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Resistivity measurement of V3Si single crystal in the mixed superconducting state
Solid State Communications,
Vol. 8, PP. 555—559, 1970.
Pergamon Press.
Printed in Great Britain
RESISTIVITY MEASUREMENT OF V3Si SINGLE CRYSTAL IN THE MIXED SUPERCONDUCTING STATE LB. Goldberg, E. Ehrenfreund and M. Weger Department of Physics, The Hebrew University of Jerusalem, Israel (Received 2 February 1970 by P.G. de Gennes)
Measurements of the resistivity of a V3Si single crystal in the mixed superconducting state, near the critical temperature T~indicate a sharp peak in the critical field H~for the onset of resistivity. In the (100) direction, H~is approximately five times larger than in the vicinity of this direction, and the width of the peak in H~is approximately 2.5°. had been Asubjected stress of order 2 inThe the crystal (100) direction. tentativetoexplanation is suggested 50 kg/cm which takes into account the domain structure caused by the martensitic transformation. The sharp peak and the large anisotropy are attributed to the possibility that the domain walls act as potential barriers to the flux flow.
INTRODUCTION
LG equations take the form
ANISOTROPY of the upper critical field H~ in type II superconductors was investigated 2 experimentally and theoretically. Tilley eta!. and Farrel et al.’ measured the anisotropy in
2~,+q)iç1i~~ —77 a~I/J~~f~2/2m[q2+ c(q + V’~) + i~rh2/2mq2(fr~ + ç&~)+ iih2/2m(q~i/i~~ + q~~ 22) (1)
pure niobium as function of temperature magnetically, and found an anisotropy order 5 per 2 investigated Nb,of Nb—Ta, cent; Reed et al. V 3Ge and V3S1 by measuring the resistivity as function of the magnetic field, and found anisotropies of 4theattribute same order. byanisotropy Tilley theseTheories effects to andthe others in band structure (the effective mass) in non-cubic crystals; for cubic crystals, a theory of Hohenberg and Werthamer4 attributes the anisotropy to non-local corrections to the Landau—Ginzburg (LG) equation.. The electronic band structure and superconducting properties of V 3 Si and V3 Ge may perhaps be accounted for by 5 Barisic and de Gennes6 the linear model.to this model, for cubic applied thechain LG theory symmetry, assuming different order parameters for different electronic bands. For three families of linear chains, in the x,y, and z directions, the
The other two equations by permutation of x, y, z. being a is deduced the usualfrom LG (1) parameter; çlr~ = () is the order parameter for the chains in the x-direction; qeffective = ih V mass, 2e/cmt/rn A; c isassumed the anisotropy in the small compared with unity in the linear chain model; 77, ILL, i are coupling constants between different chains. Neglecting the coupling between chains, Barisic and de Gennes obtained (1/H 2 a mm ~[H~+ (H~+ H)/] 02) —
—
~,
+ (H~+ H~/] [H~ + (H ~ + H)/ 1 This differs from the theories based on a single order parameter, and the previous experimental results, by predicting a large anisotropy even for cubic symmetry, and a local L G theory. In essence, if the linear chain model applies, and
555
556
RESISTIVITY MEASUREMENT OF V3Si SINGLE CRYSTAL
DC
Vol.8, No.7
mugnstlc fl.td (1(0.)
10
FIG. 1. Recorder traces of resistance R vs. magnetic field H in the vicinity of the (100) direction. The geometry of the crystal and the current is shown in the lower right corner.
T .~.IS‘K
3
strsu 5kg/cm
0
DC
mipiubc
fisid
(1(0.)
10
FIG. 2. Resistance vs. magnetic field for several current densities. The onset of resistivity for low current densities occurs at approximately the same field at which the resistivity reaches the normal value for high
current densities. a magnetic field is applied along a chain direction,
be large; thus maxima of H
the electrons moving along this chain are essentially unaffected by the magnetic field, and H~2should
the (100) directions.
02 are expected along
Vol.8, No.7
RESISTIVITY MEASUREMENT OF V3 Si SINGLE CRYSTAL
557
EXPERIMENTAL We have measured the resistivity of a single crystal V3 Si disc, as a function of the intensity of the magnetic field (up to 20 koe); its orientation with respectstress to the crystal(100) axes, temperaturn, and uniaxial direction 2). TypicalinRthe vs. H curves, for (up to 50kg/cm several magnetic field orientations are shown in Fig. 1.
