ARTICLE IN PRESS

Journal of Magnetism and Magnetic Materials 272–276 (2004) e1087–e1088

Evidence for zero and p phase from superconducting transition
temperature in Nb/Co superconducting multilayers
Yoshihisa Obia,*, Hiroyuki Fujishirob, Manabu Ikebeb
aInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Sendai 980-8577, Japanb
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan

Abstract
The oscillating phenomena of Tc as a function of ferromagnetic layer thickness have been observed for both theNb/Co superconductor(S)/ferromagnet(F) tri-layer series (F/S/F) and penta-layer series (F/S/F/S/F). The oscillating
characteristics are different between tri-layer and penta-layer, reﬂecting the 0-phase and p-phase forming of neighboring
S-layers, which provides a ﬁrst evidence of Tc oscillation distinguishing both the phases.
r 2003 Elsevier B.V. All rights reserved.
PACS: 74.78.Fk; 74.50.þr
Keywords: Niobium-cobalt; Multilayer; Superconductivity; Transition temperature

1. Introduction
In the several decades, the superconducting propertiesof superconductor(S)/ferromagnet(F) multilayer haveattracted much interest because of its peculiar oscillation
behavior of superconducting transition temperature (Tc )as a function of ferromagnetic layer thickness (dF ). First
experimental observation of Tc -oscillation was reported
for Nb/Gd multilayers [1], where the oscillation behavior has been considered as caused by the p-phaseforming as predicted theoretically by Radovic! et al. [2].
The similar oscillation behavior has been found in Nb/
Fe bilayer [3], where the p-phase geometry is impossible.
In this case the oscillation behavior has been considered
to be due to the magnetic origin. Until now there havebeen several experimental studies of Tc oscillation or Tc
anomaly but no clear conﬁrmation concerning the phasefactor has been obtained yet. Because the oscillation
phenomena are still a matter of theoretical controversy
concerning whether it originates from the appearance ofp-phase or from the 0-phase of the superconducting*Corresponding author. Tel.: +81-22-215-2097; fax: +8122-215-2096.
E-mail address: obi@imr.tohoku.ac.jp (Y. Obi).

order parameter. Theoretical possibility of Tc oscillation
has ﬁrst be proposed by Radovi!c et al. [2] and recently
Tagirov [4] developed the theory including the interface
transparency. According to their theory 0-phase and pphase takes a different ground state, which can beexperimentally conﬁrmed by the difference of oscillation
form between both phases. The 0-phase has Tc minimum
and while p-phase has Tc maximum at nearly the same
thickness of dF : In order to expose the Tc difference
between 0-phase and p-phase it is necessary to prepare
the samples with layering sequences including only oneand at least two Nb layers [5,6]. The purpose of thispaper is to ﬁnd the difference of Tc oscillation between
0-phase and p-phase.

2. Experimental
Multilayers forming 0- and p-phase are realized
by preparing Coðx=2 nmÞ=Nbð30 nmÞ=Coðx=2 nmÞ
tri-layers
andCoðx=2 nmÞ=Nbð30 nmÞ=Coðx nmÞ=Nbð30 nmÞ=Coðx=2 nmÞ penta-layers, where x changes
from 0:8 to 5 nm: The thickness of Co-edge layer istaken as x=2 so as to satisfy the boundary condition.
These multilayers have been synthesized by the RF-0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2003.12.644

ARTICLE IN PRESS
Y. Obi et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e1087–e1088

e1088

7

1.4

Co(x/2)/Nb(300)/Co(x)/Nb(300)/Co(x/2)

1.2

61

2.6
0.6

5

4.2

3.4

3.0

X=1.4

2.2

0.4

Tc (K)

R/Rn0.8

1.8

0.2

30−0.2
3.6

4

3.8

4

4.4

4.8

5.2

5.6

6

6.4

T (K)

2

penta−layertri−layer
01

2X (nm)345Fig. 1. Normalized resistivity vs. temperature for one of thepresent penta-layer series. x denotes dCo :Fig. 2. Tc vs. dCo ðxÞ for present tri-layer (open symbols) andpenta-layer (closed symbols) series.

sputtering techniques. Multilayer formation has been
conﬁrmed by low angle X-ray diffraction. Tc measurements have been performed by a four-terminal electricalresistance method. Tc is decided as the middle point
between 10% and 90% change in resistivity.

phase. As mentioned above, theory predicted theoccurrence of the Tc oscillation for the S/F multilayersirrespective of 0-phase or p-phase. Under a propercondition, Tc of 0-phase multilayer can take a re-entrant
behavior at certain dF where p-phase takes a local
maximum. Present behavior just conﬁrms the theory
except for the re-entrant behavior. The missing of the reentrant behavior of present tri-layers may be caused by
the low interface transparency for the pair wave function
and/or the interface roughness. The present results are
the ﬁrst ﬁnding of Tc oscillation behavior in multilayer,
which distinguishes the 0-phase and p-phase.

3. Results and discussion
Fig. 1 shows the electrical resistivity R=Rn (where Rn
is a resistance just above Tc ) versus temperature curves
for one of the present penta-layers. The superconducting
transition occurs within the range of 0:1 K between 10%
and 90% change of R=Rn except for x ¼ 3:8 and 4:2 nm;
showing the good quality for almost all the samples.
Fig. 2 shows the transition temperature Tc as afunction of dCo ðxÞ: In this ﬁgure the six different curves
for three of penta-layer series and other three of tri-layer
series are shown, where the same symbols are given forthe samples sputtered by the same run. The threedifferent curves for tri-layer and penta-layer series areslightly scattered. Despite the scattered behavior, thedifferent tendency between tri-layer series and pentalayer one is clear. The tri-layer series take a local broad
minimum in Tc around xB2:6 nm; while at around thesame position the penta-layer series take a local
maximum. This different behavior is a clear evidenceof the difference in the Tc oscillation in 0-phase and p-Acknowledgements
We thank Prof. L.R.Tagirov for valuable discussions
and suggestions.

References[1] J.S. Jiang, et al., Phys. Rev. Lett. 74 (1995) 314.
[2] Z. Radovi!c, et al., Phys. Rev. B 44 (1991) 759.
[3] T. Muhge,.
et al., Phys. Rev. Lett. 77 (1996) 1857.
[4] L.R. Tagirov, Physica C 307 (1998) 145.
[5] L.R. Tagirov, Private communication.
[6] B.P. Vodopyanov, et al., Physica C 366 (2001) 31.