Impact of Disorder on the Superconducting Phase Diagram in BaFe_2(As_{1-x}P_x)_2
Yuta Mizukami, Marcin Konczykowski, Kohei Matsuura, Tatsuya Watashige, Shigeru Kasahara, Yuji Matsuda, Takasada Shibauchi
aa r X i v : . [ c ond - m a t . s up r- c on ] J u l Journal of the Physical Society of Japan
LETTERS
Impact of Disorder on the Superconducting Phase Diagram in BaFe (As − x P x ) Yuta Mizukami ∗ , Marcin Konczykowski , Kohei Matsuura , Tatsuya Watashige , Shigeru Kasahara ,Yuji Matsuda , Takasada Shibauchi Department of Advanced Materials Science, University of Tokyo, Kashiwa, Chiba 277-8561, Japan Laboratoire des Solides Irradi´es, ´Ecole Polytechnique, CNRS, CEA, Universit´e Paris-Saclay, F-91128 Palaiseau,France Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan
In many classes of unconventional superconductors, the question of whether the superconductivity is enhanced bythe quantum-critical fluctuations on the verge of an ordered phase remains elusive. One of the most direct ways ofaddressing this issue is to investigate how the superconducting dome traces a shift of the ordered phase. Here, we studyhow the phase diagram of the iron-based superconductor BaFe (As − x P x ) changes with disorder via electron irradiation,which keeps the carrier concentrations intact. With increasing disorder, we find that the magneto-structural transition issuppressed, indicating that the critical concentration is shifted to the lower side. Although the superconducting transitiontemperature T c is depressed at high concentrations ( x & x . This implies thatthe superconducting dome tracks the shift of the antiferromagnetic phase, supporting the view of the crucial role playedby quantum-critical fluctuations in enhancing superconductivity in this iron-based high- T c family. In strongly correlated electron systems such as heavyfermions, cuprates, and organic materials, superconductivityoften emerges when the antiferromagnetic (AFM) order issuppressed through control parameters such as pressure andchemical composition.
1, 2)
A striking feature in these materi-als is that, in several cases, physical properties that deviatefrom the conventional Fermi-liquid theory (i.e., non-Fermiliquid properties) also appear when the AFM transition istuned to zero temperature ( T ), suggesting the existence ofan AFM quantum critical point (QCP). Although it is widelybelieved that quantum-critical fluctuations originating fromthe QCP are closely related to the superconductivity throughunconventional pairing mechanisms,
3, 4) it remains unclearwhether the QCP actually exists inside the superconductingdome. The recently discovered iron pnictides also exhibitsuperconductivity in the vicinity of AFM order accompany-ing tetragonal-to-orthorhombic structural transitions. Thesemagneto-structural transitions can be suppressed by pressureor chemical substitution, but the quantum criticality is oftenavoided by a first-order transition in several systems. Amongthe iron pnictides, Phosphorus(P)-substituted BaFe As is aparticularly clean system, and moreover, is unique in the factthat there is growing evidence for the existence of a QCPinside the superconducting dome near the optimal composi-tion. Although a QCP located at the maximum T c natu-rally leads to the consideration that the quantum-critical fluc-tuations help to enhance superconductivity, there has been nodirect evidence against a scenario that it is just a coincidence.A direct test to address this issue is to investigate how thesuperconducting dome traces when the AFM phase is shifted.However, it has been quite challenging to perform such exper-iments without changing the carrier numbers or bandwidth,whose e ff ects on the QCP and superconductivity are nontriv-ial. In fact, in heavy-fermion superconductors, it was high-lighted that chemical substitution of dopant atoms may pre-vent the appearance of quantum criticality altogether. ∗ [email protected] Recent advances in the study of the e ff ects of atomic-scalepoint defects in superconductors using high-energy electronbeams allows us to investigate the evolution of the electronicstates with increasing impurity scattering in a controlled man-ner. Through the use of successive electron irradiation, we canperform systematic measurements on a given sample with agradual introduction of impurity scattering induced by pointdefects, and without changing the carrier concentration orband width.
