Effects of In-Plane Impurity Substitution in Sr2ruo4

arXiv:cond-mat/0210190v1 [cond-mat.str-el] 9 Oct 2002 opud n high- and compounds smgei muiisata togpi raesand temperature breakers transition pair strong the as suppress act severely impurities magnetic as nteeegneo h novninlsuperconduc- unconventional with the of tivity. emergence the in teto ntels w eae,snehgl correlated highly since decades, f two last the in attention ovninlsprodciiy h upeso of suppression The superconductivity. conventional sdt banifraino h neligstrongly underlying both the in states on electronic been information correlated also obtain have to substitution used impurity of studies tematic break- symmetry translational ing to sensitivity the reflects pntiltpairing. spin-triplet oko us-w-iesoa em liquid Fermi quasi-two-dimensional a of work Sr ductivity systems. ecnutvt:rpdsprsinof suppression su- rapid unconventional the perconductivity: reflecting features several vealed onigoye lya seta oei h physical the in role Sr essential of an properties play oxygen rounding aee eosierteaeSr ruthenate perovskite layered em ufc ossigo he eryclnrclsheets cylindrical ( nearly three of consisting surface Fermi lcrn rgntn rmteRu the from originating electrons culation pncngrto)hbiie with hybridized configuration) spin uiisaddefects and purities eiuldniyo ttsi h uecnutn state measurements superconducting heat the specific in in states seen of density residual a o ay eas h muiiswr nrdcdac- introduced were impurities the crystals because easy, the not within was concentration impurity the of control surements. α and - 2 novninlsprodcossc shayfermion heavy as such superconductors Unconventional ee esuyteeet fsc usiuini the in substitution such of effects the study we Here, al tde fteiprt ffcsi Sr in effects impurity the of studies Early , 2) RuO β s n sacaatrsi faiorpcpiig Sys- pairing. anisotropic of characteristic a is and and 1) wv ymty omgei muiisa well as impurities nonmagnetic symmetry, -wave d 4 10) 5) eetosi hs aeil lyesnilroles essential play materials these in -electrons 6) ncnrs ocnetoa superconductivity conventional to contrast In r ecie uniaieywti h frame- the within quantitatively described are γ 13) EWRS Sr KEYWORDS: ). niae htsrn orltosaogthe among correlations strong that indicates sucnetoa,ms rbbyinvolving probably most unconventional, is 9) ugssta ohnnantcadmgei muiisi S in impurities u magnetic with and agreement nonmagnetic quantitative both in that is suggests resistivity residual of ctees iia otennantcZn nonmagnetic the to similar scatterers, o Ru for estvt otasainlsmer raigi Sr in breaking symmetry app translational of concentration to a sensitivity at completely superconductivity the 3 colo hsc n srnm,Uiest fS.Andrews, St. of University Astronomy, and Physics of School erpr oprtv usiuineet of effects substitution comparative report We hogotteaoesre fstudies, of series above the Throughout 2 oprsnwt h adsrcuecal- band-structure the with Comparison RuO 4+ Naoki 7) 11) 4 ntesi-rpe uecnutrSr superconductor spin-triplet the in T ffcso nPaeIprt usiuini Sr in Substitution Impurity In-Plane of Effects . c n ag nacmn fthe of enhancement large a and h omlsaepoete of properties state normal The 2 urtshv trce much attracted have cuprates RuO Kikugawa 4 nentoa noainCne,KooUiest,Kyoto University, Kyoto Center, Innovation International 4 1 muiyeet,uiaiyscattering unitarity effects, impurity , etr uiesLbrtr,KooUiest,Koo606- Kyoto University, Kyoto