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THE ANALOG OF THE JOSEPHSON EFFECT IN
THE SPIN SUPERCURRENT
A. Borovik-Romanov, Yu. Bunkov, V. Dmitriev, V. Makroczyova, Yu.
Mukharskii, D. Sergatskov, A. de Waard
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C8, Suppl6ment au no 12, Tome 49, dkcembre 1988
THE ANALOG OF THE JOSEPHSON EFFECT IN THE SPIN SUPERCURRENT
A. S. Borovik-Romanov (I), Yu. M. Bunkov (I), V. V. Drnitriev (I), V. Makroczyova (2),
Yu. M. Mukharskii (I), D. A. Sergatskov (I) and A. de Waard (3)
(I) Institute for Physical Problems, Moscow, U.S. S.R. (2) Institute of Ezperimental Physics, Kosice, Czechoslovakia
(3) Kamerlingh Onnes Laboratory, Leiden, The Netherlands
Abstract.
-
We have investigated the character of the flow of spin current, transferring longitudinal magnetization of 3 ~ e - ~ through a small hole. Experimentally we have verified the transition from the regime of current flow with phase slippage to a single-valued dependence of the current on the phase difference in the order parameter.We have observed a phenomenon which was ob- served earlier in superconducting weak links [3] and in mass superflow of He through a narrow orifice [4], the so-called Josephson effect.
The Cooper pairs in 3 ~ e possess a spin=l. There- fore, the order parameter of the superfluid phases has a very complicated structure and is determined by spa- tial as well as by spin coordinates. Owing to the dis- ruption of the spatial homogeneity of the Cooper pairs, not only mass superflow but also spin supercurrent should arise [5]. In a series of theoretical [6] and ex- perimental [7] papers, it has been pointed out, that in 3 ~ e - ~ a superfluid transfer of the magnetizations over mamoscopic distances can occur by means of a spin su- percurrent. As can be seen from [6] the supercurrent
of the component of the magnetization along the mag- Fig. imental chambers,
-
Sketch of the are exper-3 is the channel, 4, 5 are NMR coils, 6
netic field, s,, is determined by the phase of precession 7 are copper shields. The region of the domain bound- (a) and the angle (P) between the magnetization and ary is shown with dotted lines. Insert shows the profile of an external magnetic field: the narrowing.
X
(1-
cos 0 ) [(I-
cos 0) .ci+
(1+
cos P) .c:] V aY
(1) with ~ 1 1 , ~ denote the velocity of parallel and perpen- dicular spin waves, respectively.
Our experiments were carried out in analogy to those described in [8], where measurements of the flow of J,, along a long, narrow capillary and the obser- vation of phase slippage are described. Two experi- mental chambers, filled with 3 ~ e - ~ , are connected by a channel, 1.2 mm in diameter and 4.5 mm long. In the middle of the channel there is small narrowing, 00.48 mm, the form of which is shown in figure 1. Both coils are surrounded by copper shields to prevent in- ductive coupling and penetration of the RF field to the channel. In both chambers a domain with homo- geneous precession of the magnetization (HPD) is ex- cited. The HPD is formed at sufficient amplitude of the RF field, in those parts of the chamber where the magnetic field is less then WRF/Y. In the HPD, S is
inclined at an angle
>
104'. Therefore, a shift of the NMR frequency arises, which compensates the inhc- mogeneity of the external magnetic field, so that the frequency and the phase of the precession of S are, in first order, homogeneous within the HPD. This homo- geneity is maintained by a flow of the spin supercur- rent (cf. [6, 71). The experiments were carried out a field having homogeneous gradient, directed along the field, which enables control of the spatial location of the domain. The HPD and non-precessing domain are separated by a domain boundary with characteristic length 2X = 2 ( c ~ / w R F . ~ v H ) ~ ' ~ . Across the domain boundaryP
continuously changes from 104' to 0'. At the center of the boundary .yH = WRF [6].The phase of precession of HPD bears a one-to-one correspondence to the phase of the RF field. To create the difference of the phase at the ends of the chan- nel, the frequency of the RF fields on the chambers are detuned by
-
0.1+
0.01 Hz. A spin current arises along the channel which transports S, and, therefore,C8 - 2068 JOURNAL DE PHYSIQUE
Zeeman energy S,.H. As a result, the power absorbed
by the HPD from the RF field changes, so that, when measuring this power, we determine the size of the current of S,. The experiments were done in fields 71, 142 and 284 Oe and a t pressures 0 and 20 bar, and at temperatures down to 0.3 T,.
