- Email: [email protected]
Pt trilayers
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Low temperature divergence in the AHE and AMR of ultra-thin Pt/Co/Pt trilayers E. Zion, N. Haham, L. Klein, A. Sharoni
T
⁎
Department of Physics & Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel
A B S T R A C T
We study the anomalous Hall effect (AHE) and anisotropic magnetoresistance (AMR) in a series of ultra-thin Pt/Co(x)/Pt trilayers (0.1 nm ⩽ x⩽ 0.5 nm ). We find that the AHE exhibits a significant increase at low temperatures (T). This increase cannot be attributed to a trivial increase in magnetization or resistivity. A similar T dependence is observed in the AMR measurements. Interestingly, these effects show almost no dependence on cobalt thickness. Our measurements indicate that the deviation from common behavior can be attributed to an induced magnetic proximity effect in the Pt layers that increases at low temperatures, in agreement with previous reports. An alternative explanation related to the evolution of a non-continuous magnetic layer is considered as well.
1. Introduction A myriad of spin-related transport properties have been reported for hybrid ferromagnetic/non-magnetic (FM/NM) structures, especially those involving heavy NM metals with strong spin orbit interactions (SOI) [1–5]. Those systems exhibit rich interfacial magnetic phenomena which may be important to spintronics applications, see [6] and references within. Recent studies used an insulating FM as a means to separate effects of currents in the FM, thus showing additional magneto-resistance (MR) effects [7]. These were interpreted as spin Hall MR (SMR) that results from both spin Hall effect (SHE) and inverse SHE in the NM layer [8,9]; magnetic proximity effect (MPE) due to the proximity of a non-magnetic layer to magnetic elements [10]; Hanle magnetoresistance related only to the heavy NM properties [11]; the nonlocal anomalous Hall effect, which requires only one SHE and spindependent interface scattering [12]. One source of complication in resolving the origins of the MR measurements is the multiple contributions from different spin scattering processes, which may have different magnitudes that are material dependent. Additional experimental information, specifically by interfacing strong SOI materials with different conducting FM will help to resolve microscopic origins of the interactions [9,13]. It is experimentally challenging to separate the contribution of the FM in the standard transport measurements and more sophisticated methods are often required [9,10]. We studied Pt/Co/Pt trilayers with ultra-thin Co, ranging from 0 nm to 0.5 nm, via anisotropic MR (AMR) and anomalous Hall effect (AHE) measurements, which enable us to resolve the spin-transport origins of these effect. The AMR and AHE were previously reported in Pt/Co multilayers,
⁎
mainly due to interest in their intrinsic perpendicular magnetocrystalline anisotropy (PMA) with easy axis perpendicular to the film [14]. Recently, in Pt/Co/Pt layers (with thicker Co than we use), an additional MR was reported [15]. There is a considerable difference in magnitude of MR for magnetization in-plane that is perpendicular to the current and MR for out-of-plane magnetization, in spite of also being normal to the current. The effect is due to the interface, thus it was coined anisotropic interface MR (AIMR). The AHE is sensitive to both spin and topology, and is at the focus of considerable theoretical and experimental efforts [16,17]. It can be described phenomenologically as transverse resistivity, ρxy , linked to the intrinsic magnetization, M⊥ , of a conductor. The most common model is the extrinsic model, which relates the AHE to antisymmetric scattering processes and it provides that
ρxy = Rs M⊥,
(1)
where 2 Rs = aρxx + bρxx .
(2)
Here ρxx is the longitudinal resistivity and M⊥ is the component of magnetization perpendicular to the film. The linear term in resistivity of Rs is attributed to skew scattering and the quadratic term to side jumps [18,19]. AHE measurements of Co/Pt multilayers have been reported to follow this relation [20]. We find that the AHE in Pt/Co/Pt trilayers with ultra-thin Co (0.5 nm and below) exhibits an anomaly at low temperatures. While we can understand the high temperature AHE in terms of the extrinsic mechanism, the low temperature AHE changes significantly, although resistivity and magnetization do not exhibit any strong T dependence. A
Corresponding author. E-mail address: [email protected] (A. Sharoni).
https://doi.org/10.1016/j.jmmm.2019.04.035 Received 30 April 2017; Received in revised form 31 March 2019; Accepted 10 April 2019 Available online 19 April 2019 0304-8853/ © 2019 Published by Elsevier B.V.
