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Conductance quantization in ferromagnetic Ni nano-constriction
Journal of Magnetism and Magnetic Materials 239 (2002) 243–245
Conductance quantization in ferromagnetic Ni nano-constriction Masayoshi Shimizua, Eiji Saitoha, Hideki Miyajimaa,*, Yoshichika Otanib a
Depertment of Physics, Faculty of Science and Technology, Keio University, Hiyoshi 3-14-1, Kohoku-Ku, Yokohama 223-8522, Japan b Depertment of Materials Science, Graduate School of Engineering, Tohoku University, Aoba 02, Sendai 980-8579, Japan
Abstract The conductance in ferromagnetic Ni nano-wire is quantized in units of 2e2 =h in the absence of magnetic field, while the units switch to e2 =h in the magnetic field. The fractional units of 0:7e2 =h and 1:4e2 =h with and without magnetic field appear under the application of high bias-voltage. The spin polarization and bias-voltage play an important role in the electric conduction. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Conductance quantization; Nano-wire; Break-junction; Ferromagnetic materials
1. Introduction The conductance quantization in metallic nano-wires occurs even at room temperature. The conductance of non-magnetic nano-wire is quantized in units of G0 ð 2e2 =hÞ (=1/12906 O1) [1]. In a ferromagnetic Ni nano-wire, Ooka et al. found that the conductance quantization units 2e2 =h switches to e2 =h in the magnetic fields higher than the saturation field of Ni [2]. According to the Landauer formula, the conductance G of nano-wire is given by ! Nm Nk X e2 X G¼ ð1Þ Tim þ Tjk ; h i¼1 j¼1 where Tim and Tjk are the transmittance for the ith channel for up-spin and jth channel for down-spin, respectively, and the sums run over occupied states. Since the electrons passing through a nano-wire are regarded to be ballistic, Tim and Tjk must be 1 or 0. In the ferromagnetic nano-wire, the quantization in units of e2 =h arises from the absence of the spin degeneracy. Recently, Cost-Kr.amer et al. [3] and Abell!an et al. [4] *Corresponding author. Tel.: +81-45-566-1692; fax: +8145-566-1672. E-mail address: [email protected] (H. Miyajima).
found that the conductance quantization in Au nanowire shows nonlinear variation with the bias- voltage and argued this phenomenon in terms of the Coulomb blockade model or the Tomonaga–Luttinger liquids model. In this paper, the bias-voltage and applied magnetic field dependences of conductance quantization in a ferromagnetic Ni nano-wire are presented.
2. Experiments The point contact in this study is realized by means of a break-junction technique using a bimetal. Details of the system are described in previous papers [2,4]. Fig. 1 shows the scheme of the experimental setup. A Ni wire of 0.1 mm in diameter is suspended from end of a bimetal sheet, and a Ni film evaporated on a glass substrate is placed below the wire. At first, the wire is away from the film. When the bimetal sheet is heated, the sheet bends so as to contact the wire and the film. Cooling slowly, the bimetal sheet is going back, and then a nano-wire is formed between the wire and the film plane at the moment that the wire deviates from the film. The potential difference VR across the reference resister (R0 ¼ 1 kO) connected to the sample wire in series is measured by using an 8 bit digital oscilloscope (LeCroy
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 5 4 4 - 3
244
M. Shimizu et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 243–245
Fig. 1. Scheme of the experimental setup. The break-junction is formed between the tip of the wire and the film.
9310CL) with bandwidth 400 MHz at the time interval of 40 ns. The conductance of the nano-wire is estimated by using following equation, G¼
VR ; ðV0 VR ÞR0
and exhibits clear plateaus. This means that the conductance is obviously quantized. Fig. 3 shows the bias-voltage dependence of the conductance histograms without and with magnetic field in (a) and (b), respectively. These conductance histograms are deduced from 20 conductance curves which have at least one plateau. In the absence of magnetic field, the conductance is quantized in unit of nG0 ð¼ 2e2 =hÞðn ¼ 1; 2; 3; yÞ for low bias-voltage below 120 mV. Besides integer peaks, new quantized peaks appear gradually with increasing biasvoltage above 140 mV. The new peaks locate at the fractional numbers of 0:7nG0 and are enhanced with the increase of bias-voltage. It should be noted that both quantizations of nG0 and 0:7nG0 coexist at the biasvoltage of 140 mV and that nG0 peaks do not shift continuously to 0:7nG0 peaks. On the other hand, in the
ð2Þ
(b) Hext = 100(Oe)
(a) Hext = 0(Oe)
0.0 1.4 2.8 4.2 5.6 7.0 0.0 1.4 2.8 4.2 5.6 7.0
where V0 is the bias-voltage. The variation of G profile is measured with a change of V0 from 60 to 320 mV. The present experiment is carried out in the evacuated (B1 Torr) chamber.