Laboratory, Business Venture 2 2 RuO eateto hsc,KooUiest,Koo606-8502 Kyoto University, Kyoto Physics, of Department 4+ f 12) os(4 ions - 4 p ,4) 3, 1 hs supercon- whose , eetoso sur- of -electrons , T 2 n M mea- NMR and nrwPeter Andrew , c and yntv im- native by d 4 Rcie oebr1,2018) 18, November (Received 8) 2 ntelow the in d T RuO -electron ihthe with c fun- of 4 2+ re- T muiyi h high- the in impurity c 2 Mackenzie nonmagnetic 1 RuO iino the of sition pncngrto)soswa ermgeimat ferromagnetism weak shows configuration) spin h w-iesoa niermgei pnfluctuations at spin antiferromagnetic two-dimensional the eprtr eedneadlgrtmctemperature logarithmic respectively. linear- dependence, and showing data dependence heat specific temperature the and resistivity the aevector wave eigwith dering oe ttcsi est ae(D)by substitution. (SDW) wave Ti density spin static a comes eairse ntepr Sr pure the in seen behavior ueSr pure hc h usiuinis substitution the which et eeta nomnuaeBagpeak Bragg incommensurate an detect ments 9%, to increased ther µ uto ln h npaedrcin When direction. in-plane the along duction ac- minimal and with contamination cidental crystals conditions, quality high growth obtain the ef- constantly optimize considerable After to fort growth. crystal during cidentally st mako ytmtcsuyo h ffcso con- of Ir effects magnetic the Ru of of study substitution systematic trolled a on embark to us iha ayai ln the along axis easy an with ≥ ris eety erpre httesbttto of substitution the that prop- reported magnetic the we nonmagnetic on Recently, doping level review erties. higher to of useful effects therefore is the it superconductivity, Ti of the concentrations on low very scat- of the ions effects describing tering nonmagnetic Before even effects. with magnetic subtle, introducing be can systems tron antcodrn ihgas eairapasfor appears behavior glassy with ordering magnetic moment effective the with moment local a B nteohrhn,tesse Sr system the hand, other the On h ffc fiprt usiuinit orltdelec- correlated into substitution impurity of effect The 4 2 Q .%i Sr in 2.5% /Ti. efudta ohiprte suppress impurities both that found We . RuO ic rsn rmtensigmil nthe in mainly nesting the from arising 15) 2 4 iaiylmtsatrn.Orresult Our scattering. nitarity-limit oiaey01% eetn h high the reflecting 0.15%, roximately RuO nadto,arpdenhancement rapid a addition, In . t nrw,Ff Y69S Scotland 9SS, KY16 Fife Andrews, St. 3 Ti n Yoshiteru and 4+ h nue oethsIiganisotropy Ising has moment induced The 4+ x r Q 2 4 inelastic 2 muiyTi impurity RuO . T Ru ions. ≥ ic and 17) c cuprates. ∼ .% eito rmteFermi-liquid the from deviation 2.5%, 1 − 4 magnetic ntevcnt ftemgei or- magnetic the of vicinity the In x (2 606-8501 c ssrn potential strong as act Ti elastic π yee sn JPSJ.sty using typeset 8501 x eto cteigpa enin seen peak scattering neutron 3 2 /3, O 4+ 18) magnetic Maeno 4+ 4 2 RuO T hl epn ealccon- metallic keeping while ihnnantcTi nonmagnetic with eto cteigmeasure- scattering neutron Ir π c hs eut niaethat indicate results These (3 c 4+ 3 )i ls otepo- the to close is 0) /3, > 2 d ieto.Furthermore, direction. RuO 0 . .Ti a allowed had This K. 1.4 impurities 2 nSr in ) 4 , 4 Ir 4 4+ sosre with observed is 2 14) Ru 2 (5 RuO nonmagnetic d 1 ecnnow can we x 5 4+ − < β T)i fur- is (Ti) p ntelow the in x 16) 4 ver.1.0b eff Ir adbe- band n Ir and induces x 4+ O whose ∼ x x 4 (Ti) and (Ir) 0.5 4+ in > 2 Naoki Kikugawa, Andrew Peter Mackenzie and Yoshiteru Maeno

