Experimental Verification of Comparability between Spin-Orbit and Spin-Diffusion Lengths

0.43 MB·English

by  Yasuhiro Niimi

Experimental Verification of Comparability between Spin-Orbit and Spin-Diffusion
Lengths
Yasuhiro Niimi,1,∗ Dahai Wei,1 Hiroshi Idzuchi,1 Taro Wakamura,1 Takeo Kato,1 and YoshiChika Otani1,2
1Institute for Solid State Physics, University of Tokyo,
5-1-5 Kashiwa-no-ha, Kashiwa, Chiba 277-8581, Japan
2RIKEN-ASI, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
(Dated: January 3, 2013)
We experimentally confirmed that the spin-orbit lengths of noble metals obtained from weak
3
1 anti-localizationmeasurementsarecomparabletothespindiffusionlengthsdeterminedfromlateral
0 spinvalveones. Evenformetalswith strongspin-orbitinteractionssuchasPt,weverifiedthatthe
2 twomethodsgave comparable valueswhich were muchlarger than those obtained from recent spin
torque ferromagnetic resonance measurements. To give a further evidence for the comparability
n
between the two length scales, we measured the disorder dependence of the spin-orbit length of
a
copperbychangingthethicknessofthewire. Theobtained spin-orbitlengthnicely follows alinear
J
law as a function of the diffusion coefficient, clearly indicating that the Elliott-Yafet mechanism is
7
dominant as in thecase of the spin diffusion length.

]
l PACSnumbers: 73.20.Fz,72.25.Ba,73.63.Nm,75.75.-c
l
a
h
- Spin relaxation and spin dephasing are the central is- debates, one needs another reliable way to estimate the
s
suesinthefieldofspintronicsastheydeterminehowlong SDL or the SH angle. In this Letter, we focus on weak
e
m andfarelectronscantransferthe spininformation[1,2]. anti-localization(WAL)observedinnonmagneticmetals.
Owing to recent technological advancements [3–12], one Wefirstdemonstratethatthespin-orbit(SO)lengthL
. SO
t cancreatethespinaccumulation,i.e.,theelectrochemical obtainedfromtheWALcurveofAgiscomparabletothe
a
m potential difference between spin-up and down electrons SDL Ls estimated from the lateral spin valve measure-
at the Fermi level, 10 100 times larger than that gen- ment. We then extend a similar discussion to a strong
- ∼
d eratedin conventionallateralspin valve devices or along SO material such as Pt. In metallic systems where the
n
edges of samples with spin Hall effects (SHEs). Such elastic mean free path l is much shorter than L , the
e s
o
a large spin accumulation can induce a large pure spin dominantspinrelaxationprocessistheEliott-Yafet(EY)
c
[ current, the flow of spin angular momentum with no net mechanism[17]. WealsoconfirmthattheEYmechanism

chargecurrent[13]. Asitsmagnitudescaleswiththespin works very well for LSO by changing the diffusion coeffi-
2
relaxation length or the spin diffusion length (SDL), the cient D of Cu wires. This experimental fact also verifies
v
2 quantitative evaluation of the SDL is of importance. the comparability between LSO and Ls.
2 We prepared two types of devices, i.e., samples for
Recentreportsonmagnetizationswitchingatverythin
2
WAL measurements and those for spin injection mea-
1 ferromagnet/nonmagnet bilayer films [11, 12, 14] have
surements. Bothsampleswerefabricatedonathermally-
. triggered a heavy debate on the detailed mechanism.
1
oxidized silicon substrate using electron beam lithog-
The first realization of the switching was reported by
1
2 Miron et al. [14] who concluded that the magnetization raphy on polymethyl-methacrylate resist and a subse-
1 switching originates from the Rashba effect at the ferro- quent lift-off process. For the WAL samples, we pre-
v: magnet(Co)/nonmagnet(Pt) interface. Similar measure- pared ∼ 1 mm long and 100 nm wide Ag (99.99%), Cu
i mentswerealsoperformedbyLiuetal. withaCo/Ptbi- (99.9999%), and Pt (99.98%) wires and performed the
X standard 4-probe measurement using a 3He cryostat. In
layerfilm[11]aswellaswithaCoFeB/Tabilayerone[12].
