- Email: [email protected]
Pt] multilayer
Current Applied Physics 10 (2010) 655–658
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Large spontaneous Hall angle in [Co, CoFe/Pt] multilayer H.N. Lee a, Y.J. Cho b, J.H. Eom c, S.J. Joo d, K.H. Shin d, T.W. Kim a,* a
Department of Advanced Materials Engineering, Sejong University, Seoul, Republic of Korea Semiconductor Devices Lab., Samsung Advanced Institute of Technology, Suwon, Kyonggi-Do, Republic of Korea c Department of Physics, Sejong University, Seoul, Republic of Korea d Nano Devices Center, Korea Institute of Science and Technology, Seoul, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 10 July 2008 Received in revised form 2 February 2009 Accepted 19 August 2009 Available online 22 August 2009 PACS: 75.70.i 75.70.Cn Keywords: Spontaneous Hall effect Hall angle Magnetic multilayer Amorphous rare earth–transition metal alloy Spin polarization
a b s t r a c t We have quantitatively investigated the Hall effect in [Co, CoFe/Pt] multilayer films. The [Co, CoFe/Pt] multilayers exhibit large spontaneous Hall resistivity (qH) and Hall angle (qH/q). Even though the Hall resistivity in [Co, CoFe/Pt] multilayer films (2.7–4 107 X cm) is smaller than that of amorphous RE– TM alloy films which show large spontaneous Hall resistivity (<2 106 X cm), the Hall angle of multilayer (6–8%) is almost twice than that in amorphous rare earth–transition metal alloy films (3%). The Hall angle provides evidence of the effects of the exchange interaction of the Hall scattering. The exchange is between conduction electron spins and the localized spins of the transition metal. The large Hall angle of [Co, CoFe/Pt] multilayer can be considered due to the high spin polarization and high Curie temperature of Co and CoFe transition metal layers. Even though the role of interfaces and surfaces in the magnetic properties of multilayer films may dominate that of the bulk, the Hall effects in [Co, CoFe/Pt] multilayer may be mainly dominated by the bulk effect. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Magnetic multilayer films with perpendicular magnetic anisotropy have been extensively studied for the application of magnetic recording or magnetic-optical recording media. The spontaneous Hall effect (extraordinary Hall effect) in magnetic metals and alloys which is caused by spin–orbit interaction is substantially larger than the ordinary Hall effect due to Lorentz force. Some materials exhibit quite large spontaneous Hall effect suitable for Hall sensors. These materials include amorphous rare earth (RE)–transition metal (TM) alloy [1–4] and Pt-based magnetic multilayer. Recently, the large spontaneous Hall effect in Pt-based TM magnetic multilayer has been reported, in which it is important for the materials to have a large spontaneous Hall effect at a low magnetic field [6]. The analysis of large spontaneous Hall effect has been well studied for amorphous RE–TM alloy [1–5] but not for magnetic multilayer films. The intensive and quantitative investigation of the Hall effect in magnetic multilayer films is of great theoretical importance, since it provides us a means of understanding the electronic transport in these alloys.
