# A novel method to evaluate spin diffusion length of Pt

###### Abstract

Spin diffusion length of Pt is evaluated via proximity effect of spin orbit coupling (SOC) and anomalous Hall effect (AHE) in Pt/CoFeAl bilayers. By varying the thicknesses of Pt and CoFeAl layer, the thickness dependences of AHE parameters can be obtained, which are theoretically predicted to be proportional to the square of the SOC strength. According to the physical image of the SOC proximity effect, the spin diffusion length of Pt can easily be identified from these thickness dependences. This work provides a novel method to evaluate spin diffusion length in a material with a small value.

###### pacs:

71.70.Ej; 73.50.Jt; 75.47.Np; 75.50.BbAs a promptly growing research area, spintronics aims at using and manipulating not only the charge, but also the spin in an electronic device Wolf2001 (); I2004 (). Spin dependent transport property is the key for the application of spintronics device, and thus it has attracted great attention over the past few decades G1988 (); Nakayama2013 (); lin2014 (); Althammer2013 (); chen2013 (). Herein, spin diffusion length () is a fundamental parameter in the study of spin dependent transport, which has an inverse relationship with the intensity of spin dependent scattering. There are many methods such as lateral spin valve, spin pumping, spin-torque ferromagnetic resonance, Hall cross and spin absorption to gain the spin diffusion length in a normal metal Laczkowski2012 (); Vlaminck2013 (); Zhang2013 (); Azevedo2011 (); JC2014 (); liu (); G2009 (); Isasa2015 (). Different from above methods, a novel approach to evaluate spin diffusion length is introduced in this work, through proximity effect of spin orbit coupling (SOC) and anomalous Hall effect (AHE) Hall1881 (); Nagaosa2010 (); zhang15 ().

It is well known that spin orbit coupling plays a fundamental role in spin dependent transport properties, including anomalous Hall effect, spin Hall effect, spin transfer torque and Dzyaloshinskii-Moriya interaction etc. Hall1881 (); Sinova2004 (); Sloncz1996 (); Dzy1958 (); Mor1960 (). SOC can strongly affect the intensity of spin dependent scattering, and hence has a direct relationship with spin diffusion length. If a low dimensional layered structure consists of a nonmagnetic (NM) layer with strong SOC and a ferromagnetic (FM) layer, the conduction electrons will be repeatedly scattered in z direction by the interfaces of heterolayers, substrates and vacuum when the current is flowing, as shown in Fig. 1. The conduction electrons will be polarized by the magnetic layer and affected by the strong SOC layer meantime, causing enhanced spin dependent scattering. This phenomenon is called SOC proximity effect. When the thickness of the NM layer is over its spin diffusion length, the added NM layer will not contribute to the SOC proximity effect but continue shunting the measurement current, which leads to a suddenly weaken performance of spin dependent scattering. Catching the turning point, the spin diffusion length can consequently be evaluated.

In order to analyze spin dependent scattering, anomalous Hall effect is employed in this work. It is now firmly established that there are two categories competing mechanisms contributing to the AHE: intrinsic mechanism, which originates from the anomalous velocity of the Bloch electrons induced by the SOC Karplus1954 (); Jung2002 (); Xiao2010 (); external mechanism, which includes skew scattering and side jump Smi55 (); Ber70 (). Both intrinsic and side jump contribution obey the square relationship , where and correspond to the anomalous Hall resistivity and longitudinal resistivity, respectively Karplus1954 (); Jung2002 (); Xiao2010 (); Smi55 (). Differently, due to asymmetric scattering from impurities caused by SOC, the skew scattering contribution shows linear dependence on Ber70 (). Therefore, the measured usually obeys the empirical Eq. (1):

(1) |

where and are parameters. This relationship is known as the traditional scaling. In 2001, Crépieux and Bruno presented a theory of the AHE, where they deem that no matter skew scattering or side jump contributions, AHE parameters ( and ) always obey square relationships with strength of SOC CB theory (). Afterward, Tian et al. proposed an expanded scaling Tia09 (), where the impurity and phonon are assumed to have different contributions to the skew scattering. The scaling can be rewritten as Eq. (2):

(2) |

Here, is the residual resistivity, comes from the scattering of excited phonons, and are due to the skew scattering, and is dominated by the side jump and intrinsic contributions. In this equation, the phonon contribution is introduced by considering the inelastic scattering at finite temperatures, which was formulated in terms of a multiband tight-binding model by Shitade and Nagaosa Shitade2012 ().

