Interface enhanced spin-orbit torques and current-induced magnetization switching of Pd/Co/AlO$_x$ layers

2.4 MB·

by  Abhijit Ghosh

Interface enhanced spin-orbit torques and current-induced magnetization switching of
Pd/Co/AlO layers
x
Abhijit Ghosh, Kevin Garello, Can Onur Avci, Mihai Gabureac, and Pietro Gambardella
Department of Materials, ETH Zu¨rich, H¨onggerbergring 64, CH-8093 Zu¨rich, Switzerland
(Dated: January 10, 2017)
Magneticheterostructuresthatcombinelargespin-orbittorqueefficiency,perpendicularmagnetic
anisotropy, and low resistivity are key to develop electrically-controlled memory and logic devices.
Herewereportonvectormeasurementsofthecurrent-inducedspinorbittorquesandmagnetization
switching in perpendicularly magnetized Pd/Co/AlO layers as a function of Pd thickness. We
x
find sizeable damping-like (DL) and field-like (FL) torques, of the order of 1 mT per 107 A/cm2,
whichhavedifferentthicknessandmagnetizationangledependence. TheanalysisoftheDLtorque
7
1 efficiency per unit current density and electric field using drift-diffusion theory leads to an effective
0 spinHallangleandspindiffusionlengthofPdlargerthan0.03and7nm,respectively. TheFLSOT
2 includesasignificantinterfacecontribution,islargerthanestimatedusingdrift-diffusionparameters,
and is further strongly enhanced upon rotation of the magnetization from the out-of-plane to the
n
in-plane direction. Finally, taking advantage of the large spin-orbit torques in this system, we
a
demonstratebipolarmagnetizationswitchingofPd/Co/AlO layerswithsimilarcurrentdensityas
J x
used for Pt/Co layers with comparable perpendicular magnetic anisotropy.
7

]
i I. INTRODUCTION of the experimental data [25]. Our study is based on
c
the harmonic Hall voltage method to measure SOT [14–
s
- Spin-orbit torques (SOT) generated by current injec- 16, 27, 28] and includes a detailed magnetotransport
rl tion in normal metal/ferromagnet (NM/FM) bilayers characterization as well as the analysis of magnetother-
t mal contributions to the Hall resistance [14, 29]. We
m have attracted considerable attention as a method to in-
report strong DL and FL SOT amplitudes and efficient
ducemagnetizationswitchingofthinFMfilmsandmag-
.
t netic tunnel junction devices [1–7]. Although the bulk magnetization switching for this system, combined with
a
largeperpendicularmagneticanisotropy(PMA)andrel-
m or interface origin of the spin current giving rise to the
atively low resistivity. We further observe a distinct
damping-like(DL)andfield-like(FL)SOTcomponentsis
-
thickness dependence of the DL and FL torques and dis-
d amatterofdebate[8–11],ithasbeenestablishedthatthe
n strongestSOTarefoundinNMwithlargespin-orbitcou- cuss different models to account for the SOT efficiency.
o pling, and hence large spin Hall effect (SHE) and small The main results are summarized at the end of this pa-
c per.
spin diffusion length (λ), such as the 5d-metals Pt, W,
[
andTa[12–19]. Forthisreason, the4d-metalshavebeen

1 largelycastasideinthequestforlargeSOT,eventhough
v several studies of the SHE in these materials show size- II. EXPERIMENT
3
able spin Hall angles, of the order of γ ∼0.01 [20–24].
4 SH
Pd-based heterostructures constitute an apparent ex- Our samples are Ta(0.8nm)/Pd(t )/Co(0.6nm)/
8 Pd
1 ception to this trend: recent studies of [Pd/Co]N mul- AlOx(1.6nm) layers grown on thermally oxidized Si sub-
0 tilayers [25] and Pd/FePd/MgO trilayers [26] evidenced strates by dc magnetron sputtering in an Ar pressure of
. DL and FL effective fields of the same order of mag- 2×10−3 Torr. The Al cap layer was oxidized for 37 s
1
0 nitude or larger than those found in Pt- and Ta-based under a partial O2 pressure of 7×10−3 Torr in order to
7 structures, reaching up to more than 10 mT for an in- increasethePMAofCo/Pd. TheTaseedlayerwasused
1 jected current density of j = 107 A/cm2. The effective to improve the uniformity of Pd; because of its high re-
: spin Hall angle required to model the SOT according to sistivity and reduced thickness, such a layer plays a neg-
v
i spin diffusion theory is γSH > 1 in [Pd/Co]N (Ref. 25) ligible role in the generation of SOT, as we confirmed by
X
and γ ≈ 0.15 in Pd/FePd/MgO [26], which is sub- measuringPd/Co/AlO structuresgrownwithaTiseed.