V0 = 320 mV
V0= 200 mV
0 0
V0 = 280 mV V0= 180 mV
3. Results and discussion
2
2
2 0 7.0
I/V (e /h)
6
I/V (e /h)
4
8
5.6 4.2
(b) Hext = 0 Oe V0 = 180 mV
4
2.8
(c) Hext = 100 Oe V0 = 80 mV
V0 = 240 mV
0 V0= 160 mV 0
V0 = 200 mV 0 V0= 140 mV 0 V0 = 160 mV 0
2 0 7.0
2
2
I/V (e /h)
6
(a) Hext = 0 Oe V0 = 120 mV
I/V (e /h)
8
0
Number of points (arbitrary unit)
Fig. 2 shows an example of time evolution of the conductance as functions of the external magnetic field Hext and the bias-voltage V0 ; where Hext ¼ 0 in (a) and (b), Hext ¼ 100 Oe in (c) and (d), and the bias-voltage is 80 mV (c), 120 mV (a), 180 mV (b) and 280 mV (d). As is clearly seen, the conductance varies stepwise with time
5.6 4.2
V0= 120 mV (d) Hext = 100 Oe V0 = 280 mV
V0 = 120 mV
0 V0= 100 mV
2.8
1.4
1.4
0.0 0.0 0.2 0.4 0.6 0.8 1.0 -3 Time (10 sec)
0.0 0.0 0.2 0.4 0.6 0.8 1.0 -3 Time (10 sec)
Fig. 2. The external magnetic field Hext and bias-voltage V0 dependences of the conductance curves of Ni nano-wire; (a) Hext ¼ 0 Oe, V0 ¼ 100 mV, (b) Hext ¼ 0 Oe, V0 ¼ 180 mV, (c) Hext ¼ 100 Oe, V0 ¼ 80 mV, (d) Hext ¼ 0 Oe, V0 ¼ 280 mV.
0
0
0
2
4
I/V (e2/h)
6
0 V0 = 60 mV
0
0
1
2
3
4
5
6
7
I/V (e2/h)
Fig. 3. Conductance histograms in the absence of magnetic field (a) and in the magnetic field of 100 Oe (b).
M. Shimizu et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 243–245
magnetic field of 100 Oe, the quantized units of nG0 switch to 0:5nG0 for low bias-voltage below 240 mV, as already mentioned in a previous paper [2], and new peaks of fractional unit 0:35nG0 emerge when the biasvoltage is higher than 280 mV. It is interestingly noted that the fractional quantization units 0:35nG0 and 0:7nG0 are 0.7 times as small as units 0:5nG0 and nG0 : The former and latter are, respectively, observed in the application of high and low bias-voltage. Furthermore, the quantization units in magnetic fields switch to a half of those in the absence of magnetic field; thus, nG0 and 0:7nG0 in Hext ¼ 0 switch to 0:5nG0 and 0:35nG0 in Hext ¼ 100 Oe, respectively. These indicate that the emersion of 0:35nG0 and 0:7nG0 peaks is attributed to the same source depending on the bias-voltage. Recently, Costa-Kr.amer et al. [3] and Abell!an et al. [4] showed that the quantization units in Au wire vary continuously with increasing the bias-voltage, reflecting non-linear current and voltage relationship. Their experimental result seems to be different from present result wherein the fractional quantization units depend on the magnetic field as well as on the bias-voltage. In semiconductive wires, the existence of 0:7G0 conductance plateau has been known [5], and there are many attempts from the theoretical viewpoints to interpret the 0:7G0 problem; for example, (1) a spin-singlet and triplet bond state model formed around the nano-wire [6], (2) a spontaneous spin polarization model in nano-wires due to the electron correlation [7,8], (3) the Tomonaga and Luttinger model considering leads [9], and (4) the spindensity-functional model [10]. The 0:7nG0 problem, however, is still unsolved at the present stage. In the spin polarized case such as ferromagnetic Ni nano-wire, the switching of quantization unit from nG0 to 0:5nG0 is closely related to the spin degeneracy, while not only the existence of the fractional quantized unit but also the switching between 0:7nG0 and 0:35nG0 by
245
application of magnetic fields are hardly explained with the above models.