Two series of Pt (2.5 nm)/CoFeAl ( nm) and Pt ( nm)/CoFeAl (0.9 nm) bilayer films were deposited on the cm polished MgO(100) substrates by magnetron sputtering. All those samples were prepared under Hall bar mask and annealed at 320 C in situ. The base pressure of sputtering chamber is below Pa. The sputtering Ar gas with 99.999 purity was introduced with a constant pressure of 0.3 Pa. Film thickness was measured by X-ray reflectivity (XRR) using a D8 Discover X-ray diffractometer. The transport property was measured by physical property measurement system (PPMS) from 20 to 300 K.

Figure 2 shows the measured results of the AHE. versus curves of the samples are given in Fig. 2(a) and (b). The red lines are fitting curves. Obviously, versus is not linear relationship for almost all samples. Just when CoFeAl (CFA) layer is thicker than 5 nm, the relationship looks like linear. Hence, the traditional scaling does not work well for very thin bilayers. On the contrary, Eq. (2) can fit the data perfectly. These results are consistent with our reported data Che2014 (); q2013 (). It reveals that the dependence of versus shows a straighter line at special ratios among , and b only, such as the cases in a bulk material and a thick film.

According to the CB theory and the physical image of the SOC proximity effect, the effective SOC strength of Pt/CoFeAl can be treated using tight-binding sense, and the expression can be read as:

(3) |

where meV) represents the SOC strength of CoFeAl, meV) is the SOC strength of Pt, and is the thickness of CoFeAl(Pt) layer kota ().

If ( is the spin diffusion length of Pt), increasing the thickness of Pt layer will enhance the effective SOC (which has the meaning of squre of hereafter) monotonically obeying Eq. (3) shown in Fig. 3(b). On the contrary, increasing the thickness of the CoFeAl layer will not affect the spin diffusion in the Pt layer but reduce the effective SOC since the atomic SOC in the CoFeAl layer is much weaker than that in Pt layer, which is shown in Fig. 3(a).

If , the spin states will be lost in partial of Pt layer where the distance to the interface of the FM and NM layer is over the already. The reason is that the injected spin (along the direction) from the FM layer into Pt layer will be relaxed due to the SOC of Pt. Therefore, this part of Pt only plays a role of conducting a leakage current and a leakage current factor has to be introduced, which is simply proposed as here. Only those Pt atomic layers in the scope of can make contribution to the measured signal of spin dependent scattering, e.g. the AHE. The general behavior of factor is shown in Fig. 3(c). Taking into account the factor, the effective SOC of the bilayer system should take behavior shown in Fig. 3(d), in which the turning point occurs exactly at . Since the fitted parameters of the AHE are theoretically proportional to the effective SOC of the bilayer system, identifying the turning points in the fitted parameters of the AHE provides a powerful tool to fix the spin diffusion length in the Pt layer.

Fig. 4 shows the thickness dependences of fitted parameters from Fig. 2(a) and (b). For the samples with nm, the dependences are consistent with those in Fig. 3(a), indicating . For the samples with varied thicknesses of Pt layers but fixed thickness of CoFeAl layers, the overall behavior of , and
are found to be similar to those of theoretical prediction shown in Fig. 3(d) including the leakage current factor. Thus is evaluated around 5 nm which is approximate to that in Ref. [Mar2014, ].

In conclusion, this work demonstrates a method for determining the spin diffusion length via anomalous Hall effect and proximity effect of spin orbit coupling. We obtain the spin diffusion length of Pt is around 5 nm. This method can be used to evaluate nonmagnetic materials with short spin diffusion length. However, due to the limit of proximity effect, it does not work for thick films probably.

###### Acknowledgements.

We thank the beamline 08U1 at the Shanghai Synchrotron Radiation Facilities (SSRF) for the sample preparation and measurement. This work was supported by the National Science Foundation of China Grant Nos. 51331004, 11374228 and 11205235, the National Basic Research Program of China under Grant No. 2015CB921501, and the Innovation Program of Shanghai Municipal Education Commission No. 14ZZ038. Z. G. Zhu is supported by Hundred Talents Program of The Chinese Academy of Sciences.## References

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