Superlattices and Microstructures, Vol. 21, No. 3, 1997

Flux pinning in NbTi-based multilayers
Y. Obi, H. Fujimori
Institute for Materials Research, Tohoku University, Sendai 980, Japan

M. Ikebe, H. Fujishiro
Faculty of Engineering, Iwate University, Morioka 020, Japan(Received 8 July 1996)
Critical current density Jc and pinning force density Fp have been investigated for the superconductor/superconductor multilayers NbTi/Nb and superconductor/normal metal multilayer NbTi/Ti under parallel and perpendicular magnetic fields. The layered structure itself
has been confirmed to play as an effective flux pinning centre enhancing Fp⊥ under parallel
magnetic fields.
c 1997 Academic Press Limited
Key words: niobium-titanium, multilayer, critical current, flux pinning.

1. Introduction
Parallel critical fields Hc2k of multilayer superconductors are usually enhanced in comparison with perpendicular fields Hc2⊥ as confirmed by many reports [1]. The multilayer structure is also expected to enhance
the critical current Jck under parallel magnetic fields, because the vortex driving force is perpendicular to thelayers and the vortex motion should be impeded by the multilayer structure itself [2, 3]. Then the pinning force
density Fp⊥ in the perpendicular direction may be strongly affected by the kind of the metal of intervening
sublayer and the structural modulation wavelength λ.
By using dual sputtering technique, we have fabricated Nb65 Ti35 /Nb and Nb65 Ti35 /Ti multilayers in order tocompare the behavior of Jc and Fp of superconductor/superconductor (NbTi/Nb) and superconductor/normal
metal (NbTi/Ti) multilayers. The details of the sample preparation was reported elsewhere [4]. The thicknessof each sublayer was designed to be equal, i.e. λ/2 = dNbTi = dNb (or dTi ). The Jc measurement was performed
by a 4-terminal resistive method mainly at 1.5 K using a 10 T superconducting magnet.

2. Results and discussion
Figure 1 shows the field dependence of critical current Jc at 1.5 K under parallel (Jck ) and perpendicular (Jc⊥ )magnetic fields. The absolute values of Jc are slightly larger for NbTi/Nb multilayers (7 ∼ 10 × 105 A cm−2 )than for NbTi/Ti (5 ∼ 8×105 A cm−2 ). Because both sublayers of NbTi/Nb are superconductive, the electricalcurrent flows through both sublayers, while the current can flow only through NbTi sublayers in NbTi/Ti.
This may explain the smaller Jc values of NbTi/Ti multilayers at low fields.
From the measured values of Jck and Jc⊥ we can calculate the macroscopic pinning force densities Fpk andFp⊥ , which are defined as Fp⊥ = Jck × Hk and Fpk = Jc⊥ × H⊥ , respectively. In Fig. 2 we plot the maximum
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c 1997 Academic Press Limited

424Superlattices and Microstructures, Vol. 21, No. 3, 1997
25NbTi/NbJc//

5λ (Å)
60
1202002804001000

231054105λ (Å)
60
120
200
280
400
1000

231052204060H// (kOe)

80

100

1045λ (Å)
50
100
200
300
500
1000

2105204060
H (kOe)801001045λ (Å)
50
100
200
300
500
1000

2310520

NbTi/Ti
Jc

2NbTi/Ti
Jc//

32052–2–24NbTi/NbJc

D

51052Jc (A cm )–2Jc// (A cm )22C

510Jc// (A cm )5102B

510–2A

5Jc (A cm )21020204060H// (kOe)

80

100

0204060
H (kOe)80100Fig. 1. Critical current versus magnetic field. A, Jck of NbTi/Nb in parallel field; B, Jc⊥ of NbTi/Nb in perpendicular field; C, Jck ofNbTi/Ti in parallel field. D, Jc⊥ of NbTi/Ti in perpendicular field. Hc2 can be estimated as the field in small Jc limit.
.

.

44FmaxpFmaxp //A

1.5K

1.5K
38–3
Fpmax
// (10 dyn cm )3Fpmax (108dyn cm–3)

B

212

1
NbTi/NbNbTi/Ti0252

102λ (Å)

5NbTi/NbNbTi/Ti
103

02252

102λ (Å)

5103

2max
Fig. 2. Maximum pinning force Fpmax as a function of structural modulation wavelength λ. A, Fmaxp⊥ in parallel field; B, Fpk in
perpendicular field.
.

.

values of Fmax
as a function of the modulation wavelength λ for both multilayer systems. The characteristicpare summarized as follows: (i) Fmax
results for Fmax
ppk values under the perpendicular field H⊥ are almostvalues
are between 1 × 108 dyne cm−3 and 4 × 108 dyne cm−3
independent of λ for both systems. (ii) Fmaxp⊥depending on λ. These values are about one order smaller than those of commercial NbTi wires. (iii) In contrast
max
max
to Fmax
pk , Fp⊥ values, which are always larger than Fpk , show a broad maximum around λ = 300 Å. (iv)
The dimensionality of superconductivity changes from quasi-two-dimension (λ < 300 Å) to two-dimension(λ > 300 Å) around this λ value [4]. These results indicate that the multilayer structure really acting as aneffective pinning center in both systems.
Figure 3A shows the λ dependence of the maximum Fp field H(Fmaxp ) at which the maximum pinningmax
max
occurs. In Fig. 3A we see that H(Fmax)(=H)
valuesarelargerthanH(Fmaxp⊥kpk ) (= H⊥ ) irrespective of λ,max
max
maxi.e. Fp⊥ always occurs at a higher field than Fpk in both systems. H(Fp ) values are smaller for NbTi/NbSuperlattices and Microstructures, Vol. 21, No. 3, 1997