≥ 30% occurring concomitantly with metal-insulator amount of x. The Tc is rapidly and systematically sup- 19) transition and the end-member material Sr2IrO4 is pressed in both cases. The result reflects the high sensi- a Mott insulator with canted antiferromagnetic order- tivity to translational symmetry breaking, characteristic ing.20) Thus, substitution of high levels of Ti4+ and Ir4+ of unconventional superconductivity. The inset shows impurities in Sr2RuO4 leads to different magnetic ground the dependence of Tc on the impurity concentration x. states, presumably reflecting the different magnetic char- We can see an almost universal suppression of Tc, irre- acter of the isolated ions. spective of the kind of impurity. The broken line shows In this letter, we show that both nonmagnetic Ti4+ the universal Abrikosov-Gor’kov pair-breaking function, and magnetic Ir4+ impurities suppress the superconduc- where the formulation is generalized to the case of non- tivity of Sr2RuO4 completely by a concentration of ∼ magnetic and magnetic impurities in an unconventional 21) 0.15%. Also, both impurities act as strong potential scat- superconductor. Based on this model, Tc(x) satisfies terers with the maximum phase shift δ ∼ π/2 (unitar- 0 T 1 1 ¯hΓ ity limit), as seen in high-T cuprates with nonmagnetic ln c = Ψ − Ψ + . c T 2 2 2πk T Zn2+ (3d10) impurity. c0 B c A series of single crystals of Sr2Ru1−xTixO4 and Here Ψ is the digamma function, ¯h the Dirac constant − 1 2x 2 Sr2Ru1 xIrxO4 with x up to 3% were grown by a and the scattering rate Γ = = sin δ0 +AS(S + floating-zone method with an infrared image furnace 2τ π¯hN0 1); the first and second terms in Γ represent the potential (NEC Machinery, model SC-E15HD). The detailed pro- and magnetic spin-flip scattering contributions, respec- cedure of the crystal growth is described elsewhere.14, 15) tively, where N is the density of states in the normal We only note here that an excess of 0.15 molar Ru was 0 state. From our best fitting by fixing T as 1.5 K, the added for each 2 molar Sr for the crystal growth. The c0 initial rate dT /dx ∼ −7.5 K/x(%) is obtained for both Ti and Ir concentrations in grown crystals were ana- c Ti and Ir substitutions. The critical concentration x for lyzed by electron-probe microanalysis (EPMA). The Ti c disappearance of the superconductivity is estimated as is well substituted for Ru as reported by Minakata and x ∼ 0.15%. Maeno.15) On the other hand, we found that the Ir as c By measuring the residual resistivity ρ (Fig. 1), well as Ru was heavily evaporated during crystal growth ab0 ◦ we can see a universal trend that the superconductiv- at the high temperature of ∼2200 C, so that excess ity of Sr RuO is completely suppressed at the critical amounts had to be added for the crystal growth: the 2 4 resistivity of ρ ∼ 1.1 µΩcm for both impurities, as re- analyzed Ir concentration x (Ir) is roughly connected ab0 a ported from previous studies with native impurities and with the nominal concentration xn(Ir) by xa ∼ 0.25xn for 11) defects. The critical value ρab0 is again in good agree- xn ≤ 9%. We note that the tetragonal crystal symme- ment with the mean free path lab falling below the su- try15, 19) for both Sr Ru − Ti O and Sr Ru − Ir O 2 1 x x 4 2 1 x x 4 perconducting coherence length ξ ∼ 900Awhen˚ super- with x up to 3% was confirmed at room temperature. ab conductivity is destroyed. The induced moment by magnetic impurities is isotropic The fact that Ti4+ and Ir4+ suppress T in the same in sharp contrast to the result of Ti substituted system c way in spite of their very different magnetic characters and estimated as 0.7 µ /Ir from susceptibility measure- B suggests that the magnetic contribution to pair break- ments. This value is much smaller than the previous ing is negligible, and potential scattering dominates. Al- report using polycrystals, ∼2 