SH x
r stantially larger compared to previous estimates of γ Thermsroughnessmeasuredbyatomicforcemicroscopy
a SH
in Pd [20–24]. This comparison calls for further investi- was found to vary between 0.15 nm (t = 1.5 nm) and
Pd
gationsoftheSOTduetoPdaswellasofthepossibility 0.13 nm (t = 8 nm). The as-grown layers were pat-
Pd
ofusingPdtoinducemagnetizationswitching,whichhas terned using UV-lithography and dry etching into Hall
not been reported to date. bars of width w = 10 µm and length L = 50 µm, as
In this work we present a study of current-induced shown in Fig. 1a. For the magnetotransport characteri-
SOTandmagnetizationswitchinginPd/Co/AlO trilay- zation, the samples were mounted in the gap of an elec-
x
ers with varying Pd thickness. We focus on the simple tromagnet producing a field B and allowing for rotat-
ext
trilayer structure to avoid the complexity due to mul- ing the current direction relative to the magnetization
tiple interfaces and current paths in [Pd/Co] multi- (m). The experiments were performed at room temper-
N
layers, which complicate the analysis and interpretation ature using an ac current I = I sin(ωt) with amplitude
0
2
I and frequency ω/2π = 10 Hz. I ranged between 3 case, the four unknown coefficients in Eqs. 3, 4 must be
0 0
and 14 mA in samples with t = 1.5 and 9 nm, re- determinedbyfourindependentmeasurementsofR2ω as
Pd H
spectively, and was adjusted in order to keep the current a function of B , applied in-plane along φ = 0◦,±45◦
ext
density flowing through Pd between j = 1×107 and and 90◦. All the SOT values reported in this work have
Pd
1.5×107 A/cm2. The harmonic Hall voltage measure- been normalized to j =1×107 A/cm2 for comparison
Pd
ments were performed by taking the Fourier transform with literature data.
of the ac Hall resistance recorded for 10 s at each value
of the applied field and current. The first harmonic Hall
resistance is analogous to a dc Hall measurement and is
given by
III. RESULTS
Rω =R cosθ+R sin2θsin(2φ), (1)
H AHE PHE
A. Resistivity and magnetic anisotropy
where R and R are the anomalous and pla-
AHE PHE
nar Hall coefficients, and θ and φ represent the polar
and azimuthal angles of the magnetization, respectively. Figure 1(b) shows the resistance of the Pd/Co/AlOx
Current-induced effects were characterized by measuring layers as a function of Pd thickness. Using a simple par-
the second harmonic Hall resistance, R2ω, which arises allel resistor model, assuming that the conductivity of
H
due to the mixing of the ac current with the Hall effect Co remains constant across the series, we find that the
modulated by the oscillations of the magnetization in- resistivity of Pd varies approximately as ρPd ∝ 1/tPd
duced by the DL and FL torques [14–16, 27, 28]. This [inset of Fig. 1(b)]. This is in line with previous inves-
termaccountsfortheSOTeffectivefields,whicharepro- tigations of the resistivity of Pd thin films [33], which
portionaltoI,aswellasformagnetothermaleffectsthat behaves similarly to Pt [34], and is significantly smaller
are proportional to I2 [14, 16, 29]. Following Ref. 29, we compared to β-W and β-Ta. The Hall resistance RHω is
have shown in Fig. 1(c) as a function of Bext applied at an
angle θ = 84◦ relative to the sample normal. As cus-
B
dcosθ BI tomary in SOT investigations of PMA materials, the ex-
R2ω =[R −2R cosθsin(2φ)] θ
H AHE PHE dB sin(θ −θ) ternalfieldwasslightlytiltedoff-planeinordertoprevent
ext B
the formation of magnetic domains. Accordingly, we ob-
2cos(2φ)
+R sin2θ BI +R2ω , (2) serve that the magnetization loops are reversible as long
PHE B sinθ φ ∇T
ext B as m does not switch direction, as expected for coherent
where BθI and BφI are the polar and azimuthal com- rotation of the magnetization, and that RHω decreases