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
setting the field to zero. Next, the transverse resistance was measured during heating in two configurations that enable to extract accurately the anti-symmetric (i.e. transverse) resistance[24,25]. In Fig. 1(a) we plot the T dependence of the transverse resistivity from the zero-field Hall measurements, for all Co thicknesses. Since there is no external magnetic field, we naively attribute the measured ρxy to an AHE signal, which is proportional to M⊥. For all non-zero Co thicknesses ρxy decreases with increasing T until it drops rapidly to zero, at the vicinity of its Curie temperature, Tc . The Tc as a function of Co thickness, plotted in Fig. 1(c), displays a linear dependence, exemplifying strong sensitivity to Co thickness in this ultra-thin regime (we note that for each thickness we measured bridges from 2 to 5 samples, to ensure reproducibility). We draw attention to an unusual T dependence in the measurement, visible in the 0.3, 0.4 and 0.5 samples. Below ∼50 K ρxy increases significantly, as T decreases. A zoom of this region is plotted for the 0.3 sample in Fig. 1(b), showing the upturn. This behavior is unexpected since commonly at low temperatures both magnetization and longitudinal resistivity do not vary significantly [26], and thus, from Eq. (2) we would expect a saturation of the AHE at low temperatures. Fig. 1(d) shows the T dependence of longitudinal resistivity. The resistivity increases linearly at high temperatures, while at low temperatures it reaches a constant value for all Co thicknesses. A non-consistent systematics in the T-dependent part of the longitudinal resistivity for films with different Co may be the result of experimental issues. Since we are dealing with ultra-thin films, a small error in total Pt thickness of 1 Å in the deposition (from speed of shutter control, e.g.) would lead to a 4% error in total thickness. We note that insertion of the Co layer nearly doubles the samples’ resistivity, while the Co thickness itself does not modify the resistivity considerably [27,28]. Specifically, it does not reduce the resistivity, although Co bulk resistivity is lower than that of Pt [29]. This indicates that scattering (and resistance) of the Co/Pt
similar anomaly at low T appears in the AMR measurements of these films. By quantitatively comparing measurements of trilayers with different Co thickness, we resolve two contributions to the AHE and AMR signals - one that scales with the nominal Co thickness, and a second that shows the unexpected low T anomaly and is independent of Co thickness. We find evidence that the low T features can be related to MPE in the Pt layer, showing similar features to those previously reported [5,21]. However, we cannot rule out an additional scattering mechanism arising from temperature-dependent ferromagnetism of non-continues Co islands at the Pt/Co interfaces. 2. Experimental A series of Pt(3 nm)/Co(x)/Pt(3 nm) films were deposited by magnetron sputtering onto Si(100) wafers with 0.5 μm SiO2 insulator. For details about the films’ deposition process, see supplemental material [22]. Nominal Co thickness ranged between x = 0 to 0.5 nm in 0.1 nm steps. For simplicity, we label the samples by their Co thickness. X-ray reflectivity (XRR) measurements indicate there is some intermixing between Co and Pt at the film center [22]. The films were patterned via photolithography followed by Ar milling[23] into Hall bars (width = 50 μm and length = 200 μm, see inset of Fig. 1(b)) to allow transverse, ρxy , and longitudinal, ρxx , resistivity measurements. We performed these measurements in a commercial Quantum Design PPMS-9 cryostat, via a 4-probe configuration and as a function of temperature, magnetic field magnitude and direction. 3. Results and discussion Zero-field Hall measurements were executed by first cooling the sample to 2 K in a 0.5 T magnetic field perpendicular to the film, then
Fig. 1. (a) ρxy as function of T, Co thicknesses are marked. (b) ρxy in the low T regime for sample 0.3, dotted line is the expected extrapolation. Inset: schematic illustration of sample structure and measurement geometry. (c) Curie temperature as function of the Co thickness. (d) Longitudinal resistivity vs. T of all samples, color coding same as (a). 315
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
Fig. 2. ρxy as function of the magnetic field for the 0.4 sample, before (a) and after (b) subtracting the trivial OHE due to the applied magnetic field. The measurement temperatures are marked in the figure. (c) Fitting of ρxyAHE to the high field dependence and extrapolation to 1/ H → 0 . (d) Extracted values of ρ AHE , sat as function of the longitudinal resistivity. Red dotted line represents fitting of linear region to Eq. (2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
deviation of the AHE magnitude at low temperatures (the low resistivity values in the figure). In Fig. 3(a) we present the results of the analysis for all the samples, showing ρ AHE , sat as a function of T. In the inset, the measurements are plotted to scale. In the main frame, we subtracted from each measurement its value at 2 K, so to compare the changes as a function of T. As the Cobalt becomes thinner the AHE signal decreases, and for the 0.1 sample it approaches zero for higher temperatures (see Fig. 3(a), inset). Comparing the changes with T (main frame), we see that for all the samples there is an increase in ρ AHE , sat at low temperatures, and with similar magnitude. Additionally, the 0.3, 0.4 and 0.5 samples show an increase with raising T, as expected for the AHE, since the resistance is increasing. In the 0.1 sample, the AHE measurement decreases for all temperatures. To gain further insight we present the results as follows. In Fig. 3(b,c) we show the residual AHE signal, Δρ AHE , for the 0.3, 0.4 and 0.5 samples after subtracting the 0.1 signal (Fig. 3(b) is vs. T and 3(c) vs. ρxx ). The sharp increase at low temperatures has vanished for all the samples, and Δρ AHE has a resistivity dependence that can be fitted by Eq. 2 for the AHE (red dashed line). This supports that the source of the increase is independent of the Co amount. Now, Δρ AHE should represent contribution from scattering in the intermixing region. Fig. 4 shows the normalized Δρ AHE (for each sample) by the residual Co thickness (Cothickness – 0.1 nm). The results, plotted in Fig. 4 (in (b) vs. T and in (c) as a function of ρxx ) depict a good scaling relation. Our AHE analysis points toward two separate contributions to the AHE signal. The first contribution follows the conventional dependence of AHE on ρxx [20] and scales with Co content [33]. The second contribution increases at lower T and is nearly independent of increasing Co thickness. To gain further insight, we analyzed the AMR behavior of these films.
