Temperature dependent spin transport properties of Platinum inferred from spin Hall magnetoresistance measurements

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by  Sibylle Meyer

Temperature Dependent Spin Transport Properties of Platinum Inferred From Spin
Hall Magnetoresistance Measurements
Sibylle Meyer,1,∗ Matthias Althammer,1 Stephan Gepr¨ags,1 Matthias
Opel,1 Rudolf Gross,1,2 and Sebastian T. B. Goennenwein1
1Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, 85748 Garching, Germany
2Physik-Department, Technische Universit¨at Mu¨nchen, 85748 Garching, Germany
(Dated: June 9, 2014)
WestudythetemperaturedependenceofthespinHallmagnetoresistance(SMR)inyttriumiron
garnet/platinumhybridstructuresviamagnetizationorientationdependentmagnetoresistancemea-
surements. Our experiments show a decrease of the SMR magnitude with decreasing temperature.
4
UsingthesensitivityoftheSMRtothespintransportpropertiesofthenormalmetal,weinterpret
1
ourdataintermsofadecreaseofthespinHallangleinplatinumfrom0.11atroomtemperatureto
0
0.075 at10K, whilethe spin diffusionlength and thespin mixingconductance of theferrimagnetic
2
insulator/normal metal interface remain almost constant.

n
u
J Inametallicconductorwithfinitespin-orbitcoupling, theSMRtheory26,weextracttheeffectivespindiffusion

6 the flow of electric charge inevitably induces a spin cur- length λ(T) in Pt, the real part of the spin mixing con-
rent, and vice versa1–4. In the literature, this is usually ductance Gr(T) of the YIG/Pt interface, as well as the
]
l discussed in terms of the spin Hall effect (SHE), which spin Hall angle θSH(T) in Pt. We find that λ and Gr are
al describes the spin current induced by a charge current, about independent of temperature, while θSH decreases
h and the inverse spin Hall effect (ISHE), i.e., the charge from θ ≈0.11 at 300K to θ ≈0.075 at 10K.
SH SH
- currentarisingfromaspincurrent5. TheSHEandISHE The SMR arises from the absorption (M ⊥ σ) or reflec-
s
e are widely exploited for the generation and/or detection tion (M(cid:107)σ) of a spin current at the FMI/NM interface
m of spin currents in ferromagnet/normal metal (FM/NM) and thus depends on the orientation of the magnetiza-
hybrid structures6, e.g., in the spin Seebeck effect7–11 tion M of the FMI with respect to the spin polarization
.
at or in spin pumping experiments12–18. For a quantita- σ of the spin current26. This results in a characteris-
m tiveinterpretationofsuchexperiments,adetailedknowl- tic dependence of the resistivity ρ of the NM layer on
edge about the spin transport properties of the respec- the orientation m=M/|M| of the magnetization in the
-
d tive samples viz. their constituent materials is of key adjacent FMI:11,20–22,26
n importance. Since any quantitative analysis is compli-
o catedbythecoexistenceofelectronicandmagnonicspin ρ=ρ0+∆ρ(m·t)2 =ρ0+∆ρsin2α, (1)
c
[ currents, hybrid devices based on ferromagnetic insula- with the SMR amplitude
tors (FMI) came into focus, and resulted in particular
4 in a renewed interest in the ferrimagnetic insulator yt- ∆ρ =−2θS2Hλ2ρtGrtanh2(cid:0)2tλ(cid:1). (2)
v triumirongarnet(Y Fe O ,YIG)8,9,11,19–24. Thechar- ρ 1+2λρG coth(cid:0)t(cid:1)
7 3 5 12 0 r λ
acteristic magnetoresistive effect reported from YIG/Pt
8 Here, ρ is the intrinsic electric resistivity of the NM
7 (FMI/NM) heterostructures by different groups11,19–25, 0
layer and ∆ρ is the magnitude of the magnetization-
7 however, is controversially discussed. Huang et al.19 and
orientationdependentresistivitychangearisingfromthe
. Lu et al.23,25 ascribe the observed magnetoresistance to
1 interplayofchargeandspincurrentsattheFMI/NMin-
a static magnetic proximity effect in Pt. On the other
0 terface,tisaunitvectororthogonaltoboththedirection
4 hand, the magnetoresistance in FMI/NM hybrids can
jofchargecurrentflowandthefilmnormaln(seeFig.1),
1 alsobeunderstoodasaspincurrent-basedeffect, theso-
and α is the angle enclosed by n and the magnetization
: called spin Hall magnetoresistance (SMR)20,22,26. This
v orientation m. As evident from Eq.(2), the SMR varies
interpretation naturally accounts for both the magneti-
Xi zation orientation dependence and the magnitude of the characteristically with the thickness t of NM19–22. Thus,
the measurement of the SMR as a function of t allows
r observed magnetoresistance11,20,22,26,27.
a for a quantitative evaluation of both θ and λ of the
In this letter, we experimentally study the temperature- SH
NM. Since we here study Pt films with thicknesses down
dependent evolution of the magnetoresistance in a set
to 1nm, we explicitly take surface scattering effects into
of YIG/Pt bilayer samples with different Pt thicknesses,
account by considering that the resistivity ρ = ρ(t) de-
and interpret our observations in terms of the SMR. We
pends on the Pt film thickness22.
extract the magnitude of the SMR effect from magne-
The samples used in our experiments are YIG/Pt
toresistance measurements as a function of the magne-
thin film heterostructures deposited onto (111)-oriented
tizationorientation(angledependentmagnetoresistance,
gadolinium gallium garnet (GGG) or yttrium aluminum
ADMR). The ADMR data recorded in the temperature
garnet (YAG) single crystal substrates as described
range10K≤T ≤300KconsistentlyshowthattheSMR
earlier27. The YIG thin films with a thickness of ap-
magnitudedecreaseswithdecreasingtemperature. Using
proximately 60nm were epitaxially grown via pulsed
2
n substrate t(nm) h(nm) substrate t(nm) h(nm)
(a) H
α YAG 0.8 0.7 GGG 3.5 0.7
YAG 2.0 0.8 YAG 6.5 0.9
Pt t GGG 2.2 0.7 GGG 11.1 0.6
G GGG 2.5 0.5 GGG 17.2 0.6
YI
YAG 3.0 0.8 YAG 19.5 1.0
j
TABLE I. Substrate material, platinum thickness t and in-
558.4 terface roughness h (rms value) for all YIG/Pt bilayer het-
(b) erostructures investigated in this work.
558.2

