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Helicon - like oscillation in superconducting tin
Volume 27A. number 2
PHYSICS LETTERS
the anomalous resistance of the undeformed sample a~seen from the real curve in fig. la, and P~~~(T)one of plastically deformed samples. Fig. Tb shows the volume distribution of the portion that is associated with the different TN for the different reductions. The volume distribution is almost symmetrical with respect to the original TN. The result strongly suggests that contractive and expansive regions in the lattice exist in nearly the same proportion and introduction of compressive and tensile stresses in Cr would change the effective number of 3d electrons. It is of interest to investigate whether the upper edge of the temperature region of the TN in fig. lb reach to 475°Kobtained by Shull and Wilkinson [5], as the deformation becomes heavy.
HELICON-LIKE
3 June 1968
The authors would like to express their thanks to Drs. T.Sambongi and T.Chiba for discussions and to Prof. C. T. Tomizuka of the University of Arizona for supplying chromium specimens.
References 1. A.Arrott, in Magnetism II B, eds. G.T.Rado and H. Suhl (Academic Press Inc., New York, 1966). 2. M.E.De Morton, Nature 181 (1958) 477. 3. M.J.Marcinkowski and H.A.Lipsitt, J. App!. Phys. 32 (1961)1238. ~• T.M.Sabin~and G.W.Cox, J. Phys. Chem. Solids 5. C.G.Shull and M.K.Wilkinson, Rev. Mod. Phys. 25 (1953) 100.
OSCILLATION
IN SUPERCONDUCTING
TIN
T. OGASAWARA, K.YASUXOCHI Department of Physics, College of Science and Engineering Nihon University, Chiyoda-ku, Tokyo, Japan
and T. AKACHI Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, Japan
Received 17 April 1968
Helicon wave has been observed in the intermediate state of tin. The investigation of the Hall effect in the intermediate state and in the mixed state is one of keys to clarify the basic mechanism of the flux motion in superconductors. For this purpose, the helicon wave has been observed in indium [1,2] and niobium [3,4], since the Hall effect appears as a precessional motion of flux in the helicon experiment. In this letter, we present the first observation of helicon-like oscillation in the intermediate state of high purity tin, The specimen is a rectangular thin plate of 3, and single crystalline tin, 15 x 10 X 2.0 mm its purity is 99.9999%. The helicon experiment was made by the oscillation method: A static magnetic field H~is applied perpendicular to the large surface of the specimen. In addition to this, a small magnetic field h is applied perpendicular to H~.A pick-up coil is placed with its 108
axis orthogonal to both H~and h. In a constant field H~,h is suddenly removed. The time change in the average field in the specimen can be obtained by observing the voltage induced in the pick-up coil on an oscilloscope. It was shown that the helicon wave is excited in the normal state above the thermodynamic critical field H~= 270 Oe at l.2°Kand in whole range of the static field at 4.2°K. This helicon wave is a damped oscillation of one cycle. Tin is a compensated metal. Therefore, no helicon wave would be excited, if all the electron and the hole orbits would be closed. However, tin has open orbits, which are considered to lead to the existence of the helicon wave. The helicon-like oscillation was also observed in the intermediate state in static fields below Hc at 1.2°K. The angular frequency of the helicon wave (i’4 is plotted
Volume 27A, number 2
P H Y SIC S L E T T ER S
o 1.2K • ~2°K
100
/
80
/
/
/
/
°
// //
60
40
~ /
/
00
Hc
200
400
600 Hz(Oe)
800
Fig. 1. Oscillation frequency of the helicon wave cUd as a function of the static magnetic field H 5.