V~Si S
~~1(01O) 2
f.901
____________________________________ 1.
When H 0 •H > H ~
the
resistance isapproximately lower than due to surface currents. The current resistance densities, densities The first asisand function effect shown thenormal predominates second in of Fig. at2.at for low Itwhich several at isones. high seen that H~2is the field the
~I.57’
‘resistance starts to build up at low current densities, while ut high current densities it is approximately the field at which it becomes equal to the normal resistivity.
2 1.
Curves of the field H ~, at which the resistivity reaches 10 per cent of its normal value at low current densities, as function of the angles 0, ~ between the direction of the magnetic field and the (100) axis, are shown in •Fig. 3. These results were obtained with a they 2, though stress of approximately 10kg/cm do not depend strongly on the value of the stress. The temperature was 16.48°K(T 0 = 16.87). It is seen that H~displays a very sharp peak (-‘~‘2.5°wide), at 0 = 0. These results persist, even if the stress is removed, the sample warmed to ambient, and recooled. An experiment which was subsequently carried out on a virgin crystal (i.e. one that has never been subjected to stress) at temperatures of 13.7—14.5°K,and fields up to 60 hoe, failed to indicate the presence of the sharp peak in H,,. Under these conditions, the resistivity as function of H has a sharp discontinuity (approx. 3 koe wide), and H 02 can be determined unambiguously. H02 at 0 = 10°is approximately 2 per cent lower than at 0 = 0.
3 ~~X1) 2 1
“so.
‘(lao) I
1
e 1(d.y..s)1
I
FIG.3. Dependence of 1f~,the field at which the resistivity reaches 10 per cent of the normal value, on the polar angle 0, for several azimutal angles çb. The sharp peak in the (100) direction and the be inequivalence of (010) and (001) directions should 2. noted. The current density is about 10 A/cm INTERPRETATION Sharp maxima of critical fields in discs and films were observed? when the magnetic field was parallel to the surface of the disc. Also, broad anisotropies in critical currents8 have been observed before. However, a sharp anisotropy for a field perpendicular to the surface of a sample, has not been previously reported, to our knowledge
558
RESISTIVITY MEASUREMENT OF V3 Si SINGLE CRYSTAL
A tentative explanation for the sharp peak in the stressed crystal, may proceed as follows, When V3 Si in the tetragonal state, is pressed in the (100) direction, domains align so that the c-axes are in the (010) and (001) directions, and the are in the (011) and walls (On) between planes.9 these Thus,domains the domain walls intersect in the (100) direction. If the domain walls act as barriers to the flux flow, this action would be more effective when flux lines are parallel to these planes, and in particular, when they are parallel to both (011) and (011) planes, since then they would be trapped in domain corners. This could account for a maximum in the critical field for flux flow when the is in the direction of the stress. However, presently, this explanation must be regarded as preliminary and tentative, It should be noted that the presence of a sharp anisotropy in H~2is a critical testsuperfor the 1° model for the Labbe—Friedel—Barisic conductivity of V Si (and Nb 3Sn). According to their model, in the tetragonal state, one (or two) of the linear chain families are much less occupied than the rest, and superconductivity is due directly to these states. Thus, the values of the L G parameters (a, 77, ~i, etc) are
Vol.8, No.7
different for the three families of chains, and this results in a significant anisotropy, even when the coupling between the chains is not weak. (In the cubic state, under such conditions, H02 is isotropic, out by Barisic and 6 On as the pointed other hand, a recent de Gennes). investigation of the Fermi surface of V 3 Si by means of positron annihilation,~ seems to give support to the linear chain model. Thus, the situation regarding the application of the linear chain model to account for superconductivity in V3 Si, must probably be regarded at present as indecisive. Further work is presently being done in an attempt to understand the superconducting properties of ~—w compounds. Another feature of the experimental results is the inequivalence of the (010) and (001) directions. In the [001] plane there is a broad large peak about (010) direction whereas in the [OlOj is no such peak at all. This effect plane is notthere yet understood. Acknowledgements The experiments weredes assisted by Mr. de Laplace, of the Faculté Sciences, Orsay; Mr. J. Mock, Bell Telephone Laboratories; stimulating discussions with Prof. A.B. Pippard, and Dr. A.C. Gossard and Dr. N. Kaplan, Dr. S. Barisic and Prof. J. Labbe, are gratefully appreciated. —
REFERENCES 1.