4. Conclusion The conductance in ferromagnetic Ni nano-wire is quantized in units of 2e2 =h in the absence of magnetic field and at bias-voltage below 120 mV, while the conductance in the magnetic field is quantized in units of e2 =h when bias-voltage is lower than 240 mV. Increasing applied bias-voltage, the new fractional quantization units of 0:7ne2 =h and 0:7ð2ne2 =hÞ appear whether the magnetic field is applied or not.
References ! ! [1] J.I. Pascual, J. M!endez, J. Gomez-Herrero, A.M. Baro, N. Garc!ıa, V.T. Binh, Phys. Rev. Lett. 71 (1993) 1852. [2] T. Ono, Y. Ooka, H. Miyajima, Y. Otani, Appl. Phys. Lett. 75 (1999) 1622. [3] J.L. Costa-Kr.amer, N. Garc!ıa, P. Garc!ıa-Mochales, P.A. Serena, M.I. Marqu!es, A. Correia, Phys. Rev. B 55 (1997) 5416. ! A. Arenas, Surf. Sci. 418 (1998) [4] J. Abell!an, R. Chicon, 493. [5] K.J. Thomas, J.T. Nicholls, M.Y. Simmons, M. Pepper, D.R. Mace, D.A. Ritchie, Phys. Rev. Lett. 77 (1996) 135. [6] V.V. Flambaum, M.Yu. Kuchiev, Phys. Rev. B 61 (2000) 7869. [7] B. Spivak, F. Zhou, cond-matt/9911175. [8] H. Bruus, V.V. Cheianov, K. Flensberg, cond-matt/ 0002338. [9] D.L. Maslov, M. Stone, Phys. Rev. B 52 (1995) 5539. [10] K. Hirose, S. Li, N.S. Wingreen, Phys. Rev. Lett. 63 (2001) 33315.
Conductance quantization in ferromagnetic Ni nano-constriction Masayoshi Shimizua, Eiji Saitoha, Hideki Miyajimaa,*, Yoshichika Otanib a
Depertment of Physics, Faculty of Science and Technology, Keio University, Hiyoshi 3-14-1, Kohoku-Ku, Yokohama 223-8522, Japan b Depertment of Materials Science, Graduate School of Engineering, Tohoku University, Aoba 02, Sendai 980-8579, Japan
Abstract The conductance in ferromagnetic Ni nano-wire is quantized in units of 2e2 =h in the absence of magnetic field, while the units switch to e2 =h in the magnetic field. The fractional units of 0:7e2 =h and 1:4e2 =h with and without magnetic field appear under the application of high bias-voltage. The spin polarization and bias-voltage play an important role in the electric conduction. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Conductance quantization; Nano-wire; Break-junction; Ferromagnetic materials
1. Introduction The conductance quantization in metallic nano-wires occurs even at room temperature. The conductance of non-magnetic nano-wire is quantized in units of G0 ð 2e2 =hÞ (=1/12906 O1) [1]. In a ferromagnetic Ni nano-wire, Ooka et al. found that the conductance quantization units 2e2 =h switches to e2 =h in the magnetic fields higher than the saturation field of Ni [2]. According to the Landauer formula, the conductance G of nano-wire is given by ! Nm Nk X e2 X G¼ ð1Þ Tim þ Tjk ; h i¼1 j¼1 where Tim and Tjk are the transmittance for the ith channel for up-spin and jth channel for down-spin, respectively, and the sums run over occupied states. Since the electrons passing through a nano-wire are regarded to be ballistic, Tim and Tjk must be 1 or 0. In the ferromagnetic nano-wire, the quantization in units of e2 =h arises from the absence of the spin degeneracy. Recently, Cost-Kr.amer et al. [3] and Abell!an et al. [4] *Corresponding author. Tel.: +81-45-566-1692; fax: +8145-566-1672. E-mail address: [email protected] (H. Miyajima).
found that the conductance quantization in Au nanowire shows nonlinear variation with the bias- voltage and argued this phenomenon in terms of the Coulomb blockade model or the Tomonaga–Luttinger liquids model. In this paper, the bias-voltage and applied magnetic field dependences of conductance quantization in a ferromagnetic Ni nano-wire are presented.
