Gross R., Sidorenko A., Tagirov L. Nanoscale Devices

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Origin of the Resistive Transition Broadening for

Superconducting Magnesium Diboride

A. S. Sidorenko

Institute of Electronic Engineering and Industrial Technologies ASM,

MD-2028 Kishinev, Moldova

Abstract: The origin of the superconducting transition broadening for the novel

superconductor MgB

is investigated. The dominant role of two-

dimensional fluctuations and thermally activated flux flow in the

vicinity of the critical temperature is found to be responsible for the

resistivity of MgB

near the superconducting transition. The reasons

of the observed extraordinary strong magnetic field dependence of

the activation energy of the flux motion are discussed.

Keywords: superconducting transition broadening, fluctuations, flux flow

Introduction

The discovery of superconductivity in MgB

[1] with the highest critical

temperature, T

= 39 K, for a simple intermetallic compound triggered

various expectations of big-scale technical applications of this novel

material. This superconductor with a large Ginzburg-Landau parameter

≈ 26, a big magnetic penetration length λ(0) = 140-180 nm and short

coherence

lengths, ξ

(0) = 2.3 nm, ξ

(0) = 6.8 nm has a rather high

critical current density, j

~ 1.6×10

A/cm

at 15 K [2], what makes

magnesium

diboride a very attractive candidate as a high current

conductor. On the other hand, the broadening of the superconducting

transition,

as found in resistivity measurements, could limit the

applicability of MgB

. Obviously, it is important to clarify the mechanisms

responsible for the appearance of resistivity.

339

R. Gross et al. (eds.), Nanoscale Devices - Fundamentals and Applications, 339–348.

340 A. S. Sidorenko

Superconducting transition broadening may have different reasons. It

may be caused by an inhomogeneous microstructure of polycrystalline

samples with additional phases having different T

values. Furthermore,

thermodynamical fluctuations play an important role in the vicinity of the

superconducting transition, especially for low-dimensional and layered

superconductors with a short coherence length and a high T

, as in the case

of MgB

. Finally, the thermally activated flow of flux quanta leads to

dissipation and results in a broadening of the transition.

The first reason of superconducting transition broadening can be

eliminated by improving the technological process of sample preparation.

The other two mechanisms are of fundamental nature and, therefore, are

more interesting for experimentalists and theorists.

Superconducting Fluctuations

The fluctuations governing the superconducting transition broadening have

been investigated for high quality homogeneous MgB

films [3] and single

crystals [4]. It was shown, that there exists an intrinsic transition width of

the resistive transition of a superconductor caused by thermodynamic

fluctuations of the order parameter. This minimal width, ∆T

, is given by

the Ginzburg criterion [5], ∆T

= GiT

Gi = [2

(0)

]

(1)

where Gi is the Ginzburg parameter, B

(0) the critical flux density at

T = 0 K,

= h v

/ 2

= 4

×10

-7

Vs/Am, k

the Boltzmann

constant, and v

the Fermi velocity. The value of Gi is extremely small for

pure 3D conventional superconductors like bulk Pb and Al (G ~ 10

-13

However, it increases by many orders of magnitude for dirty and low

dimensional systems making the fluctuation effects observable

experimentally [6]. For layered superconductors with a small coherence

length

, the normalized intrinsic width ∆T

/ T

may be much larger, up to

Gi ~ 10

-2

for high-T

superconductors like YBa

7-x

[7]. Due to the

layered character of MgB

with its small coherence length it is expected

that fluctuation effects resulting in a broadening of the resistive transition

can be directly detected.

