Creating, manipulating and detecting spin polarized carriers are the key
elements of spin based electronics. Most practical devices use a perpendicular
geometry in which the spin currents, describing the transport of spin angular
momentum, are accompanied by charge currents. In recent years, new sources of
pure spin currents, i.e., without charge currents, have been demonstrated and
applied. In this paper, we demonstrate a conceptually new source of pure spin
current driven by the flow of heat across a ferromagnetic/non-magnetic metal
(FM/NM) interface. This spin current is generated because the Seebeck
coefficient, which describes the generation of a voltage as a result of a
temperature gradient, is spin dependent in a ferromagnet. For a detailed study
of this new source of spins, it is measured in a non-local lateral geometry. We
developed a 3D model that describes the heat, charge and spin transport in this
geometry which allows us to quantify this process. We obtain a spin Seebeck
coefficient for Permalloy of -3.8 microvolt/Kelvin demonstrating that thermally
driven spin injection is a feasible alternative for electrical spin injection
in, for example, spin transfer torque experiments

A Brataas

A. Slachter

AA Tulapurkar

B. J. van Wees

C Chappert

C Kittel

F. L. Bakker

FJ Albert

FJ Jedema

G Schmidt

GE Bauer

H Yu

I Zutic

J Xiao

J-P. Adam

K Uchida

L Gravier

M Hatami

MN Baibich

MV Costache

NF Mott

PC van Son

RD Barnard

SI Kiselev

SO Valenzuela

SP Dash

T Valet

T Yang

V Vlaminck

X Lou

Y Dubi

Y Tserkovnyak

English

arXiv

Slachter, A.

Bakker, F. L.

Adam, J-P.

van Wees, B. J.