r ordertoobtainaverysmallWALsignalcomparedtothe
They claimed that the switching is due to the perpen-
a
backgroundresistance,we useda bridge circuit [18]. For
dicularly induced spin currents via the SHE of Pt and
the spin injection (or spin valve) measurement, we first
Ta. To discussthe conversionefficiency fromchargecur-
prepared two Permalloy (Ni Fe ; hereafter Py) wires,
rent to spin current i.e., the spin Hall (SH) angle, in 81 19
whichworkasspininjectoranddetector. TomeasureL
their devices, they performed the spin torque induced s
of a strong SO material such as Pt, we inserted it in be-
ferromagnetic resosnance (FMR) measurements and es-
tweenthetwoPywires. Thethreewireswerebridgedby
timated the SH angle of Pt and Ta to be 0.07 and 0.15,
a thicker Cu wire to transfer a pure spin current gener-
respectively[10–12]. TheseSHangles,however,arequite
ated at the Py/Cu interface. To check the reproducibil-
different from those obtained from the spin absorption
ity, we measured at least a few different samples on the
method (0.02 for Pt and 0.004 fo Ta) [15]. Furthermore
Liu et al. [16] pointed out that the overestimationof the same batch both for the WAL and spin valve measure-
ments.
SDLs reported in Ref. [15] results in a large underesti-
mation of the SH angles. To settle down such heavy In order to clarify whether L from WAL measure-
SO
2
2647 that the spin relaxation rate 1/τ = D/L2 is twice the
Ag s s
spin-flipscatteringrate,i.e.,1/τ =1/τ +1/τ . Atsuf-
t = 50 nm s ↑↓ ↓↑
T = 4 K L = 0.55 mm ficiently low temperatures, the contribution of phonons
2646
can be neglected and one obtains
) √3
WR ( 2645 T = 0.4 K Ls = 2 LSO, (2)
10 m m within the EY mechanism from isotropic impurity scat-
D R
2644 tering. Since Ag is a monovalent metal with an almost
sphericalFermisurface,onecanadaptEq.(2)toconvert
fromL toL . WethusobtainL =650 40nm,which
SO s s
±
2643 is quantitatively consistent with L ( 600 nm) obtained
s
-500 0 500 ∼
from the lateral spin valve measurements [4, 23].
B (G)
Next we discuss the SDL of a strongSO materialsuch
asPtwhichisthemoststandardSHEmaterial. Asmen-
FIG. 1: (Color online) WAL curves of Ag wire measured at
tionedintheintroduction,thisisoneofthecausesofthe
T =0.4and4K.ThebrokenlinesarethebestfitsofEq.(1).
The inset shows a scanning electron micrograph of the Ag big debates, i.e., Ls = 11 nm from the spin absorption
wire. measurements[15]andLs =1.4nmfromthespintorque
FMR measurements [16]. To solve the problem, here we
performtwo differentmeasurementsto obtainL orL
SO s
of Pt; WAL and spin absorptionin the lateralspin valve
ments is equivalent to L from spin valve ones, we first
s
devices. NotethatthePtwiresfortheWALandspinab-
measure WAL curves of a weak SO material. Figure 1
sorption measurements were prepared at the same time.
shows typical WAL curves of a Ag wire measured at
Figure 2(a) shows a typical WAL curve of Pt. The field
T = 0.4 and 4 K. Unlike a normal weak localization
scale is 20 times largerthan that for Ag wires, which in-
(WL) curve, the resistance increases with increasing the
dicates that L is much shorter. We observe maxima
perpendicular magnetic field B because of the SO in- SO
of the WAL curve at around 0.9 T. From the best fit
teraction. With decreasing temperature, the phase co- ±
of Eq. (1), we obtain L =12 nm. We have performed
herence of electrons gets larger and the WAL peak also SO
similar measurements for 5 different samples and using
gets sharper. The WAL peak of quasi one-dimensional
Eq.(2)wehavedeterminedL ofPttobe10 2nm[24].