We performed measurements of the upper critical field and the resistive

transition for MgB

films grown on MgO and sapphire single crystalline

substrates

by dc -magnetron sputtering. The x-ray diffraction study

revealed a (101)-textured structure of the films. SEM-characterization of

the samples demonstrated a polycrystalline very smooth and homogeneous

Origin of the Resistive Transitions Broadening 341

morphology of the films with ~ 100 nm crystallites size. The resistive

transitions R(T) in constant external magnetic fields were measured by a

conventional four-probe method. The observed linear temperature

dependence of the upper critical field demonstrates a 3D character of

superconductivity in our samples below T

as discussed in [3]. In contrast,

resistivity measurements yield a temperature dependence of the fluctuation

conductivity above T

which agrees with the Aslamazov-Larkin (AL)

theory [8] for a 2D superconductor in the weak fluctuation region. Our

experimental results indicate a quasi two-dimensional origin of the

nucleation of superconductivity in MgB

34 35 36 37 38 39

"b"

"a"

R, Ohm

T, K

Fig. 1. Resisitive transition broadening for a MgB

film (thickness d = 5.6 µm,

substrate MgO). Fluctuations manifest themselves in the region marked as “a” in

the R(T) curve.

Fig. 1 shows the resistive transition R(T) at zero magnetic field for one of

the investigated MgB

samples. The transition width ∆T

is about 0.7 K

(0.1R

-0.9R

criterion), demonstrating a high homogeneity of the film. The

fluctuation or excess conductivity,

≡

1/R(T) – 1/R

, strongly depends on

the superconductor dimensionality D. For a two-dimensional

superconductor (D = 2) in the weak fluctuation region the excess

conductivity

´ ~ (T / T

– 1)

(D-4)/2

is expected to be inversely proportional

to the temperature

[

´(T)]

-1

= (R

)(T - T

)/ T

(2)

where

= (R

) /16 h , and R

is the sheet resistance of the film [8].

342 A. S. Sidorenko

Fig. 2. Linear behaviour of the fluctuation conductivity on 1/T in the fluctuation

region, i.e. the upper part of the resistive transition, marked as “a” in Fig.1. The

solid line corresponds to the AL-theory for a 2D-superconductor, crossing the T-

axis at T

(marked by the arrow).

Figure 2 presents the results of Fig. 1 in the (σ

/ σ´) vs T plot, indicating

that the resistive behavior of the MgB

film is really caused by

superconducting fluctuations according to eq. (2). The fit of the

experimental results in Fig. 2 by equation (2) gave us the values of R

and

gives the critical temperature T

= 36.77 K, which is higher than the mid-

point value of T

0.5Rn

= 35.67 K as the result of the critical temperature shift

due to fluctuations. The procedure of the precise determination of the

normal state resistance, R

, is shown in Fig. 3. From the transition width of

the film ∆T

= 0.7 K we obtain the experimental value of the Ginzburg

parameter, G = ∆T

/ T

= 0.02, which is comparable with the value Gi = 10

for high- T

superconductors.

. According to eq. (2), the intersection of the linear fit with the T-axis

Origin of the Resistive Transitions Broadening 343

0 5 10 15 20

0,02

0,03

0,04

0,05

0,06

1/B

perp

(Tesla

-1

)

1/R (Ohm

-1

)

T = 36.0K

T = 37.0K

T = 40.0K

Fig. 3. Precise determination of the normal-state resistance of the measured

sample. The intersection of the 1/R vs 1/B curves, measured at different

temperatures, with the 1/R-axis gives the value R

= 42.185 Ohm.

Thermally Assisted Flux Flow (TAFF)

A further mechanism causing a broadening of the superconducting

transition of MgB

in the lower part of the R(T) curve (marked as “b” in

Fig.1) was found. The resistivity in that region is governed by the flux-flow

processes.

In a type-II superconductor like magnesium diboride, in the mixed state

the flux lines are fixed at “pinning centers” formed by defects or impurities.

The main mechanism of flux creep resulting in a broadening of the resistive

transition in an applied magnetic field, is the thermally activated motion of

flux lines over the energy barrier, U

, of the pinning center [9].

The layered structure of MgB

is expected to influence the magnetic flux

penetration and motion leading to a resistive transition broadening similar

to the case of high-T

superconductors and artificially multilayered systems

[10, 11]. Moreover, magnesium diboride exhibits an exceptional magnetic

behavior with dendritic magnetic instabilities for vortex penetration [12]

and “noise-like” jumps of the magnetization in an applied magnetic field

[13], which should influence the resistive behavior of this novel

superconducting material.