against H5 in fig. 1. A significant difference exists between the normal state and the intermediate state. In the normal state, cUd is proportional to H5, while, in the intermediate state, cUd is nearly independent of H5. The behavior is the same as that obtained for indium [1,2]. In the normal state, the frequency cUd [5] jS given by 2]2 . 7~~4~H , 2 (1) cUd=[1+(d/a) 2 +(d/b) 5/4d where AH is the Hall coefficient, d is the thickness, and a and b are the dimensions of the large surface of the specimen. The data of cUd at 1.2°K and eq. (1) yield the Hall coefficient in the normal state, AH = 7.6 X i0~ e.m.u. The helicon-like oscillation observed in the intermediate state may be considered to be caused by the precessio-
3 June 1968
nal motion of the flux-tube around its equilibrium position. On the basis of their flux-tube model, De Gennes and Nozières [6] proposed the dispersion relation of the vibrational mode, wd = = where k = ir/d, A is the penetration depth and = eHc/rnc is the cyclotron frequency in the core of the flux-tube. Therefore, the frequency (i~dhas a constant value independent of H~in the intermediate state. Our results agree qualitatively with this prediction. Two direct observations were carried out on the dynamic behavior of the intermediate state pattern in disk specimens of high purity tin. DeSorbo [7] showed that flux-tubes move straightforward to the center of the specimen when the external field is increased. In contrast to this result, Haenssler and Rinderer [8] found that the flux-tube moves along spiral path. Thismotion spiral motion corresponds to athe precessional of flux-tubes in the helicon experiment. Therefore, our result is in accord with that obtained by Haenssler and Rinderer.
References 1. B. W. Maxfield and E. F. Johnson. Phys. Rev. Letters 15 (1965) 677. 2. G.J.Van Gurp and C.A.A.J. 3. W.F.Druyvesteyn, W.F.Druyvesteyn and C.A.A.J.Greebe. Phys. Greebe. Phys. Letters 22 (1966) 248. Letters 22 (1966) 17. ~ B.W.Maxfield. Solid State Commun. 5 (1967) 585. 5. R.G.Chambers and B.K.Jones. Proc. Roy. Soc. A 270 (1962) 417. 6. P.G.De Gennes and P. Nozleres. Phys. Letters 15 7. W.DeSorbo Phil. Mag. 11(1965) 853. 8. F.Haenssler and L.Rinderer. Phys. Letters 16 (1965) 29: Helv. Phys. Acta 40 (1967) 659.
109
PHYSICS LETTERS
the anomalous resistance of the undeformed sample a~seen from the real curve in fig. la, and P~~~(T)one of plastically deformed samples. Fig. Tb shows the volume distribution of the portion that is associated with the different TN for the different reductions. The volume distribution is almost symmetrical with respect to the original TN. The result strongly suggests that contractive and expansive regions in the lattice exist in nearly the same proportion and introduction of compressive and tensile stresses in Cr would change the effective number of 3d electrons. It is of interest to investigate whether the upper edge of the temperature region of the TN in fig. lb reach to 475°Kobtained by Shull and Wilkinson [5], as the deformation becomes heavy.
HELICON-LIKE
3 June 1968
The authors would like to express their thanks to Drs. T.Sambongi and T.Chiba for discussions and to Prof. C. T. Tomizuka of the University of Arizona for supplying chromium specimens.
References 1. A.Arrott, in Magnetism II B, eds. G.T.Rado and H. Suhl (Academic Press Inc., New York, 1966). 2. M.E.De Morton, Nature 181 (1958) 477. 3. M.J.Marcinkowski and H.A.Lipsitt, J. App!. Phys. 32 (1961)1238. ~• T.M.Sabin~and G.W.Cox, J. Phys. Chem. Solids 5. C.G.Shull and M.K.Wilkinson, Rev. Mod. Phys. 25 (1953) 100.