TILLEY D.R., VAN GURP G.J. and BERGHOUT C.W., Phys. Lett. 12, 305 (1964); FARREL LLE., CHANDRASEKHAR B.S. and HUANG S., Phys. Rev. 176, 562 (1968).
2.
3.
REED W.A., FAWCETT E., MEINCKE P.P.M., HOHENBERG P.C. and WERTHAMER N.R., Proc. Tenth liii. Conf. Low-Temperature Phys. Moscow, (1966) (edited by MALKOV M.P.) Proizvodstrenno Izdatel’skii Kombinat, VINITI, Moscow, (1967). TILLEY D.R, Proc. Phys. Soc. (London) 86, 289 (1965); 86, 675 (1965).
4.
HOHENBERG P.C. and WERTHAMER N.R., Phys. Rev. 153, 493 (1967).
5. 6.
WEGER M., Rev. Mod. Phys. 36, 175 (1964). BARISIC S. and DE GENNES P.G., Solid State Commun. 6, 281 (1967).
7. 8.
HARPER F.E. and TINKHAM M., Phys. Rev. 172, 441 (1968). TEDMON CS. Jr., ROSE R.M. and WTJLFF J., J. appi. Phys. 36, 829 (1965).
9.
BATTERMAN B.W. and BARRETT C.S., Phys. Rev. 145, 296 (1966).
—
J.
and FRIEDEL
J.,
10.
LABBE
J. Phys. Radium 27, 153, 303 (1966).
11.
BERKO S. and WEGER M., to be published in Phys. Rev. Lelt.
Vol.8, No.7
RESISTIVITY MEASUREMENT OF V3Si SINGLE CRYSTAL Nous avons mesuré Ia résistivité d’un monocristal de V3 Si dans l’état supraconducteur, prés de la temperature de Ia transition, dans un champ magnétique. Nous avons trouvé un pic aigu du champ critique H~pour le commencement de la résistance, autour de la direction (100). H~est approximativement cinq fois plus grand dans la direction (100) qu’au alentour de cette direction, et Ia largeur du pic de H3, est approximativement Le cristal étépeut soumis 2 dans la2.5°. direction (100). aOn essayer une pression d’expliqucr de 50kg/cm ce pic par l’effet des parois des domains tétragonaux, qui freinent le mouvement des fluxoids.
559
Vol. 8, PP. 555—559, 1970.
Pergamon Press.
Printed in Great Britain
RESISTIVITY MEASUREMENT OF V3Si SINGLE CRYSTAL IN THE MIXED SUPERCONDUCTING STATE LB. Goldberg, E. Ehrenfreund and M. Weger Department of Physics, The Hebrew University of Jerusalem, Israel (Received 2 February 1970 by P.G. de Gennes)
Measurements of the resistivity of a V3Si single crystal in the mixed superconducting state, near the critical temperature T~indicate a sharp peak in the critical field H~for the onset of resistivity. In the (100) direction, H~is approximately five times larger than in the vicinity of this direction, and the width of the peak in H~is approximately 2.5°. had been Asubjected stress of order 2 inThe the crystal (100) direction. tentativetoexplanation is suggested 50 kg/cm which takes into account the domain structure caused by the martensitic transformation. The sharp peak and the large anisotropy are attributed to the possibility that the domain walls act as potential barriers to the flux flow.
INTRODUCTION
LG equations take the form
ANISOTROPY of the upper critical field H~ in type II superconductors was investigated 2 experimentally and theoretically. Tilley eta!. and Farrel et al.’ measured the anisotropy in
2~,+q)iç1i~~ —77 a~I/J~~f~2/2m[q2+ c(q + V’~) + i~rh2/2mq2(fr~ + ç&~)+ iih2/2m(q~i/i~~ + q~~ 22) (1)
pure niobium as function of temperature magnetically, and found an anisotropy order 5 per 2 investigated Nb,of Nb—Ta, cent; Reed et al. V 3Ge and V3S1 by measuring the resistivity as function of the magnetic field, and found anisotropies of 4theattribute same order. byanisotropy Tilley theseTheories effects to andthe others in band structure (the effective mass) in non-cubic crystals; for cubic crystals, a theory of Hohenberg and Werthamer4 attributes the anisotropy to non-local corrections to the Landau—Ginzburg (LG) equation.. The electronic band structure and superconducting properties of V 3 Si and V3 Ge may perhaps be accounted for by 5 Barisic and de Gennes6 the linear model.to this model, for cubic applied thechain LG theory symmetry, assuming different order parameters for different electronic bands. For three families of linear chains, in the x,y, and z directions, the
The other two equations by permutation of x, y, z. being a is deduced the usualfrom LG (1) parameter; çlr~ = (
—
~,
+ (H~+ H~/] [H~ + (H ~ + H)/ 1 This differs from the theories based on a single order parameter, and the previous experimental results, by predicting a large anisotropy even for cubic symmetry, and a local L G theory. In essence, if the linear chain model applies, and
555
556
RESISTIVITY MEASUREMENT OF V3Si SINGLE CRYSTAL
DC
Vol.8, No.7
mugnstlc fl.td (1(0.)