ponents of the current-induced effective fields, respec- when increasing Bext as m tilts away from z. When
t(∇iveTly×,imnc)lu·dyinisgtbhoeththSeOrmTaalnHdalOlerresstisetdanficeelda,sasnodciRat∇2eωdT t∝o φus=to0d◦e,r9i0v◦e,tRheHωainsgpleroθp=ortcioosn−a1l(tRoHωm/R·AzH,Ew)haicshaaflulonwcs-
the anomalous Nernst effect. The latter is caused by tion of applied field. We observe also that the maximum
the unintentional out-of-plane and in-plane temperature amplitude of RHω decreases with increasing Pd thickness
gradients∇T producedbyJouleheatingandasymmetric owingtothedecreaseoftheAHEduetocurrentshunting
heatdissipationinthetrilayer[29]. ToseparatetheSOT through Pd [Fig. 1(d)]. Our data indicate that both the
contributions from R2ω , we exploit the different behav- AHE and PHE are roughly proportional to t−3 rather
∇T Pd
ior of BI and R2ω as a function of B , as explained thantoρ /t ∝t−2,aswouldbeexpectedforaparal-
θ,φ ∇T ext Pd Pd Pd
in detail in Refs. 29 and 30. Finally, in order to explicit lel resistor model of the Co and Pd layers. This suggests
the relationship between BI and BI in Eq. 2 and the that the AHE and the magnetoresistance are enhanced
θ φ
DL and FL SOT effective fields, we express the latter in at the Pd/Co interface relative to bulk Co, in agreement
spherical coordinates [14]: with studies of the AHE in [Co/Pd] multilayers [35].
N
BDL =BDLcosφe −BDLcosθsinφe , (3) The inset of Fig. 1(d) shows the effective magnetic
θ θ φ φ anisotropy field calculated by using the macrospin ap-
BFL =−BθFLcosθsinφeθ−BφFLcosφeφ, (4) proximation: BK = Bext(sinθB/sinθ − cosθB/cosθ).
We find that B varies between 0.7 and 0.9 T, with no
where the coefficients BDL, BFL, BDL, and BFL repre- K
θ θ φ φ systematic variation as a function of Pd thickness and
sent the polar and azimuthal amplitudes of the DL and
independently of the in-plane direction of the magneti-
FL SOT. In the ”isotropic torque” limit usually consid-
zation. The corresponding uniaxial magnetic anisotropy
ered in the SOT literature, Eqs. 3, 4 are obtained by
energy is thus K =B M /2+µ M2/2=(1.5±0.1)×
projecting BDL = BDL(m×y) and BFL = BFL[m× u K s 0 s
0 0 106 J/m3, where M = 1.27×106 A/m is the satura-
(m×y)]ontotheunitvectorse ande andbyassuming s
θ φ tion magnetization measured by SQUID. Interestingly,
BDL =BDL andBFL =BFL. GeneralmodelsandSOT
θ,φ 0 θ,φ 0 K for Pd/Co/AlO is comparable or larger relative to
u x
vector measurements, however, have shown that BDL
θ,φ [Pd/Co]N multilayers [36–38], which we attribute to the
and BFL can be functions of the magnetization orien- top oxide layer favoring strong PMA through the forma-
θ,φ
tation [14, 31, 32]. When this occurs, as in the present tion of Co-O bonds [39, 40].
3
B. Spin-orbit torques 42]. Remarkably, we find that the ratio BDL/j in-
0 Pd
creases with increasing t , whereas BFL/j has a non
Pd 0 Pd
The SOT measurements were performed by analyzing monotonic dependence on tPd. This is a first indica-
thesecondharmonicHallresistancethatarisesduetothe tion that the interface and bulk contributions to the two
mixing of the ac current with the ac oscillations of the torques differ in magnitude. Moreover, we observe that
magnetizationinducedbytheDLandFLtorques(Eq.2). theSOTefficiencydependsontheorientationofthemag-
Because the DL torque is larger when m is oriented in netizationrelativetothecurrentdirection. Inparticular,
the xz plane, whereas the FL torque tends to align m the angular dependence of the FL SOT is much stronger
towards y, measurements taken at φ = 0◦ (φ = 90◦) re- than that of the DL SOT [Fig. 3(b)], such that the total
flect mainly the strength of the DL (FL) effective fields. FL torque is larger than the total DL torque when the
Figures 2(a) and (b) show R2ω measured at φ = 0◦ and magnetization is tilted in-plane [Fig. 3(c)].