University of Groningen Research Database

  
 University of Groningen
Thermally driven spin injection from a ferromagnet into a non-magnetic metal
Slachter, A.; Bakker, F. L.; Adam, J-P.; van Wees, Bart
Published in:
Nature Physics
DOI:
10.1038/NPHYS1767
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from
it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
2010
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Slachter, A., Bakker, F. L., Adam, J-P., & van Wees, B. J. (2010). Thermally driven spin injection from a
ferromagnet into a non-magnetic metal. Nature Physics, 6(11), 879-882. DOI: 10.1038/NPHYS1767
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 10-02-2018
SUPPLEMENTARY INFORMATION
doi: 10.1038/nPHYS1767
nature PHYSicS | www.nature.com/naturephysics 1
1
I. SUPPLEMENTARY INFORMATION A
Here we calculate what happens when heat is sent
through the FM/NM system in ﬁgure 1. We begin by
writing the spin dependent currents:
J↑,↓ = −σ↑,↓(
1
e
∇µ↑,↓ + S↑,↓∇T ) (1)
here µ↑,↓ is the spin dependent chemical potential. When
a heat current Q is sent through the bulk of a ferromag-
net in the absence of a charge current, a spin current
Js = J↑ − J↓ = −σF (1 − P 2)Ss∇T/2 ﬂows, driven by
the spin dependent Seebeck coeﬃcient, which we deﬁne
as Ss ≡ S↑−S↓. Here P is the conductivity polarization
P = (σ↑ − σ↓)/(σ↑ + σ↓) of the FM and σF is the con-
ductivity of the ferromagnet. Charge and spin current
conservation1,2 leads to the thermoelectric spin diﬀusion
equation:
∇2µs =
µs
λ2
− e(
dSs
dT
(∇T )2 + Ss∇
2T ) (2)
where µs is the spin accumulation µ↑ − µ↓. In addition
to the Valet-Fert spin diﬀusion equation ∇2µs =
µs
λ2 two
source terms are present. Both terms can in principle
µ↑
µ↓
Q
∆µ
FM NM
λF λN
FIG. 1: Thermal spin injection by the spin depen-
dent Seebeck coeﬃcient across a FM/NM interface.
Schematic ﬁgure showing the resulting spin dependent chem-
ical potentials µ↑,↓ across a FM/NM interface when a heat
current Q = −k∇T crosses it. Heat current is taken to be
continuous across the interface leading to a discontinuity in
∇T . No currents are allowed to leave the FM, nevertheless, a
spin current proportional to the spin dependent Seebeck co-
eﬃcient ﬂows through the bulk FM which needs to become
unpolarized in the bulk NM. This injects a spin imbalance
µ↑−µ↓ at the boundary which relaxes in the FM and NM with
the length scale of their respective spin relaxation lengths λi.
A thermoelectric interface potential ∆µ = Pµs also builds
up1,2. On the left side no spin current is allowed to leave
leading to an opposite spin accumulation.
create (albeit small) bulk spin accumulations. We note
that we ignored such terms in deriving the above spin
current Js = −σF (1 − P 2)Ss∇T/2 ﬂowing through the
bulk ferromagnet such that we have µ↑ = µ↓.
In ﬁgure 1 we sent a heat current Q through the
FM/NM interface while we allow no charge or spin cur-
rent to leave. The heat current Q = −k∇T needs to be
continuous throughout the system, leading to ∇TFM =
kNM/kFM∇TNM at the interface. Since ∇T is constant
in both regions individually, and for ﬁrst order eﬀects we
may assume Ss is constant, the source terms in equation
2 are irrelevant. Therefore, we may use the standard
Valet-Fert spin diﬀusion equation to solve the bulk spin
accumulation leading to the general expression for the
spin dependent potentials in the bulk:
µ↑,↓(x) = A+Bx± C/σ↑,↓e
−x/λi ±D/σ↑,↓e
x/λi (3)
with A-D the parameters to be solved in both regions.
At the FM/NM interface we take the chemical poten-
tials µ↑,↓ to be continuous as well as the spin dependent
currents J↑,↓. At the outer interfaces we set the spin de-
pendent currents to zero. This leads to a set of equations
which can be solved. We obtain:
B = e
σ↑S↑ + σ↓S↓
σ↑ + σ↓
∇TFM ≡ eSFM∇TFM (4)
where we use the deﬁnition of the conventional Seebeck
coeﬃcient of a ferromagnet SFM 3. The spin accumula-
tion at the interface is:
B (mT) B (mT)
0 100
-20
-10
R 1
 (
µΩ
)
0 100
8.42
8.41R
2 
(µ
V/
m
A2
)
a)
c)
b)
d)
1
2
34
5
FIG. 2: Previous device results. a) Coloured SEM ﬁgure
of the device. The sample consist of the same two ferromag-
nets which are now placed 400 nm apart. It is connected by
a copper V shape instead of a funnel. b) Non local spin valve
signal by sending current from contact 1 to 3 and measuring
the potential from contact 5 to 4. c,d) Thermal spin injection
result. The current is now sent from contact 1 to 2 while the
potential was measured between contacts 5 and 4.
2 nature PHYSicS | www.nature.com/naturephysics
SUPPLEMENTARY INFORMATION doi: 10.1038/nPHYS1767
2
µs
∇TFM
= −eλFSsRmis (5)
where Rmis = RN/(RN +RF /(1−P 2)) is a conductivity
mismatch4 factor in which Ri = λi/σi are the spin resis-
tances determined by the relaxation lengths λi and the
conductivities σi.
For the explanation of the results of Uchida et al.5 a
similar derivation was made6. However, they introduce
an extra source term for spin accumulation to equation 2
which does not decay on the scale of the spin relaxation
length. This allows in their analysis to have a spin accu-
mulation in the bulk at interface distances further than
the spin relaxation length.
As a consequence, their experiment is interpreted as a
result of spin accumulation in the bulk which is probed
by the inverse spin Hall eﬀect at diﬀerent locations.
In contrast, our eﬀect cannot produce a bulk spin ac-
cumulation since we exclude the higher order eﬀects men-
tioned before. It can only arise at the interface where it
can inject spins into the NM region.
We note that our deﬁnition of the spin dependent
Seebeck coeﬃcient SS ≡ S↑ − S↓ is in principle the
same as their deﬁnition of the spin Seebeck coeﬃcient
SS ≡ 1e