15, 16)
In general, impurity scattering reduces the T c in unconventional superconductors, where the suppres-sion rate depends on the gap structures. Indeed, the super-conducting dome shrinks with the introduction of scatteringvia chemical substitution in cuprates and heavy-fermion su-perconductors.
18, 19)
Here, we report on the changes of themagneto-structural transition temperature ( T N ) and supercon-ducting transition temperature ( T c ) in the T -dependence ofresistivity ρ ( T ) with increasing defect density across the en-tire superconducting dome of BaFe (As − x P x ) , revealing amonotonic decrease of T N and highly composition-dependentchanges of T c . In particular, the superconductivity initiallyexhibits an unusual enhancement at low P concentrationswith increasing disorder. After irradiation, the superconduct-ing dome exhibits a shift of the optimal composition toward alower P concentration. This implies that the superconductingdome tracks the AFM phase, supporting the suggested crucialrole of quantum-critical fluctuations on the superconductivityin these high- T c superconducting materials.Single crystals of BaFe (As − x P x ) were synthesized by theself-flux method. The quality of the single crystals was con-firmed by their sharp superconducting transitions and quan-tum oscillation measurements. In order to introduce uni-form point defects into the BaFe (As − x P x ) single crystals,we irradiated the sample with an electron beam with an in-cident energy of 2.5 MeV, which is far above the thresh-old energy required for the formation of vacancy-interstitial(Frenkel) pairs. The sample was kept at 20 K to preventdefect migration and clustering e ff ects during the irradiation.
1. Phys. Soc. Jpn.
LETTERS ρ ( µ Ω c m ) T (K) x=0.05 pristine 0.48 C/cm ρ ( µ Ω c m ) T (K) x=0.16 pristine 1.5 C/cm ρ ( µ Ω c m ) T (K) x=0.28 pristine 1.7 C/cm ρ ( µ Ω c m ) T (K) x=0.29 pristine 1.2 C/cm ρ ( µ Ω c m ) T (K) x=0.3 pristine 1.1 C/cm ρ ( µ Ω c m ) T (K) x=0.45 pristine 0.7 C/cm ρ ( µ Ω c m ) T (K) x=0.24 pristine 0.8 C/cm ρ ( µ Ω c m ) T (K) x = 0 pristine 0.3 C/cm ρ - ρ ( T c ) ( a . u . ) ρ - ρ ( T c ) ( a . u . ) T T cN (a) (b) (c) (d)(e) (f) (g) (h) Fig. 1. (Color online) (a)–(h) The ρ ( T ) at di ff erent irradiation levels for x =
0, 0.05, 0.16, 0.24, 0.28, 0.29, 0.3, and 0.45, respectively. The di ff erent colorsrepresent di ff erent irradiation levels. The blue (red) arrow represents T N ( T c ). The inset in (c) and (d) shows ρ ( T ) which has been shifted vertically for clarity. In order to evaluate the change in ρ ( T ) with irradiation ac-curately, we repeated the process of ρ ( T ) measurement andirradiation on the same crystal without removing the elec-trodes for each composition. During the irradiation process, ρ ( T ) was monitored to confirm the increase of ρ ( T ) inducedby defects.In Figure 1(a)–(h), ρ ( T ) curves are shown at several irradia-tion levels for x =
0, 0.05, 0.16, 0.24, 0.28, 0.29, 0.3, and 0.45,respectively. For the x = T N which correspond to 130 K (Figure 1(a)) and 122K (Figure 1(b)) in pristine samples, respectively. Irradiatingthe sample with electrons causes the observed kinks to splitinto an upturn and subsequent downturn upon cooling, whichis similar to the doping dependence of ρ ( T ) in BaFe As .