H
φ=90◦ after the subtraction of R2ω [30]. These curves Next, we analyze the SOT amplitudes normalized by
are, respectively, odd and even wit∇hTrespect to magneti- theappliedelectricfieldBDL,FL/E,showninFig.4(a-c).
zationreversal, reflectingthedifferentsymmetryofBDL The motivation for this analysis is that the resistivity of
and BFL [14]. Similarly to Rω, we observe that the am- Pdisstronglythicknessdependent,asshowninFig.1(b).
H
plitude of R2ω decreases with increasing Pd thickness, Therefore,evenwithinasinglesample,thecurrentisnot
H
which limits the signal-to-noise ratio and, consequently, homogeneously distributed across the Pd layer. More-
therangeofourSOTmeasurementstot ≤8nm. Fig- over, the current profile in Pd will vary from sample to
Pd
ures 2(c) and (d) show the effective fields BDL and BFL sampleinawaythatisnotdescribedbyasimpleparallel
θ θ
as a function of θ, obtained by R2ω using Eqs. 2-4. We resistor model. The electric field E = ρj = ρPdjPd, on
H
findthattheDLandFLfieldshavethesamesignasmea- the other hand, is the primary force driving the charge
suredforPt/Co/AlO [1,14,41]andincreaseasthemag- and spin currents [9] and is constant throughout the
x
netization rotates towards the plane of the layers. Com- thickness of the whole sample, which makes it a practi-
patibly with the uniaxial symmetry of the system, the cal unit for thickness dependent studies of SOT [15, 42].
angulardependenceoftheDLandFLfieldscanbemod- Accordingly, in analogy with Eq. 5 and for the purpose
elledbyaFourierseriesexpansionofthetypeBDL,FL = ofcomparingtheSOTindifferentsystems,wedefinethe
θ SOT efficiency per unit electric field [42]
BDL,FL+BDL,FLsin2θ+BDL,FLsin4θ+...,whereasthe
0 2 4
azimuthal components are only weakly angle dependent
vaanldueasreofapthperozxeimroathte,dsebcyonBdφD,La,nFdLf≈ouBrt0DhLo,FrdLer[1B4]D. LT,FhLe ξEDL(FL) = 2¯heMstCoBDLE(FL) = ξjDρLP(FdL). (6)
θ
coefficients are obtained by fitting the data in Fig. 2(c)
Figure 4(a) shows that the thickness dependence of the
and (d) according to this expansion. Additionally, we
electric field-normalized SOT is very different from that
present data obtained using the small angle approxima-
of the current-normalized SOT: BDL/E increases in an
tθio≈n0[2◦8[]s,tawrhsicyhmybioellsdsinacFciugr.a2t(ec)vaalnudes(fdo)r].BT0DhLis,FaLppwrhoexn- almostlinearwayinthewholerang0eoftPd whileB0FL/E
has a monotonic dependence on t and extrapolates to
Pd
imation is valid as long as R2ω varies linearly with the
H a nonzero value at tPd = 0. The angular amplitudes
applied field, as shown in the inset of Figs. 2(a) and (b), BDL/E, on the other hand, are very small relative to
2+4
and is equivalent to Eq. 2 in this limit.
BDL/E and only weakly thickness dependent, contrary
Figures 3(a-c) report the isotropic and angle- 0
to the FL components BFL/E, which have a strong de-
dependent SOT amplitudes as a function of t , nor- 2+4
Pd pendenceont ,asshowninFig.4(b). Theimplications
malizedtoj =107 A/cm2. ToobtaintheisotropicFL Pd
Pd of these results are discussed below.