* Corresponding author. Fax: +82 2 3408 4342. E-mail address: [email protected] (T.W. Kim). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.08.011
In this study, we focused on [Co/Pt] multilayer and [CoFe/Pt] multilayer. [CoFe/Pt] multilayer films show a large spontaneous Hall resistivity (qH) and Hall angle (qH/q). The Hall angle provides evidence of the importance of the exchange energy and spin polarization in their effect on the Hall Scattering. The aim of the study is to quantitatively research the effect of Curie temperature and spin polarization to spontaneous Hall effect in magnetic multilayer using Hall resistivity and Hall angle. 2. Experiments The [Ta50 Å/Pt 4 Å/(Co3 Å/Pt8 Å)]10,15 multilayer films and [Ta50 Å/Pt4 Å/(Co90Fe103 Å/Pt8 Å)]10,15 multilayer films were deposited on in a DC magnetron sputtering system at room temperature. Argon was used as the sputtering gas. Initial pressure was 7 108 Torr and the deposition pressure was in the range of 1–6 mTorr. Magnetic properties were measured by using a vibrating sample magnetometer with a maximum magnetic field of 10 kOe. The transport properties including the Hall effect were measured by using the van der Pauw method at magnetic fields up to 3.5 kOe. The field was applied in the direction perpendicular to the film plane. Four indium wire contacts were formed at right angles. With an applied field of 100 lA, voltage was measured at the rest two adjacent ones. All measurements were done at room
656
H.N. Lee et al. / Current Applied Physics 10 (2010) 655–658
temperature. The Hall resistivity (qH) and Hall angle (qH/q) were calculated on the basis of the measured Hall voltage (VH) and sample resistivity (q). 3. Results and discussion For a material with a saturated spontaneous magnetic moment Ms, the Hall resistivity is given in cgs units by [5];
qH ¼ Ro B þ Rs 4pMs
ð1Þ
where Ro is the ordinary Hall coefficient and Rs is the extraordinary coefficient or the spontaneous Hall coefficient. The change of qH with applied field is the same with that of magnetization with applied field. Therefore, qH has a same shape of magnetization hysteresis loop. 4pMs is the field necessary to overcome demagnetization perpendicular to the plane of the film. In a magnetic multilayer, because Ro is much smaller than Rs, the Hall resistivity can be described by:
qH ¼ Rs 4pMs
ð2Þ
[Co, CoFe/Pt] multilayer films showed a strong perpendicular magnetic anisotropy, which exhibits a rectangular hysteresis loop when the magnetic field is applied perpendicular to the film plane. Hysteresis loops measured with the applied field perpendicular to the film plane were saturated at the field range of 200 Oe–1.2 kOe. On the contrary, Hysteresis loops measured with the applied field par-
Fig. 1. qH and qH/q -H loops of [Co/Pt]10 multilayer. (qH: 2.7 107 X cm, qH/q: 6% and q: 5.4 106 X cm).
allel to the film plane were saturated at the field range of 4–6 kOe. In Fig. 1 are shown the qH -H and qH/q -H loops for [Co/Pt]10 multilayer. No correction was made with respect to the demagnetization field. The hysteresis of qH -H loop is the same as that observed in an ordinary M–H loop, indicating that the sign of Rs is positive. The saturation of Hall resistivity reached at about 850 Oe, and the Hall resistivity (qH) and Hall angle (qH/q) are 2.7 107 X cm and 6%, respectively. The ease of saturation and the existence of hysteresis can be understood from the fact that the [Co/Pt] multilayer possesses the perpendicular anisotropy. Fig. 2 shows the qH -H and qH/q -H loops for the [Co/Pt]15 multilayer. The saturation of Hall resistivity reached at about 1.2 kOe, and the qH and qH/q are 2.7 107 X cm and 6%, which are the same values with those of [Co/Pt]10 multilayer. Another important point to note in [Co/Pt]15 multilayer is that the way qH varies with H is opposite to that observed in an ordinary M–H loop. Specifically, the value of qH decreases (increases) with increasing (decreasing) H, indicating that the sign of Rs is negative. [Co/Pt] multilayer films exhibit the different sign of Hall effect with the number of layers. In order to explain the positive and negative Hall effects, McGuire and Gambino have proposed the model on Hall effect of amorphous RE–TM alloys in which ferromagnetic exchange-coupled RE and TM sublattices both contribute to Hall resistivity (qH). The resulting Hall voltage is the sum of the two sublattices which are pointed antiparallel to each other in amorphous RE–TM alloys [2]. On the basis of the sublattice model, both [Co/Pt]10 and [Co/Pt]15 multilayers have the same Co sublattice, which seem to induce the same
Fig. 2. qH and qH/q -H loops of [Co/Pt]15 multilayer. (qH: 2.7 107 X cm, qH/q: 6% and q: 5.4 106 X cm).
