.1 K. The bottom curves are the fieldderivative d R /d B at 0.03 K. B c ( T ) K Fe As sample H1B // abB // cWHH orbital limit12.512.011.5 B c ( T ) K Fe As sample H1B // abWHH fit all temperatures T > 2 K (a)(b) FIG. 3. (color online) (a) Temperature dependence of theupper critical field in sample H1 and (b) enlargement of alow-temperature part for B k ab . Upward and downward tri-angles correspond to up- and down-field data, respectively.The dashed curve for B k ab is a WHH fit in the whole tem-perature range, while the solid one is a fit in a temperaturerange T > B k c is a WHH orbitallimit curve. B c ( T ) θ (degrees)Ba K Fe As field up field down GL (orbital only) GL (orbital + spin)sample H1 sample H2 FIG. 4. (color online) (a) Angle dependence of the upper crit-ical field in samples H1 and H2. Upward and downward trian-gles correspond to up- and down-field data, respectively. Thedashed and solid curves are calculated with the anisotropicGinzburg-Landau theory. The former do not include the para-magnetic effect, while the latter do. of the paramagnetic critical field from T c , B po = 15.1T. A WWH fit to the ab -plane data in the whole tem-perature range gives the dashed line, which deviates up-wards around T = 2 K and then downwards below 1K [Fig. 3(b)]. If we use only data points above 2 K,we obtain an excellent fit down to 2 K as shown by thesolid line. In either fit, B c ( T ) decreases with decreasing T below T ∼ this sug-gests that the superconducting transition becomes firstorder in the low temperature region. Experimentally,the hysteresis is observed below ∼ ∼ T axis, and hence it follows from the Clapeyronequation d B/ d T = −△ S/ △ M that the entropy differ-ence between the superconducting and normal phases atthe phase boundary is nearly zero. It would therefore bevery difficult to see this phase boundary via heat capacitymeasurementsWe also note that the experimental B c (0) of 8.0 Tfor B k c is larger than the orbital critical field B ∗ c (0)= 6.4 T estimated from the initial slope. The solid linedrawn for the c -axis data shows a B c ( T ) curve for theWHH orbital limit without the paramagnetic effect. Theupward deviation of the experimental data indicates theimportance of multi-band effects. Figure 4 shows the angular dependences of B c forsamples H1 and H2. Within the anisotropic Ginzburg-Landau (GL) theory, B ∗ c ( θ ) = B ∗ c ( θ = 0) /δ ( θ )with δ ( θ ) = p cos θ + ǫ sin θ , where ǫ = B ∗ c ( θ =0) /B ∗ c ( θ = 90 ◦ ). Neglecting the paramagnetic effect,namely identifying B ∗ c with B c , these formulas are oftenused to describe the angular dependence of B c . How-ever, they fail in the present cases. The dashed curves -0.3-0.2-0.10.0 M a g n e t i c t o r q u e ( a r b . un i t s ) R ( m Ω ) Ba K Fe As sample H2B // ab1 23-15-10-50 M a g n e t i c t o r q u e ( a r b . un i t s ) R ( m Ω ) Ba K Fe As sample H2 θ = 87¡T = 0.03 K (a)(b) FIG. 5. (color online) (a) Magnetic torque in sample H2 mea-sured at θ = 87 ◦ . The R ( B ) curves at the same angle areshown for comparison. (b) Magnetic torque for B k ab withinexperimental accuracy ( ∼ ◦ ). The solid and dashed curvescorrespond to T = 0.03 and 1.5 K, respectively. Note thatthe vertical scale is roughly two orders-of-magnitudes smallerthan that in (a). The R ( B ) curves at 0.03 K for B k ab areshown for comparison. Kinks appear in the torque curves at0.03 K as indicated by the grey vertical bars attached to thefield-down curve. The kink structures may also be explicableas due to two-step jumps in the torque as illustrated with thefield-up curves. The hysteresis in the torque up to the highestshown field may be ascribed to surface superconductivity (seetext). are drawn using the experimental values of B ∗ c ( θ = 0)and ǫ . They clearly deviate from the experimental data.When the paramagnetic effect is important, the angu-lar dependence of B c is modified: B c ( θ ) = [ B ∗ c ( θ =0) − aB c ( θ )] /δ ( θ ), where a is a parameter describing thestrength of the paramagnetic effect. This gives excellentfits to the experimental data as shown by the solid curves,again confirming the presence of the strong paramagneticeffect. The fitted parameters are [ B ∗ c ( θ = 0), a , ǫ ] =[11.6(4), 0.058(5), 0.17(4)] and [8.5(1), 0.067(2), 0.07(2)]for samples H1 and H2, respectively, with B ∗ c ( θ = 0) and a − in Tesla.Finally, we show magnetic torque data measured ona small piece cut from sample H2. Figure 5(a) shows the torque measured for the field direction θ = 87 ◦ overa wide field range. The U-shaped torque curves witha peak approximately at B c /2 can be explained in theframework of the anisotropic GL theory, albeit the dif-ference between the field-up and -down curves, which isdue to vortex pinning. The field-down curve indicates aweak peak effect in a field range ∼ R ( B ) curve measured at the same angle.The present torque curves bear a general resemblance tothose reported for MgB . Figure 5(b) shows the torque curves for B k ab withinexperimental accuracy ( ∼ . ◦ ) measured at T = 0.03 K(solid) and 1.52 K (dashed). The R ( B ) curve at T = 0.03K for B k ab is also shown for comparison. The torquecurves at T = 0.03 K show kinks in the field region of theresistive transition as indicated by grey vertical bars forthe field-down curve, and they approximately