- Email: [email protected]
Vortex-glass transition and vortex phase diagram in a thick amorphous MgxB1−x film
Physica C 408–410 (2004) 493–494 www.elsevier.com/locate/physc
Vortex-glass transition and vortex phase diagram in a thick amorphous MgxB1x film S. Okuma *, K. Amemori, S. Togo Research Center for Low Temperature Physics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro-ku, Tokyo 152-8551, Japan
Abstract We present superconducting properties and vortex states in a thick amorphous Mgx B1x film with x ¼ 0:31. Measurements of dc and ac complex resistivities in the mixed state reveal the presence of the vortex-glass transition in three dimensions. Based on the data, we construct the vortex phase diagram in the field–temperature plane. We find that there is the relatively large vortex-liquid phase, which persists down to low temperatures. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Fy; 74.60.Ec; 74.62.)c Keywords: Mixed state; Vortex-glass transition; Amorphous films; MgB2
1. Introduction
2. Experimental
We have recently reported the observation of superconductivity in thick amorphous (a-)Mgx B1x films with x ¼ 0:29–0.39 [1,2]. The transition temperature Tc is found to change smoothly as a function of x, exhibiting a peak (Tc 6:1 K) at x 0:33 ( xp ). Seven films studied are classified into two groups. For films with x < xp the slope of the critical field B0:01% ðT Þ where the dc resistivity q vanishes is larger than that for films with x P xp , indicating that there is the difference in the electronic and/or vortex states between two groups. However, the vortex states in a-Mgx B1x films have not been fully determined yet. In this work we perform measurements of dc and ac complex resistivities. We find the power-law temperature dependence of q and vortex-relaxation time sg , as well as the crossing behavior of the phase / (of ac resistivity) vs. T curves at various frequencies f . These results provide evidence for the vortex-glass transition (VGT) [3]. Based on the data, we construct the vortex phase diagram in the field–temperature (B–T ) plane. The preliminary results will be presented elsewhere [4].
A 290-nm-thick a-Mgx B1x film with x ¼ 0:31 was prepared by coevaporation of pure Mg (99.9%) and B (99.9%) from electron beam crucibles onto the glass substrate held at room temperature. The vacuum was 1010 Torr before the deposition and 108 Torr during deposition. Amorphous structure was confirmed by a transmission electron micrograph and an electron diffraction pattern [2]. The linear dc resistivity q was measured by the four-terminal method. The ac data, f dependence of the amplitude and phase /, were also taken in the linear regime as a function of T and B employing the four-terminal method [5]. The magnetic field was applied perpendicular to the plane of the film.
*
Corresponding author. Tel.: +81-3-5734-3252; fax: +81-35734-2749. E-mail address: [email protected] (S. Okuma).
3. Results and discussion The temperature dependence of dc qðT Þ in different B [2,4] is shown in the inset of Fig. 1. The transition temperature Tc ¼ 5:7 K in B ¼ 0, which we define as the temperature at which q falls to 0.01% of normal-state resistivity qn at 10 K, is much lower than Tc ¼ 39 K for MgB2 crystals [6–9]. In the main panel of Fig. 1 we plot the temperature dependence of the characteristic fields extracted from the qðT Þ data at various B values on the
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.03.188
494
S. Okuma et al. / Physica C 408–410 (2004) 493–494 6
7T
600
NORMAL ρ (µΩcm)
6
B c2(T)
400
0.5T 200 5T
0.1T
4
B (T)
0 0
4 32 1
0T 5
T (K)
VORTEX LIQUID
B g(T) 2
VORTEX GLASS
0 0
2
4
6
T (K)
Fig. 1. B90% ðT Þ (open squares) and B0:01% ðT Þ (open circles), which denote the points where q falls to 90% and 0.01% of qn (10 K), respectively. Full circles represent Bg ðT Þ determined from ac resistivity. A full square corresponds to the temperature at which q ¼ 0 in B ¼ 0. (Inset) qðT Þ in different B.
