A novel method to evaluate spin diffusion length of Pt

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by  Y. Q. Zhang

A novel method to evaluate spin diffusion length of Pt
Y. Q. Zhang,1 N. Y. Sun,1 W. R. Che,1 R. Shan,1,a) and Z. G. Zhu2,3,b)
1)Shanghai Key Laboratory of Special Artificial Microstructure and Pohl Institute of Solid State
Physics and School of Physics Science and Engineering, Tongji University, Shanghai 200092,
China
2)School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences,
Beijing 100049, China.
3)Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory,
College of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049,
China.
6
1 (Dated: 8 January 2016)
0
Spin diffusion length ofPt is evaluated via proximityeffect of spin orbitcoupling (SOC) andanomalousHall
2
effect (AHE) in Pt/Co FeAl bilayers. By varying the thicknesses of Pt and Co FeAl layer, the thickness
2 2
n dependences ofAHE parameterscanbe obtained, whichare theoreticallypredictedto be proportionalto the
a
square of the SOC strength. According to the physical image of the SOC proximity effect, the spin diffusion
J
length of Pt can easily be identified from these thickness dependences. This work provides a novel method
7
to evaluate spin diffusion length in a material with a small value.

]
i PACS numbers: 71.70.Ej;73.50.Jt; 75.47.Np; 75.50.Bb
c
s
-
l
r As a promptly growingresearcharea,spintronicsaims
mt at using and manipulating not only the charge, but also
thespininanelectronicdevice1,2. Spindependenttrans-
.
t portpropertyisthekeyfortheapplicationofspintronics
a
device,andthusithasattractedgreatattentionoverthe
m
past few decades3–7. Herein, spin diffusion length (λ)
-
d is a fundamental parameter in the study of spin depen-
n dent transport, which has an inverse relationship with
o the intensity of spin dependent scattering. There are
c many methods such as lateral spin valve, spin pumping,
[
spin-torque ferromagneticresonance,Hall crossandspin

1 absorption to gain the spin diffusion length in a normal
v metal8–15. Different from above methods, a novel ap- FIG. 1. (Color online) Physical image of AHE in FM/NM
1 proach to evaluate spin diffusion length is introduced in bilayer. Gray arrow (M) indicates the magnetic moment di-
7 rection of FM layer. Yellow line indicates possible motion
thiswork,throughproximityeffectofspinorbitcoupling
3 (SOC) and anomalous Hall effect (AHE)16–18. It is well pathoftheconductionelectrons. tNM andλisthicknessand
1 spin diffusion length of NM layer, respectively.
known that spin orbit coupling plays a fundamental role
0
. inspindependenttransportproperties,includinganoma-
1
lous Halleffect, spinHalleffect, spintransfertorque and
0 not contribute to the SOC proximity effect but continue
Dzyaloshinskii-Moriya interaction etc.17,19–22. SOC can
6 shuntingthe measurementcurrent,whichleadstoasud-
1 stronglyaffecttheintensityofspindependentscattering, denly weaken performance of spin dependent scattering.
: and hence has a direct relationship with spin diffusion
v Catchingthe turning point, the spindiffusion lengthcan
length. If a low dimensionallayeredstructure consistsof
i consequently be evaluated.
X a nonmagnetic (NM) layer with strong SOC and a fer-
In orderto analyze spin dependent scattering, anoma-
r romagnetic (FM) layer, the conduction electrons will be
a repeatedly scattered in z direction by the interfaces of lous Hall effect is employed in this work. It is now
firmly established that there are two categories com-
heterolayers,substrates and vacuum when the current is
peting mechanisms contributing to the AHE: intrinsic
flowing, as shown in Fig. 1. The conduction electrons
mechanism, which originates from the anomalous veloc-
will be polarized by the magnetic layer and affected by
ity of the Bloch electrons induced by the SOC23–25; ex-
the strong SOC layer meantime, causing enhanced spin
ternal mechanism, which includes skew scattering and
dependent scattering. This phenomenon is called SOC
sidejump26,27. Bothintrinsicandsidejumpcontribution
proximity effect. When the thickness of the NM layer is
over its spin diffusion length, the added NM layer will obey the square relationshipρAH ∝ρ2xx, where ρAH and
ρxx correspondtotheanomalousHallresistivityandlon-
gitudinalresistivity,respectively23–26. Differently,dueto
asymmetric scattering from impurities caused by SOC,
a)Electronicmail: [email protected] theskewscatteringcontributionshowslineardependence
b)Electronicmail: [email protected] onρxx27. Therefore,themeasuredρAH usuallyobeysthe
2