intermixing is significant (diffusive), and is almost not influenced by the amount of Co for this range (as shown in Fig. 1(d))[30,31]. The zero field measurements qualitatively reveal the temperature dependence of the AHE. However, temperature driven changes of the domain structure cannot be ruled out. Hence, in order to accurately determine the AHE contribution of the samples for different temperatures (including the T dependence of saturation magnetization) the following procedure is preformed: Since we do not have a direct measurement of M⊥ , we assess the AHE for saturation magnetization in the following way. We measure the dependence of the transverse resistivity on the perpendicular magnetic field, up to 8 T, exemplified in Fig. 2(a) for the 0.4 sample and three different temperatures, 2 K, 70 K and OHE 140 K. We extract the ordinary Hall effect (OHE) resistivity, ρxy , from the high field slope of ρxy at 2 K, where the AHE is nearly field independent [32]. The OHE is dominantly due to the Pt layers, which are OHE 6 nm. Since OHE of Pt has no T dependence [7], we may subtract ρxy from ρxy for any temperature and field, resulting in ρxyAHE . This is presented in Fig. 2(b) for the 0.4 sample and three different temperatures. For the 2 K measurement ρxyAHE reaches a plateau at high fields, but as T increases, ρxyAHE has a considerable field dependence even at high fields. We expand in first order the high field behavior of magnetization to M = Ms (1 − a/ H ) , where Ms is the saturation magnetization, which is T independent, and a is a constant. By extrapolating to large fields, i.e. 1/ H → 0 , we can find ρ AHE , sat = Ms Rs . Now we can compare Rs for every T, up to the constant Ms , by fitting
ρ AHE = ρ AHE , sat (1 − a/ H )
(3)
to the high field dependence in our measurements, depicted in Fig. 2(c) for the same three temperatures. Rs Ms is shown as a function of resistivity in Fig. 2(d) for the 0.4 sample. The red dotted line is a fit to Eq. 2. While the high resistivity (and high T) fits well, there is still a 316
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
Fig. 3. (a) ρ AHE , sat subtracted from its value at T = 2 K, as function of T. Inset: ρ AHE , sat vs. T, no scaling. (b,c) Residual Δρ AHE as function of T (b) and as function of longitudinal resistivity, ρxx (c). Red Dashed lines represent fits to Eq. (2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
ρ (ϕ) = ρ⊥ + (ρ‖ − ρ⊥) cos 2 ϕ
In Fig. 5(a) we plot the angle dependent AMR measurements of the 0.4 sample, measured at 70 K and an external magnetic field of 8 T while rotating the sample in three different planes, depicted in the inset of the figure. Generally, the AMR angle dependence should follow a cosine square relation:
(4)
where ρ⊥ and ρ‖ are the resistivity for magnetization oriented perpendicular and parallel to the current, respectively [23]. We find that the AMR magnitude for rotating in plane (α , red curve) is similar to rotation from parallel to out-of-plane (γ , blue curve), and considerably larger
Fig. 4. AHE signal in saturation, after subtraction and normalized the Co thickness differences between each sample (see legend) and sample 0.1, as function of (a) temperature, (b) longitudinal resistivity. 317
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
Fig. 5. (a) Longitudinal resistiviy as function of the angle between current and applied external magnetic field. Data presented in three different planes of the film according to the schematic illustration in the inset. (b) Δρ/ ρ vs. T, extracted from the AMR measurement in the film plane, at 8 T, for the 0.5 (black), 0.4 (red), 0.3 (green) and 0.1 (blue) samples. (c) Δρ/ ρ after subtraction of the AMR signal of the 0.1 sample, as function of T, for samples 0.3–0.5 (same color coding as b). (d) Δρ/ ρ as function of T, after subtraction and normalizing to the thickness differences of each sample with sample 0.1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
numerical simulation based on Comsol, see supplementary [22] for details. To conclude, we studied the T dependence of the AHE and AMR in Pt/Co/Pt trilayers with nominally ultrathin Co, having some intermixing (<1 nm) with the Pt layers. We do not find evidence for SMR in these samples, probably since the ultrathin cobalt is thinner than the spin diffusion length. Both the AHE and AMR show an increasing signal with lowering temperatures, which we attribute to the development of a MPE in the Pt layers. The MPE contribution to the AHE signal is rather small, while it has a comparable magnitude to the ordinary AMR. While a MPE effect is in agreement with previous reports [15,34,36], a much thicker FM was used. One could imagine that in the ultra-thin regime, the SOI will modify an intrinsic change in the band structure which is influenced by the mere proximity to Co islands rather than the amount of Co and will probably disappear in much smaller Co coverage ratios [37]. Finally, we have shown that using ultrathin metallic FM layers can be an efficient way of studying their interaction with NM layers, without overwhelming the MR measurements, in addition to reducing SMR effects. This finding is important in light of ongoing efforts to clarify the relevance of MPE and other SOI effects in FM/NM systems and their physical mechanisms which can be of practical significance in spintronics devices and MR applications.
than rotation between perpendicular and out-of-plane (β , green). Thus, there is no significant SMR effect [3,32]. And, the non-zero but small β dependence is likely due to an AIMR effect [15]. In order to minimize contributions from the AIMR [15,34] we perform all AMR measurements rotating the sample in the film plane. AMR results for samples 0.1 and 0.3–0.5 are shown in Fig. 5(b). We extract Δρ = ρ‖ − ρ⊥ , and plot Δρ / ρ - the AMR resisitivity ratio [16]. All samples show a decrease of Δρ / ρ with T. We follow the same procedure performed for the AHE data, to asses the presence of two contributions to the AMR signal. In Fig. 5(c) we show the effect of subtracting the AMR of the 0.1 nm sample from the other samples, and in Fig. 5(d) after scaling with the Co thickness. Clearly, all curves collapse to nearly one line and interestingly, the AMR magnitude and T-dependence we observed after subtraction is similar to that reported for Pt/Insulating-FM films [35]. We conjecture there are indeed two separate contributions to the AHE and AMR measurements arising from different regions in the trilayer. The first is the common scattering in a FM material, in this case the region of Co and Co-Pt intermixing, and thus depends on nominal Co thickness. The second is attributed to the clean Pt layers, and is nearly independent of the Co amount. This may be due to a MPE between the layers, which was previously reported and shown to increase at low temperatures [35]. In this scenario, the AHE or AMR signal in the 0.1 sample is mainly from the MPE. Now, since the contributions are cumulative, we could subtract the MPE signal from all other samples, resulting in a standard AHE or AMR of a FM layer. The FM content of our samples is much smaller than usually reported in measurements, so it does not overwhelm the smaller contribution of the proximity induced magnetism, enabling us to asses it without the use of an insulating FM. Finally, we also verified that the presented scenario is reasonable, i.e., the scattering contribution of the thin Co layer relative to the thicker Pt layers results in a linear dependence, by performing
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.jmmm.2019.04.035. References [1] E. Saitoh, M. Ueda, H. Miyajima, G. Tatara, Appl. Phys. Lett. 88 (2006) 182509 .