basis of two different criteria: onset B90% (open squares) and completion B0:01% (open circles) of qðT Þ curves [2,4]. Here, B90% and B0:01% , respectively, represent the points where q decreases to 90% and 0.01% of qn (10 K). Usually, this type of diagram is roughly identified with the vortex phase diagram. In the present study, however, in order to determine the vortex states experimentally, we have performed measurements of ac complex resistivity. Fig. 2(a) representatively displays the T dependence of / of ac resistivity at various f in B ¼ 2 T. The / vs. T curves merge to the same value 73° at T 2:95 K, indicating the occurrence of the VGT in three dimensions (3D) at this temperature (Tg ¼ 2:95 0:03 K) [3]. Using the critical value of /g ¼ 73 2°, the dynamical exponent z is immediately obtained to be 5.3 ± 0.7 from the relation /g ¼ ðp=2Þðz 1Þ=z. The dc qðT Þ is also reproduced by a predicted functional form qðT Þ /
=2T 6
10
f (Hz)
50
0
75 k 99.8 k 133 k 177 k 235 k 313 k 417 k 555 k 75 k 983 k 1.19 M 1.58 M
3
T (K)
ν(z1) = 4.5 1.58 MHz
(a)
3.5
8
10
10
1/τg (1/s)
Tg = 2.95±0.03 K B φg = 73±2° z = 5.3±0.7
ρ (Ωm)
φ (deg)
100
10
6
B=2T Tg = 2.95 K νz = 4.9 (b)
5
0.3
0.4
0.5
0.6
T–T g (K)
Fig. 2. (a) / vs. T at various f in 2 T. f is listed in the figure (from left to right). Open circles represent dc qðT Þ in 2 T and a full line is the fit of the data to the formula predicted by the 3D VG theory and (b) log 1=sg vs. logðT Tg Þ in 2 T. A straight line indicates the fit of the data to the 3D VGT formula.
ðT =Tg 1Þmðz1Þ using Tg ¼ 2:92 0:03 K and mðz 1Þ ¼ 4:5 0:3 of reasonable magnitude [3]. In order to see the critical slowing down of vortex dynamics on the liquid side of the second-order transition, we plot in Fig. 2(b) log 1=sg against logðT Tg Þ, where 1=sg is defined as a frequency at which / starts to rise (/ ¼ 10°). We can see a power-law relationship (shown with a straight line) expressed as 1=sg ðT Tg Þmz with mz ¼ 4:9 0:3 and Tg ¼ 2:95 0:03 K in B ¼ 2 T. The power-law temperature dependence of sg ðT Þ and qðT Þ, and the crossing behavior of the / vs. T curves at various f , which are characteristic of the 3D VGT, are observed in all of the fields (B ¼ 1, 2, and 3 T) studied. We find that the true VGT field, Bg ðT Þ (full circles in Fig. 1), which corresponds to the data point of Tg ðBÞ obtained above in the B–T plane, is close to B0:01% ðT Þ (open circles) determined from q=qn ¼ 0:01%. We thus regard B0:01% and B90% in Fig. 1 as the VGT field and the upper critical field Bc2 , respectively. We notice that the vortex-liquid phase persists down to low temperatures, suggestive of the quantum-vortex-liquid phase at T ! 0 [5]. To demonstrate it convincingly, ac resistivity measurements down to 30 mK are now in progress. Finally, we compare the phase diagram for aMgx B1x films with that for other related systems. The liquid phase for a-Mgx B1x films [1,2] is generally broader than that for a-Mox Si1x films [5] but remarkably narrower than that for crystalline MgB2 samples [7]. The strength of both thermal and quantum fluctuations is determined by qn and dimensionality of the sample. Thus, the broader liquid phase for a-Mgx B1x films than that for a-Mox Si1x films whose qn , thickness, Tc , and Bc2 are of the same order of magnitude as those for the a-Mgx B1x films is most likely attributed to weaker pinning effects in a-Mgx B1x films.
References [1] S. Okuma, S. Togo, K. Amemori, Phys. Rev. B 67 (2003) 172508. [2] S. Okuma, S. Togo, K. Amemori, in: S. Tsukamoto (Ed.), Proceedings of the 15th International Symposium on Superconductivity, 2002, Yokohama, Phys. C 392–396 (2003) 336. [3] D.S. Fisher, M.P.A. Fisher, D.A. Huse, Phys. Rev. B 43 (1991) 130. [4] S. Okuma, S. Togo, K. Amemori, in: J.D. Fan (Ed.), Proceedings of the 4th Int. Conference on New Superconductors and Related Materials, 2003, San Diego, Int. J. Mod. Phys. B 17 (2003) 3688. [5] S. Okuma, Y. Imamoto, M. Morita, Phys. Rev. Lett. 86 (2001) 3136. [6] J. Nagamatsu et al., Nature (London) 410 (2001) 63. [7] H.H. Wen et al., Phys. Rev. B 64 (2001) 134505. [8] Yu. Eltsev et al., Phys. Rev. B 65 (2001) 140501. [9] A.K. Pradhan et al., Phys. Rev. B 64 (2001) 212509.
