Extreme type II superconductors: universal trends

PHYSICA

Physica B 194-196 (1994) 1789-1790 North-Holland

Extreme Type II Superconductors: Universal Trends T. Schneider a and tt. Keller b a I B M Research Division, Zurich Research Laboratory, 8803 Rfischlikon, Switzerland bphysik-Institut der Universit/it Ziirich, Sch6nberggasse 9, 8001 Zfirich, Switzerland Motivated by the Uemura plot, which relates the measured 7 c to the zero temperature /,SR relaxation rate [1-3], and by the hyperuniversal relation between 7 c and critical amplitudes of the London penetration depth and phase correlation length [4-6], we propose a simple "universal" scaling ansatz, where the plot of the rescaled transition temperature versus rescaled /zSR relaxation rate should fall on a single parabola. This scaling ansatz is remarkably consistent with the t~SR data for a large class of cuprate and Chevrel-phase superconductors. In agreement with experiment, it also implies universal trends in the pressure (a) and isotope (9) coefficients. t~SR measurements strongly suggest that m a n y extreme type II superconductors share the unique property that their transition temperature Tc is closely related to the zero temperature value of the uSR relaxation rate a(0) [1-3] which is proportional to the square of the inverse zero temperature penetration depth [6]. Moreover, extended studies of the pressure [7] and isotope mass [8-11] dependence of T c in various cuprates, measured in terms of the coefficients a-

1

d~

Tc

dP

and fl =

dln r~ dlnm

,

(1)

revealed remarkable generic trends. Indeed, for various compounds, ~ and fl fall into c o m m o n 7c-a and Tc-.fl regions, respectively, forming two branches, one for systems with positive and the other for compounds with negative pressure or isotope coefficient. The two branches merge at the m a x i m u m T c where the coefficients vanish and the magnitude of the coefficients ~ and fl decreases with increasing T c. These trends appear to be a c o m m o n feature of a large class of doped extreme type II superconductors, sharing a rather unique dependence of the transition temperature on the inverse zero temperature penetration depth squared (a(0) cc 1/2~(0) oc nslMI). Indeed, the assumption of a 16arabolie rfiaximum a(0) yields the simple scaling form [5,6] Tc =

2~(1

T c = Tc/Tcm,

- ~/2),

~ = a(0)/am(0).

Elsevier Science B . V . SSDI 0921-4526(93)1526-R

(2)

Thus in plotting Tc versus a(0), a particular family forms a unique parabolic branch characterised by 7cm and am(0). As it should be, 7 c vanishes at a ( 0 ) = 0, implying a vanishing condensate density or an infinite effective mass (a(0) ,:xZns(O)lMll!." ttowever, T c is also supposed to vanish at a(0) = 2am(0), corresponding to a finite zero temperature condensate density. Accordingly superconductivity is suppressed at finite temperatures. The plot of T c versus ~, shown in Fig. 1 for various cuprate and Chevrel phase superconductors, reveals remarkable agreement with experiment. The corresponding T m and am(0) values, as determined from a fit to Eq. (2), turned out to be nearly proportional to each other. To ensure that this behavior is not just an artifact of the gSR technique, sample preparation and quality, we next consider the pressure and isotope effect coefficients. Adopting Eq. (2), pressure and isotope mass can enter only via a(0), am(0) and Tcm. In principle all these quantities depend on pressure. Assuming that both pressure and isotope coefficient are dominated by a(0), we obtain from Eq. (2)

a-

1 Tc =

dTc I =+2 dp P=0 -

~l-Tc _ 7c

m

dTc

x/1 - Tc

7~

dm

- + 2

7=~

a0 ,

(3) ~o

where ~0 = 1/am(0) (da(O)/dP)le=o and t0 = -m/am(O)(da(O)/dm). The signs + a n d - refer

1790

V A 0.4

0.8

0,2 |

~~

~

0.6

-0.2~

o

II--

0.4

-0.4

0.2

-0.6 0.5

1

~

0.3

1.5

0.4

0.5

0,6

0.7

0.8

0.9

TC

Fig. 1: Tc versus a. [From Ref. 6]. ® T12Ba2Ca2Cu30~o, Tlo.sPbo.sSr2Ca2Cu309, Bi2_xpbx Sr2Ca2Cu 3016 <~ Yl_xPrxBa2Cu306.97 ~, YBa2Cu30 x V La2_xSrxCuO4 Bi2Sr2Cal_xYxCu208+ 6 [] LaMo6Se 8, SnMo6Ss, PbMo6Ss, SnMo6S4Se4 SnM°6S7Se, SnM°6SISe7, I.aMo6S s, PbMo6S4Se 4. The parabolas are fits to Eq. (2) with 7cm and am(0). ]From Ref. 6]. to a(0) < am(0) and a(0) > am(0), respectively. I towever, because the condensate density (a(0) oc ps(0) = nslMii) increases with decreasing volume, the coeffiEients s 0 and fl0 are expected to vary from system to system. Thus, the universal behavior of isotope effect and pressure coefficients_ is restricted to trends implied by the 7c-dependent part of E_q. (3), namely, vanishing fl in the limit T c ~ l ~ increasing magnitude of fl with decreasing T c and the appearance of two symmetric branches, one for positive and the other for negative /~ values. The pressure coefficient data [7] confirms these trends remarkably well. As shown in Fig. 2, remarkable agreement is also obtained f,_)r the oxygen isotope coefficient in Lal.asSr~.lsCUl_xNix04, YBa2_xLaxCusOz, and Yl_xPrxCayBa2Cu307 for flo = 0.125.

~g. r=

2: Isotope effect coefficient fl versus r c / r m for

A Lal.ssSr0.15 Cul_xNixO 4 [10], <3 YBa2_xLaxCu30z [91, Yl_xPrxCavBa2Cu307 [9]. The line corresponds to Eq. (3) with fl0 = 0.35. [From Ref. 51. 1. Y.J. Uemura et al., Phys. Rev. Lett. 62, 2317 (1989); Phys. Rev. B 38, 909 (1988). 2. Y.J. Uemura et al., Physica C 162-164, 857 (1989). 3. Y.J. Uemura, Phys. Rev. Lett. 66, 2665 (1991). 4. T. Schneider, Z. Phys. B 88, 249 (1992). 5. T. Schneider and H. Keller, Phys. Rev. Lett. 69, 3374 (1993). 6. J'. Schneider and It. Keller, Physica C 207, 366 (1993). 7. It. Mori in: The Physics and Chemistry of Oxide Superconductors, edited by Y. Iye and H. Yasuoka (Springer-Verlag, Berlin, 1992). 8. J.P. Franck et al., Physica C 162-164, 733 (1989); ibid. 185-189, 1379 (1991); Phys. Rev. B 44, 5318 (1991). 9. H.J. Bornemann, D.E. Morris and ll.B. Liu, Physica C 182, 132 (1991), H..I. Bornemann et al., preprint. 10. N. Babushkina et al., Physica C 185-189, 901 (1991). 11. K.A. Mtiller, Z. Phys. B 70, 193 (1990).