Physica B 284}288 (2000) 857}858

Flux pinning characteristics in NbTi/Nbsuperconductor/superconductor multilayers
Y. Obi *, M. Ikebe, H. Fujishiro, H. Fujimori
Institute for Materials Research, Tohoku University, Katahira, Aoba-Ku, Sendai 980-8577, Japan
Faculty of Engineering, Iwate University, Morioka 020-8551, Japan

Abstract
Flux pinning characteristics have been investigated for superconductor(S)/superconductor(S) NbTi/Nb multilayers.
The maximum of the perpendicular pinning force (F) as a function of the structure modulation length K has a peak, in the quasi-two-dimensional superconductivity region. The large perpendicular pinning force observed in the S/S
multilayer is caused by Nb layers, which act as the repulsive pinning centers.  2000 Elsevier Science B.V. All rights
reserved.
Keywords: Multilayers; Niobium}titanium; Pinning strength

In superconductor(S)/normal metal(N) multilayers, theperpendicular pinning force F acting in the perpen,
dicular direction to the layer plane is usually much enhanced compared to the parallel pinning force F . In
S/N multilayers, the N layer works as an attractive pin
center for vortices. Recently, Matsushita et al. [1,2] suggested that in S/S structures (m (m ), the large enhanceYment is possible in F , where the boundary works asa repulsive pinning center. We investigate Fin,
NbTi/Nb (S/S) multilayers in this note. We discuss about
the size of F with respect to the GL coherence length,m of NbTi layer.
Three series of NbTi/Nb (Nb Ti /Nb(N1), 
Nb Ti /Nb(N2) and Nb Ti /Nb(N4)) multilayers  have been fabricated by an RF dual sputtering ontoquartz substrates. Samples have equal sublayer thicknesses, d"d "(1/2)K, where dand d denote,2,
,2,
the thickness of NbTi and Nb layer, respectively, and K is
the modulation wavelength. The critical current density
J was determined resistively at 1.5 K for the three seriesof N1, N2 and N4. F and F were estimated from,J as F "J ;H and F "J ;H , where H and,,
* Corresponding author. Tel.: #81-22-215-2097; fax: #8122-215-2096.
E-mail address: obi@imr.tohoku.ac.jp (Y. Obi)

H are applied "elds parallel and perpendicular to the,layer. The current J is always applied along the layer.
Our recent experimental study [3] revealed that in S/S
multilayers, the maximum pinning force Fis compa 
rable to that of S/N multilayer NbTi/Ti. These results
indicate that in NbTi/Nb, Nb layers actually act as
equally strong repulsive pinning centers as Ti layers inNbTi/Ti which act as attractive pinning centers. Wede"ne Fas the maximum value of the J ;H curve
, 

and F
as a function of K is shown in Fig. 1. All, Fversus K curves have a broad peak at around, K"200}300 As . The peak value of F
is the largest
, for Nb Ti /Nb. The di!erence in the peak values should originate from the di!erence in the coherence
length m of each NbTi layer. According to the Hmeasurement [4], m (0) of each material at 0 K is esti
mated as 100.0, 63.4, 58.9 and 42.4 As for Nb, Nb Ti , 
Nb Ti and Nb Ti , respectively.
  The energy of a single vortex line per unit length ismade up of contributions from inside and outside of thecore. In a parallel #ux con"guration to the layer, thecontribution from outside of the core is averaged overseveral S and S layers and may roughly be independentof the vortex core site. The superconducting condensation energy is almost the same for Nb and NbTi sublayers. Then the main di!erence in the vortex core energyof S and S layers comes from the kinetic energy term,

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Y. Obi et al. / Physica B 284}288 (2000) 857}858

Fig. 1. Ffor Nb Ti /Nb, Nb Ti /Nb,   Nb Ti /Nb as a function of K at 1.5 K.
 and( "W")/2mH, in the GL free energy density, which isapproximately equal to pBm/k . Dividing the energy
di!erence by 2m , the elementary pinning force f by this,
term is estimated to beB (m !m)
 ,f K0.5p  Y(1),kmwhere B is the thermodynamic critical "eld and k is the
permeability of vacuum. Thus, f and, as a result, the,maximum macroscopic pinning force F
is expected, to depend linearly on g(m )"(m !m)/m . In Fig. 2, we plot the maximum F
as a function of g(m ). We can, 
see from the plot that Fversus g(m ) approximately, follows a linear relation.
In summary, the S/S multilayer, NbTi/Nb, has a large
F
which is comparable to that of NbTi/Ti [3].
, Three series of NbTi/Nb having di!erent Ti composi-Fig. 2. Maximum F
as a function of g(m ) for three, 
NbTi/Nb series at 1.5 K. The broken line is a guide to the eye.

tions show a broad peak in their F
versus K curve in, the quasi-2D superconductivity region. The peak value ofF
as a function of g(m ) has nearly a linear relation.
, This should originate from the Nb sublayers which
act as repulsive pinning centers in the parallel #ux
con"guration.

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