Vortex-glass transition and vortex phase diagram in a thick amorphous MgxB1x film S. Okuma *, K. Amemori, S. Togo Research Center for Low Temperature Physics, Tokyo Institute of Technology, 2-12-1 Ohokayama, Meguro-ku, Tokyo 152-8551, Japan
Abstract We present superconducting properties and vortex states in a thick amorphous Mgx B1x film with x ¼ 0:31. Measurements of dc and ac complex resistivities in the mixed state reveal the presence of the vortex-glass transition in three dimensions. Based on the data, we construct the vortex phase diagram in the field–temperature plane. We find that there is the relatively large vortex-liquid phase, which persists down to low temperatures. Ó 2004 Elsevier B.V. All rights reserved. PACS: 74.25.Fy; 74.60.Ec; 74.62.)c Keywords: Mixed state; Vortex-glass transition; Amorphous films; MgB2
1. Introduction
2. Experimental
We have recently reported the observation of superconductivity in thick amorphous (a-)Mgx B1x films with x ¼ 0:29–0.39 [1,2]. The transition temperature Tc is found to change smoothly as a function of x, exhibiting a peak (Tc 6:1 K) at x 0:33 ( xp ). Seven films studied are classified into two groups. For films with x < xp the slope of the critical field B0:01% ðT Þ where the dc resistivity q vanishes is larger than that for films with x P xp , indicating that there is the difference in the electronic and/or vortex states between two groups. However, the vortex states in a-Mgx B1x films have not been fully determined yet. In this work we perform measurements of dc and ac complex resistivities. We find the power-law temperature dependence of q and vortex-relaxation time sg , as well as the crossing behavior of the phase / (of ac resistivity) vs. T curves at various frequencies f . These results provide evidence for the vortex-glass transition (VGT) [3]. Based on the data, we construct the vortex phase diagram in the field–temperature (B–T ) plane. The preliminary results will be presented elsewhere [4].
A 290-nm-thick a-Mgx B1x film with x ¼ 0:31 was prepared by coevaporation of pure Mg (99.9%) and B (99.9%) from electron beam crucibles onto the glass substrate held at room temperature. The vacuum was 1010 Torr before the deposition and 108 Torr during deposition. Amorphous structure was confirmed by a transmission electron micrograph and an electron diffraction pattern [2]. The linear dc resistivity q was measured by the four-terminal method. The ac data, f dependence of the amplitude and phase /, were also taken in the linear regime as a function of T and B employing the four-terminal method [5]. The magnetic field was applied perpendicular to the plane of the film.
*
Corresponding author. Tel.: +81-3-5734-3252; fax: +81-35734-2749. E-mail address: [email protected] (S. Okuma).
3. Results and discussion The temperature dependence of dc qðT Þ in different B [2,4] is shown in the inset of Fig. 1. The transition temperature Tc ¼ 5:7 K in B ¼ 0, which we define as the temperature at which q falls to 0.01% of normal-state resistivity qn at 10 K, is much lower than Tc ¼ 39 K for MgB2 crystals [6–9]. In the main panel of Fig. 1 we plot the temperature dependence of the characteristic fields extracted from the qðT Þ data at various B values on the
0921-4534/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2004.03.188
494
S. Okuma et al. / Physica C 408–410 (2004) 493–494 6
7T
600
NORMAL ρ (µΩcm)
6
B c2(T)
400
0.5T 200 5T
0.1T
4
B (T)
0 0
4 32 1
0T 5
T (K)
VORTEX LIQUID
B g(T) 2
VORTEX GLASS
0 0
2
4
6
T (K)
Fig. 1. B90% ðT Þ (open squares) and B0:01% ðT Þ (open circles), which denote the points where q falls to 90% and 0.01% of qn (10 K), respectively. Full circles represent Bg ðT Þ determined from ac resistivity. A full square corresponds to the temperature at which q ¼ 0 in B ¼ 0. (Inset) qðT Þ in different B.