10
FIG. 1. Recorder traces of resistance R vs. magnetic field H in the vicinity of the (100) direction. The geometry of the crystal and the current is shown in the lower right corner.
T .~.IS‘K
3
strsu 5kg/cm
0
DC
mipiubc
fisid
(1(0.)
10
FIG. 2. Resistance vs. magnetic field for several current densities. The onset of resistivity for low current densities occurs at approximately the same field at which the resistivity reaches the normal value for high
current densities. a magnetic field is applied along a chain direction,
be large; thus maxima of H
the electrons moving along this chain are essentially unaffected by the magnetic field, and H~2should
the (100) directions.
02 are expected along
Vol.8, No.7
RESISTIVITY MEASUREMENT OF V3 Si SINGLE CRYSTAL
557
EXPERIMENTAL We have measured the resistivity of a single crystal V3 Si disc, as a function of the intensity of the magnetic field (up to 20 koe); its orientation with respectstress to the crystal(100) axes, temperaturn, and uniaxial direction 2). TypicalinRthe vs. H curves, for (up to 50kg/cm several magnetic field orientations are shown in Fig. 1.
V~Si S
~~1(01O) 2
f.901
____________________________________ 1.
When H 0
the
resistance isapproximately lower than due to surface currents. The current resistance densities, densities The first asisand function effect shown thenormal predominates second in of Fig. at2.at for low Itwhich several at isones. high seen that H~2is the field the
~I.57’
‘resistance starts to build up at low current densities, while ut high current densities it is approximately the field at which it becomes equal to the normal resistivity.
2 1.
Curves of the field H ~, at which the resistivity reaches 10 per cent of its normal value at low current densities, as function of the angles 0, ~ between the direction of the magnetic field and the (100) axis, are shown in •Fig. 3. These results were obtained with a they 2, though stress of approximately 10kg/cm do not depend strongly on the value of the stress. The temperature was 16.48°K(T 0 = 16.87). It is seen that H~displays a very sharp peak (-‘~‘2.5°wide), at 0 = 0. These results persist, even if the stress is removed, the sample warmed to ambient, and recooled. An experiment which was subsequently carried out on a virgin crystal (i.e. one that has never been subjected to stress) at temperatures of 13.7—14.5°K,and fields up to 60 hoe, failed to indicate the presence of the sharp peak in H,,. Under these conditions, the resistivity as function of H has a sharp discontinuity (approx. 3 koe wide), and H 02 can be determined unambiguously. H02 at 0 = 10°is approximately 2 per cent lower than at 0 = 0.
3 ~~X1) 2 1
“so.