correspondto the onset of the resistive hysteresis, a kink in the R ( B )curve, and the end of the hysteresis. The kink structuresmay also be interpreted as due to two successive jumpsin the torque as illustrated for the field-up curves. Thekink structures are not seen in the torque curves at T =1.52 K, where the resistive transition is not hysteretic.One might think that the observed jumps were too bluntfor a first-order transition. However, we note that mag-netic torque measurements measure the component of themagnetization that is perpendicular to the field. Magne-tization jumps along the field direction could be muchlarger. Indeed, it has been reported that the ab -planemagnetization for B k ab in KFe As exhibits an abruptincrease at B c at low temperatures. The field-up and -down curves at T = 0.03 K do notmerge in the shown field region, and the resistance curvesare concave up to the highest shown field. These may beascribed to surface superconductivity, which can persistup to B c ∼ . B c . Although it is difficult to preciselydetermine B c in this sample because of drift in the mea-surement equipment (compare the two field-up curves 1and 3), the torque did not show clear irreversibility be-yond the drift when the field sweep direction was reversedat 17 T from up (curve 1) to down (curve 2). The surfacesuperconductivity was previously reported for MgB , for example.The magnetic torque for field directions close to B k c exhibits de Haas-van Alphen (dHvA) oscillations forfields above ∼
16 T, confirming the good quality of thesample. Using the observed dHvA frequency of F ≈ l > ∼
50 nm, which is much longer than ξ ab indicating thatthe sample is in the clean limit.Theoretically, the superconducting transition in simpleparamagnetically limited superconductors becomes firstorder below 0.56 T c . Since the first order region wouldshrink in realistic cases with the orbital effect, the presentnarrow hysteretic region (
T < ∼ . T c ) does not conflictwith the theoretical prediction. Because the Maki param-eter α for B k c is less than one, the paramagnetic effectbecomes less important as the field is tilted from the ab plane, which explains the disappearance of the hysteresisfor θ < ◦ . We also consider the FFLO states, since thesamples are in the clean limit. An early theoretical studypredicted a possible occurrence of the FFLO state for α > . The maximum temperature of the FFLO re-gion was estimated to be 0.55 T c for α = ∞ but was shownto decrease with decreasing α . With this model, thetransition from the mixed state to the FFLO state wasfound first order, while that from the FFLO to the nor-mal state second order. However, recent theories predictmore complicated phase diagrams, in most cases witha first-order transition line in some parts of them, and whether the FFLO-to-normal transition is first or secondorder depends on parameters of models considered. Thus, the present observation of the resistive hysteresisdoes not contradict possibility of the FFLO state.
IV. SUMMARY
The temperature and field angle dependences of B c in Ba . K . Fe As indicate a strong paramagnetic ef-fect for B k ab , and the observed resistive hysteresis canbe attributed to a first-order superconducting transition.The features observed in the magnetic torque data maybe regarded as a sign of magnetization jumps. For example, see M. Decroux and Ø. Fischer, in
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Supplemental material: First-order superconducting resistive transition inBa . K . Fe As Taichi Terashima,
1, 2
Kunihiro Kihou,
2, 3
Megumi Tomita, Satoshi Tsuchiya, Naoki Kikugawa, Shigeyuki Ishida,
2, 3
Chul-Ho Lee,
2, 3
Akira Iyo,
2, 3
Hiroshi Eisaki,
2, 3 and Shinya Uji
1, 2 National Institute for Materials Science, Tsukuba, Ibaraki 305-0003, Japan JST, Transformative Research Project on Iron Pnictides (TRIP), Chiyoda, Tokyo 102-0075, Japan National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan (Dated: June 23, 2018)
PACS numbers: 74.70.Xa, 74.25.Dw, 74.25.Op A m p li t u d e ( a r b . un i t s ) α Ba K Fe As sample H2 O s c ill a t o r y p a r t o f t o r q u e θ = 10¡T = 0.03 K(c) FIG. S 1. Fourier transform of dHvA torque oscillations at θ = 10 ◦ with background subtracted (inset). The magnetic torque for field directions close to B k c exhibits de Haas-van Alphen (dHvA) oscillations. Theinset of Fig. 1 shows the oscillatory part of the torquefor θ = 10 ◦ . The Fourier transform (main panel) shows a clear peak at about F = 2000 T, which corresponds to the α frequency observed in KFe As [1]. (The inset suggeststhe existence of another much lower frequency F ∼
200 T,but it is not resolved by Fourier transformation becauseof the too narrow field range.) The observation of thedHvA oscillations indicates that the Landau level spac-ing ¯ hω c is comparable to the Landau level broadening Γ= ¯ h/ τ due to impurity/defect scattering at these fields( B ∼
16 T). Using the observed dHvA frequency, we canestimate the carrier mean free path to be l = τ v F > ∼ ξ ab indicating that thesample is in the clean limit. [1] T. Terashima, M. Kimata, N. Kurita, H. Satsukawa,A. Harada, K. Hazama, M. Imai, A. Sato, K. Ki-hou, C. H. Lee, H. Kito, H. Eisaki, A. Iyo, T. Saito,H. Fukazawa, Y. Kohori, H. Harima, and S. Uji,J. Phys. Soc. Jpn.79