SOT component, BFL, the Oersted field is calculated as
0
BOe =µ j t /2 [open triangles in Fig. 3(a)] and sub-
0 Pd Pd
tractedfromthetotalFLeffectivefieldderivedfromR2ω
H C. Discussion of the spin-orbit torque dependence
(opendots). ThecoefficientsBDL(FL),shownin(a),rep- on Pd thickness
0
resent the magnetic field induced by the DL (FL) torque
when m (cid:107) z, whereas BDL(FL), shown in (b), represent We discuss first the thickness dependence of the
2+4
theangle-dependentcontributions,andB0D+L2(+F4L),shown isotropic DL torque B0DL/jPd in terms of the drift-
in (c), represent the total amplitude of the field when diffusion approach widely employed in the analysis of
m (cid:107) x(y). For comparison with literature data, we plot SOT and spin pumping experiments. Assuming that
also the SOT efficiency (right scale), defined by the spin current flowing from the NM into the FM is
uniquely due to the bulk SHE of the NM and entirely
2e BDL(FL) absorbed at the NM/FM boundary [12], the simplest
ξDL(FL) = M t , (5)
j ¯h s Co j drift-diffusion model gives a dependence of the type
Pd
ξDL = γ [1 − sech(t /λ)]. A fit according to this
j SH Pd
whichrepresentstheratioofthespincurrentabsorbedby function [grey line in Fig. 3(a)] yields γ = 0.03 and
SH
theFMtothechargecurrentinjectedintheNMlayer[12, λ=2 nm, with an incertitude of about 10%. There are,
4
however, several reasons that caution against drawing SOT in Pd/Co/AlO relative to what is expected from
x
conclusions from such a simplified model. First, within thebareSHEofPd. TheamplitudeoftheDLSOT,how-
drift-diffusion theory, one should take into account the ever,remainssmallerthanreportedforPt/Co/AlO [14]
x
spin backflow into the NM [8, 43] and spin memory loss and Pt/Co/MgO [42]. We remark that the observed
at the NM/FM interface [44, 45]. Second, as pointed variation of the torques cannot be related to changes of
out in Ref. 42, drift-diffusion models assume constant the film roughness [52], which is approximately constant
ρ , γ , and λ throughout the NM layer, whereas the across the whole Pd/Co/AlO series. We also note that
NM SH x
strong dependence of ρ on t typical of ultrathin a refinement of the drift-diffusion model that considers
NM NM
films [Fig. 1(b)] invalidates this hypothesis. Third, both a thickness-dependent λ rescaled such that the product
first-principle electronic calculations [10, 11] and optical ρ λ is constant and equal to the bulk value ρ∞λ∞,
Pd Pd
measurements [46] suggest the existence of an ”interface consistently with the Elliott-Yafet mechanism of spin re-
SHE”, which can be significantly larger than the bulk laxation [42], gives σ = (5±2)×105 Ω−1m−1 and
SH
SHE. This interface SHE is ascribed to the current car- λ = (18±8) nm, showing that the fitted values of σ
SH
riedbyinterfacestates,similarlytotheRashba-Edelstein andλarestronglymodeldependent. Evensucharefined
effect [47]. Additionally, spin-dependent scattering at model, however, does not take into account the interface
the FM/NM interface can also lead to a spin polarized enhancement of the SHE [10, 11, 48, 49] and cannot jus-
current and generate DL and FL SOT [48, 49]. Keep- tify the presence of a large FL SOT.
ing track of all these effects together leads to an over- A similar analysiscan be performedon BDL , corre-
0+2+4
parameterized problem, which makes it difficult to draw sponding to the SOT efficiency for the in-plane magne-
a firm conclusion on either γSH or λ. tization [Fig. 3(c)]; the main result in this case is a re-
An alternative approach is to consider the SOT values duction of λ by 20-40% relative to the out-of-plane case
normalized by the applied electric field. According to discussed above. Such a result is not so surprising if
drift-diffusion theory and including spin back flow [8], one considers that spin diffusion in the limit of t ≥ λ
Pd
the SOT efficiency per unit electric field due to the bulk is strongly influenced by the NM/FM interface, where
SHE is given by spin-orbitcouplingisresponsibleforinducinganisotropic
electron scattering processes. For the same reason, one
(cid:18) (cid:19)
γ t
ξDL =4λ SH sinh2 may expect also the spin mixing conductance and spin
E ρ 2λ memory loss to depend on the magnetization direction.