H.N. Lee et al. / Current Applied Physics 10 (2010) 655–658
657
Hall effect, both positive or both negative. The inconsistency between the sign of Hall effect and the number of layers in [Co/Pt] multilayer films is hard to be explained. Figs. 3 and 4 show the qH -H and qH/q -H loops for [CoFe/Pt]10 and [CoFe/Pt]15 multilayers, respectively. The [CoFe/Pt] multilayers exhibit negative Hall effects for both multilayers. In [CoFe/ Pt]10 multilayer, the saturation of Hall resistivity reached at about 500 Oe, and the qH and qH/q are 4 107 X cm and 8%. In [CoFe/ Pt]15 multilayer, the saturation of Hall resistivity reached at about 200 Oe, and the qH and qH/q are 6.5 107 X cm and 10%. Even though the resistivity of [CoFe/Pt]15 multilayer (q: 6.5 106 X cm) is somewhat higher than that of [CoFe/Pt]10 multilayer (q: 5 106 X cm), the qH and qH/q of [CoFe/Pt]15 multilayer are higher than those of [CoFe/Pt]10 multilayer. As the spontaneous Hall effect is related the magnetic moment in magnetic layer, the Hall resistivity would be suppressed by the decrease of magnetic moment. Therefore, it can be though that the difference of Hall resistivity between two [CoFe/Pt] multilayers would be caused by the formation of magnetic dead layer at the interface in case of [CoFe/Pt]10 multilayer. The magnetic dead layer can make the Hall resistivity decrease. The relation between qH and a fraction of the dead layer contribution to qH can be described by:
jqH j ¼ jqHmax jx jqHmax jð1 xÞ jqH =qHmax j ¼ 2x 1
ð3Þ
Fig. 4. qH and qH/q -H loops of CoFe/Pt]15 multilayer. (qH: 6.5 107 X cm, qH/q: 10% and q: 6.5 106 X cm).
Fig. 3. qH and qH/q -H loops of [CoFe/Pt]10 multilayer. (qH: 4 107 X cm, qH/q: 8% and q: 5 106 X cm).
where qH max is the maximum of Hall resistivity which can be provided by the reference multilayer with maximum Hall resistivity, and x is a fraction of Hall resistivity in the multilayer with dead layer. Assuming that the maximum Hall resistivity is 6.5 107 X cm of [CoFe/Pt]15 multilayer, the fractional Hall resistivity |qH/qH max| is about 0.57 using the Hall resistivity (qH) of [CoFe/ Pt]10 multilayer with magnetic dead layer. Inserting the absolute fraction, |qH/qH max|, to Eq. (3), a fraction of 0.78 (78%) is obtained. The fraction of magnetic dead layer contribution to qH is 0.22 (22%). Therefore, the above analysis might explain the reason that [CoFe/ Pt]10 multilayer has the lower value of Hall resistivity (78%) to [CoFe/Pt]15 multilayer. The Hall effect can better be characterized by the ratio qH/q (or also frequently called the tangent of the Hall angle) (where q is the electrical resistivity), since both qH and q arise from the same atomic scattering sources [5]. Therefore, the Hall angle (qH/q) provides the evidence of the importance of the exchange energy in its effect on the Hall scattering. In RE metals and alloys the RKKY exchange mechanism is believed to be dominant. This exchange is between conduction electron spins and the localized spins of the rare earth. The conduction electrons are polarized by this exchange and the strength of the exchange is related to the Curie temperature or Curie Weiss h. The increase in spin polarization of the conduction electrons enhances the intrinsic spin–orbit coupling [5]. On the basis of the effect of spin-polarized conduction electrons, it is possible to explain the large Hall angle (qH/q) in transition me-
658
H.N. Lee et al. / Current Applied Physics 10 (2010) 655–658
tal multilayer films. The [Co, CoFe/Pt] multilayer films exhibit a large spontaneous Hall angle compared to amorphous TbCo alloy films which show large spontaneous Hall effect. Even though the qH in [Co, CoFe/Pt] multilayer films (2.7–4 107 X cm) is smaller than that in amorphous RE–TM alloy films (<2 106 X cm), the Hall angle of multilayer (6–8%) is almost twice than that in amorphous TbCo alloy films (3%). The large Hall angle of [CoFe/Pt] multilayer films can be considered due to the high spin polarization and high Curie temperature of Co or CoFe transition metal layer. From Figs. 1–4, it can be seen that [CoFe/Pt] multilayers have the larger qH and qH/q than [Co/Pt] multilayers. Though the pure Co has a higher Curie temperature than CoFe alloys [7], the qH and qH/q of [Co/Pt] multilayer are smaller than those of [CoFe/Pt] multilayer. The lager Hall angle of [CoFe/Pt] multilayer compared to [Co/Pt] multilayer would be mainly due to the higher spin polarization of CoFe magnetic layer in [CoFe/Pt] multilayer than that of pure Co magnetic layer in [Co/Pt] multilayer [8]. From the results of qH and qH/q for [Co, CoFe/Pt] multilayer films, even though the role of interfaces and surfaces in the magnetic properties of multilayer films may dominate that of the bulk, the Hall effects in [Co, CoFe/ Pt] multilayer films may be mainly dominated by the bulk effect of magnetic layer in multilayer. 4. Conclusions Recently, the large spontaneous Hall effect in magnetic multilayers has been reported. The quantitative study on spontaneous