For the spin current in 3 ~ e - ~ we can introduce the length [ which is analogous to the Ginzburg-Landau coherence length in superconductors [Q]; [ is depen- dent on the precession frequency of the HPD and the Larmor frequency in the channel w,, as follows:
When w, is near WRF, we can expect that [ is of the order of the dimensions of the small hole in the chan- nel and the current-phase relationship becomes single- valued. The largest region where the Josephson effect manifests itself was obtained at 71 Oe and P = 0 bar. It may be connected with the fact that spin wave ve- locity increases with the decreasing of the pressure. In figure 2 a typical plot of the current us. the precession
phase difference is shown, together with its dependence on a small change in H. Curve 1 corresponds to the smallest value of H and so to the smallest
<.
It demon- strates phase slippage. As H is increased, the single- valued relationship shown in graphs 2, 4, is observed.Fig. 2.
-
Experimental dependence of the spin supercur- rent on the phase difference between the HPD's Differ- ent curves correspond t o different values of H. 1) V H = 0.9 Oe/cm, A H = H-
w c / 7 "24 mOe, C$ =! 0.6 mm; 2) V H = 0.9 Oe/cm, A H"
17 mOe, C$ 0.75 mm; 3) V H = 0.9 Oe/cm, A H e! 6 mOe, C$ E 1.25 mm; 4) V H = 0.15 Oe/cm, A H E 12 mOe, C$ =! 0.9 mm.A further increase of H brings the current-phase re- lationship closer to sinusoidal and decreases its initial slope (curve 3j. As can be seen from equation (1) the value of the initial slope remains constant in the HPD since ,tJ w const there. So this decrease means that the channel is only partially filled with HPD. Joseph- son behaviour was observed only under this condition. This means that [ is inhomogeneous across the channel and thus complicates the comparison with theory [lo].
However, curve 4 is close to the unusual "triangle1' current-phase dependence predicted in [lo]. It is con- nected, probably, with the smaller value of the field gradient.
The unavoidable presence of the boundary within the channel is caused by the rather large size of the narrowing (d)
.
[ increases along the HPD towards the domain boundary and goes to infinity at the center of the boundary. To make<
larger than the size of the narrowing, the distance between the domain border and the narrowing must be smaller than the bound- ary thickness. If the field gradient is decreased, the boundary becomes thicker then d and<
becomes homo- geneous, but this enhances the influence of the bound- ary surface tension. Making a much smaller narrowing will solve this problem since one can observe Joseph- son behaviour at smaller values of[.
The reason we have chosen a rather large narrowing size was because we did not expect the HPD to penetrate the channel as easily as it does.Acknowledgements
We express our deepest gratitude to I. A. Fomin and
A. V. Markelov for their helpful helpful discussions on this work.
[l] Institute of Experimental Physics, Kosice, Czechoslovakia.
[2] Kamerlingh Onnes Laboratory, Leiden, the Netherlands.
[3] Likharev, K. K., Rev. Mod. Phys. 5 1 (1979) 101.
[4] Avenel, 0 . and Varoquaux, E., Jpn J. Appl. Fhys. 26 (Suppl. 26-3) (1987) 1798.
[5] Leggett, A. J., Rev. Mod. Phys. 4 7 (1975) 331. [6] Fomin, I. A., Sow. Phys. JETP 6 1 (1985) 1207. [7] Borovik-Romanov, A. S., Bunkov, Yu. M.,
Dmitriev, V. V., Mukharskii, Yu. M. and Flach- bart, K., Sov. Phys. JETP 61 (1985) 1199. [8] Borovik-Romanov, A. S., Bunkov, Yu. M.,
Dmitriev, V. V. and Mukharskii, Yu. M., JETP Lett. 45 (1987) 98.
[9] Fomin, I. A., JETP Lett. 45 (1987) 106.