344 A. S. Sidorenko

20 25 30 35

7 5 4 3 2 1 0

ρ (

µΩ

cm )

T (K)

Fig. 4. Resistive transitions ρ(T) for a 400 nm thick MgB

film on a sapphire

substrate measured at different values of the magnetic field perpendicular to the

film plane: curves 0 to 7 correspond to B = 0, 1, 2, 3, 4, 5, 7 Tesla.

Figure 4 shows the resistive transitions

(T) at several magnetic fields

B, applied perpendicular to the MgB

film plane for one of the investigated

samples grown on a sapphire substrate. The transition width is about 0.3 K

in zero and low magnetic fields but increases up to ~ 2 K for high fields.

Usually, for layered superconductors the broadening of the lower parts of

the resistive transition,

(T) < 1 %

(

is the resistivity in the normal

state just above the transition), in a magnetic field is interpreted in terms of

the dissipation of energy caused by the motion of vortices. This

interpretation is based on the fact that in the low-resistance region the creep

of vortices represents a thermally activated process so that the

()T

dependences are described by the Arrhenius equation

[

]

00B

(, ) exp /TB U kT

ρρ

=−

(1)

Origin of the Resistive Transitions Broadening 345

0,8 1,0 1,2 1,4 1,6

1E-5

1E-3

0,1

=7T

=5T

=4T

=3T

=2T

=1T

=0T

(

µΩ

cm )

/ T

Fig. 5. Arrhenius plot

(T)

B=const

presents the data of Fig. 4 as ln(

) vs (T

/ T).

From the slope of the linear parts of the curves the values of the activation energy

are obtained.

Here, U

is the energy barrier that has to be overcome by thermal activation

and

is a field-independent pre-exponential factor. Investigations of high-

superconductors and artificial multilayers showed that the activation

energy exhibits weak power-law dependences on the applied magnetic

field, U

(B)~B

-n

with an exponent n ~ 1 [10, 11]. Since eq. (1) with a

temperature-independent U

is used, the values of U

should be deduced

only from the limited temperature intervals below T

, in which the data of

the Arrhenius plot of

()T

yield straight lines.

The

straight-line behavior over five orders of magnitude of the

resistance really indicates that the resistive behavior of the lower parts of

the resistive transition is caused by the TAFF-process as described by the

Arrhenius law, Eq. (1). The best fit of the experimental data for

()T



B=const

yields values of the activation energy, ranging from

= 10000 K in low magnetic field down to 300 K in the high field

region, as shown in Fig. 6. Compared to the power law U

(B)~B

-n

usually

observed for other layered systems, MgB

shows a much stronger field

dependence of the activation energy in the high magnetic field region

(B > 1 T). This is clearly demonstrated by Fig. 6, where data for the

investigated MgB

sample are shown together with a typical U

(B)

346 A. S. Sidorenko

dependence for a high-T

superconductor (data for a Bi-Sr-Ca-Cu-O sample,

taken from Palstra et al. [14]).

0,1 1 10

100

10000

(K)

B (T)

MgB

on Al

BiSrCaCuO

Fig. 6. Dependence of the activation energy U

/ k

on applied magnetic field for

the investigated 400 nm thick MgB

film deposited on sapphire (solid squares). For

comparison, the weak power-law dependence U

~ B

-n

, n = 1/6 and n = 1/3 in two

linear parts of the U

(B) dependence, observed for a high-T

superconductor (solid

circles, data for Bi-Sr-Ca-Cu-O sample [14]) is given.