318
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
[2] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, E. Saitoh, Nature 455 (2008) 778. [3] H. Nakayama, M. Althammer, Y.T. Chen, K. Uchida, Y. Kajiwara, D. Kikuchi, T. Ohtani, S. Geprägs, M. Opel, S. Takahashi, et al., Phys. Rev. Lett. 110 (2013) 206601 . [4] K. Garello, I.M. Miron, C.O. Avci, F. Freimuth, Y. Mokrousov, S. Blugel, S. Auffret, O. Boulle, G. Gaudin, P. Gambardella, Nat. Nano 8 (2013) 587. [5] J.X. Li, M.W. Jia, Z. Ding, J.H. Liang, Y.M. Luo, Y.Z. Wu, Phys. Rev. B 90 (2014) 214415 . [6] F. Hellman, A. Hoffmann, Y. Tserkovnyak, G.S.D. Beach, E.E. Fullerton, C. Leighton, A.H. MacDonald, D.C. Ralph, D.A. Arena, H.A. Dürr, et al., Rev. Mod. Phys. 89 (2017) 025006 . [7] S.Y. Huang, X. Fan, D. Qu, Y.P. Chen, W.G. Wang, J. Wu, T.Y. Chen, J.Q. Xiao, C.L. Chien, Phys. Rev. Lett. 109 (2012) 107204 . [8] Y.-T. Chen, S. Takahashi, H. Nakayama, M. Althammer, S.T.B. Goennenwein, E. Saitoh, G.E.W. Bauer, Phys. Rev. B 87 (2013) 144411 . [9] C.O. Avci, K. Garello, A. Ghosh, M. Gabureac, S.F. Alvarado, P. Gambardella, Nat. Phys. 11 (2015) 570. [10] F. Maccherozzi, M. Sperl, G. Panaccione, J. Minár, S. Polesya, H. Ebert, U. Wurstbauer, M. Hochstrasser, G. Rossi, G. Woltersdorf, et al., Phys. Rev. Lett. 101 (2008) 267201 . [11] S. Vélez, V.N. Golovach, A. Bedoya-Pinto, M. Isasa, E. Sagasta, M. Abadia, C. Rogero, L.E. Hueso, F.S. Bergeret, F. Casanova, Phys. Rev. Lett. 116 (2016) 016603 . [12] S.S.L. Zhang, G. Vignale, Phys. Rev. Lett. 116 (2016) 136601 . [13] L. Liu, C.-F. Pai, Y. Li, H.W. Tseng, D.C. Ralph, R.A. Buhrman, Science 336 (2012) 555. [14] P.F. Carcia, J. Appl. Phys. 63 (1988) 5066. [15] A. Kobs, S. Heße, W. Kreuzpaintner, G. Winkler, D. Lott, P. Weinberger, A. Schreyer, H.P. Oepen, Phys. Rev. Lett. 106 (2011) 217207 . [16] N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, N.P. Ong, Rev. Modern Phys. 82
[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
[30] [31] [32] [33] [34] [35] [36] [37]
319
(2010) 1539. Z. Wang, C. Tang, R. Sachs, Y. Barlas, J. Shi, Phys. Rev. Lett. 114 (2015) 016603 . C. Zeng, Y. Yao, Q. Niu, H.H. Weitering, Phys. Rev. Lett. 96 (2006) 037204 . J. Kötzler, W. Gil, Phys. Rev. B 72 (2005) 060412 . C.L. Canedy, X.W. Li, G. Xiao, J. Appl. Phys. 81 (1997) 5367. Y.M. Lu, J.W. Cai, S.Y. Huang, D. Qu, B.F. Miao, C.L. Chien, Phys. Rev. B 87 (2013) 220409 . Supplementary information regarding XRR, simulations and AMR measurements are available in the supplementary information file. (2017). Y. Kachlon, N. Kurzweil, A. Sharoni, J. Appl. Phys. 115 (2014) 173911 . T. Yamin, Y.M. Strelniker, A. Sharoni, Sci. Rep. 6 (2016) 19496. S. Seri, M. Schultz, L. Klein, Phys. Rev. B 87 (2013) 125110 . J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, 2010. R. Dimmich, J. Phys. F: Met. Phys. 15 (1985) 2477. A.R. Fert, Mater. Sci. Forum 59 (1991) 439. W.M. Haynes, CRC Handbook of Chemistry and Physics: A Ready-reference Book of Chemical and Physical Data, CRC Press, Taylor & Francis Group, Boca Raton, Florida, 2013. A. Kobs, H.P. Oepen, Phys. Rev. B 93 (2016) 014426 . A.F. Mayadas, M. Shatzkes, Phys. Rev. B 1 (1970) 1382. X. Zhou, L. Ma, Z. Shi, W.J. Fan, J.-G. Zheng, R.F.L. Evans, S.M. Zhou, Phys. Rev. B 92 (2015) 060402 . A. Fert, A. Friederich, A. Hamzic, J. Magn. Magn. Mater. 24 (1981) 231. X. Xiao, J.X. Li, Z. Ding, J.H. Liang, L. Sun, Y.Z. Wu, Appl. Phys. Lett. 108 (2016) 222402 . Y.M. Lu, Y. Choi, C.M. Ortega, X.M. Cheng, J.W. Cai, S.Y. Huang, L. Sun, C.L. Chien, Phys. Rev. Lett. 110 (2013) 147207 . C.O. Avci, K. Garello, J. Mendil, A. Ghosh, N. Blasakis, M. Gabureac, M. Trassin, M. Fiebig, P. Gambardella, Appl. Phys. Lett. 107 (2015). A.I. Buzdin, Phys. Rev. Mater. 2 (2018) 011401 .