∂µch↑
∂T

n↑
−

∂µch↓
∂T

n↓

by virtue of the deﬁ-
nition of the Seebeck coeﬃcients (eq. 1).
II. SUPPLEMENTARY INFORMATION B
In this section we report on the measurements of a
previous sample. A SEM picture is shown in ﬁgure 2 (a).
A regular spin valve signal was measured by sending a
current from contact 1 to 3 and measuring the potential
between contact 5 and 4 of which the result is shown
in ﬁgure 2 (b). In this case a 13.8 mΩ background Rb1
is observed on top of a non local spin valve signal Rs1
of 3 mΩ. The background is originating from Peltier
heating/cooling of the FM/NM interfaces7. Both signals
are close to the calculated 14.1 mΩ and 4.1 mΩ.
When the current is sent from contact 1 to 2, we ob-
tain the results shown in ﬁgure 2 (c,d). A regular spin
valve signal Rs1 of 10 µΩ is observed on top of a small -15
µΩ background Rb1. This is somewhat diﬀerent then the
calculated -100 µΩ background and -4 µΩ spin valve sig-
nal. However, these eﬀects are highly dependent on the
exact geometry and are due to the small 30 x 30 nm2 size
of the contact. This makes sure grain size, lithographic
precision and ballistic eﬀects dominate.
Thermal spin injection was observed and is shown in
ﬁgure 2 (d). The background Rb2 is again larger then the
calculated 3.4 µV/mA2. If we compensate for this in the
modelling we obtain from the observed ≈ -7 nV/mA2
signal a spin dependent Seebeck coeﬃcient for Permalloy
of ≈ -5 µV/K.
We conclude that also in this device we have good
agreement between observed and calculated thermoelec-
tric voltages when we apply a similar correction for the
Joule heating. A very similar value for the spin Seebeck
coeﬃcient was found.
III. SUPPLEMENTARY INFORMATION C
Here we exclude any inﬂuence of possible nonlinear
behaviour of the physical eﬀect represented by the Rs1I
signal on our measured thermally driven spin injection
signal Rs2I
2.
We start by reasoning what happens if the amount of
current ﬂowing through, or the spin injection eﬃciency
of, the Py1/Cu interface depends on the temperature.
In that case, a Peltier heating/cooling induced change
of the physical eﬀect represented by the Rs1I signal can
give a contribution to the Rs2I
2 signal. However, from the
modeling we know that at the typical current of 1 mA we
used, the eﬀective Joule heating is ≈10 times larger. The
Rs3I
3 signal, then representing the Joule heating induced
change, should therefore be ≈10 times larger than the
Rs2I
2 signal. However, R3I3 was simultaneously mea-
sured and found absent. This excludes any thermally
related contributions to our measured Rs2I
2 signal.
Our contacts are highly ohmic, causing the Rs1I signal
in the ﬁrst place. In the case of tunnel contacts, electrical
spin injection can depend on the bias voltage applied. We
can reason that if our contacts are slightly tunnelling,
the eﬀect represented by the Rs1I signal can still have
an inﬂuence on our thermally driven spin injection signal
Rs2I
2 without being present in the R3I3 signal.
By checking the magnitude of such eﬀects in previous
samples7 which have been prepared in an identical way,
we can also rule out such eﬀects. We note that at a typi-
cal current of 1 mA Rs1I ≈ 20 nV, while R
s
2I
2 ≈ -15.6 nV.
We see from previous measurements7 that at these cur-
rents the change in electrical spin injection visible in the
Rs2I
2 signal is less then 5%. Any signal in theRs2I
2 should
then be less then 1 nV. On top of that, it should also be
of diﬀerent sign then our observed thermally driven spin
injection signal.
Finally, we note that the Rs1I signal for our device
is of diﬀerent sign then that observed in a previous de-
vice reported on in the previous section. However, the
thermally driven spin injection signal is of identical sign,
showing the fact that there are no spurious contributions.
1 van Son, P.C., van Kempen, H. & Wyder, P. Boundary Re-
sistance of the Ferromagnetic-Nonferromagnetic Metal In-
terface. Phys. Rev. Lett. 58, 2271-2273 (1987)
nature PHYSicS | www.nature.com/naturephysics 3
SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS1767
3
2 Valet, T. & Fert, A. Theory of the perpendicular mag-
netoresistance in magnetic multilayers. Phys. Rev. B. 48,
7099-7113 (1993)
3 Barnard R.D. Thermoelectricity in metals and alloys. (Tay-
lor and Francis LTD., London, 1972)
4 Schmidt, G., Ferrand, D., Molenkamp, L.W., Filip, A.T.
& van Wees, B.J. Fundamental obstacle for electrical spin
injection from a ferromagnetic metal into a diﬀusive semi-
conductor. Phys. Rev. B 62, R4790 (2000)
5 Uchida, K. et al. Observation of the Spin Seebeck eﬀect.
Nature 455, 778-781 (2008)
6 Uchida, K. et al. Phenomenological analysis for spin-
Seebeck eﬀect in metallic magnets. J. Appl. Phys. 105,
07C908 (2009)
7 Bakker, F.l., Slachter, A., Adam, J.-P. & van Wees, B.J.
Interplay of Peltier and Seebeck eﬀects in nanoscale nonlo-
cal spin valves, arXiv:1004.0118v1 (submitted to Phys. Rev.
Lett.)