(cid:104) (cid:105)
2λG2cosh(t)+G 2λG cosh(t)+ 1sinh(t) We now discuss the thickness dependence of the FL
i λ r r λ ρ λ
, (7) SOT, which is qualitatively different compared to the
(cid:2)2Giλcosh(λt)(cid:3)2+(cid:104)2λGrcosh(λt)+ ρ1sinh(λt)(cid:105)2 DL SOT. The B0FL/jPd ratio [full dots in Fig. 3(a)] has
a nonmonotonic behavior as a function of t , with a
Pd
minimum around 3.5 nm. This behavior compounds the
(cid:18) (cid:19)
ξFL =4λγSH sinh2 t FL SOT thickness dependence with the uneven current
E ρ 2λ distribution in the Pd/Co bilayer. Analysing the ratio
BFL/E [full dots in Fig. 4(a)] obviates the problem of
1G sinh(t) 0
ρ i λ , (8) the current distribution, revealing a monotonic increase
(cid:2)2Giλcosh(λt)(cid:3)2+(cid:104)2λGrcosh(λt)+ ρ1sinh(λt)(cid:105)2 ohfowBe0FvLer/,EBwFitLh/iEncreexatsrianpgotlPatde.sDtiofferaenntolynzfreoromvBa0DluLe/Eat,
0
where ρ and t are the resistivity and thickness of the tPd = 0, evidencing a significant contribution from the
normal metal layer (Pd in our case), while G and G Pd/Co interface akin to a Rashba-Edelstein magnetic
r i
are the real and imaginary parts of the spin mixing con- field [41, 53]. Moreover, an attempt to fit ξFL using
E
ductance. The grey line in Fig. 3(c) is a fit of BDL/E the SHE drift-diffusion theory (Eq. 8) adding a constant
0
according to Eq. 7, which gives a spin Hall conductivity term for the interface contribution yields σSH about one
σ =γ /ρ=(4±1)×105Ω−1m−1andλ=(7±1)nm, orderofmagnitudelargerthanderivedfromtheanalysis
SH SH
assuming ρ∞ =1.4×109 Ωm for the bulk Pd resistivity of ξDL. Similar considerations apply to BFL . The
Pd E 0+2+4
(measured for a 30 nm thick Pd film), and the spin mix- comparison between BFL and BDL in Fig. 4(b) fur-
2+4 2+4
ingconductancecalculatedforapermalloy/Pdinterface, thershowsthattheFLtorquehasastrongeranisotropic
G =7.75×1014 Ω−1m−2 andG =G /7[50]. Although component relative to the DL torque, and that such
r i r
λ = 7 nm is in good agreement with recent first prin- anisotropy is thickness dependent. This is in contrast
ciples calculations of Pd [51], σ exceeds the intrinsic withthestandardformoftheSOTderivedfromthebulk
SH
valueof2.1×105 Ω−1m−1 calculatedforbulkPd[50]and SHE using either the drift-diffusion model or the Boltz-
γ =ρ∞σ ≈0.055 is consistently larger than previ- mann transport equation, exemplified by Eqs. 7 and 8,
SH Pd SH
ouslyreportedforPd/permalloybilayersinspinpumping which only predict the existence of the isotropic terms
experiments [20–24, 44, 50]. An even larger estimate of BDL andBDL [8]. Althoughthereispresentlynotheory
0 0
σ is obtained if we use G to 5.94×1014 calculated providingacompletedescriptionofthetorqueanisotropy
SH r
for a Co/Pt interface [8]. This analysis suggests that ex- in realistic FM/HM systems including both bulk and
trinsic or interface-related effects may enhance the DL interfacial spin-orbit coupling, a possible explanation is
5
that the angular dependence of the torques arises from D. Magnetization switching
anisotropicspin-dependentscatteringattheFM/HMin-
terface or inside the FM, which affects the amplitude of
Finally, we address the question of whether the SOT
the nonequilibrium spin currents in the bilayer.