OSCILLATION
IN SUPERCONDUCTING
TIN
T. OGASAWARA, K.YASUXOCHI Department of Physics, College of Science and Engineering Nihon University, Chiyoda-ku, Tokyo, Japan
and T. AKACHI Faculty of Engineering, University of Tokyo, Bunkyo-ku, Tokyo, Japan
Received 17 April 1968
Helicon wave has been observed in the intermediate state of tin. The investigation of the Hall effect in the intermediate state and in the mixed state is one of keys to clarify the basic mechanism of the flux motion in superconductors. For this purpose, the helicon wave has been observed in indium [1,2] and niobium [3,4], since the Hall effect appears as a precessional motion of flux in the helicon experiment. In this letter, we present the first observation of helicon-like oscillation in the intermediate state of high purity tin, The specimen is a rectangular thin plate of 3, and single crystalline tin, 15 x 10 X 2.0 mm its purity is 99.9999%. The helicon experiment was made by the oscillation method: A static magnetic field H~is applied perpendicular to the large surface of the specimen. In addition to this, a small magnetic field h is applied perpendicular to H~.A pick-up coil is placed with its 108
axis orthogonal to both H~and h. In a constant field H~,h is suddenly removed. The time change in the average field in the specimen can be obtained by observing the voltage induced in the pick-up coil on an oscilloscope. It was shown that the helicon wave is excited in the normal state above the thermodynamic critical field H~= 270 Oe at l.2°Kand in whole range of the static field at 4.2°K. This helicon wave is a damped oscillation of one cycle. Tin is a compensated metal. Therefore, no helicon wave would be excited, if all the electron and the hole orbits would be closed. However, tin has open orbits, which are considered to lead to the existence of the helicon wave. The helicon-like oscillation was also observed in the intermediate state in static fields below Hc at 1.2°K. The angular frequency of the helicon wave (i’4 is plotted
Volume 27A, number 2
P H Y SIC S L E T T ER S
o 1.2K • ~2°K
100
/
80
/
/
/
/
°
// //
60
40
~ /
/
00
Hc
200
400
600 Hz(Oe)
800
Fig. 1. Oscillation frequency of the helicon wave cUd as a function of the static magnetic field H 5.
against H5 in fig. 1. A significant difference exists between the normal state and the intermediate state. In the normal state, cUd is proportional to H5, while, in the intermediate state, cUd is nearly independent of H5. The behavior is the same as that obtained for indium [1,2]. In the normal state, the frequency cUd [5] jS given by 2]2 . 7~~4~H , 2 (1) cUd=[1+(d/a) 2 +(d/b) 5/4d where AH is the Hall coefficient, d is the thickness, and a and b are the dimensions of the large surface of the specimen. The data of cUd at 1.2°K and eq. (1) yield the Hall coefficient in the normal state, AH = 7.6 X i0~ e.m.u. The helicon-like oscillation observed in the intermediate state may be considered to be caused by the precessio-
3 June 1968
nal motion of the flux-tube around its equilibrium position. On the basis of their flux-tube model, De Gennes and Nozières [6] proposed the dispersion relation of the vibrational mode, wd = = where k = ir/d, A is the penetration depth and = eHc/rnc is the cyclotron frequency in the core of the flux-tube. Therefore, the frequency (i~dhas a constant value independent of H~in the intermediate state. Our results agree qualitatively with this prediction. Two direct observations were carried out on the dynamic behavior of the intermediate state pattern in disk specimens of high purity tin. DeSorbo [7] showed that flux-tubes move straightforward to the center of the specimen when the external field is increased. In contrast to this result, Haenssler and Rinderer [8] found that the flux-tube moves along spiral path. Thismotion spiral motion corresponds to athe precessional of flux-tubes in the helicon experiment. Therefore, our result is in accord with that obtained by Haenssler and Rinderer.
References 1. B. W. Maxfield and E. F. Johnson. Phys. Rev. Letters 15 (1965) 677. 2. G.J.Van Gurp and C.A.A.J. 3. W.F.Druyvesteyn, W.F.Druyvesteyn and C.A.A.J.Greebe. Phys. Greebe. Phys. Letters 22 (1966) 248. Letters 22 (1966) 17. ~ B.W.Maxfield. Solid State Commun. 5 (1967) 585. 5. R.G.Chambers and B.K.Jones. Proc. Roy. Soc. A 270 (1962) 417. 6. P.G.De Gennes and P. Nozleres. Phys. Letters 15 7. W.DeSorbo Phil. Mag. 11(1965) 853. 8. F.Haenssler and L.Rinderer. Phys. Letters 16 (1965) 29: Helv. Phys. Acta 40 (1967) 659.
109