empirical Eq. (1):
ρAH =aρxx+bρ2xx, (1) (a) 3 Pt (2.5 nm)/CFA (tCFA nm)
whereaandbareparameters. Thisrelationshipisknown
0.6 nm
as the traditional scaling. In 2001, Cr´epieux and Bruno 2 0.73 nm
presentedatheoryoftheAHE,wheretheydeemthatno 0.9 nm
matter skew scattering or side jump contributions, AHE 1.1 nm
parameters (a and b) always obey square relationships 2.2 nm
1
withstrengthofSOC28. Afterward,Tianet al. proposed m 5 nm
an expanded scaling29, where the impurity and phonon c 10 nm
are assumed to have different contributions to the skew
60 70 80 90
scattering. The scaling can be rewritten as Eq. (2):
H
A
ρAH =a′ρxx0+a′′ρxxT +bρ2xx (2) 3 Pt (tPt nm)/CFA (0.9 nm)
Here, ρxx0 is the residual resistivity, ρxxT comes from
′ ′′
the scattering of excited phonons, a and a are due to 2
theskewscattering,andbisdominatedbythe sidejump 1.5 nm
andintrinsiccontributions. Inthis equation,the phonon 2.5 nm
1
contribution is introduced by considering the inelastic 5 nm
scattering at finite temperatures, which was formulated 10 nm
(b)
in terms of a multiband tight-binding model by Shitade 0 20 nm
and Nagaosa30.
20 40 60 80
TwoseriesofPt(2.5nm)/Co2FeAl(tCFA nm) andPt xx cm
o(tnPtthnem1)×/C1o2cFme2Aplo(l0is.9hendmM)gbOila(y1e0r0)filsmubsswtrearteesdebpyomsitaegd- FIG. 2. (Color online) ρAH/ρxx versus ρxx curves for (a) Pt
(2.5 nm)/Co2FeAl (tCFA nm) and (b) Pt (tPt nm)/Co2FeAl
netron sputtering. All those samples were prepared un-
(0.9 nm) bilayers. All scattered symbols represent experi-
◦
der Hall bar mask and annealed at 320 C in situ. The
mental data. All red lines were fitted results by ρAH =
basepressureofsputteringchamberisbelow3×10−6Pa. a′ρxx0+a′′ρxxT +bρ2xx.
The sputtering Ar gas with 99.999% purity was intro-
ducedwithaconstantpressureof0.3Pa. Filmthickness
was measured by X-ray reflectivity (XRR) using a D8
If t < λ (λ is the spin diffusion length of Pt),
Discover X-ray diffractometer. The transport property Pt Pt Pt
increasing the thickness of Pt layer will enhance the ef-
wasmeasuredby physicalpropertymeasurementsystem
fectiveSOC(whichhasthe meaningofsqureofζ here-
(PPMS) from 20 to 300 K. eff
after)monotonicallyobeyingEq. (3)showninFig.3(b).
Onthe contrary,increasingthe thickness ofthe Co FeAl
Figure 2 shows the measured results of the AHE. 2
layer will not affect the spin diffusion in the Pt layer
ρAH/ρxx versus ρxx curves of the samples are given in
but reduce the effective SOC since the atomic SOC in
Fig. 2(a) and (b). The red lines are fitting curves. Ob-
the Co FeAl layer is much weaker than that in Pt layer,
viously, ρAH/ρxx versus ρxx is not linear relationship 2
which is shown in Fig. 3(a).
for almost all samples. Just when Co FeAl (CFA) layer
2
is thicker than 5 nm, the relationship looks like linear. If tPt > λPt, the spin states will be lost in partial
Hence,thetraditionalscalingdoesnotworkwellforvery of Pt layer where the distance to the interface of the
thin bilayers. On the contrary, Eq. (2) can fit the data FM and NM layer is over the λPt already. The reason
perfectly. These results are consistent with our reported is that the injected spin (along the M direction) from
data31,32. ItrevealsthatthedependenceofρAH/ρxx ver- the FM layer into Pt layer will be relaxed due to the
susρxx showsastraighterlineatspecialratiosamonga′, SOC of Pt. Therefore, this part of Pt only plays a role
a′′ and bρxx0 only, such as the cases in a bulk material of conducting a leakage current and a leakage current
and a thick film. factor has to be introduced, which is simply proposedas
According to the CB theory and the physical image L(tPt) = (λPt+tCFA)/(tPt+tCFA) here. Only those Pt
of the SOC proximity effect, the effective SOC strength atomic layers in the scope of λPt can make contribution
of Pt/Co FeAl can be treated using tight-binding sense, to the measuredsignalof spin dependent scattering, e.g.
2
and the expression can be read as: the AHE. The generalbehaviorof factorL(tPt) is shown
in Fig. 3(c). Taking into account the L(t ) factor, the
ζ t +ζ t Pt
ζ = CFA CFA Pt Pt, (3) effective SOC of the bilayersystem shouldtake behavior
eff
t +t
CFA Pt shown in Fig. 3(d), in which the turning point occurs
whereζ (=53.8meV)representsthe SOCstrengthof exactly at t = λ . Since the fitted parameters of the
CFA Pt Pt
Co FeAl,ζ (=554meV)istheSOCstrengthofPt,and AHE are theoretically proportional to the effective SOC
2 Pt
t is the thickness of Co FeAl(Pt) layer33. of the bilayer system, identifying the turning points in
CFA(Pt) 2
3
80
2 (/)effCFA 40 Pt (2.5 nm)/CFA (tCFA nm) Without fPatc t(otPrt nLm)/CFA (0.9 nm) 80 2 (/)effCFA -2 a’ (10) 1200 Pt (2.5 nm)/CFA (tCFA( nam)) Pt (tPt nm)/CFA (0.9( dnm)) 10
(a) (b) 40 0 0