Hall effect in magnetic multilayers has not been done yet. [Co, CoFe/Pt] multilayer films showed a large spontaneous Hall angle compared to amorphous TbCo alloy films which show large spontaneous Hall effect. From the analysis of Hall resistivity (qH) and Hall angle (qH/q), it can be though that a large Hall angle of [Co, CoFe/Pt] multilayer films is due to the high spin polarization and high Curie temperature of transition metal layer and the Hall effects in [Co, CoFe/Pt] multilayer films may be mainly dominated by the bulk effect of magnetic layer in multilayer. Acknowledgement This work was supported by the faculty research fund of the National Program for Tera-level Nanodevices as a 21st Century Frontier Program. References [1] [2] [3] [4] [5]
T.R. McGuire, R.J. Gambino, R.C. Taylor, IEEE Trans. Magn. 13 (1977) 1598. T.R. McGuire, R.J. Gambino, R.C. Taylor, J. Appl. Phys. 48 (1977) 2965. T.W. Kim, R.J. Gambino, J. Appl. Phys. 87 (4) (2000) 1869. T.W. Kim, S.H. Lim, R.J. Gambino, J. Appl. Phys. 89 (11) (2001) 7212. T.R. McGuire, R.J. Gambino, R.C. O’Handley, Hall effect in amorphous metals, in: C.L. Chien, C.R. Westgate (Eds.), The Hall Effect and Its Applications, Plenum Publishing Corp., New York, 1980, p. 137. [6] Y. Zhu, J.W. Cai, Appl. Phys. Lett. 90 (2007) 1869. [7] R.C. O’Handley, Modern Magnetic Materials Principles and Applications, John Wiley & Sons, 2000. [8] H. Kikuchi, M. Sato, K. Kobayashi, J. Appl. Phys. 87 (2000) 6055.
Contents lists available at ScienceDirect
Current Applied Physics journal homepage: www.elsevier.com/locate/cap
Large spontaneous Hall angle in [Co, CoFe/Pt] multilayer H.N. Lee a, Y.J. Cho b, J.H. Eom c, S.J. Joo d, K.H. Shin d, T.W. Kim a,* a
Department of Advanced Materials Engineering, Sejong University, Seoul, Republic of Korea Semiconductor Devices Lab., Samsung Advanced Institute of Technology, Suwon, Kyonggi-Do, Republic of Korea c Department of Physics, Sejong University, Seoul, Republic of Korea d Nano Devices Center, Korea Institute of Science and Technology, Seoul, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 10 July 2008 Received in revised form 2 February 2009 Accepted 19 August 2009 Available online 22 August 2009 PACS: 75.70.i 75.70.Cn Keywords: Spontaneous Hall effect Hall angle Magnetic multilayer Amorphous rare earth–transition metal alloy Spin polarization
a b s t r a c t We have quantitatively investigated the Hall effect in [Co, CoFe/Pt] multilayer films. The [Co, CoFe/Pt] multilayers exhibit large spontaneous Hall resistivity (qH) and Hall angle (qH/q). Even though the Hall resistivity in [Co, CoFe/Pt] multilayer films (2.7–4 107 X cm) is smaller than that of amorphous RE– TM alloy films which show large spontaneous Hall resistivity (<2 106 X cm), the Hall angle of multilayer (6–8%) is almost twice than that in amorphous rare earth–transition metal alloy films (3%). The Hall angle provides evidence of the effects of the exchange interaction of the Hall scattering. The exchange is between conduction electron spins and the localized spins of the transition metal. The large Hall angle of [Co, CoFe/Pt] multilayer can be considered due to the high spin polarization and high Curie temperature of Co and CoFe transition metal layers. Even though the role of interfaces and surfaces in the magnetic properties of multilayer films may dominate that of the bulk, the Hall effects in [Co, CoFe/Pt] multilayer may be mainly dominated by the bulk effect. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Magnetic multilayer films with perpendicular magnetic anisotropy have been extensively studied for the application of magnetic recording or magnetic-optical recording media. The spontaneous Hall effect (extraordinary Hall effect) in magnetic metals and alloys which is caused by spin–orbit interaction is substantially larger than the ordinary Hall effect due to Lorentz force. Some materials exhibit quite large spontaneous Hall effect suitable for Hall sensors. These materials include amorphous rare earth (RE)–transition metal (TM) alloy [1–4] and Pt-based magnetic multilayer. Recently, the large spontaneous Hall effect in Pt-based TM magnetic multilayer has been reported, in which it is important for the materials to have a large spontaneous Hall effect at a low magnetic field [6]. The analysis of large spontaneous Hall effect has been well studied for amorphous RE–TM alloy [1–5] but not for magnetic multilayer films. The intensive and quantitative investigation of the Hall effect in magnetic multilayer films is of great theoretical importance, since it provides us a means of understanding the electronic transport in these alloys.