9, 20)
The T N of each composition is monotonically suppressed withincreasing irradiation. Above T N , ρ ( T ) shows an almost paral-lel shift with irradiation that is caused by T -independent im-purity scattering, indicating the non-magnetic nature of thepoint defects. On the other hand, below T N , the change in ρ ( T )exhibits some T -dependent term whose magnitude becomeslarger upon cooling. Such T -dependent impurity scatteringwas also observed with increasing irradiation in the previous α -particle irradiation experiment on iron-based superconduc-tor NdFeAs(O,F), and can be understood with the assump-tion that the magnetic moments of the defects induce Kondo-like scattering, similar to the case of heavy-fermion materials.Although no discernible magnetic moment was observed af-ter irradiation in the paramagnetic state down to 0.1 K in oursystem, this observation indicates that non-magnetic holescreated in the AFM networks induce a T -dependent scatter-ing process that deserves further investigation to elucidate itsorigin. For x = ρ ( T )exhibits a reduction at low temperatures due to the onset of su-perconductivity. Here, T c is defined as the temperature where ρ ( T ) starts to drop from the extrapolated linear curve, as in-dicated in Figure 1(c). Upon the introduction of disorder, weobserve a remarkable feature at several initial stages of irradi-ation: T c gradually increases by ≈ ≈ / cm . Although ρ ( T ) does not reachzero for x = T c can be clearly seenfor both x = x = ρ ( T ) is shifted verti-cally to compare the T c at di ff erent impurity levels, as shownin the inset of Figure 1(c) and (d). For x = T N decreases with increasing irradiation andeven disappears above ≈ / cm for x = x = x = T N is evident, and we observethe monotonic suppression of T c with increasing irradiationdosage.Figure 2(a) shows the T -dependence of the Hall coe ffi cient R H ( T ) for x =
0, 0.24, 0.29, and 0.30 at several irradiation lev-els. In the AFM state, the value of R H ( T ) after electron irradi-ation exhibits a slight change for x = T -dependent scattering process, asin the case for ρ ( T ). Here, it should be noted that in the para-magnetic state, the change of R H ( T ) with irradiation is almostnegligible compared to the reported change induced by chem-ical substitution.
9, 22, 23)
This result indicates that electron irra-diation does not essentially change the carrier concentration,and mainly introduces impurity scattering. In Figure 2(b)–(d),the T -derivative of the resistivity, d ρ / d T ( T ), is shown for thesamples near the optimal compositions x = ff erent irradiation levels. The presented data was ob-tained by di ff erentiating the ρ ( T ) data shown in Figures 1(e)–(g). For the x = ρ / d T ( T ) exhibits asharp dip due to magneto-structural transitions but otherwiseremains constant at high temperatures. For x = ρ / d T ( T )
2. Phys. Soc. Jpn.
LETTERS (a) (b)(c) (d) -2.0-1.5-1.0-0.500.51.0 d ρ / d T ( µ Ω c m / K ) T (K) x=0.3 pristine 1.1 C/cm -2.0-1.5-1.0-0.500.51.0 d ρ / d T ( µ Ω c m / K ) T (K) x=0.29 pristine 1.2 C/cm -2.0-1.5-1.0-0.500.51.0 d ρ / d T ( µ Ω c m / K ) T (K) x=0.28 pristine 1.7 C/cm - R H ( - c m / C ) T (K) x = 0 (0, 4.7, 8.6 C/cm ) x = 0.29 (0, 3.0 C/cm ) x = 0.3 (0, 1, 4.5 C/cm ) x = 0.24 (0, 1.6, 4.7 C/cm ) T N Fig. 2. (Color online) (a) Change of R H ( T ) with increasing irradiation for x = ff erent colors represent the di ff erent irradiationlevels. The blue arrow marks the position of T N where the Hall coe ffi cientsexperience a jump due to magneto-structural transitions. (b)–(d) Change ofd ρ / d T ( T ) with irradiation for x = ff erentiating the ρ ( T ) data presented in Figures 1(e)–(g). is constant across a wide T range (reflecting the T -linear de-pendence of ρ ( T )), and is not a ff ected by the irradiation level.This result demonstrates that electron irradiation does not in-duce T -dependent inelastic scattering, which is in sharp con-trast to carrier-doped systems in iron-based superconductorswhere the change of T c is concomitant with the drastic evolu-tion of ρ ( T ). Thus, the change of T N and T c with irradiation isnot due to a change in carrier number or