558.0
300K

netic field is intentionally chosen much larger than the
m)439.6 (c) anisotropy and demagnetizing fields of YIG, in order to
Ω
n ensure that the YIG magnetization M is always satu-
ρ (439.4 100K rated and oriented along H, αH = α. By choosing the
oopj rotation geometry, we can separate the SMR sig-
390.4
nalfromananisotropicmagnetoresistance(AMR)inthe
(d)
polycrystallinePtlayer. Inparticular,onewouldnotex-
390.2
pectamagnetizationorientationdependenceoftheresis-
10K tivityinthisconfigurationforAMR,asdiscussedin22,23.
390.0
The longitudinal resistivity ρ(α)=V (α)/(Jl) of the
0° 90° 180° 270° 360° long
α samplecanthenstraightforwardlybecalculatedfromthe
voltage drop V (α) along the direction of charge cur-
long
rentflowandthemagnitudeJ ofthechargecurrentden-
FIG. 1. Resistivity ρ versus angle α for a YIG/3.5nm Pt
hybrid structure in oopj - ADMR measurements at 1T, per- sity. Figure 1 shows a typical set of ρ(α) ADMR curves,
formed at (b) 300K, (c) 100K and (d) 10K. The different recorded in the YIG/Pt sample with t = 3.5nm at dif-
offsetvaluesareduetothetemperaturedependenceofthere- ferent, constant temperatures while rotating a magnetic
sistivityinthePtlayer[cf.Fig2(a)]. Thesketchin(a)shows field |µ H| = 1T. In a series of ADMR measurements
0
the coordinate system defined by j, t, and n in our YIG/Pt atdifferentmagneticfields(notshownhere), wefurther-
hybrid structures and the definition of the positive rotation more checked that ρ(α) does not depend on the field
angle α.
magnitude for 0.5T ≤ µ H ≤ 7T. As evident from
0
Fig. 1, the measured resistivity shows a sin2(α)-behavior
withrespecttothemagnetizationorientation,asalsore-
laserdepositionfromastoichiometricpolycrystallinetar- ported in earlier SMR experiments22. We now address ρ
get, utilizing a KrF excimer laser with a wavelength of of the normal metal Pt in more detail. We observe an
248nm at a repetition rate of 10Hz. The deposition was increaseofρwithdecreasingt,whichweattributetothe
carried out in an oxygen atmosphere at a pressure of finite roughness of the YIG/Pt interface. Upon decreas-
25 × 10−3mbar and a substrate temperature of 500◦C ing the temperature from room temperature to 10K, ρ
(YAG) or 550◦C (GGG), respectively. After cooling
the sample to room temperature, we in-situ deposited a
polycrystalline Pt layer of thickness t via electron beam
7 (a) (b)
erevsaoplourtaiotnionX-ornaytorpefloefcttohmeeYtrIyG(HfilRm-X. RWRe)atpopdlieetderhmiginhe- Ωm) -40)10
t for all samples, using the Software Package LEPTOS -7 05 (x1
(Bruker AXS), (see Tab. I). We patterned the YIG/Pt 1 ρ
bilayers into Hall bar structures (width w =80µm, con- ρ (x ∆ρ/5
tact separation l = 600µm) using optical lithography 3 −
andargonionbeammilling(seeFig.1(a)),andmounted
0
them in the variable temperature inset of a supercon- 0 100 200 300 0 100 200 300
ducting magnet cryostat for magnetoresistance measure- T (K) T (K)