* Corresponding author. Fax: +82 2 3408 4342. E-mail address: [email protected] (T.W. Kim). 1567-1739/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cap.2009.08.011
In this study, we focused on [Co/Pt] multilayer and [CoFe/Pt] multilayer. [CoFe/Pt] multilayer films show a large spontaneous Hall resistivity (qH) and Hall angle (qH/q). The Hall angle provides evidence of the importance of the exchange energy and spin polarization in their effect on the Hall Scattering. The aim of the study is to quantitatively research the effect of Curie temperature and spin polarization to spontaneous Hall effect in magnetic multilayer using Hall resistivity and Hall angle. 2. Experiments The [Ta50 Å/Pt 4 Å/(Co3 Å/Pt8 Å)]10,15 multilayer films and [Ta50 Å/Pt4 Å/(Co90Fe103 Å/Pt8 Å)]10,15 multilayer films were deposited on in a DC magnetron sputtering system at room temperature. Argon was used as the sputtering gas. Initial pressure was 7 108 Torr and the deposition pressure was in the range of 1–6 mTorr. Magnetic properties were measured by using a vibrating sample magnetometer with a maximum magnetic field of 10 kOe. The transport properties including the Hall effect were measured by using the van der Pauw method at magnetic fields up to 3.5 kOe. The field was applied in the direction perpendicular to the film plane. Four indium wire contacts were formed at right angles. With an applied field of 100 lA, voltage was measured at the rest two adjacent ones. All measurements were done at room
656
H.N. Lee et al. / Current Applied Physics 10 (2010) 655–658
temperature. The Hall resistivity (qH) and Hall angle (qH/q) were calculated on the basis of the measured Hall voltage (VH) and sample resistivity (q). 3. Results and discussion For a material with a saturated spontaneous magnetic moment Ms, the Hall resistivity is given in cgs units by [5];
qH ¼ Ro B þ Rs 4pMs
ð1Þ
where Ro is the ordinary Hall coefficient and Rs is the extraordinary coefficient or the spontaneous Hall coefficient. The change of qH with applied field is the same with that of magnetization with applied field. Therefore, qH has a same shape of magnetization hysteresis loop. 4pMs is the field necessary to overcome demagnetization perpendicular to the plane of the film. In a magnetic multilayer, because Ro is much smaller than Rs, the Hall resistivity can be described by:
qH ¼ Rs 4pMs
ð2Þ
[Co, CoFe/Pt] multilayer films showed a strong perpendicular magnetic anisotropy, which exhibits a rectangular hysteresis loop when the magnetic field is applied perpendicular to the film plane. Hysteresis loops measured with the applied field perpendicular to the film plane were saturated at the field range of 200 Oe–1.2 kOe. On the contrary, Hysteresis loops measured with the applied field par-
Fig. 1. qH and qH/q -H loops of [Co/Pt]10 multilayer. (qH: 2.7 107 X cm, qH/q: 6% and q: 5.4 106 X cm).