425

120

0.8
Hmax(NbTi/Nb)//
Hmax (NbTi/Nb)
Hmax(NbTi/Ti)//
Hmax (NbTi/Ti)

B

1.5 K
0.7

80
1.5 K

h(Fpmax)H(Fpmax) (kOe)

100

A

60

0.6

0.5

40hmax(NbTi/Nb)//hmax (NbTi/Nb)
hmax(NbTi/Ti)//
hmax (NbTi/Ti)

0.4

200252102λ (Å)

510302252102λ (Å)

51032maxmax
Fig. 3. A, Maximum pinning field Hmax versus λ. N, Hmax
pk of NbTi/Nb; M, Hp⊥ of NbTi/Nb; ●, Hpk of NbTi/Ti;
NbTi/Ti. B, Reduced maximum pinning field h max = Hmax /Hc2 versus λ. Symbols are the same as A.
.

.

, Hmaxp⊥ ofTable 1: Parameters for various Nb65 Ti35 /Nb and Nb65 Ti35 /Ti multilayers.
Tc(K)

Hc2k(kOe)
1.5 K

Hc2⊥(kOe)
1.5 K

Nb65 Ti35 /Nb60
7.76
120
7.71
200
7.40
280
7.42
400
7.92
1000
8.59

51536260
5338

363633333234λ(Å)

Fmax
Fmaxp⊥pk
8(10 dyn cm−3 )1.5 K 1.5 K

λ(Å)

1.58
2.05
2.43
3.11
2.67
1.84

1.41
1.62
1.55
1.64
1.80
1.26

Tc(K)

Hc2k(kOe)
1.5 K

Hc2⊥(kOe)
1.5 K

Nb65 Ti35 /Ti
50
6.91
100
6.46
200
6.49
300
6.82
500
7.61
1000
8.12

98
100
110
93
81
76

80
58
51
50
57
65

Fmax
Fmax
p⊥
pk
−38(10 dyn cm )
1.5 K
1.5 K
2.08
2.32
3.04
3.50
2.76
2.57

1.56
1.45
1.31
1.33
1.72
1.75

system than for NbTi/Ti system. The origin for the low H(Fmaxp ) is attributable to the lower Hc2 values ofNbTi/Nb than those of NbTi/Ti multilayers.
max
max
max
Figure 3B shows h(Fmaxp ) = H(Fp )/Hc2 versus λ. In terms of the reduced field, h(Fpk ) (= h ⊥ ) values of
NbTi/Nb are somewhat larger than corresponding values of NbTi/Ti. No systematic λ dependence of h(Fmaxp )max
is confirmed except for h(Fmaxp ) of NbTi/Ti. The values of h(Fp ) of NbTi/Ti increased with increasing λ up
to λ = 500 Å and then saturated.
Finally we make a brief comment on the pinning mechanisms operating in these multilayer systems.
For Nb/Ti, the superconductor/normal metal multilayer, the fluxoids are stabilized in Ti sublayers and thesuperconducting condensation energy is the main vortex pinning energy. The elementary pinning force fp
across the interface may be estimated from the core interaction formula, e.g. fp ≈ 0.3ξNT H2c (1 − H/Hc2 ) withthermodynamical critical field Hc and the coherence length ξNT of NbTi layer. In contrast, for NbTi/Nb, thesuperconductor/superconductor multilayer with almost the same condensation energy of both layers, the main
origin of the pinning force comes from h̄ 2 (∇ψ)2 /2m∗ term of the GL free energy (ψ: order parameter, m ∗ :426Superlattices and Microstructures, Vol. 21, No. 3, 1997

effective mass), which stabilizes the fluxoids in NbTi sublayers [5]. It is noteworthy that the overall featuresof Fmaxp⊥ versus λ curve are similar for NbTi/Nb and NbTi/Ti multilayers in spite of the different vortex siteand different pinning mechanisms between the two systems.
As a summary, the multilayer structures of NbTi/Nb and NbTi/Ti systems have been confirmed to enhance
the pinning force density Fp⊥ perpendicular to the layer plane. Although the pinning mechanisms are different between these superconductor/superconductor and superconductor/normal metal multilayers, the mosteffective pinning occurs near the quasi-two-dimension to two-dimension transition of superconductivity inboth systems. In comparison with NbTi/Ti, Fp⊥ in NbTi/Nb is enhanced at lower magnetic fields. Important
superconducting material parameters are summarized in Table 1 for multilayers studied in this report.

References.

[1] See} for example, B. Y. Jin and J. B Ketterson, Adv. in Phys. 38, 189 (1989).
} Tachiki and S. Takahashi, Solid State Commun. 70, 291 (1989).
[2] M.
} Obi, M. Ikebe, and H. Fujimori, Jpn. J. Appl. Phys. 31, 1134 (1992).
[3] Y.
} Obi, S. Takahashi, H. Fujimori, M. Ikebe, and H. Fujishiro, J. Low Temp. Phys. 96, 1 (1994).
[4] Y.
} Matsushita et al. to be published in Adv. Cryog. Eng. Mater. 42 (1996).
[5] T.
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