ments (10K ≤ T ≤ 300K). We performed ADMR
0.8 nm 2.2 nm 3.0 nm 6.5 nm 17.2 nm
measurements22,28,29 by rotating an external magnetic 2.0 nm 2.5 nm 3.5 nm 11.1 nm 19.5 nm
field of constant magnitude µ H ≤7T in the plane per-
0
pendiculartothecurrentdirectionj(oopjgeometry)and FIG. 2. Temperature dependence of (a) the resistivity ρ and
recordingtheevolutionofthesample’sresistivityρ(αH). (b) the SMR signal −∆ρ/ρ0 in YIG/Pt with different values
Here, αH denotes the angle between the magnetic field t of the Pt thickness at µ0H = 1T. The lines are guides to
Handthesurfacenormaln. Themagnitudeofthemag- the eye.
3
decreases by a factor of about 1.5 [cf. Fig. 2(a)] for all and p the fraction of electrons scattered at the metal
samples as expected for metals. In order to take the film surface. Here we assume a diffusive limit (p = 0) and
thicknessandtemperaturedependenceofρintoaccount, choose ρ (T)= ρ(19.5nm,T) (the thickest film studied
∞
we use a thickness dependent resistivity21,30 ρ(t,T)31: is assumed to be bulk-like) and (cid:96) = 3nm from a
∞
fit of Eq. (3) to the experimental data as exemplarily
(a) shown in Fig.3(a) for the 10K data. To enable a
(a) (b)

Ωm)6 10K a.u.)10-1 HR-XRR sthtriackignhetsfso,riw.ea.r,dacfirtososfstehveerdalatsaamapsleas,fuwnectuisoenoonfetahnedfitlhme
-7(x104 ensity (1100--32 sraoallumgseahmnavepselsreas(.gdeeArrimsveesdvvifdarloeunmetoHfrfRohm-X=FRiR0g..7a2ns(mbli)s,ftoetrdhteihnmetaainbgtn.eIirt)fuafdoceer
ρ 2 nt10-4 of the SMR signal ∆ρ/ρ decreases with decreasing
I 0
0 5 10 15 20 1 2 3 4 5 temperature for all samples. Upon plotting ∆ρ/ρ as a
t (nm) angle (°) 0
function of t for different T as shown in Fig. 3(c)-(e), a
(c) clear maximum in the SMR signal magnitude at around
12 300K t ≈ 3nm becomes evident. Note that according to
250K Eq. (2) the SMR should show a maximum at t ≈ 2λ.
9
200K Fig. 3(c)-(e) reveals that this maximum appears at the
6 same t value of about 3nm for all temperatures within