basis of two different criteria: onset B90% (open squares) and completion B0:01% (open circles) of qðT Þ curves [2,4]. Here, B90% and B0:01% , respectively, represent the points where q decreases to 90% and 0.01% of qn (10 K). Usually, this type of diagram is roughly identified with the vortex phase diagram. In the present study, however, in order to determine the vortex states experimentally, we have performed measurements of ac complex resistivity. Fig. 2(a) representatively displays the T dependence of / of ac resistivity at various f in B ¼ 2 T. The / vs. T curves merge to the same value 73° at T 2:95 K, indicating the occurrence of the VGT in three dimensions (3D) at this temperature (Tg ¼ 2:95 0:03 K) [3]. Using the critical value of /g ¼ 73 2°, the dynamical exponent z is immediately obtained to be 5.3 ± 0.7 from the relation /g ¼ ðp=2Þðz 1Þ=z. The dc qðT Þ is also reproduced by a predicted functional form qðT Þ /
=2T 6
10
f (Hz)
50
0
75 k 99.8 k 133 k 177 k 235 k 313 k 417 k 555 k 75 k 983 k 1.19 M 1.58 M
3
T (K)
ν(z1) = 4.5 1.58 MHz
(a)
3.5
8
10
10
1/τg (1/s)
Tg = 2.95±0.03 K B φg = 73±2° z = 5.3±0.7
ρ (Ωm)
φ (deg)
100
10
6
B=2T Tg = 2.95 K νz = 4.9 (b)
5
0.3
0.4
0.5
0.6
T–T g (K)
Fig. 2. (a) / vs. T at various f in 2 T. f is listed in the figure (from left to right). Open circles represent dc qðT Þ in 2 T and a full line is the fit of the data to the formula predicted by the 3D VG theory and (b) log 1=sg vs. logðT Tg Þ in 2 T. A straight line indicates the fit of the data to the 3D VGT formula.
ðT =Tg 1Þmðz1Þ using Tg ¼ 2:92 0:03 K and mðz 1Þ ¼ 4:5 0:3 of reasonable magnitude [3]. In order to see the critical slowing down of vortex dynamics on the liquid side of the second-order transition, we plot in Fig. 2(b) log 1=sg against logðT Tg Þ, where 1=sg is defined as a frequency at which / starts to rise (/ ¼ 10°). We can see a power-law relationship (shown with a straight line) expressed as 1=sg ðT Tg Þmz with mz ¼ 4:9 0:3 and Tg ¼ 2:95 0:03 K in B ¼ 2 T. The power-law temperature dependence of sg ðT Þ and qðT Þ, and the crossing behavior of the / vs. T curves at various f , which are characteristic of the 3D VGT, are observed in all of the fields (B ¼ 1, 2, and 3 T) studied. We find that the true VGT field, Bg ðT Þ (full circles in Fig. 1), which corresponds to the data point of Tg ðBÞ obtained above in the B–T plane, is close to B0:01% ðT Þ (open circles) determined from q=qn ¼ 0:01%. We thus regard B0:01% and B90% in Fig. 1 as the VGT field and the upper critical field Bc2 , respectively. We notice that the vortex-liquid phase persists down to low temperatures, suggestive of the quantum-vortex-liquid phase at T ! 0 [5]. To demonstrate it convincingly, ac resistivity measurements down to 30 mK are now in progress. Finally, we compare the phase diagram for aMgx B1x films with that for other related systems. The liquid phase for a-Mgx B1x films [1,2] is generally broader than that for a-Mox Si1x films [5] but remarkably narrower than that for crystalline MgB2 samples [7]. The strength of both thermal and quantum fluctuations is determined by qn and dimensionality of the sample. Thus, the broader liquid phase for a-Mgx B1x films than that for a-Mox Si1x films whose qn , thickness, Tc , and Bc2 are of the same order of magnitude as those for the a-Mgx B1x films is most likely attributed to weaker pinning effects in a-Mgx B1x films.
References [1] S. Okuma, S. Togo, K. Amemori, Phys. Rev. B 67 (2003) 172508. [2] S. Okuma, S. Togo, K. Amemori, in: S. Tsukamoto (Ed.), Proceedings of the 15th International Symposium on Superconductivity, 2002, Yokohama, Phys. C 392–396 (2003) 336. [3] D.S. Fisher, M.P.A. Fisher, D.A. Huse, Phys. Rev. B 43 (1991) 130. [4] S. Okuma, S. Togo, K. Amemori, in: J.D. Fan (Ed.), Proceedings of the 4th Int. Conference on New Superconductors and Related Materials, 2003, San Diego, Int. J. Mod. Phys. B 17 (2003) 3688. [5] S. Okuma, Y. Imamoto, M. Morita, Phys. Rev. Lett. 86 (2001) 3136. [6] J. Nagamatsu et al., Nature (London) 410 (2001) 63. [7] H.H. Wen et al., Phys. Rev. B 64 (2001) 134505. [8] Yu. Eltsev et al., Phys. Rev. B 65 (2001) 140501. [9] A.K. Pradhan et al., Phys. Rev. B 64 (2001) 212509.