providedbyPdaresufficienttoreversethemagnetization
of the Co layer in a controlled way. To our knowledge,
SOT-drivenswitchingusing4dmetallayershasnotbeen
reported so far. Figure 5(a) shows the results of a typ-
ical switching experiment, performed by injecting 0.3 s
long current pulses of positive and negative polarity in
a Pd(4nm)/Co(0.6nm)/AlO Hall bar. The plot shows
The observation of a thickness-independent FL SOT x
the change of the Hall resistance after each pulse due to
andofstronglyenhancedDLandFLamplitudesrelative
switchingofthemagnetizationfromuptodownandvice
to those expected from the bulk SHE of Pd leads to the
versa duringa singlesweepof thein-plane externalfield,
conclusion that interface effects contribute significantly
from -0.82 to 0.82 T. An alternative demonstration of
to the current-induced SOT in Pd/Co/AlO . Such ef-
x
current-inducedswitchingisreportedinFig.5(b),where
fects are ubiquitous, but may be particularly evident in
the Hall resistance is recorded as a function of current
Pd because of the reduced bulk SHE compared to 5d
for a constant in-plane field. As discussed in previous
metalsystems. Thestandarddrift-diffusiontheoryofthe
work [1, 2], the purpose of the in-plane field is to break
SHE[8,43],whichisroutinelyusedtoextractγ andλ
SH
the symmetry of the DL SOT and univocally determine
fromspinpumpingandSOTmeasurements,doesnotac-
the switching direction, which occurs through the ex-
countforeitherinterfaceterms,thickness-dependentspin
pansion of chiral domain walls [6]. Figure 5(c) shows
diffusionparameters,orangle-dependentSOT.Similarly,
the difference of the Hall resistance ∆Rω measured af-
two-dimensional models of the Rashba-Edelstein effect H
ter two consecutive current pulses, one positive and one
donotproperlydescribethespinaccumulationprofilein
negative, normalised to its saturation value. Switching
FM/HMlayersandneglectthebulkSHEoftheHM[53].
is obtained whenever |∆Rω| > 0. We observe that the
Morerecenttheoreticalworkconsequentlypointsoutthe H
minimum field required to achieve deterministic switch-
need to include the bulk- and interface-generated spin
ing, B , decreases linearly with increasing current, as
accumulation on the same footing in three-dimensional m
shown in Fig. 5(d), similarly to Pt/Co/AlO [1] and
models of electron transport [48, 49]. A key prediction x
Ta/CoFeB/MgO [16]. Such a linear behavior is found
of this later work is that interfacial spin-orbit scattering
in all samples, albeit with a different slope, which we
createssubstantialspincurrentsthatflowawayfromthe
attribute to differences in the domain nucleation field.
FM/HM interface, generating both DL and FL torques.
The minimum current density required to achieve de-
Interestingly,thethicknessdependenceofthetwotorques
terministic switching depends on t , and is generally
differs, withtheinterfacialFLtorquebeingnearlythick- Pd
smaller in the thicker samples, as expected due to the
nessindependentandtheinterfacialDLtorqueincreasing
overall increase of the SOT with increasing t shown
with the thickness of the NM layer [49]. This is quali- Pd
in Fig.3. Remarkably, the dc current density required to
tatively consistent with the results reported in Fig. 4,
switch Pd/Co/AlO is similar (within a factor two) to
namely a FL torque comprising a thickness-independent x
that used to switch Pt/Co/MgO and Pt/Co/AlO dots
term and a DL torque that is strongly thickness de- x
with comparable PMA [2, 5], which is in agreement with
pendent. In this scenario, both torques would include
the relatively large SOT efficiency reported in this work.
bulk and interface contributions of comparable magni-
tude. Another prediction of this theory is that the inter-
facial scattering amplitudes depend on the magnetiza-
tion direction, which naturally leads to anisotropic SOT IV. CONCLUSIONS
as well as magnetoresistance [48, 49]. In this respect it
is interesting to draw a parallel between the angular de- In summary, we have performed magnetotransport,
pendence of the SOT and magnetoresistance in metallic magnetic anisotropy, and SOT vector measurements of
FM/HM bilayers. Figures 3 and 4 show that the SOT Pd/Co(0.6nm)/AlO layers as a function of Pd thick-
x
amplitude increases strongly when m is tilted towards ness. We found that the PMA of Pd/Co is reinforced
the y direction and only moderately when m is tilted to- by optimum oxidation of the Al capping layer relative to
wards the x direction. This is similar to the behavior Pd/Co multilayers, yielding a magnetic anisotropy en-
ofthemagnetoresistanceinFM/HMlayers,whichshows ergy of (1.5±0.1)×106 J/m3, which is nearly indepen-
much larger changes when m is rotated in the yz plane dent of t . Current injection in Pd/Co/AlO leads to
Pd x
relative to rotations in the xz plane [54, 55]. Exploring sizeable DL and FL SOT that have the same order of
this connection goes beyond the scope of this work, but magnitude, about 1 mT per 107 A/cm2, but different
we believe that additional studies of the correlation be- thickness and angular dependence. The analysis of the
tween SOT and anisotropic magnetoresistance [19] may DL SOT yields a relatively large effective spin Hall an-
helptounderstandtransportatinterfaceswithspin-orbit gle for Pd, γ ≈ 0.03−0.06, or a spin Hall conduc-
SH
coupling. tivity σ = (4±1)×105 Ω−1m−1, depending on the
SH
6
modelusedtofitthedata. TheDLspintorqueefficiency nontrivial thickness and angle dependence of the SOT
per unit electric field is of the order of 105 Ω−1m−1, observed here. Finally, we report bipolar magnetization
only a factor of two smaller relative to Pt/Co/MgO lay- switching in Pd/Co/AlO for j =3−6×107 A/cm2,
x Pd
ers of comparable thickness [42]. γ is enhanced com- dependingonthePdthicknessandin-planeappliedfield.