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Research articles
Low temperature divergence in the AHE and AMR of ultra-thin Pt/Co/Pt trilayers E. Zion, N. Haham, L. Klein, A. Sharoni
T
⁎
Department of Physics & Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 5290002, Israel
A B S T R A C T
We study the anomalous Hall effect (AHE) and anisotropic magnetoresistance (AMR) in a series of ultra-thin Pt/Co(x)/Pt trilayers (0.1 nm ⩽ x⩽ 0.5 nm ). We find that the AHE exhibits a significant increase at low temperatures (T). This increase cannot be attributed to a trivial increase in magnetization or resistivity. A similar T dependence is observed in the AMR measurements. Interestingly, these effects show almost no dependence on cobalt thickness. Our measurements indicate that the deviation from common behavior can be attributed to an induced magnetic proximity effect in the Pt layers that increases at low temperatures, in agreement with previous reports. An alternative explanation related to the evolution of a non-continuous magnetic layer is considered as well.
1. Introduction A myriad of spin-related transport properties have been reported for hybrid ferromagnetic/non-magnetic (FM/NM) structures, especially those involving heavy NM metals with strong spin orbit interactions (SOI) [1–5]. Those systems exhibit rich interfacial magnetic phenomena which may be important to spintronics applications, see [6] and references within. Recent studies used an insulating FM as a means to separate effects of currents in the FM, thus showing additional magneto-resistance (MR) effects [7]. These were interpreted as spin Hall MR (SMR) that results from both spin Hall effect (SHE) and inverse SHE in the NM layer [8,9]; magnetic proximity effect (MPE) due to the proximity of a non-magnetic layer to magnetic elements [10]; Hanle magnetoresistance related only to the heavy NM properties [11]; the nonlocal anomalous Hall effect, which requires only one SHE and spindependent interface scattering [12]. One source of complication in resolving the origins of the MR measurements is the multiple contributions from different spin scattering processes, which may have different magnitudes that are material dependent. Additional experimental information, specifically by interfacing strong SOI materials with different conducting FM will help to resolve microscopic origins of the interactions [9,13]. It is experimentally challenging to separate the contribution of the FM in the standard transport measurements and more sophisticated methods are often required [9,10]. We studied Pt/Co/Pt trilayers with ultra-thin Co, ranging from 0 nm to 0.5 nm, via anisotropic MR (AMR) and anomalous Hall effect (AHE) measurements, which enable us to resolve the spin-transport origins of these effect. The AMR and AHE were previously reported in Pt/Co multilayers,
⁎
mainly due to interest in their intrinsic perpendicular magnetocrystalline anisotropy (PMA) with easy axis perpendicular to the film [14]. Recently, in Pt/Co/Pt layers (with thicker Co than we use), an additional MR was reported [15]. There is a considerable difference in magnitude of MR for magnetization in-plane that is perpendicular to the current and MR for out-of-plane magnetization, in spite of also being normal to the current. The effect is due to the interface, thus it was coined anisotropic interface MR (AIMR). The AHE is sensitive to both spin and topology, and is at the focus of considerable theoretical and experimental efforts [16,17]. It can be described phenomenologically as transverse resistivity, ρxy , linked to the intrinsic magnetization, M⊥ , of a conductor. The most common model is the extrinsic model, which relates the AHE to antisymmetric scattering processes and it provides that
ρxy = Rs M⊥,
(1)
where 2 Rs = aρxx + bρxx .
(2)
Here ρxx is the longitudinal resistivity and M⊥ is the component of magnetization perpendicular to the film. The linear term in resistivity of Rs is attributed to skew scattering and the quadratic term to side jumps [18,19]. AHE measurements of Co/Pt multilayers have been reported to follow this relation [20]. We find that the AHE in Pt/Co/Pt trilayers with ultra-thin Co (0.5 nm and below) exhibits an anomaly at low temperatures. While we can understand the high temperature AHE in terms of the extrinsic mechanism, the low temperature AHE changes significantly, although resistivity and magnetization do not exhibit any strong T dependence. A
Corresponding author. E-mail address: [email protected] (A. Sharoni).
https://doi.org/10.1016/j.jmmm.2019.04.035 Received 30 April 2017; Received in revised form 31 March 2019; Accepted 10 April 2019 Available online 19 April 2019 0304-8853/ © 2019 Published by Elsevier B.V.