the accuracy of our measurements, suggesting that
3
the spin diffusion length λ is only weakly temperature
dependent. Finally, we use Eq. (2) to extract the Pt
(d)
4)12 150K
-0
1 100K
x 9 (a) (b)
ρ/ρ (0 6 75K -210)10 m)1.6
∆ x
− 3 (SH λ (n
θ
8
(e)
12 50K 1.4
20K
9 10K -2m)6 (c) -1m)4 (d)
6 -1Ω -1Ω
3 14 50
0 1
0 5 t (n1m0) 15 20 G (x1r4 σ(x Spin3
0 100 200 300 0 100 200 300
FIG.3. (a)Thicknessdependenceofρ(symbols)forthe10K T (K) T (K)
dataandafitusingEq.(3)(solidline). Panel(b)showsexem-
plary HR X-ray reflectometry (HR-XRR) data for a sample
FIG. 4. Temperature dependence of (a) the spin Hall angle
with a Pt thickness of t=2.5nm. The red line shows a HR-
θ , (b) the spin diffusion length λ and (c) the spin mixing
XRR fit for a thickness of the YIG layer of t = 53.4nm SH
YIG conductanceG forPtextractedfromafittoourSMRdata.
and a roughness of h=0.49nm. The SMR effect −∆ρ/ρ in r
0 Full black symbols represent the values obtained using three
YIG/PtbilayersplottedversusthePtthicknesstattempera-
free parameters θ (T), G (T) and λ(T), red open symbols
turesbetween300Kand10Kisshowninpanels(c)-(e). The SH r
indicate simulations with constant G¯ = 4×1014Ω−1m−2
symbolsrepresenttheexperimentaldatatakenatµ H =1T r
0 and λ¯ = 1.5nm. Panel (d) shows σ calculated using the
andthesolidlinesdepicttheSMRcalculatedfromEq.(2)us- spin
temperaturedependentresistivityρ(t)fromourexperimental
ingtheparametersθ ,G andλshowninFig.4. Theblack
SH r data for a sample with t=3nm.
dashed line indicates the maximum of the observed SMR at
t≈3nm=2λ.
spin transport parameters from our set of experimental
data. As discussed above, Eq. (2) depends on four
(cid:18) (cid:19)
3 parameters: θ (T), λ(T), ρ(t,T) and G (T). Since we
ρ(t,T)=ρ (T) 1+ (cid:96) (1−p) , (3) SH r
∞ 8(t−h) ∞ use ρ(t,T) calculated from Eq. (3), this leaves θSH(T),
λ(T), and G (T) as free parameters. Fitting the data
r
where ρ is the resistivity for t → ∞, h the rms then yields θ (T), λ(T) and G (T) as given by the
∞ SH r
interface roughness, (cid:96) the mean free path for t → ∞ full symbols in Fig. 4. The parameters consistently
∞
4
describe our entire set of experimental data, as depicted dependence that does not substantially change within
by the solid lines in Fig. 3(c)-(e). As the temperature the temperature range investigated, with a magnitude
dependence of G and λ is rather weak and comparable σ = (3.6±0.3)×105Ω−1m−1 quantitatively consis-
r spin
to the fitting error, we performed a second analysis with tent with other measurements32.
temperature independent G¯ = 4.0×1014Ω−1m−2 and In summary, we have investigated the SMR in YIG/Pt
r
λ¯ = 1.5nm values [cf. Fig. 4(c)]. The θ (T) values heterostructureswithdifferentPtthicknessesviaADMR
SH
obtained from this simple analysis [cf. red open symbols measurements at temperatures between 10K and room
in Fig. 4(a)] are very similar to the ones obtained from temperature. We observe a decrease of the SMR at
the full fit. This suggests that the real part of the low temperatures for all Pt thicknesses. We used the
spin mixing conductance G¯ is almost independent of SMR theory to extract the temperature dependence
r
temperature, as one might naively expect considering of the spin mixing conductance G for the YIG/Pt
r
that the density of states in Pt does not significantly interface, as well as the spin Hall angle θ and the
SH
change with T. The spin diffusion length λ¯ obtained spin diffusion length λ in Pt. Our data suggests λ and
from our fit is comparable to earlier results33. However, G to be almost T-independent, while θ decreases
r SH
since the spin diffusion strongly depends on the density from 0.11 at room temperature to 0.075 at 10K.
andtypeofimpuritiesintheNM,asignificantdifference Nevertheless, the spin Hall conductivity in Pt does not
ofvaluesforλspreadingfrom1.25nm33 to(14±6)nm34 substantially change as a function of temperature, with
is reported in the literature. σ =(3.6±0.3)×105Ω−1m−1 .
spin
From the relation θ = σ /σ, we can calculate the
SH spin
temperature dependent spin Hall conductivity σ (T) We thank T. Brenninger for technical support, A. Erb
spin
using the temperature dependent θ (T) from the for the fabrication of the stoichiometric YIG target and
SH
simulation and the measured electrical conductivity G.E.W. Bauer and M. Schreier for fruitful discussions.
σ(t,T) = ρ−1(t,T). Figure 4(d) shows σ (T) ex- Financial support by the Deutsche Forschungsgemein-
spin
emplary for the t = 3nm sample [the ρ(T)-evolution schaft via SPP 1538 (project no. GO 944/4) and the
is very similar in all samples studied, see Fig. 2(a)]. German Excellence Initiative via the ”Nanosystems Ini-
From both simulation approaches, we obtain a σ (T) tiative Munich (NIM)” is gratefully acknowledged.
spin
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