SH
pared to Pd/permalloy bilayers [20–24], but significantly These results show that Pd/Co/oxide layers with rela-
smaller than reported for [Pd/Co] multilayers [25] and tivelylowresistivitycanbeusedtocombinestrongPMA
N
Pd/FePd/MgO [26]. Additionally, our data evidence a with efficient current-induced magnetization switching,
strong FL SOT, with an interface contribution that ex- opening the possibility of using Pd as an alternative ma-
trapolates to a finite value at t = 0, and up to a terial to Pt, Ta, and W in SOT devices.
Pd
three-fold enhancement of the FL SOT efficiency when
themagnetizationrotatesfromtheout-of-planetothein-
planedirectiontransversetothecurrent. Overall,ourre- V. ACKNOWLEDGMENTS
sultsindicatethatSOTmodelsbasedonone-dimensional
drift-diffusion theory and a bulk SHE do not adequately This work was supported by the Swiss National Sci-
capture the SOT dependence on Pd thickness, at least enceFoundation(GrantNo. 200021-153404)andtheEu-
based on a single set of σSH, λ, Gr, and Gi parameters. ropean Commission under the Seventh Framework Pro-
A possible scenario is that spin currents driven by inter- gram(spOtproject,GrantNo. 318144). WethankJunx-
facial spin-orbit scattering add up to the spin currents iao Feng and Luca Persichetti for performing the rough-
induced by the bulk SHE of Pd [49], resulting in the ness measurements.
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FIG. 1. (a) Schematic of the experimental geometry and scanning electron micrograph of a Pd/Co/AlO Hall bar. (b)
x
Resistance as a function of Pd thickness. Inset: Pd resistivity as a function of inverse thickness; the solid line is a linear fit.
(c) First harmonic Hall resistance Rω of three representative samples as a function of external field applied at θ =84◦ and
H B
φ = 0◦. Inset: detail of the low field region of the 4 nm sample. (d) R as a function of Pd thickness. Inset: Anisotropy
AHE
field B .
K
FIG. 2. Second harmonic Hall resistance R2ω as a function of applied field at φ = 0◦ (a) and φ = 90◦ (b). The insets show
H
R2ω inthesmallanglelimit(θ≤7◦). (c)BDL and(d)BFL extractedfromthedatain(a)and(b),respectively,asafunction
H
of the polar magnetization angle θ. BDL and BFL obtained using the small angle approximation are indicated by a star.
10
FIG.3. SOTfieldsperunitcurrentdensityasafunctionoft . (a)IsotropicamplitudesBDL/j andBFL/j ,corresponding
Pd 0 Pd 0 Pd
to perpendicular magnetization. (b) Angle-dependent amplitudes BDL/j and BFL/j . (c) Total amplitudes for in-plane
2+4 Pd 2+4 Pd
magnetization, BDL /j and BFL /j . The SOT efficiency ξDL(FL) is shown on the right scale.
0+2+4 Pd 0+2+4 Pd j
FIG. 4. SOT fields per unit electric field as a function of t . (a) Isotropic amplitudes BDL/E and BFL/E, corresponding
Pd 0 0
to perpendicular magnetization. (b) Angle-dependent amplitudes BDL/E and BFL/E. (c) Total amplitudes for in-plane
2+4 2+4
magnetization, BDL /E and BFL /E. The SOT efficiency ξDL(FL) is shown on the right scale.
0+2+4 0+2+4 E