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
setting the field to zero. Next, the transverse resistance was measured during heating in two configurations that enable to extract accurately the anti-symmetric (i.e. transverse) resistance[24,25]. In Fig. 1(a) we plot the T dependence of the transverse resistivity from the zero-field Hall measurements, for all Co thicknesses. Since there is no external magnetic field, we naively attribute the measured ρxy to an AHE signal, which is proportional to M⊥. For all non-zero Co thicknesses ρxy decreases with increasing T until it drops rapidly to zero, at the vicinity of its Curie temperature, Tc . The Tc as a function of Co thickness, plotted in Fig. 1(c), displays a linear dependence, exemplifying strong sensitivity to Co thickness in this ultra-thin regime (we note that for each thickness we measured bridges from 2 to 5 samples, to ensure reproducibility). We draw attention to an unusual T dependence in the measurement, visible in the 0.3, 0.4 and 0.5 samples. Below ∼50 K ρxy increases significantly, as T decreases. A zoom of this region is plotted for the 0.3 sample in Fig. 1(b), showing the upturn. This behavior is unexpected since commonly at low temperatures both magnetization and longitudinal resistivity do not vary significantly [26], and thus, from Eq. (2) we would expect a saturation of the AHE at low temperatures. Fig. 1(d) shows the T dependence of longitudinal resistivity. The resistivity increases linearly at high temperatures, while at low temperatures it reaches a constant value for all Co thicknesses. A non-consistent systematics in the T-dependent part of the longitudinal resistivity for films with different Co may be the result of experimental issues. Since we are dealing with ultra-thin films, a small error in total Pt thickness of 1 Å in the deposition (from speed of shutter control, e.g.) would lead to a 4% error in total thickness. We note that insertion of the Co layer nearly doubles the samples’ resistivity, while the Co thickness itself does not modify the resistivity considerably [27,28]. Specifically, it does not reduce the resistivity, although Co bulk resistivity is lower than that of Pt [29]. This indicates that scattering (and resistance) of the Co/Pt
similar anomaly at low T appears in the AMR measurements of these films. By quantitatively comparing measurements of trilayers with different Co thickness, we resolve two contributions to the AHE and AMR signals - one that scales with the nominal Co thickness, and a second that shows the unexpected low T anomaly and is independent of Co thickness. We find evidence that the low T features can be related to MPE in the Pt layer, showing similar features to those previously reported [5,21]. However, we cannot rule out an additional scattering mechanism arising from temperature-dependent ferromagnetism of non-continues Co islands at the Pt/Co interfaces. 2. Experimental A series of Pt(3 nm)/Co(x)/Pt(3 nm) films were deposited by magnetron sputtering onto Si(100) wafers with 0.5 μm SiO2 insulator. For details about the films’ deposition process, see supplemental material [22]. Nominal Co thickness ranged between x = 0 to 0.5 nm in 0.1 nm steps. For simplicity, we label the samples by their Co thickness. X-ray reflectivity (XRR) measurements indicate there is some intermixing between Co and Pt at the film center [22]. The films were patterned via photolithography followed by Ar milling[23] into Hall bars (width = 50 μm and length = 200 μm, see inset of Fig. 1(b)) to allow transverse, ρxy , and longitudinal, ρxx , resistivity measurements. We performed these measurements in a commercial Quantum Design PPMS-9 cryostat, via a 4-probe configuration and as a function of temperature, magnetic field magnitude and direction. 3. Results and discussion Zero-field Hall measurements were executed by first cooling the sample to 2 K in a 0.5 T magnetic field perpendicular to the film, then
Fig. 1. (a) ρxy as function of T, Co thicknesses are marked. (b) ρxy in the low T regime for sample 0.3, dotted line is the expected extrapolation. Inset: schematic illustration of sample structure and measurement geometry. (c) Curie temperature as function of the Co thickness. (d) Longitudinal resistivity vs. T of all samples, color coding same as (a). 315
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
Fig. 2. ρxy as function of the magnetic field for the 0.4 sample, before (a) and after (b) subtracting the trivial OHE due to the applied magnetic field. The measurement temperatures are marked in the figure. (c) Fitting of ρxyAHE to the high field dependence and extrapolation to 1/ H → 0 . (d) Extracted values of ρ AHE , sat as function of the longitudinal resistivity. Red dotted line represents fitting of linear region to Eq. (2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
deviation of the AHE magnitude at low temperatures (the low resistivity values in the figure). In Fig. 3(a) we present the results of the analysis for all the samples, showing ρ AHE , sat as a function of T. In the inset, the measurements are plotted to scale. In the main frame, we subtracted from each measurement its value at 2 K, so to compare the changes as a function of T. As the Cobalt becomes thinner the AHE signal decreases, and for the 0.1 sample it approaches zero for higher temperatures (see Fig. 3(a), inset). Comparing the changes with T (main frame), we see that for all the samples there is an increase in ρ AHE , sat at low temperatures, and with similar magnitude. Additionally, the 0.3, 0.4 and 0.5 samples show an increase with raising T, as expected for the AHE, since the resistance is increasing. In the 0.1 sample, the AHE measurement decreases for all temperatures. To gain further insight we present the results as follows. In Fig. 3(b,c) we show the residual AHE signal, Δρ AHE , for the 0.3, 0.4 and 0.5 samples after subtracting the 0.1 signal (Fig. 3(b) is vs. T and 3(c) vs. ρxx ). The sharp increase at low temperatures has vanished for all the samples, and Δρ AHE has a resistivity dependence that can be fitted by Eq. 2 for the AHE (red dashed line). This supports that the source of the increase is independent of the Co amount. Now, Δρ AHE should represent contribution from scattering in the intermixing region. Fig. 4 shows the normalized Δρ AHE (for each sample) by the residual Co thickness (Cothickness – 0.1 nm). The results, plotted in Fig. 4 (in (b) vs. T and in (c) as a function of ρxx ) depict a good scaling relation. Our AHE analysis points toward two separate contributions to the AHE signal. The first contribution follows the conventional dependence of AHE on ρxx [20] and scales with Co content [33]. The second contribution increases at lower T and is nearly independent of increasing Co thickness. To gain further insight, we analyzed the AMR behavior of these films.