0
5 10 0 5 10 15 20 ) 30
tCFA (nm) tPt (nm) -2 0 40
L(t) Pt01..50 (c) PPPPtttt====5812 With factor L PPPPtttt====1285 4800 2 (/)L(t)effCFAPt -1a" (1m)2000 (b) (e) 012000
(d)
0.0 0 c-1
0 5 10 15 20 0 5 10 15 20
-2
tPt (nm) tPt (nm) m-2 (c) (f)
(
FIG. 3. (Color online) Thickness dependence of (ζeff/ζCFA)2 b -3 -4
given by Eq. (3) for (a) Pt (2.5 nm)/Co2FeAl (tCFA nm) 0 5 10 0 5 10 15 20
and (b) Pt (tPt nm)/Co2FeAl (0.9 nm) bilayers. (c) Thick-
nessdependenceofL(tPt)forPt(tPt nm)/Co2FeAl(0.9nm) tCFA (nm) tPt (nm)
bilayer. L(tPt) is a factor resulting from the leakage cur- FIG. 4. (Color online) Thickness dependences of a′, a′′ and
rent for a thicker Pt layer. L(t ) = 1 when t ≤ λ ;
Pt Pt Pt b for Pt (2.5 nm)/Co FeAl (t nm) in (a)-(c) and Pt (t
simply L(tPt) = (λPt+tCFA)/(tPt +tCFA) when tPt > λPt. nm)/Co FeAl (0.9 nm2) bilayeCrFsAin (d)-(f). Here, a′ and aP′t′
(d) Thickness dependence of (ζ /ζ )2L(t ) for Pt (t 2
eff CFA Pt Pt indicate the contributions of skew scattering from impurities
nm)/Co FeAl (0.9 nm) bilayer, corresponding to the values
2 and phonons;b represents theintrinsic andside jump contri-
with the leakage current factor revision. λ is Pt diffusion
Pt butions.
length, which is arbitrarily taken as 1, 2, 5, 8 nm in (c) and
(d).
Grant Nos. 51331004, 11374228 and 11205235, the Na-
tionalBasicResearchProgramofChinaunderGrantNo.
the fitted parameters of the AHE provides a powerful 2015CB921501,andtheInnovationProgramofShanghai
tool to fix the spin diffusion length in the Pt layer. Municipal Education Commission No. 14ZZ038. Z. G.
Fig. 4 shows the thickness dependences of fitted pa- Zhu is supported by Hundred Talents Program of The
rameters from Fig. 2(a) and (b). For the samples with Chinese Academy of Sciences.
t = 2.5 nm, the t dependences are consistent with
Pt CFA
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