µ /Ir at x(Ir) ∼ 5%.19) B though it could also be explained in other ways, this For the resistivity measurements, the crystals were cut observation is qualitatively consistent with the existence into rectangles with a typical size of 3.5 × 0.4 × 0.05 of a spin-triplet state. Magnetic impurities break singlet mm3. The shortest dimension was along the c axis. Sil- pairs essentially because of exchange splitting of the sin- ver paste (Dupont, 6838) was used for attaching elec- ◦ gle particle state; equal spin paired triplet states would trodes and cured at 500 C for 5 minutes; the contact not be subject to such an effect. Similar observations resistances were below 0.4 Ω. The in-plane resistivity of negligible magnetic pair breaking have also been re- ρ measurements were performed by a standard four- ab ported in UPt .3) probe dc method between 4.2 and 300 K and by a low 3 In Fig. 2, the impurity concentration depen- frequency ac method between 0.3 and 5 K. Before mea- dence of ρab0 is displayed for Sr2Ru1−xTixO4 and suring the ρab of Sr2Ru1−xTixO4 and Sr2Ru1−xIrxO4, Sr Ru − Ir O . The enhancement of ρ shows the we examined the absolute value of the ρ for Sr RuO 2 1 x x 4 ab0 ab 2 4 same behavior for both impurities with a slope dρ /dx crystals without Ti and Ir substitutions but with various ab0 ∼ 500 µΩcm/x. For potential scattering, the residual T (1.42 K, 1.24 K and less than 0.3 K) in order to remove c resistivity in a two dimensional system is given as the uncertainty due to the size error and the inhomoge- neous current path. The resistivity of these crystals were 4¯h x ρ = sin2 δ , 121 ± 2 µΩcm at 300 K. Moreover, the residual resistiv- ab0 e2 α,β,γ 0 i ni ity ρ were 0.15, 0.40 and 1.6 µΩcm, respectively, in ab0 where, n is the carrier concentrationP for each Fermi sur- the order of decreasing T . Here, the ρ was defined by i c ab0 face (α,β,γ).9) Using the relation n = k2 /2πd, where the extrapolation of the the low temperature resistivity i Fi k i is each Fermi wave number in cylindrical Fermi sur- to T = 0. The T vs. ρ agreed well with the previous F c ab0 face approximation9) and d the interlayer distance, we data.11) can obtain dρ /dx = 425 µΩcm/x in Sr RuO , drawn Figure 1 shows the temperature dependence of ρ ab0 2 4 ab as a broken line in Fig. 2. Here we have assumed the in Sr2Ru1−xTixO4 and Sr2Ru1−xIrxO4 with a small Effects of In-Plane Impurity Substitution in Sr2RuO4 3 unitarity limit, namely with the maximum phase shift Physica B 223&224 (1996) 44. δ0 = π/2. The estimated value is in good agreement 4) For instance, F. Kromor, M. Lang, N. Oeschler, P. Hinze, C. 62 with the experimental results. Also, by assuming only Langhammer and F. Steglich: Phys. Rev. B (2000) 12477, and references therein; B. Arfi, H. Bahlouli, C.J. Pethick and potential scattering contribution with δ0 = π/2, we es- 60 dT π¯hΓ 1 D. Pines: Phys. Rev. Lett. (1988) 2206. timated c = − ∼ −10 K/x(%) and the criti- 5) For instance, Y.Fukuzumi, K. Mizuhashi, K. Takenaka and dx 2kB x S. Uchida: Phys. Rev. Lett. 76 (1996) 684; S.H. Pan, E.W. cal concentration for disappearance of the superconduc- Hudson, K.M. Lang, H. Eisaki, S. Uchida and J.C. Davis: π2k T N 1 ∼ B c0 0 ∼ Nature 403 (2000) 746; E.W. Hudson, K.M. Lang, V. Mad- tivity xc 2 0.1%. Here, γ is the 4γ sin δ0 havan, S.H. Pan, H. Eisaki, S. Uchida and J.C. Davis: Nature Euler constant. These values are consistent with the ex- 411 (2001) 920. perimental values ∼ −7.5 K/x% and ∼ 0.15%, respec- 6) Y. Maeno, H. Hashimoto, K. Yoshida, A. Nishizaki, T. Fujita, 372 tively. These results again suggest that both nonmag- J.G. Bednorz and F. Lichtenberg: Nature (1994) 532. 