Thermally driven spin injection from a ferromagnet into a non-magnetic metal

Creation, manipulation and detection of spin-polarized carriers are the key elements of spin-based electronics. Most practical devices use a perpendicular geometry in which the spin currents are accompanied by charge currents. In recent years, new sources of pure spin currents (that is, transport of spin angular momentum without charge currents) have been demonstrated and applied. Here we demonstrate a conceptually new source of pure spin current driven by the flow of heat across the interface between a ferromagnet and a non-magnetic metal. This spin current is generated because, in a ferromagnet, the Seebeck effect—which describes the generation of a voltage as a result of a temperature gradient—is spin dependent. We studied this new source of spin currents experimentally in a non-local lateral geometry and developed a three-dimensional model that describes the heat, charge and spin transport in this geometry, enabling us to quantify this process. We obtain a spin-dependent Seebeck coefficient for Permalloy of -3.8 µV K-1, suggesting that thermally driven spin injection is a feasible alternative for electrical spin injection in, for example, spin-transfer-torque experiments.

Slachter, A.,

Bakker, F.L.,

Adam, J-P.,

Wees, B.J. van,

University of Groningen Digital Archive

Creation, manipulation and detection of spin-polarized carriers are the key elements of spin-based electronics(1,2). Most practical devices(3-5) use a perpendicular geometry in which the spin currents are accompanied by charge currents. In recent years, new sources of pure spin currents ( that is, transport of spin angular momentum without charge currents) have been demonstrated(6-9) and applied(10-12). Here we demonstrate a conceptually new source of pure spin current driven by the flow of heat across the interface between a ferromagnet and a non-magnetic metal. This spin current is generated because, in a ferromagnet, the Seebeck effect-which describes the generation of a voltage as a result of a temperature gradient-is spin dependent(13,14). We studied this new source of spin currents experimentally in a non-local lateral geometry and developed a three-dimensional model that describes the heat, charge and spin transport in this geometry, enabling us to quantify this process(15). We obtain a spin-dependent Seebeck coefficient for Permalloy of -3.8 mu VK(-1), suggesting that thermally driven spin injection is a feasible alternative for electrical spin injection in, for example, spin-transfer-torque experiments(16).</p

