Novel flux phases in superconductors with a periodic pinning array

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PHYSICA Physica C 282-287 (1997) 379-382

Novel flux phases in superconductors with a periodic pinning array* V.V. Moshchalkov, M. Baert, E. Rosseel, V.V. Metlushko, M. J. Van Bael, and Y. Bruynseraede ~ Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Flux-line confinement by triangular and square regular arrays of microholes ("antidots") has been studied in superconducting films (Pb, WGe) and multilayers (Pb/Ge). For relatively large antidots sharp cusp-like magnetization anomalies appear at the matching fields Hm. These anomalies are caused by the formation of the multi-quanta vortex lattices at each subsequent Hm. The multi-quanta vortex lattices make possible a peacefull coexistence of the flux penetration at the antidots and the presence of a substantial superfluid density in the space between them. This leads to a very strong enhancement of the critical current density in films with an antidot lattice. For smaller antidots the vortices are forced to occupy the interstitial positions after the saturation of the pinning sites at antidots. This leads to the formation of the novel composite flux-fine lattices consisting from the interpenetrating sublattices of weakly pinned interstitial single-quantum vortices and multi-quanta vortices strongly pinned by the antidots. When the interstitial flux-fine lattice melts, it forms the interstitial flux liquid coexisting with the flux solid at antidots.

1.

INTRODUCTION

In homogeneous superconductors the formation of the flux line (FL) lattices consisting of multiquanta vortices is energetically unfavorable [1]. Contrary to this, relatively large artificial pin-

ning centers can stabilize multi-quanta vortices. The m a x i m u m possible number of the FL trapped by the single insulating inclusion with the radius r is determined by the saturation number ns = r/2~(T), where ~(T) is the t e m p e r a t u r e dependent coherence length [2]. For regular arrays of artificial pinning centers the vortex-vortex interactions make the situation more complicated, but still multi-quanta FL lattices can exist, provided that the radius r is sufficiently large [3]. Following the pioneering work of Hebard et al. [4], we have shown recently [5-7] that the regular arrays of submicron holes (Fig. 1) ("antidots" (Fig. 1), this definition has been borrowed from the publications [8] on similar nanostructured semiconducting films) can be successfully used to stabilize novel flux phases consisting of multi-quanta and interstitial vortices in superconducting films with the antidot lattices. The form*Supported by the Belgian IUAP, Flemish FWO, GOA Programs and the Research Council of the K.U.Leuven. 0921-4534/97/$17.00 © Elsevier Science B.V. All rights reserved. PII S0921-4534(97)00280-3

ation of these novel phases leads to the appearance of the magnetization anomalies observed at matching fields H = Hm. Here the matching fields Hm = m. ¢o/S are determined by the unit cell area of the antidot lattice, S, and integer m. In what follows, we briefly characterize the main features of the novel flux phases, induced by the presence of regular pinning arrays. 2. M U L T I - Q U A N T A

VORTEX

LATTICE

Superconducting films with relatively large antidots can successfully stabilize multi-quanta vortices. In this case puzzling sharp cusp-like magnetization anomalies appearing at Hm (Fig. 2) are somewhat similar to the well-known M(H) cusp at lower critical field He1, but for the onset of multi-quanta vortices trapping by antidots : 2¢0 at H = H1, 3¢0 at H = H2, etc. Using the London limit expression for M(H), we have shown [9] that exactly at the matching fields Hm, magnetization is given by the relation M(H,,) oc -m¢o/2A2(T), where A(T) is the t e m p e r a t u r e dependent penetration depth in thin films. Between the matching fields Hm < H < Hm+l, M(H) follows the logarithmic behavior M oc - l n ( H - Hm) typical for the system of strongly interacting FL. In other words, the

V.g Moshchalkov et al./Physica C 282-287 (1997) 379-382

380

"H4

"H3 -H 2

-H 1

~

0

,

H1

,

H2

H3

Pb/Ge

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ot I

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.

.

.

oe

H4

}

)

.

,1

5 tJm

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Figure 1. An AFM picture of a single Pb(5001~)film with a square lattice of submicron antidots (period d = lpm, radius r = 0.2pro).

-96

-72

-48

-24

0

3.

COMPOSITE

FLUX LATTICES

The crossover between the multiquanta and composite [6] vortex lattices is realized in fields

48

72

96

H(G)

Figure 2. Magnetization loop

well known M o¢ - l n ( H ) behaviour of type-II superconductors in the London limit in the case of films with multi-quanta vortex lattices stabilized by the antidot lattice should be rewritten as M cx - l n ( H - H,~). Therefore, the whole magnetization curve of superconducting films with an antidot lattice is now successfully described (see solid line in Fig. 2 by the simple M(H) expression, derived for interacting multi-quanta vortices in the London limit. This consistent quantitative analysis of the magnetic behavior convincingly demonstrates the existence of multiple-Oo FL lattices in superconducting films with antidot lattices and opens new possibilities to control the width of the M(H) hysteresis loop and critical current in nanostructured superconducting films. In films with antidot lattices the strongly enhanced critical current is close to its theoretical limit - depairing current [10].