7) Y. Maeno, T.M. Rice and M. Sigrist: Physics Today 54 (2001) netic and magnetic impurities act mainly as strong po- 42 and references therein. tential scatterers in Sr2RuO4. This unitarity scattering 8) Y. Maeno, K. Yoshida, H. Hashimoto, S. Nishizaki, S. Ikeda, in Sr2RuO4 is similar to the substitution effect of non- M. Nohara, T. Fujita, A.P. Mackenzie, N.E. Hussy, J.G. Bed- 2+ 5) norz and F. Lichtenberg: J. Phys. Soc. Jpn. 66 (1997) 1405. magnetic (Zn ) impurity in high-Tc cuprates. Table I summarizes the nonmagnetic and magnetic 9) A.P. Mackenzie, S.R. Julian, A.J. Diver, G.J. McMullan, M.P. Ray, G.G. Lonzarich, Y. Maeno, S. Nishizaki and T. Fujita: substitution effects in Sr2RuO4, in comparison with Phys. Rev. Lett. 76 (1996) 3786. those in the high-Tc cuprates. For both impurities, 10) T. Oguchi: Phys. Rev. B 51 (1995) R1385; D.J. Singh: Phys. further substitution leads to different magnetic ground Rev. B 52 (1995) 1358. state, namely spin glass behavior coexisting with in- 11) A.P. Mackenzie, R.K.W. Haselwimmer, A.W. Tyler, G.G. 15, 16) Lonzarich, Y. Mori, S. Nishizaki and Y. Maeno: Phys. Rev. commensurate magnetic order and weak ferromag- 80 19, 20) Lett. (1998) 161; Z.Q. Mao, Y. Mori and Y. Maeno: Phys. netism for nonmagnetic and magnetic impurities, Rev. B. 60 (1999) 610. respectively. At very low doping levels, however, we have 12) S. NishiZaki, Y. Maeno and Z.Q. Mao: J. Low Temp. Phys. shown here that both impurities have very similar effects 117 (1999) 1581. on transport and magnetic properties. In order to clarify 13) K. Ishida, H. Mukuda, Y. Kitaoka, Z.Q. Mao, H. Fukazawa 84 the similarity and the difference in more detail, it is very and Y. Maeno: Phys. Rev. Lett. (2000) 5387. 14) Z.Q. Mao, Y. Maeno and H. Fukazawa: Mat. Res. Bull. 35 important to investigate how the spin fluctuation at Qic (2000) 1813. is modified by the magnetic impurity, as has been done 15) M. Minakata and Y. Maeno: Phys. Rev. B. 63 (2001) for the nonmagnetic impurity.16) R180504. In summary, we report systematic comparison of the 16) M. Braden, O. Friedt, Y. Sidis, P. Bourges, M. Minakata and 88 substitution effects of nonmagnetic and magnetic im- Y. Maeno: Phys. Rev. Lett. (2002) 197002. 17) Y. Sidis, M. Braden, P. Bourges, B. Hennion, S. NishiZaki, purities in the spin-triplet superconductor Sr2RuO4. Ir- Y. Maeno and Y. Mori: Phys. Rev. Lett. 83 (1999) 3320. respective of leading to different magnetic ordering at 18) N. Kikugawa and Y. Maeno: Phys. Rev. Lett. 89 (2002) high levels of substitution, we found universal behavior 117001. 19) R.J. Cava, B. Batlogg, K. Kiyono and H. Takagi: Phys. Rev. for both impurities in the suppression of Tc and the en- B. 49 (1994) 11890. hancement of ρab , in accordance with the strong poten- 0 20) G. Cao, J. Bolivar, S. McCall, J.E. Crow and R.P. Guertin: tial scattering with δ0 = π/2. Our result suggests that Phys. Rev. B. 57 (1998) 11039; M.K. Crawford, M.A. Subra- both nonmagnetic and magnetic impurities in Sr2RuO4 manian, R.L. Harlow, J.A. Fernandez-Baca, Z.R. Wang and break pairs due to strong potential scattering, and that D.C. Johnston: Phys. Rev. B. 50 (1994) 9419. magnetic scattering does not play an important role. 21) For instance, R.J. Radtke, K Levin, H.-B. Schüttler and M.R. 48 The authors thank H. Fukazawa, K. Deguchi and M. Norman: Phys. Rev. B. (1993) 653. 22) P. Mendels, J. Bobroff, G. Collin, H. Alloul, M. Gabay, J.F. Yoshioka, P.D.A. Mann and D. Herd for useful discus- Marucco, N. Blanchard and B. Grenier: Europhys. Lett. 46 sions and technical support. They also thank T. No- (1999) 678. mura and M. Sigrist for useful discussions, Y. Shibata, 23) S. Uchida and K.M. Kojima: private communication. J. Hori and T. Fujita for EPMA measurements at Hi- roshima University. This work was mainly supported by Core Research for Evolutional Science and Technology (CREST) of Japan Science and Technology Corporation, and by the Grant-in-Aid for Scientific Research on Pri- ority Area ”Novel Quantum Phenomena in Transition Metal Oxides” from the Ministry of Education, Culture, Sports, Science and Technology.