ARTS repository - University of Groningen

   University of GroningenThermally driven spin injection from a ferromagnet into a non-magnetic metalSlachter, A.; Bakker, F. L.; Adam, J-P.; van Wees, B. J.Published in:Nature PhysicsDOI:10.1038/NPHYS1767IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2010Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Slachter, A., Bakker, F. L., Adam, J-P., & van Wees, B. J. (2010). Thermally driven spin injection from aferromagnet into a non-magnetic metal. Nature Physics, 6(11), 879-882.https://doi.org/10.1038/NPHYS1767CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 30-10-2023SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS1767nature PHYSicS | www.nature.com/naturephysics 11I. SUPPLEMENTARY INFORMATION AHere we calculate what happens when heat is sentthrough the FM/NM system in figure 1. We begin bywriting the spin dependent currents:J↑,↓ = −σ↑,↓(1e∇µ↑,↓ + S↑,↓∇T ) (1)here µ↑,↓ is the spin dependent chemical potential. Whena heat current Q is sent through the bulk of a ferromag-net in the absence of a charge current, a spin currentJs = J↑ − J↓ = −σF (1 − P 2)Ss∇T/2 flows, driven bythe spin dependent Seebeck coefficient, which we defineas Ss ≡ S↑ −S↓. Here P is the conductivity polarizationP = (σ↑ − σ↓)/(σ↑ + σ↓) of the FM and σF is the con-ductivity of the ferromagnet. Charge and spin currentconservation1,2 leads to the thermoelectric spin diffusionequation:∇2µs =µsλ2− e(dSsdT(∇T )2 + Ss∇2T ) (2)where µs is the spin accumulation µ↑ − µ↓. In additionto the Valet-Fert spin diffusion equation ∇2µs = µsλ2 twosource terms are present. Both terms can in principleµ↑µ↓Q∆µFM NMλF λNFIG. 1: Thermal spin injection by the spin depen-dent Seebeck coefficient across a FM/NM interface.Schematic figure showing the resulting spin dependent chem-ical potentials µ↑,↓ across a FM/NM interface when a heatcurrent Q = −k∇T crosses it. Heat current is taken to becontinuous across the interface leading to a discontinuity in∇T . No currents are allowed to leave the FM, nevertheless, aspin current proportional to the spin dependent Seebeck co-efficient flows through the bulk FM which needs to becomeunpolarized in the bulk NM. This injects a spin imbalanceµ↑−µ↓ at the boundary which relaxes in the FM and NM withthe length scale of their respective spin relaxation lengths λi.A thermoelectric interface potential ∆µ = Pµs also buildsup1,2. On the left side no spin current is allowed to leaveleading to an opposite spin accumulation.create (albeit small) bulk spin accumulations. We notethat we ignored such terms in deriving the above spincurrent Js = −σF (1 − P 2)Ss∇T/2 flowing through thebulk ferromagnet such that we have µ↑ = µ↓.In figure 1 we sent a heat current Q through theFM/NM interface while we allow no charge or spin cur-rent to leave. The heat current Q = −k∇T needs to becontinuous throughout the system, leading to ∇TFM =kNM/kFM∇TNM at the interface. Since ∇T is constantin both regions individually, and for first order effects wemay assume Ss is constant, the source terms in equation2 are irrelevant. Therefore, we may use the standardValet-Fert spin diffusion equation to solve the bulk spinaccumulation leading to the general expression for thespin dependent potentials in the bulk:µ↑,↓(x) = A + Bx± C/σ↑,↓e−x/λi ±D/σ↑,↓ex/λi (3)with A-D the parameters to be solved in both regions.At the FM/NM interface we take the chemical poten-tials µ↑,↓ to be continuous as well as the spin dependentcurrents J↑,↓. At the outer interfaces we set the spin de-pendent currents to zero. This leads to a set of equationswhich can be solved. We obtain:B = eσ↑S↑ + σ↓S↓σ↑ + σ↓∇TFM ≡ eSFM∇TFM (4)where we use the definition of the conventional Seebeckcoefficient of a ferromagnet SFM3. The spin accumula-tion at the interface is:B (mT) B (mT)0 100-20-10R 1 (µΩ)0 1008.428.41R2 (µV/mA2)a)c)b)d)12345FIG. 2: Previous device results. a) Coloured SEM figureof the device. The sample consist of the same two ferromag-nets which are now placed 400 nm apart. It is connected bya copper V shape instead of a funnel. b) Non local spin valvesignal by sending current from contact 1 to 3 and measuringthe potential from contact 5 to 4. c,d) Thermal spin injectionresult. The current is now sent from contact 1 to 2 while thepotential was measured between contacts 5 and 4.2 nature PHYSicS | www.nature.com/naturephysicsSUPPLEMENTARY INFORMATION doi: 10.1038/nPHYS17672µs∇TFM= −eλFSsRmis (5)where Rmis = RN/(RN +RF /(1−P 2)) is a conductivitymismatch4 factor in which Ri = λi/σi are the spin resis-tances determined by the relaxation lengths λi and theconductivities σi.For the explanation of the results of Uchida et al.5 asimilar derivation was made6. However, they introducean extra source term for spin accumulation to equation 2which does not decay on the scale of the spin relaxationlength. This allows in their analysis to have a spin accu-mulation in the bulk at interface distances further thanthe spin relaxation length.As a consequence, their experiment is interpreted as aresult of spin accumulation in the bulk which is probedby the inverse spin Hall effect at different locations.In contrast, our effect cannot produce a bulk spin ac-cumulation