A possible reason for the unusually strong magnetic field dependence of

the activation energy of the TAFF process in MgB

may be the appearance

of thermo-magnetic instabilities, leading to a complex flux dynamics, such

as the dendritic flux instability found recently for c-axis textured MgB

films in a magnetic field perpendicular to the film plane. The magneto-

optical measurements demonstrate a “fractal-like“ structure of the flux

penetration with increasing amount of the flux-dendrite density with

increasing applied magnetic field [12]. More generally, thermal

instabilities, analyzed by M. Tinkham [15], lead to disastrous consequences

for superconducting magnets and cables because the material rapidly heats

up due to the dissipation of energy caused by the flux creep. Therefore, for

thermal stability of a superconductor, an increase in local heat production

needs an increased outflow of heat to the surrounding material which has to

respond to the increased dissipation due to flux motion.

Origin of the Resistive Transitions Broadening 347

Conclusion

From the reported experimental results one may conclude that the resistive

transitions broadening for good quality MgB

films has a fundamental

reason: fluctuations in the upper part of the resistive transition and flux-

flow processes for the lower part. The rapid decrease of the activation

energy for MgB

in the magnetic field region B > 1T reflects a dramatic loss

of the current carrying capabilities of this superconductor due to the

weakening of the flux-line pinning with increasing magnetic field. The

unusual flux creep behavior of magnesium diboride needs further

investigation, especially in view of future technical applications, an

increase of the flux line pinning and a thermal stabilization of wires and

cables are necessary for electrical transport with high current density.

Acknowledgments

I am very grateful to Jan Klamut, Andrei Varlamov, Paul Ziemann, Jan

Aarts, Serghej Prischepa, Armin Reller for useful and stimulating

discussions, Thomas Schimmel, Thomas Koch, Achim Wixforth, Siegfried

Horn, Reinhard Tidecks, Valery Ryazanov and Lenar Tagirov for long-term

fruitful collaboration, as well as to the A. v. Humboldt Foundation for the

donation of “Coolpower-4.2GM” and “PLN-106” refrigerators. This work

was partially supported by BMBF, Project Nr. MDA02/002, and by the

International Laboratory of Strong Magnetic Fields and Low Temperatures

(Wroclaw).

References

1. Namagatsu J, Nagakawa N, Muranaka T, Zenitani Y, Akimitsu J (2001).

Nature 410:63

2. Kim HJ, WN Kang, Choi EM, Kim MS, Kim KHP (2001). Lee SI, Phys Rev

Lett 87:087002

3. Sidorenko A, Tagirov L, Rossolenko A, Ryazanov V, Klemm M, Tidecks R

(2002) Evidence fort wo-dimensional superconductivity in MgB

. Europhys

Lett 59:272-276

4. Masui T, Lee S, Tajima S (2003). Physica C 383:299

5. Schmidt VV (2000) Introduction to the Physics of Superconductors. Ryazanov

VV and Feigelman MF (eds) 2nd Russian edition, MCNMO Publishers,

Moskow. Chapter III, §19

6. Fogel NYa, Sidorenko AS, Rybalchenko LF, Dmitrenko IM (1979). Sov. Phys

JETP 50:120

348 A. S. Sidorenko

7. Kapitulnik A (1988). Physica C153-155:520

8. Aslamazov LG and Larkin AI (1968). Phys Lett 26A:238

9. Yeshurn Y, Malozemoff AP (1988). Phys Rev Lett 60:2202

10. Fogel NY, Cherkasova VG, Koretzkaya OA, Sidorenko AS (1997). Phys Rev

B 55:85

11. Graybeal JM, Beasley MR (1986). Phys Rev Lett 56:173

12. Johansen TH, Bazilevich M, Shantsev DV, Goa PE, Galperin YM, Kang WN,

Kim HJ, Choi EM, Kim MS, Lee SI (2002). Europhys Lett 59:599

13. Jin S, Mavoori H, Bower C, Dover RB (2001). Nature 411:563

14. Palstra TTM, Batlogg B, Schneemeyer LF, Waszczak JV (1988). Phys Rev

Lett. 61:1662

15. Tinkham M (1996) Introduction to Superconductivity. 2nd ed, McGraw Hill,

New York

Gross R., Sidorenko A., Tagirov L. Nanoscale Devices - Fundamentals and Applications

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