‘(lao) I
1
e 1(d.y..s)1
I
FIG.3. Dependence of 1f~,the field at which the resistivity reaches 10 per cent of the normal value, on the polar angle 0, for several azimutal angles çb. The sharp peak in the (100) direction and the be inequivalence of (010) and (001) directions should 2. noted. The current density is about 10 A/cm INTERPRETATION Sharp maxima of critical fields in discs and films were observed? when the magnetic field was parallel to the surface of the disc. Also, broad anisotropies in critical currents8 have been observed before. However, a sharp anisotropy for a field perpendicular to the surface of a sample, has not been previously reported, to our knowledge
558
RESISTIVITY MEASUREMENT OF V3 Si SINGLE CRYSTAL
A tentative explanation for the sharp peak in the stressed crystal, may proceed as follows, When V3 Si in the tetragonal state, is pressed in the (100) direction, domains align so that the c-axes are in the (010) and (001) directions, and the are in the (011) and walls (On) between planes.9 these Thus,domains the domain walls intersect in the (100) direction. If the domain walls act as barriers to the flux flow, this action would be more effective when flux lines are parallel to these planes, and in particular, when they are parallel to both (011) and (011) planes, since then they would be trapped in domain corners. This could account for a maximum in the critical field for flux flow when the is in the direction of the stress. However, presently, this explanation must be regarded as preliminary and tentative, It should be noted that the presence of a sharp anisotropy in H~2is a critical testsuperfor the 1° model for the Labbe—Friedel—Barisic conductivity of V Si (and Nb 3Sn). According to their model, in the tetragonal state, one (or two) of the linear chain families are much less occupied than the rest, and superconductivity is due directly to these states. Thus, the values of the L G parameters (a, 77, ~i, etc) are
Vol.8, No.7
different for the three families of chains, and this results in a significant anisotropy, even when the coupling between the chains is not weak. (In the cubic state, under such conditions, H02 is isotropic, out by Barisic and 6 On as the pointed other hand, a recent de Gennes). investigation of the Fermi surface of V 3 Si by means of positron annihilation,~ seems to give support to the linear chain model. Thus, the situation regarding the application of the linear chain model to account for superconductivity in V3 Si, must probably be regarded at present as indecisive. Further work is presently being done in an attempt to understand the superconducting properties of ~—w compounds. Another feature of the experimental results is the inequivalence of the (010) and (001) directions. In the [001] plane there is a broad large peak about (010) direction whereas in the [OlOj is no such peak at all. This effect plane is notthere yet understood. Acknowledgements The experiments weredes assisted by Mr. de Laplace, of the Faculté Sciences, Orsay; Mr. J. Mock, Bell Telephone Laboratories; stimulating discussions with Prof. A.B. Pippard, and Dr. A.C. Gossard and Dr. N. Kaplan, Dr. S. Barisic and Prof. J. Labbe, are gratefully appreciated. —
REFERENCES 1.
TILLEY D.R., VAN GURP G.J. and BERGHOUT C.W., Phys. Lett. 12, 305 (1964); FARREL LLE., CHANDRASEKHAR B.S. and HUANG S., Phys. Rev. 176, 562 (1968).
2.
3.
REED W.A., FAWCETT E., MEINCKE P.P.M., HOHENBERG P.C. and WERTHAMER N.R., Proc. Tenth liii. Conf. Low-Temperature Phys. Moscow, (1966) (edited by MALKOV M.P.) Proizvodstrenno Izdatel’skii Kombinat, VINITI, Moscow, (1967). TILLEY D.R, Proc. Phys. Soc. (London) 86, 289 (1965); 86, 675 (1965).
4.
HOHENBERG P.C. and WERTHAMER N.R., Phys. Rev. 153, 493 (1967).
5. 6.
WEGER M., Rev. Mod. Phys. 36, 175 (1964). BARISIC S. and DE GENNES P.G., Solid State Commun. 6, 281 (1967).
7. 8.
HARPER F.E. and TINKHAM M., Phys. Rev. 172, 441 (1968). TEDMON CS. Jr., ROSE R.M. and WTJLFF J., J. appi. Phys. 36, 829 (1965).
9.
BATTERMAN B.W. and BARRETT C.S., Phys. Rev. 145, 296 (1966).
—
J.
and FRIEDEL
J.,
10.
LABBE
J. Phys. Radium 27, 153, 303 (1966).
11.
BERKO S. and WEGER M., to be published in Phys. Rev. Lelt.
Vol.8, No.7
RESISTIVITY MEASUREMENT OF V3Si SINGLE CRYSTAL Nous avons mesuré Ia résistivité d’un monocristal de V3 Si dans l’état supraconducteur, prés de la temperature de Ia transition, dans un champ magnétique. Nous avons trouvé un pic aigu du champ critique H~pour le commencement de la résistance, autour de la direction (100). H~est approximativement cinq fois plus grand dans la direction (100) qu’au alentour de cette direction, et Ia largeur du pic de H3, est approximativement Le cristal étépeut soumis 2 dans la2.5°. direction (100). aOn essayer une pression d’expliqucr de 50kg/cm ce pic par l’effet des parois des domains tétragonaux, qui freinent le mouvement des fluxoids.
559