2. Experiments The point contact in this study is realized by means of a break-junction technique using a bimetal. Details of the system are described in previous papers [2,4]. Fig. 1 shows the scheme of the experimental setup. A Ni wire of 0.1 mm in diameter is suspended from end of a bimetal sheet, and a Ni film evaporated on a glass substrate is placed below the wire. At first, the wire is away from the film. When the bimetal sheet is heated, the sheet bends so as to contact the wire and the film. Cooling slowly, the bimetal sheet is going back, and then a nano-wire is formed between the wire and the film plane at the moment that the wire deviates from the film. The potential difference VR across the reference resister (R0 ¼ 1 kO) connected to the sample wire in series is measured by using an 8 bit digital oscilloscope (LeCroy
0304-8853/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 1 ) 0 0 5 4 4 - 3
244
M. Shimizu et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 243–245
Fig. 1. Scheme of the experimental setup. The break-junction is formed between the tip of the wire and the film.
9310CL) with bandwidth 400 MHz at the time interval of 40 ns. The conductance of the nano-wire is estimated by using following equation, G¼
VR ; ðV0 VR ÞR0
and exhibits clear plateaus. This means that the conductance is obviously quantized. Fig. 3 shows the bias-voltage dependence of the conductance histograms without and with magnetic field in (a) and (b), respectively. These conductance histograms are deduced from 20 conductance curves which have at least one plateau. In the absence of magnetic field, the conductance is quantized in unit of nG0 ð¼ 2e2 =hÞðn ¼ 1; 2; 3; yÞ for low bias-voltage below 120 mV. Besides integer peaks, new quantized peaks appear gradually with increasing biasvoltage above 140 mV. The new peaks locate at the fractional numbers of 0:7nG0 and are enhanced with the increase of bias-voltage. It should be noted that both quantizations of nG0 and 0:7nG0 coexist at the biasvoltage of 140 mV and that nG0 peaks do not shift continuously to 0:7nG0 peaks. On the other hand, in the
ð2Þ
(b) Hext = 100(Oe)
(a) Hext = 0(Oe)
0.0 1.4 2.8 4.2 5.6 7.0 0.0 1.4 2.8 4.2 5.6 7.0
where V0 is the bias-voltage. The variation of G profile is measured with a change of V0 from 60 to 320 mV. The present experiment is carried out in the evacuated (B1 Torr) chamber.
V0 = 320 mV
V0= 200 mV
0 0
V0 = 280 mV V0= 180 mV
3. Results and discussion
2
2
2 0 7.0
I/V (e /h)
6
I/V (e /h)
4
8
5.6 4.2
(b) Hext = 0 Oe V0 = 180 mV
4
2.8
(c) Hext = 100 Oe V0 = 80 mV
V0 = 240 mV
0 V0= 160 mV 0
V0 = 200 mV 0 V0= 140 mV 0 V0 = 160 mV 0
2 0 7.0
2
2
I/V (e /h)
6
(a) Hext = 0 Oe V0 = 120 mV
I/V (e /h)
8
0
Number of points (arbitrary unit)
Fig. 2 shows an example of time evolution of the conductance as functions of the external magnetic field Hext and the bias-voltage V0 ; where Hext ¼ 0 in (a) and (b), Hext ¼ 100 Oe in (c) and (d), and the bias-voltage is 80 mV (c), 120 mV (a), 180 mV (b) and 280 mV (d). As is clearly seen, the conductance varies stepwise with time
5.6 4.2
V0= 120 mV (d) Hext = 100 Oe V0 = 280 mV
V0 = 120 mV
0 V0= 100 mV
2.8
1.4
1.4
0.0 0.0 0.2 0.4 0.6 0.8 1.0 -3 Time (10 sec)
0.0 0.0 0.2 0.4 0.6 0.8 1.0 -3 Time (10 sec)
Fig. 2. The external magnetic field Hext and bias-voltage V0 dependences of the conductance curves of Ni nano-wire; (a) Hext ¼ 0 Oe, V0 ¼ 100 mV, (b) Hext ¼ 0 Oe, V0 ¼ 180 mV, (c) Hext ¼ 100 Oe, V0 ¼ 80 mV, (d) Hext ¼ 0 Oe, V0 ¼ 280 mV.