intermixing is significant (diffusive), and is almost not influenced by the amount of Co for this range (as shown in Fig. 1(d))[30,31]. The zero field measurements qualitatively reveal the temperature dependence of the AHE. However, temperature driven changes of the domain structure cannot be ruled out. Hence, in order to accurately determine the AHE contribution of the samples for different temperatures (including the T dependence of saturation magnetization) the following procedure is preformed: Since we do not have a direct measurement of M⊥ , we assess the AHE for saturation magnetization in the following way. We measure the dependence of the transverse resistivity on the perpendicular magnetic field, up to 8 T, exemplified in Fig. 2(a) for the 0.4 sample and three different temperatures, 2 K, 70 K and OHE 140 K. We extract the ordinary Hall effect (OHE) resistivity, ρxy , from the high field slope of ρxy at 2 K, where the AHE is nearly field independent [32]. The OHE is dominantly due to the Pt layers, which are OHE 6 nm. Since OHE of Pt has no T dependence [7], we may subtract ρxy from ρxy for any temperature and field, resulting in ρxyAHE . This is presented in Fig. 2(b) for the 0.4 sample and three different temperatures. For the 2 K measurement ρxyAHE reaches a plateau at high fields, but as T increases, ρxyAHE has a considerable field dependence even at high fields. We expand in first order the high field behavior of magnetization to M = Ms (1 − a/ H ) , where Ms is the saturation magnetization, which is T independent, and a is a constant. By extrapolating to large fields, i.e. 1/ H → 0 , we can find ρ AHE , sat = Ms Rs . Now we can compare Rs for every T, up to the constant Ms , by fitting
ρ AHE = ρ AHE , sat (1 − a/ H )
(3)
to the high field dependence in our measurements, depicted in Fig. 2(c) for the same three temperatures. Rs Ms is shown as a function of resistivity in Fig. 2(d) for the 0.4 sample. The red dotted line is a fit to Eq. 2. While the high resistivity (and high T) fits well, there is still a 316
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
Fig. 3. (a) ρ AHE , sat subtracted from its value at T = 2 K, as function of T. Inset: ρ AHE , sat vs. T, no scaling. (b,c) Residual Δρ AHE as function of T (b) and as function of longitudinal resistivity, ρxx (c). Red Dashed lines represent fits to Eq. (2). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
ρ (ϕ) = ρ⊥ + (ρ‖ − ρ⊥) cos 2 ϕ
In Fig. 5(a) we plot the angle dependent AMR measurements of the 0.4 sample, measured at 70 K and an external magnetic field of 8 T while rotating the sample in three different planes, depicted in the inset of the figure. Generally, the AMR angle dependence should follow a cosine square relation:
(4)
where ρ⊥ and ρ‖ are the resistivity for magnetization oriented perpendicular and parallel to the current, respectively [23]. We find that the AMR magnitude for rotating in plane (α , red curve) is similar to rotation from parallel to out-of-plane (γ , blue curve), and considerably larger
Fig. 4. AHE signal in saturation, after subtraction and normalized the Co thickness differences between each sample (see legend) and sample 0.1, as function of (a) temperature, (b) longitudinal resistivity. 317
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
Fig. 5. (a) Longitudinal resistiviy as function of the angle between current and applied external magnetic field. Data presented in three different planes of the film according to the schematic illustration in the inset. (b) Δρ/ ρ vs. T, extracted from the AMR measurement in the film plane, at 8 T, for the 0.5 (black), 0.4 (red), 0.3 (green) and 0.1 (blue) samples. (c) Δρ/ ρ after subtraction of the AMR signal of the 0.1 sample, as function of T, for samples 0.3–0.5 (same color coding as b). (d) Δρ/ ρ as function of T, after subtraction and normalizing to the thickness differences of each sample with sample 0.1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
numerical simulation based on Comsol, see supplementary [22] for details. To conclude, we studied the T dependence of the AHE and AMR in Pt/Co/Pt trilayers with nominally ultrathin Co, having some intermixing (<1 nm) with the Pt layers. We do not find evidence for SMR in these samples, probably since the ultrathin cobalt is thinner than the spin diffusion length. Both the AHE and AMR show an increasing signal with lowering temperatures, which we attribute to the development of a MPE in the Pt layers. The MPE contribution to the AHE signal is rather small, while it has a comparable magnitude to the ordinary AMR. While a MPE effect is in agreement with previous reports [15,34,36], a much thicker FM was used. One could imagine that in the ultra-thin regime, the SOI will modify an intrinsic change in the band structure which is influenced by the mere proximity to Co islands rather than the amount of Co and will probably disappear in much smaller Co coverage ratios [37]. Finally, we have shown that using ultrathin metallic FM layers can be an efficient way of studying their interaction with NM layers, without overwhelming the MR measurements, in addition to reducing SMR effects. This finding is important in light of ongoing efforts to clarify the relevance of MPE and other SOI effects in FM/NM systems and their physical mechanisms which can be of practical significance in spintronics devices and MR applications.
than rotation between perpendicular and out-of-plane (β , green). Thus, there is no significant SMR effect [3,32]. And, the non-zero but small β dependence is likely due to an AIMR effect [15]. In order to minimize contributions from the AIMR [15,34] we perform all AMR measurements rotating the sample in the film plane. AMR results for samples 0.1 and 0.3–0.5 are shown in Fig. 5(b). We extract Δρ = ρ‖ − ρ⊥ , and plot Δρ / ρ - the AMR resisitivity ratio [16]. All samples show a decrease of Δρ / ρ with T. We follow the same procedure performed for the AHE data, to asses the presence of two contributions to the AMR signal. In Fig. 5(c) we show the effect of subtracting the AMR of the 0.1 nm sample from the other samples, and in Fig. 5(d) after scaling with the Co thickness. Clearly, all curves collapse to nearly one line and interestingly, the AMR magnitude and T-dependence we observed after subtraction is similar to that reported for Pt/Insulating-FM films [35]. We conjecture there are indeed two separate contributions to the AHE and AMR measurements arising from different regions in the trilayer. The first is the common scattering in a FM material, in this case the region of Co and Co-Pt intermixing, and thus depends on nominal Co thickness. The second is attributed to the clean Pt layers, and is nearly independent of the Co amount. This may be due to a MPE between the layers, which was previously reported and shown to increase at low temperatures [35]. In this scenario, the AHE or AMR signal in the 0.1 sample is mainly from the MPE. Now, since the contributions are cumulative, we could subtract the MPE signal from all other samples, resulting in a standard AHE or AMR of a FM layer. The FM content of our samples is much smaller than usually reported in measurements, so it does not overwhelm the smaller contribution of the proximity induced magnetism, enabling us to asses it without the use of an insulating FM. Finally, we also verified that the presented scenario is reasonable, i.e., the scattering contribution of the thin Co layer relative to the thicker Pt layers results in a linear dependence, by performing
Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.jmmm.2019.04.035. References [1] E. Saitoh, M. Ueda, H. Miyajima, G. Tatara, Appl. Phys. Lett. 88 (2006) 182509 .