allel to the film plane were saturated at the field range of 4–6 kOe. In Fig. 1 are shown the qH -H and qH/q -H loops for [Co/Pt]10 multilayer. No correction was made with respect to the demagnetization field. The hysteresis of qH -H loop is the same as that observed in an ordinary M–H loop, indicating that the sign of Rs is positive. The saturation of Hall resistivity reached at about 850 Oe, and the Hall resistivity (qH) and Hall angle (qH/q) are 2.7 107 X cm and 6%, respectively. The ease of saturation and the existence of hysteresis can be understood from the fact that the [Co/Pt] multilayer possesses the perpendicular anisotropy. Fig. 2 shows the qH -H and qH/q -H loops for the [Co/Pt]15 multilayer. The saturation of Hall resistivity reached at about 1.2 kOe, and the qH and qH/q are 2.7 107 X cm and 6%, which are the same values with those of [Co/Pt]10 multilayer. Another important point to note in [Co/Pt]15 multilayer is that the way qH varies with H is opposite to that observed in an ordinary M–H loop. Specifically, the value of qH decreases (increases) with increasing (decreasing) H, indicating that the sign of Rs is negative. [Co/Pt] multilayer films exhibit the different sign of Hall effect with the number of layers. In order to explain the positive and negative Hall effects, McGuire and Gambino have proposed the model on Hall effect of amorphous RE–TM alloys in which ferromagnetic exchange-coupled RE and TM sublattices both contribute to Hall resistivity (qH). The resulting Hall voltage is the sum of the two sublattices which are pointed antiparallel to each other in amorphous RE–TM alloys [2]. On the basis of the sublattice model, both [Co/Pt]10 and [Co/Pt]15 multilayers have the same Co sublattice, which seem to induce the same
Fig. 2. qH and qH/q -H loops of [Co/Pt]15 multilayer. (qH: 2.7 107 X cm, qH/q: 6% and q: 5.4 106 X cm).
H.N. Lee et al. / Current Applied Physics 10 (2010) 655–658
657
Hall effect, both positive or both negative. The inconsistency between the sign of Hall effect and the number of layers in [Co/Pt] multilayer films is hard to be explained. Figs. 3 and 4 show the qH -H and qH/q -H loops for [CoFe/Pt]10 and [CoFe/Pt]15 multilayers, respectively. The [CoFe/Pt] multilayers exhibit negative Hall effects for both multilayers. In [CoFe/ Pt]10 multilayer, the saturation of Hall resistivity reached at about 500 Oe, and the qH and qH/q are 4 107 X cm and 8%. In [CoFe/ Pt]15 multilayer, the saturation of Hall resistivity reached at about 200 Oe, and the qH and qH/q are 6.5 107 X cm and 10%. Even though the resistivity of [CoFe/Pt]15 multilayer (q: 6.5 106 X cm) is somewhat higher than that of [CoFe/Pt]10 multilayer (q: 5 106 X cm), the qH and qH/q of [CoFe/Pt]15 multilayer are higher than those of [CoFe/Pt]10 multilayer. As the spontaneous Hall effect is related the magnetic moment in magnetic layer, the Hall resistivity would be suppressed by the decrease of magnetic moment. Therefore, it can be though that the difference of Hall resistivity between two [CoFe/Pt] multilayers would be caused by the formation of magnetic dead layer at the interface in case of [CoFe/Pt]10 multilayer. The magnetic dead layer can make the Hall resistivity decrease. The relation between qH and a fraction of the dead layer contribution to qH can be described by:
jqH j ¼ jqHmax jx jqHmax jð1 xÞ jqH =qHmax j ¼ 2x 1
ð3Þ
Fig. 4. qH and qH/q -H loops of CoFe/Pt]15 multilayer. (qH: 6.5 107 X cm, qH/q: 10% and q: 6.5 106 X cm).
Fig. 3. qH and qH/q -H loops of [CoFe/Pt]10 multilayer. (qH: 4 107 X cm, qH/q: 8% and q: 5 106 X cm).