(1D) wire can be fitted by the Hikami-Larkin-Nagaoka s ±
The spin absorption measurement into the Pt wire is
formula [19];
shown in Fig. 2(b). For comparison, Py middle-wire de-
vices were prepared since the SDL of Py is well-known
∆R = 1 R∞  23 21 (1) from other experiments [25]. We have performed nonlo-
R∞ πL~/e2 qL12ϕ + 34L12SO + 31wl4B2 − qL12ϕ + 31wl4B2 cal spin valve (NLSV) measurements with and without
the middle wires [8, 9, 15]. The in-plane magnetic field
where ∆R, R∞, L, and w are respectively the WL cor- Bk is applied parallel to the two Py wires [see the in-
rection factor, the resistance of the wire at high enough set of Fig. 2(b)]. A pure spin current generated from
field, the length and width of the quasi-1D wire. e, ~, Py1isabsorbedperpendicularlyintothemiddlewirebe-
and lB = p~/eB are respectively the electron charge, cause of the strong SO interaction of Pt (or Py). As
thereducedPlankconstant,andthemagneticlength. In shown in Fig. 2(b), the NLSV signal detected at Py2 is
Eq. (1), we have only two unknown parameters; Lϕ and reduced by inserting the Pt or Py wire compared to the
LSO. According to the Fermi liquid theory [20], Lϕ does one without any middle wire. To extract the SDLs of
depend on temperature ( T−1/3), while LSO is almost Pt and Py, we first use the 1D analytical model based
∝
constant at low temperatures [21]. Based on this fact, on the Takahashi-Maekawa formula [13]. In this model,
we fix LSO at both temperatures to fit the WAL curves. the normalized NLSV signal ∆RSwith/∆RSwithout can be
We obtain Lϕ = 4.20 and 1.95 µm at T = 0.4 and 4 K, expressed as follows [8, 9];
respectively, while L = 800 nm [22]. The two L val-
SO ϕ
ues meet the Fermi liquid theory Lϕ T−1/3. We have ∆RSwith 2RMsinh(d/LCsu)
∝
measured 4 different Ag wires on the same batch and ∆RSwithout ≈ RCu{cosh(d/LCsu)−1}+2RMsinh(d/LCsu)
obtained L =760 50 nm. (3)
SO
±
L should be closely related to L . This relation has whereR andR arethespinresistancesofCuandthe
SO s Cu M
been theoretically discussed in Ref. [1]. The SO scat- middle wire(PtorPy),respectively. Thespinresistance
tering rate 1/τ = D/L2 includes both spin-flip and R ofmaterial“X”isdefinedasρ LX/(1 p2)A ,where
SO SO X X s − X X
spin-conserving processes, resulting in 1/τ = 3/(2τ ) ρ , LX, p and A are respectively the electrical resis-
SO ↑↓ X s X X
where 1/τ is the spin-flip scattering rate. We also note tivity, the SDL, the spin polarization, and the effective
↑↓
3
(a) thusconcludethattheSDLofPtitselfisnot oftheorder
Pt of 1 nm but about 10 nm.
t = 20 nm
The reasonwhy L of Pt reported in Ref. [16] is much
101.3 L = 1.9 mm s
L = 12 nm shorter than ours is that in the FMR measurement, the
SO
) ferromagnet/nonmagnet bilayer is always used. In such
WR (k abilayersystem,onecannotavoidthe contributionfrom
themagneticdampingeffect[16,27,28]. Asaresult,the
101.29 real SDL of nonmagnet can be modulated by the FMR,
whichresultsinamuchshorterSDL.Thus,suchashorter
T = 3 K
SDLcannot beadaptedtothecaseofthespinaborption
-10000 0 10000 method and the SH angle of Pt should be about a few
B (G) percent[15],should not beenhancedupto7%asclaimed
(b) by Liu et al [16]. Recently, Kondou et al. [29] measured
d= 700 nm the SH angle of Pt using the same method as Liu et
al. [10–12, 16] but they carefully studied the thickness
0.5
dependence of ferromagnetand nonmagnet. They found
Pt: r = 10 W(cid:215)m cm
) thatthesymmetricpartofFMRspectra,fromwhichthe
Wm 0 DR with Py: r = 19 W(cid:215)m cm SH angle is extracted, does depend on the thickness of
(S S
R ferromagnet and one should take the zero-limit to avoid
Py1
DR without Pt or Py any effects from the ferromagnet [29]. The extrapolated
-0.5 S Py2 SH angle is 0.022 for Pt, which is quantitatively consis-
T = 10 K Cu V
tent with that in Ref. [15].
B
-1000 0 1000 //
TofurthersupportthecomparabilitybetweenL and
B (G) SO
// L , we study the disorder effect on L . In metallic sys-
s SO
tems where l < L , the EY mechanism is dominant for
FIG.2: (Coloronline)(a)WALcurveofPtwiremeasuredat e s
T =3K.ThebrokenlineisthebestfitofEq.(1). (b)NLSV the spin relaxation process. If Eq. (2) is valid in metal-
signals with Pt (RSwith; red) and Py (blue) wires in between lic systems, LSO should also follows the EY mechanism.