electron correlations,but is mainly due to an increase in impurity scattering.To see the changes in T N and T c caused by irradiation inentire compositions, the dependence of T N and T c on the ir-radiation level is shown in Figure 3. In Figure 3(a) (3(b)), thechange of T N ( T c ) from its pristine value T N ( T c ), ∆ T N = T N − T N ( ∆ T c = T c − T c ), is normalized by T N ( T c ). Al-though T N is reduced by electron irradiation in all composi-tions, the change of T c with the irradiation dose displays largecomposition dependence. For low P concentrations, x = T c is initially increasedand then further levels of irradiation tend to suppress the su-perconductivity. On the other hand, T c is monotonically re-duced following irradiation for all other compositions, wherethe magnitude of suppression is larger for higher P concen-trations. Figure 3(c) shows the change of T c with irradiationdose for compositions near the optimal composition, x = T c is attainedfor x = T c forall three compositions. For increased irradiation dose levels,the T c of x = x = / cm , which can be seen by the crossing ofthe two curves. Moreover, the T c for the x = x = / cm .These results originate from the fact that the suppression rateof superconductivity becomes gradually larger in cases with T c ( K ) dose (C/cm ) x = 0.3 0.290.28 -0.4-0.200.2 ∆ T c / T c dose (C/cm ) x = 0.16 x = 0.24 x = 0.28 x = 0.29 x = 0.30 x = 0.45 -0.3-0.2-0.10 ∆ T N / T N dose (C/cm ) x = 0.16 x = 0.28 x = 0 x = 0.24 x = 0.05 (a) (b) (c) Fig. 3. (Color online) (a) Change of T N from its initial value in a pristinesample T N , and normalized by T N for x =
0, 0.05, 0.16, 0.24, and 0.28. (b)Change of T c from the pristine sample’s value T c , and normalized by T c for x = T c closeto the optimal composition, x = T c for the x = T c in the paramagnetic(AFM) state for each composition. high P concentrations, as seen in Figure 3(b).In Figure 4(a), we illustrate the phase diagram obtainedfrom the dose dependence of T N and T c in Figure 3. In thephase diagram of the pristine sample, the optimal P concen-tration coincides with the extrapolated end point of the AFMphase, where the AFM QCP is considered to be located. Here we make the phase diagram for the 2.0 C / cm case byinterpolating the data points linearly in the dose dependenceof T N and T c . The monotonic decrease of T N for each compo-sition leads to a shift of the AFM phase. On the other hand, ifwe look at the change in T c , it displays a strong variation inthe magnitude of the suppression, as we mentioned when dis-cussing Figure 3(b). T c is increased for low P concentrations,but largely suppressed at high P concentration, as shown bythe T c curve for 2.0 C / cm in Figure 4(a). It is worth notingthat there is a clear shift of the optimal composition toward alower P concentration when we consider the 2.5 C / cm phasediagram, as shown in Figure 4(b).Recently, the e ff ect of point defects on T c on the en-tire superconducting dome has been reported in hole-dopedBa − x K x Fe As . Although the suppression of superconduc-tivity in this system is minimal at optimal doping, and in-creases away from the optimal doping level, T c is monotoni-cally reduced at all doping levels for an increasing number ofdefects. This can be understood in terms of the suppressionof superconductivity, which is governed by the magnitude ofthe gap anisotropy. In the BaFe (As − x P x ) case, however, thechange of the phase diagram on irradiation is qualitatively dif-ferent. Here, the superconductivity is enhanced at low P con-centrations. Although an increase of T c due to the introduc-tion of scattering was experimentally reported in Zn-dopedLaFeAs(O − x F x ), it is not obvious whether Zn substitutionintroduces only impurity scattering, or whether it involves ad-ditional e ff ects such as carrier doping and changes in the lat-tice parameters. More recently, electron-irradiated FeSe ex-hibited a slight increase of T c ≈ However, the e ff ectof irradiation in FeSe with very small Fermi energies is notwell understood, and further investigation is needed to con-firm the e ff ect of impurity scattering. Therefore, our result is