where qH max is the maximum of Hall resistivity which can be provided by the reference multilayer with maximum Hall resistivity, and x is a fraction of Hall resistivity in the multilayer with dead layer. Assuming that the maximum Hall resistivity is 6.5 107 X cm of [CoFe/Pt]15 multilayer, the fractional Hall resistivity |qH/qH max| is about 0.57 using the Hall resistivity (qH) of [CoFe/ Pt]10 multilayer with magnetic dead layer. Inserting the absolute fraction, |qH/qH max|, to Eq. (3), a fraction of 0.78 (78%) is obtained. The fraction of magnetic dead layer contribution to qH is 0.22 (22%). Therefore, the above analysis might explain the reason that [CoFe/ Pt]10 multilayer has the lower value of Hall resistivity (78%) to [CoFe/Pt]15 multilayer. The Hall effect can better be characterized by the ratio qH/q (or also frequently called the tangent of the Hall angle) (where q is the electrical resistivity), since both qH and q arise from the same atomic scattering sources [5]. Therefore, the Hall angle (qH/q) provides the evidence of the importance of the exchange energy in its effect on the Hall scattering. In RE metals and alloys the RKKY exchange mechanism is believed to be dominant. This exchange is between conduction electron spins and the localized spins of the rare earth. The conduction electrons are polarized by this exchange and the strength of the exchange is related to the Curie temperature or Curie Weiss h. The increase in spin polarization of the conduction electrons enhances the intrinsic spin–orbit coupling [5]. On the basis of the effect of spin-polarized conduction electrons, it is possible to explain the large Hall angle (qH/q) in transition me-
658
H.N. Lee et al. / Current Applied Physics 10 (2010) 655–658
tal multilayer films. The [Co, CoFe/Pt] multilayer films exhibit a large spontaneous Hall angle compared to amorphous TbCo alloy films which show large spontaneous Hall effect. Even though the qH in [Co, CoFe/Pt] multilayer films (2.7–4 107 X cm) is smaller than that in amorphous RE–TM alloy films (<2 106 X cm), the Hall angle of multilayer (6–8%) is almost twice than that in amorphous TbCo alloy films (3%). The large Hall angle of [CoFe/Pt] multilayer films can be considered due to the high spin polarization and high Curie temperature of Co or CoFe transition metal layer. From Figs. 1–4, it can be seen that [CoFe/Pt] multilayers have the larger qH and qH/q than [Co/Pt] multilayers. Though the pure Co has a higher Curie temperature than CoFe alloys [7], the qH and qH/q of [Co/Pt] multilayer are smaller than those of [CoFe/Pt] multilayer. The lager Hall angle of [CoFe/Pt] multilayer compared to [Co/Pt] multilayer would be mainly due to the higher spin polarization of CoFe magnetic layer in [CoFe/Pt] multilayer than that of pure Co magnetic layer in [Co/Pt] multilayer [8]. From the results of qH and qH/q for [Co, CoFe/Pt] multilayer films, even though the role of interfaces and surfaces in the magnetic properties of multilayer films may dominate that of the bulk, the Hall effects in [Co, CoFe/ Pt] multilayer films may be mainly dominated by the bulk effect of magnetic layer in multilayer. 4. Conclusions Recently, the large spontaneous Hall effect in magnetic multilayers has been reported. The quantitative study on spontaneous
Hall effect in magnetic multilayers has not been done yet. [Co, CoFe/Pt] multilayer films showed a large spontaneous Hall angle compared to amorphous TbCo alloy films which show large spontaneous Hall effect. From the analysis of Hall resistivity (qH) and Hall angle (qH/q), it can be though that a large Hall angle of [Co, CoFe/Pt] multilayer films is due to the high spin polarization and high Curie temperature of transition metal layer and the Hall effects in [Co, CoFe/Pt] multilayer films may be mainly dominated by the bulk effect of magnetic layer in multilayer. Acknowledgement This work was supported by the faculty research fund of the National Program for Tera-level Nanodevices as a 21st Century Frontier Program. References [1] [2] [3] [4] [5]
T.R. McGuire, R.J. Gambino, R.C. Taylor, IEEE Trans. Magn. 13 (1977) 1598. T.R. McGuire, R.J. Gambino, R.C. Taylor, J. Appl. Phys. 48 (1977) 2965. T.W. Kim, R.J. Gambino, J. Appl. Phys. 87 (4) (2000) 1869. T.W. Kim, S.H. Lim, R.J. Gambino, J. Appl. Phys. 89 (11) (2001) 7212. T.R. McGuire, R.J. Gambino, R.C. O’Handley, Hall effect in amorphous metals, in: C.L. Chien, C.R. Westgate (Eds.), The Hall Effect and Its Applications, Plenum Publishing Corp., New York, 1980, p. 137. [6] Y. Zhu, J.W. Cai, Appl. Phys. Lett. 90 (2007) 1869. [7] R.C. O’Handley, Modern Magnetic Materials Principles and Applications, John Wiley & Sons, 2000. [8] H. Kikuchi, M. Sato, K. Kobayashi, J. Appl. Phys. 87 (2000) 6055.