the two Py wires. As a reference signal, we plot the NLSV For this purpose, we have chosen copper which has a
signal without the middle wire (RSwithout; black). The width weak SO interactionand then simply changed the thick-
and thickness of the Pt or Py middle wire are 100 nm and
ness t of the copper wire. Figure 3(a) shows WAL
Cu
20 nm, respectively. The other dimensions are the same as
curves of 20, 30, 80 nm thick Cu wires. It is obvious
in Refs. [8] and [9]. A pair of arrows on the top indicates
that the maximum position (triangle in the figure) due
the magnetizations of Py1 and Py2. The inset shows the
schemetic of ourlateral spin valvedevice. to the SO interaction shifts toward lower fields with in-
creasingt . Thispositioncorrespondstothefieldwhere
Cu
2/L =w/l2,i.e.,B∗ =2~/(ewL ). Fromthe fitting,
SO B SO
we obtain L = 340, 550, 920 nm for t = 20, 30,
SO Cu
cross sectional area involved in the equations of the 1D 80 nm respectively.
spin diffusion model [8, 9]. d is the distance between the In Fig. 3(b) we plot LSO of Cu as a function of D.
two Py wires, in the present case d=700 nm. Although Note that D is determined from the Einstein relation
the spinabsoprtionrate∆Rwith/∆Rwithout isalmostthe D = 1/(e2ρN) where N is the density of state at the
S S
same for the Pt and Py middle wires, the obtained Ls Fermi level [30]. LSO nicely follows a linear law down
fromEq.(3)are11( 2)nm forPtand5( 1)nm forPy. to 20 nm thick Cu wires. According to the EY mecha-
± ±
This is because the resistivity of Pt is nearly half of Py. nism, τs consists of the phonon and impurity contribu-
The SDL of Pt coincides well with that from our WAL tions as follows; 1/τs = 1/τsimp+1/τsph. Since we focus
measurement and the SDL of Py is also consistent with on the low temperature part, we can neglect the phonon
other experimental results [25]. contribution [21] and concentrate on the discussion only
Wehavealsousedthethree-dimensional(3D)spindif- about the spin relaxation from impurities, which makes
fusion model based on the Valet-Fert formalism [26] to theanalysismuchsimpler[31]. Inaddition,theimpurity
obtain Ls of Pt. This has been done in order to refute contribution can be expressed as τsimp = τe/εimp where
the claim made by Liu et al. that Ls of Pt extracted τe andεimp aretheelesticscatteringtimeandtheproba-
from the 1D model might be overestimated [16]. As de- bility of spin-flip scattering, respectively [32]. Thus, one
tailed in Ref. [9], SDLs obtained from the two methods obtains the following equation;
donotdiffersignificantlywhentheSDLsarecomparable
2 2D 2l
e
orsmallerthanthe thicknessofthe middle wire. Infact, LSO = Ls = = (4)
√3 vF√εimp 3√εimp
wehaveconfirmedthatthe3DanalysisforthePtmiddle
wire gives almost the same value as the 1D model. We where v is the Fermi velocity. As can be seen in
F
4
(a) 10442 t = 20 nm CESRmeasurements[34]. We also showLSO andle as a
Cu
L = 0.55 mm functionoft onthe sameplotinthe insetofFig.3(b).
Cu
) 10440 B* LSO = 340 nm BothLSO andle follow the same dependency. When tCu
WR ( 10438 is much larger than le, the impurity and defect contri-
butions come mainly from the inside of the wires. With
10436 decreasingtCu, le is limited by tCu. This means that the
presentsystemis perfectlydiffusiveandthereis nospec-
11182 t = 30 nm
Cu ular scattering from the surface [18]. In this case, the
L = 1.35 mm
11180 surface scattering can be regarded as a kind of impurity
)
WR ( 11178 LSO = 550 nm or defect, and thus Eq. (4) works down to our lowest D.
Inconclusion,wehaveexperimentallyverifiedthecom-
11176 parability between the SO lengths and the SDLs of no-
ble metals using the WAL and spin absorptionmethods.
3783.4 tCu = 80 nm This comparability works not only for weak SO mate-
L = 1.9 mm
3783.2 LSO = 920 nm rials but also for strong SO materials such as Pt. We
)
have also studied the disorder effect on the SO lengths
WR ( 3783 of Cu by changing the thickness of wires. The obtained
3782.8 T = 4 K
SO length nicely follows a linear law as a function of D,
-500 0 500 which clearly verifies the EY mechanism in the present
B (G) system.
(b) 1500 We acknowledge helpful discussions with C. B¨auerle,
Cu S. Maekawa,S. Takahashi,S. KasaiandK. Kondou. We
20 nm
wouldalsoliketothankY.IyeandS.Katsumotoforthe
30 nm
1000 50 nm useofthelithographyfacilities. Thisworkwassupported
m) 80 nm tCu (nm) by KAKENHI.
(n 100 nm 0 50 100
O le (nm) LSO (nm)
LS 500 T = 4 K 40 1000
20
0 0 ∗
0 Electronic address: [email protected]
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