24

M(H) at T

= 6K of a and without the triangular antidot lattice (d = l#m). The solid line is a fit following the logarithmic dependence of the magnetization between the matching fields Hm and Hm+1. The dashed line is demonstrating the validity of the linear behaviour of M ( H . O. The loops were measured for M > 0 and syrnmetrized for clarity for M < 0.

(Pb(100A)/Ge(50A))2multilayers with

H > Hns when the antidots are saturated and ~o -vortices are forced to occupy interstices. The characteristic crossover field follows the temperature dependence expected from the saturation number ns -- r/2~(T). The composite flux lattices are observed when the radii of the antidots are sufficiently small o r / a n d temperature is not too close to Tc and H exceeds the limiting field H . s. Also the pinning potential at interstices should not be very shallow to provide a weaker, but still sufficient pinning to form a softer interstitial flux solid. The composite flux lattices are characterized by the coexistence of the two

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V.V. Moshchalkov et al./Physica C 282-287 (1997) 3 79-382

caged interstitial pinning Oo-vortices. The melting transition as a function of magnetic field is then observed exactly at H = H,~ s (see for example the transition at H = H2, T = 6.7 K in Fig. 4, where for H > H2 there is still a finite width of the hysteresis loop, or a very abrupt first order phase transition at H = H1 and T = 6.8 K in Ref. 6). In other words, the homogeneous mO0-vortex solid with m = n s produces in this case only the B = c o n s t a n t background while the melting of the interstitial Oo-vortex phase causes the very sharp magnetization drop at H = H,~s . The interstitial vortex fluid reversibly responses to the field variation and this results in a zero width of the hysteresis loop in fields H > H~ s. The novel flux phases listed above can exist at

-H 4 -H 3 -H 2 -H 1

0

H1

H 2 H 3 H4

10 8

Figure 3. Schematic presentation, using an AFM picture, of the flux line lattice (arrows) in a

6

(Pb(100A)/Ge(50A))2 multilayer with the antidot

4

lattice at the third ( H = H3) matching field. The composite flux lattice is characterized by the coexistence of the two interpenetrating flux lattices at interstices (Oo-vortices) and at antidots (200vortices).

%" E

2

'9

0

Pb/Ge

~

T = 6.7 K

O

~; -2 -4 -6

-weakly and strongly pinned - interpenetrating flux lattices at interstices (Oo-vortices) and antidots (mO0-vortices), respectively (Fig. 3)[6,9,10]. These coexisting lattices have recently been directly visualized in the Lorentz-microscopy [11] and magnetic decoration [12] experiments. 4. M U L T I - Q U A N T A VORTEX LATTICE COEXISTING WITH THE INTERSTITIAL VORTEX FLUID This flux phase is formed when T -+ Tc and the interstitial pinning potential becomes very shallow and thus can not prevent the melting of the

-8

e--

-10 -96

-72

-48

-24

o ~thou~antidot

I

I

I

I

0

24

48

72

96

H(G)

Figure 4. Magnetization loop M ( H ) of a (Pb(100/~)/Ge(f0A))2 multilayer with and without the antidot lattice at T - 6.7 K At H -- H2 the interstitial flux solid melts, thus producing a sharp magnetization jump.

382

~g Mo~h~nitaYo~4al./PhysicaC 282"287'(1997)379-382

temperatures not too far from To, since at lower temperatures the tendency to form a conventional Bean profile starts to dominate arid matching anomalies are suppressed, for ~xample for Pb/Ge we barely see any M(H) matching anomalies below 5 K. 5. C O N C L U S I O N S In conclusion, the superconducting film With a lattice of relatively large arltidots seems to demonstrate the novel single-terrace critical state [9] which appears at temperatures sufficiently close to Tc due to the multiple connee~ivi~t~ hi" the film and the stabilization of the m@~:tlux lattices. The separation of the areas where flux penetrates from those where superconducting order parameter nucleates provides a kind of a "peaceful coexistence" of FLs pinned by antidots with the superconducting condensate in the space between them. Fabricating an antidot lattice to let flux go through, we are thus helping the order parameter between the antidots to sustain much higher currents and magnetic fields. Moreover, superconductors with an antidot lattice, having substantially reduced low critical fields He1 and enhanced He2 [13], still keep the product He1 • H~2 = Hc constant. The presence of the antidot lattice also broadens the H - T area where the London limit is valid. Using the two essential assumptions: B --- constant (single-terrace critical state, especially at matching fields H = Hm) and I~] = constant, we have reached close to T~ a convincing quantitative description of the magnetization loops, including linear behavior of M(H) at matching fields M(H,n) and logarithmic behavior elsewhere: M(Hm < H < Hm+l) - ln(H - Hm). The existence of several novel flux phases - multiquanta vortex lattice, composite flux lattice and interstitial fro-vortex fluid coexisting with the m~o-vortex lattices at antidots - has been made possible by fabricating regular arrays of antidots. REFERENCES

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these proceedings.