1) For instance, N.D. Mathur, F.M. Grosche, S.R. Julian, I.R. Walker, D.M. Freye, R.K.W. Haselwimmer and G.G. Lon- zarich: Nature 394 (1998) 39. 2) For instance, Y. Kitaoka, K. Ishida and K. Asayama: J. Phys. Soc. Jpn. 63 (1994) 2052. 3) Y. Dalichaouch, M.C. de Andrade, D.A. Gajewski, R. Chau, P. Visani and M.B. Maple: Phys. Rev. Lett. 75 (1995) 3938; H.G.M. Duijn, N.H. van Dijk, A. de Visser and J.J.M. Franse: 4 Naoki Kikugawa, Andrew Peter Mackenzie and Yoshiteru Maeno

Sr2Ru1–x MxO4 (M = Ti, Ir) 5 2.0 1.5 Ti

(K) Ir 1.0 4 c T 0.5 x c ~ 0.15%

cm) 0

Ω 0 0.2 0.4 0.6 µ 3 x (%) (

ab x (Ti) = 0.5% ρ 2

1.1µΩcm 1 x (Ti) = 0.10% x (Ir) = 0.11% Table I. Substitution eﬀects of nonmagnetic and magnetic impu- x (Ir) = 0.07% rity in (a) Sr2RuO4, (b) underdoped and (c) overdoped cuprates. 0 x = 0% 0 1 2 3 4 (a) Sr2RuO4 T (K) Sr2Ru1−xTixO4 Sr2Ru1−xIrxO4

phase shift (δ0) π/2 π/2 15) peff 0.5 µB/Ti 0.7 µB/Ir 15) 19) Fig. 1. Temperature dependence of the in-plane resistivities ρab magnetic order x(Ti) ≥ 2.5% x(Ir) ≥ 30% 19) in Sr2Ru1−xTixO4 and Sr2Ru1−xIrxO4. Inset: Superconduct- SDW and spin glass weak ferromagnetism ing transition temperature Tc as a function of the impurity concentration x. The broken line shows the best fitting by (b) high-T cuprates (underdoped) Abrikosov-Gor’kov pair-breaking function. c nonmagnetic (Zn2+) magnetic (Ni2+) 5) 5) phase shift (δ0) π/2 0.36π 22) 22) peff 1 µB/Zn 1.6 µB/Ni magnetic order − −

nonmagnetic (Zn2+) magnetic (Ni2+) 5) 23) 25 phase shift (δ0) π/2 0.32 - 0.36π 22) 22) peﬀ 0.4 µB/Zn 1.2 µB/Ni Sr Ru Ti O − − 20 2 1–x x 4 magnetic order Sr2Ru1–xIrxO4 cm) 15 Ω µ (

0 10 ab ρ 5 unitarity limit 425x µΩcm 0 0 0.01 0.02 0.03 Impurity concentration x

Fig. 2. Residual resistivity ρab0 as a function of x for Sr2Ru1−xTixO4 and Sr2Ru1−xIrxO4. The broken line repre- sents the unitarity scattering with the phase shift δ0 = π/2.