3. Phys. Soc. Jpn.
LETTERS T ( K ) x T N T c C/cm C/cm C/cm C/cm T ( K ) x x max (0 C/cm ) x max (2.5 C/cm ) T N T c (a) (b) Fig. 4. (Color online) (a) The entire phase diagram for 0 and 2.0 C / cm .The open (filled) squares and circles represent T N and T c for 0 (2.0) C / cm ,respectively. The value of T c for the x = / cm and 2.5 C / cm .The open (filled) squares and circles represent T N and T c for 0 (2.5) C / cm ,respectively. The arrows indicate the compositions where T c is maximum( x max ) for each irradiation level. the first clear observation of a significant increase in T c merelyby impurity scattering.Indeed, it was already pointed out theoretically that the su-perconductivity may be enhanced in the AFM regime with theintroduction of disorder based on a spin-fluctuation-mediatedpairing, if there is competition between the AFM orderingand superconductivity.
28, 29)
When the enhancement of T c dueto the suppression of AFM order surpasses the reduction of T c purely from impurity scattering, T c may be increased asa result of the competing e ff ects. In this scenario, it is ex-pected that the suppression of T c is largely enhanced whenthe AFM order is absent. However, we do not observe anysignificant di ff erence in the suppression rate of T c between x = x = T N disappears rapidly for x = ff ect of impurityscattering on superconductivity remains, and causes the su-perconducting dome to shrink. In addition to this e ff ect, ifwe assume that the entire superconducting dome shifts to-ward a lower P composition, then we can naturally explainthe change of T c for the entire phase diagram. It should benoted here that the monotonic decrease of T N naturally leadsto the fact that the QCP may also shift its location toward alower P concentration. Indeed, this is implied by the constantd ρ / d T , reflecting the fact that the T -linear dependence in ρ ( T )is extended toward lower temperatures with irradiation for x = ρ / d T value is universal between x = T -dependence of ρ ( T ) in the x = x = T c superconductors. Such a change of the phase diagram has notbeen observed in cuprates, which may be related to the factthat the pseudogap temperature does not change significantlywith disorder. Acknowledgment
We thank H. Kontani, V. Mishra, and R. Prozorov forfruitful discussions. We also thank B. Boizot, O. Cavani, J. Losco, and V.Metayer for technical assistance. This work was supported by the Grants-in-Aid for Scientific Research (KAKENHI) program from the Japan Societyfor the Promotion of Science (JSPS), and by the “Topological Quantum Phe-nomena” (No. 25103713) Grant-in Aid for Scientific Research on InnovativeAreas from the Ministry of Education, Culture, Sports, Science, and Tech-nology (MEXT) of Japan. The irradiation experiments were supported by theEMIR network, proposal no. 11-10-8071 and no. 15-1580.1) T. Park, F. Ronning, H. Q. Yuan, M. B. Salamon, R. Movshovich,J. L. Sarrao, and J. D. Thompson, Nature , 65 (2006).2) B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen,Nature , 179 (2015).3) P. Gegenwart, Q. Si, and F. Steglich, Nature Phys. , 186 (2008).4) D. M. Broun, Nature Phys. , 170 (2008).5) H. Hosono, and K. Kuroki, Physica C , 399 (2015).6) P. Dai, Rev. Mod. Phys. , 855 (2015).7) J. Paglione, and R. L. Greene, Nature Phys. , 645 (2010).8) T. Shibauchi, A. Carrington, and Y. Matsuda, Annu. Rev. Condens. Mat-ter Phys. , 113 (2014).9) 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 , 184519 (2010).10) Y. Nakai, T. Iye, S. Kitagawa, K. Ishida, H. Ikeda, S. Kasahara,H. Shishido, T. Shibauchi, Y. Matsuda, and T. Terashima, Phys. Rev.Lett. , 107003 (2010).11) 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. Mat-suda, T. Shibauchi, and A. Carrington, Phys. Rev. Lett. , 057008(2010).12) K. Hashimoto, K. Cho, T. Shibauchi, S. Kasahara, Y. Mizukami, R. Kat-sumata, Y. Tsuruhara, T. Terashima, H. Ikeda, M. A. Tanatar, H. Kitano,N. Salovich, R. W. Giannetta, P. Walmsley, A. Carrington, R. Prozorov,and Y. Matsuda, Science , 1554 (2012).13) P. Walmsley, C. Putzke, L. Malone, I. Guillam´on, D. Vignolles,C. Proust, S. Badoux, A. I. Coldea, M. D. Watson, S. Kasahara,Y. Mizukami, T. Shibauchi, Y. Matsuda, and A. Carrington, Phys. Rev.Lett. , 257002 (2013).14) S. Seo, X. Lu, J-X. Zhu, R. R. Urbano, N. Curro, E. D. Bauer,V. A. Sidorov, L. D. Pham, T. Park, Z. Fisk, and J. D. Thompson, NaturePhys. , 120 (2013).15) R. Prozorov, M. Konczykowski, M. A. Tanatar, A. Thaler, S. L. Bud’ko,P. C. Canfield, V. Mishra, and P. J. Hirschfeld, Phys. Rev. X , 041032(2014).16) Y. Mizukami, M. Konczykowski, Y. Kawamoto, S. Kurata, S. Kasa-hara, K. Hashimoto, V. Mishra, A. Kreisel, Y. Wang, P. J. Hirschfeld,Y. Matsuda, and T. Shibauchi, Nat. Commun. , 5657 (2014).17) A. V. Balatsky, I. Vekhter, and J.-X. Zhu, Rev. Mod. Phys. , 373(2006).18) H. Alloul, J. Bobro ff , M. Gabay and P. J. Hirschfeld, Rev. Mod. Phys. , 45 (2009).19) S. Seo, E. Park, E. D. Bauer, F. Ronning, J. N. Kim, J.-H. Shim,J. D. Thompson, and T. Park, Nat. Commun. , 6433 (2015).20) N. Ni, M. E. Tillman, J-Q. Yan, A. Kracher, S. T. Hannahs,S. L. Bud’ko, and P. C. Canfield, Phys. Rev. B , 214515 (2008).21) C. Tarantini, M. Putti, A. Gurevich, Y. Shen, R. K. Singh, J. M. Rowell,N. Newman, D. C. Larbalestier, P. Cheng, Y. Jia, and H. H. Wen, Phys.Rev. Lett. , 087002 (2010).22) L. Fang, H. Luo, P. Cheng, Z. Wang, Y. Jia, G. Mu, B. Shen, I. I. Mazin,L. Shan, C. Ren, and H-H. Wen, Phys. Rev. B , 140508(R) (2009).23) B. Shen, H. Yang, Z-S. Wang, F. Han, B. Zeng, L. Shan, C. Ren, andH-H. Wen, Phys. Rev. B , 184512 (2011).24) K. Cho, M. Konczykowski, S. Teknowijoyo, M. A. Tanatar, Y. Liu,T. A. Lograsso, W. E. Straszheim, V. Mishra, S. Maiti, P. J. Hirschfeld,4. Phys. Soc. Jpn. LETTERS and R. Prozorov, Sci. Adv. , e1600807 (2016).25) Y. Li, J. Tong, Q. Tao, C. Feng, G. Cao, W. Chen, F. Zhang, and Z. Xu,New J. Phys. , 083008 (2010).26) S. Teknowijoyo, K. Cho, M. A. Tanatar, J. Gonzales, A. E. B¨ohmer,O. Cavani, V. Mishra, P. J. Hirschfeld, S. L. Bud’ko, P. C. Canfield, andR. Prozorov, Phys. Rev. B , 064521 (2016).27) S. Kasahara, T. Watashige, T. Hanaguri, Y. Kohsaka, T. Yamashita, Y. Shimoyama, Y. Mizukami, R. Endo, H. Ikeda, K. Aoyama,T. Terashima, S. Uji, T. Wolf, H. v. L¨ohneysen, T. Shibauchi, andY. Matsuda, Proc. Natl. Acad. Sci. USA , 16309 (2014).28) R. M. Fernandes, M. G. Vavilov, and A. V. Chubukov, Phys. Rev. B ,140512 (2012).29) V. Mishra, Phys. Rev. B91