0
0
0
2
4
I/V (e2/h)
6
0 V0 = 60 mV
0
0
1
2
3
4
5
6
7
I/V (e2/h)
Fig. 3. Conductance histograms in the absence of magnetic field (a) and in the magnetic field of 100 Oe (b).
M. Shimizu et al. / Journal of Magnetism and Magnetic Materials 239 (2002) 243–245
magnetic field of 100 Oe, the quantized units of nG0 switch to 0:5nG0 for low bias-voltage below 240 mV, as already mentioned in a previous paper [2], and new peaks of fractional unit 0:35nG0 emerge when the biasvoltage is higher than 280 mV. It is interestingly noted that the fractional quantization units 0:35nG0 and 0:7nG0 are 0.7 times as small as units 0:5nG0 and nG0 : The former and latter are, respectively, observed in the application of high and low bias-voltage. Furthermore, the quantization units in magnetic fields switch to a half of those in the absence of magnetic field; thus, nG0 and 0:7nG0 in Hext ¼ 0 switch to 0:5nG0 and 0:35nG0 in Hext ¼ 100 Oe, respectively. These indicate that the emersion of 0:35nG0 and 0:7nG0 peaks is attributed to the same source depending on the bias-voltage. Recently, Costa-Kr.amer et al. [3] and Abell!an et al. [4] showed that the quantization units in Au wire vary continuously with increasing the bias-voltage, reflecting non-linear current and voltage relationship. Their experimental result seems to be different from present result wherein the fractional quantization units depend on the magnetic field as well as on the bias-voltage. In semiconductive wires, the existence of 0:7G0 conductance plateau has been known [5], and there are many attempts from the theoretical viewpoints to interpret the 0:7G0 problem; for example, (1) a spin-singlet and triplet bond state model formed around the nano-wire [6], (2) a spontaneous spin polarization model in nano-wires due to the electron correlation [7,8], (3) the Tomonaga and Luttinger model considering leads [9], and (4) the spindensity-functional model [10]. The 0:7nG0 problem, however, is still unsolved at the present stage. In the spin polarized case such as ferromagnetic Ni nano-wire, the switching of quantization unit from nG0 to 0:5nG0 is closely related to the spin degeneracy, while not only the existence of the fractional quantized unit but also the switching between 0:7nG0 and 0:35nG0 by
245
application of magnetic fields are hardly explained with the above models.
4. Conclusion The conductance in ferromagnetic Ni nano-wire is quantized in units of 2e2 =h in the absence of magnetic field and at bias-voltage below 120 mV, while the conductance in the magnetic field is quantized in units of e2 =h when bias-voltage is lower than 240 mV. Increasing applied bias-voltage, the new fractional quantization units of 0:7ne2 =h and 0:7ð2ne2 =hÞ appear whether the magnetic field is applied or not.
References ! ! [1] J.I. Pascual, J. M!endez, J. Gomez-Herrero, A.M. Baro, N. Garc!ıa, V.T. Binh, Phys. Rev. Lett. 71 (1993) 1852. [2] T. Ono, Y. Ooka, H. Miyajima, Y. Otani, Appl. Phys. Lett. 75 (1999) 1622. [3] J.L. Costa-Kr.amer, N. Garc!ıa, P. Garc!ıa-Mochales, P.A. Serena, M.I. Marqu!es, A. Correia, Phys. Rev. B 55 (1997) 5416. ! A. Arenas, Surf. Sci. 418 (1998) [4] J. Abell!an, R. Chicon, 493. [5] K.J. Thomas, J.T. Nicholls, M.Y. Simmons, M. Pepper, D.R. Mace, D.A. Ritchie, Phys. Rev. Lett. 77 (1996) 135. [6] V.V. Flambaum, M.Yu. Kuchiev, Phys. Rev. B 61 (2000) 7869. [7] B. Spivak, F. Zhou, cond-matt/9911175. [8] H. Bruus, V.V. Cheianov, K. Flensberg, cond-matt/ 0002338. [9] D.L. Maslov, M. Stone, Phys. Rev. B 52 (1995) 5539. [10] K. Hirose, S. Li, N.S. Wingreen, Phys. Rev. Lett. 63 (2001) 33315.