318
Journal of Magnetism and Magnetic Materials 485 (2019) 314–319
E. Zion, et al.
[2] K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, E. Saitoh, Nature 455 (2008) 778. [3] H. Nakayama, M. Althammer, Y.T. Chen, K. Uchida, Y. Kajiwara, D. Kikuchi, T. Ohtani, S. Geprägs, M. Opel, S. Takahashi, et al., Phys. Rev. Lett. 110 (2013) 206601 . [4] K. Garello, I.M. Miron, C.O. Avci, F. Freimuth, Y. Mokrousov, S. Blugel, S. Auffret, O. Boulle, G. Gaudin, P. Gambardella, Nat. Nano 8 (2013) 587. [5] J.X. Li, M.W. Jia, Z. Ding, J.H. Liang, Y.M. Luo, Y.Z. Wu, Phys. Rev. B 90 (2014) 214415 . [6] F. Hellman, A. Hoffmann, Y. Tserkovnyak, G.S.D. Beach, E.E. Fullerton, C. Leighton, A.H. MacDonald, D.C. Ralph, D.A. Arena, H.A. Dürr, et al., Rev. Mod. Phys. 89 (2017) 025006 . [7] S.Y. Huang, X. Fan, D. Qu, Y.P. Chen, W.G. Wang, J. Wu, T.Y. Chen, J.Q. Xiao, C.L. Chien, Phys. Rev. Lett. 109 (2012) 107204 . [8] Y.-T. Chen, S. Takahashi, H. Nakayama, M. Althammer, S.T.B. Goennenwein, E. Saitoh, G.E.W. Bauer, Phys. Rev. B 87 (2013) 144411 . [9] C.O. Avci, K. Garello, A. Ghosh, M. Gabureac, S.F. Alvarado, P. Gambardella, Nat. Phys. 11 (2015) 570. [10] F. Maccherozzi, M. Sperl, G. Panaccione, J. Minár, S. Polesya, H. Ebert, U. Wurstbauer, M. Hochstrasser, G. Rossi, G. Woltersdorf, et al., Phys. Rev. Lett. 101 (2008) 267201 . [11] S. Vélez, V.N. Golovach, A. Bedoya-Pinto, M. Isasa, E. Sagasta, M. Abadia, C. Rogero, L.E. Hueso, F.S. Bergeret, F. Casanova, Phys. Rev. Lett. 116 (2016) 016603 . [12] S.S.L. Zhang, G. Vignale, Phys. Rev. Lett. 116 (2016) 136601 . [13] L. Liu, C.-F. Pai, Y. Li, H.W. Tseng, D.C. Ralph, R.A. Buhrman, Science 336 (2012) 555. [14] P.F. Carcia, J. Appl. Phys. 63 (1988) 5066. [15] A. Kobs, S. Heße, W. Kreuzpaintner, G. Winkler, D. Lott, P. Weinberger, A. Schreyer, H.P. Oepen, Phys. Rev. Lett. 106 (2011) 217207 . [16] N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, N.P. Ong, Rev. Modern Phys. 82
[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29]
[30] [31] [32] [33] [34] [35] [36] [37]
319
(2010) 1539. Z. Wang, C. Tang, R. Sachs, Y. Barlas, J. Shi, Phys. Rev. Lett. 114 (2015) 016603 . C. Zeng, Y. Yao, Q. Niu, H.H. Weitering, Phys. Rev. Lett. 96 (2006) 037204 . J. Kötzler, W. Gil, Phys. Rev. B 72 (2005) 060412 . C.L. Canedy, X.W. Li, G. Xiao, J. Appl. Phys. 81 (1997) 5367. Y.M. Lu, J.W. Cai, S.Y. Huang, D. Qu, B.F. Miao, C.L. Chien, Phys. Rev. B 87 (2013) 220409 . Supplementary information regarding XRR, simulations and AMR measurements are available in the supplementary information file. (2017). Y. Kachlon, N. Kurzweil, A. Sharoni, J. Appl. Phys. 115 (2014) 173911 . T. Yamin, Y.M. Strelniker, A. Sharoni, Sci. Rep. 6 (2016) 19496. S. Seri, M. Schultz, L. Klein, Phys. Rev. B 87 (2013) 125110 . J.M.D. Coey, Magnetism and Magnetic Materials, Cambridge University Press, 2010. R. Dimmich, J. Phys. F: Met. Phys. 15 (1985) 2477. A.R. Fert, Mater. Sci. Forum 59 (1991) 439. W.M. Haynes, CRC Handbook of Chemistry and Physics: A Ready-reference Book of Chemical and Physical Data, CRC Press, Taylor & Francis Group, Boca Raton, Florida, 2013. A. Kobs, H.P. Oepen, Phys. Rev. B 93 (2016) 014426 . A.F. Mayadas, M. Shatzkes, Phys. Rev. B 1 (1970) 1382. X. Zhou, L. Ma, Z. Shi, W.J. Fan, J.-G. Zheng, R.F.L. Evans, S.M. Zhou, Phys. Rev. B 92 (2015) 060402 . A. Fert, A. Friederich, A. Hamzic, J. Magn. Magn. Mater. 24 (1981) 231. X. Xiao, J.X. Li, Z. Ding, J.H. Liang, L. Sun, Y.Z. Wu, Appl. Phys. Lett. 108 (2016) 222402 . Y.M. Lu, Y. Choi, C.M. Ortega, X.M. Cheng, J.W. Cai, S.Y. Huang, L. Sun, C.L. Chien, Phys. Rev. Lett. 110 (2013) 147207 . C.O. Avci, K. Garello, J. Mendil, A. Ghosh, N. Blasakis, M. Gabureac, M. Trassin, M. Fiebig, P. Gambardella, Appl. Phys. Lett. 107 (2015). A.I. Buzdin, Phys. Rev. Mater. 2 (2018) 011401 .