since we exclude the higher order effects men-tioned before. It can only arise at the interface where itcan inject spins into the NM region.We note that our definition of the spin dependentSeebeck coefficient SS ≡ S↑ − S↓ is in principle thesame as their definition of the spin Seebeck coefficientSS ≡ 1e∂µch↑∂Tn↑−∂µch↓∂Tn↓by virtue of the defi-nition of the Seebeck coefficients (eq. 1).II. SUPPLEMENTARY INFORMATION BIn this section we report on the measurements of aprevious sample. A SEM picture is shown in figure 2 (a).A regular spin valve signal was measured by sending acurrent from contact 1 to 3 and measuring the potentialbetween contact 5 and 4 of which the result is shownin figure 2 (b). In this case a 13.8 mΩ background Rb1is observed on top of a non local spin valve signal Rs1of 3 mΩ. The background is originating from Peltierheating/cooling of the FM/NM interfaces7. Both signalsare close to the calculated 14.1 mΩ and 4.1 mΩ.When the current is sent from contact 1 to 2, we ob-tain the results shown in figure 2 (c,d). A regular spinvalve signal Rs1 of 10 µΩ is observed on top of a small -15µΩ background Rb1. This is somewhat different then thecalculated -100 µΩ background and -4 µΩ spin valve sig-nal. However, these effects are highly dependent on theexact geometry and are due to the small 30 x 30 nm2 sizeof the contact. This makes sure grain size, lithographicprecision and ballistic effects dominate.Thermal spin injection was observed and is shown infigure 2 (d). The background Rb2 is again larger then thecalculated 3.4 µV/mA2. If we compensate for this in themodelling we obtain from the observed ≈ -7 nV/mA2signal a spin dependent Seebeck coefficient for Permalloyof ≈ -5 µV/K.We conclude that also in this device we have goodagreement between observed and calculated thermoelec-tric voltages when we apply a similar correction for theJoule heating. A very similar value for the spin Seebeckcoefficient was found.III. SUPPLEMENTARY INFORMATION CHere we exclude any influence of possible nonlinearbehaviour of the physical effect represented by the Rs1Isignal on our measured thermally driven spin injectionsignal Rs2I2.We start by reasoning what happens if the amount ofcurrent flowing through, or the spin injection efficiencyof, the Py1/Cu interface depends on the temperature.In that case, a Peltier heating/cooling induced changeof the physical effect represented by the Rs1I signal cangive a contribution to the Rs2I2 signal. However, from themodeling we know that at the typical current of 1 mA weused, the effective Joule heating is ≈10 times larger. TheRs3I3 signal, then representing the Joule heating inducedchange, should therefore be ≈10 times larger than theRs2I2 signal. However, R3I3 was simultaneously mea-sured and found absent. This excludes any thermallyrelated contributions to our measured Rs2I2 signal.Our contacts are highly ohmic, causing the Rs1I signalin the first place. In the case of tunnel contacts, electricalspin injection can depend on the bias voltage applied. Wecan reason that if our contacts are slightly tunnelling,the effect represented by the Rs1I signal can still havean influence on our thermally driven spin injection signalRs2I2 without being present in the R3I3 signal.By checking the magnitude of such effects in previoussamples7 which have been prepared in an identical way,we can also rule out such effects. We note that at a typi-cal current of 1 mA Rs1I ≈ 20 nV, while Rs2I2 ≈ -15.6 nV.We see from previous measurements7 that at these cur-rents the change in electrical spin injection visible in theRs2I2 signal is less then 5%. Any signal in the Rs2I2 shouldthen be less then 1 nV. On top of that, it should also beof different sign then our observed thermally driven spininjection signal.Finally, we note that the Rs1I signal for our deviceis of different sign then that observed in a previous de-vice reported on in the previous section. However, thethermally driven spin injection signal is of identical sign,showing the fact that there are no spurious contributions.1 van Son, P.C., van Kempen, H. & Wyder, P. Boundary Re-sistance of the Ferromagnetic-Nonferromagnetic Metal In-terface. Phys. Rev. Lett. 58, 2271-2273 (1987)nature PHYSicS | www.nature.com/naturephysics 3SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS176732 Valet, T. & Fert, A. Theory of the perpendicular mag-netoresistance in magnetic multilayers. Phys. Rev. B. 48,7099-7113 (1993)3 Barnard R.D. Thermoelectricity in metals and alloys. (Tay-lor and Francis LTD., London, 1972)4 Schmidt, G., Ferrand, D., Molenkamp, L.W., Filip, A.T.& van Wees, B.J. Fundamental obstacle for electrical spininjection from a ferromagnetic metal into a diffusive semi-conductor. Phys. Rev. B 62, R4790 (2000)5 Uchida, K. et al. Observation of the Spin Seebeck effect.Nature 455, 778-781 (2008)6 Uchida, K. et al. Phenomenological analysis for spin-Seebeck effect in metallic magnets. J. Appl. Phys. 105,07C908 (2009)7 Bakker, F.l., Slachter, A., Adam, J.-P. & van Wees, B.J.Interplay of Peltier and Seebeck effects in nanoscale nonlo-cal spin valves, arXiv:1004.0118v1 (submitted to Phys. Rev.Lett.)

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Creation, manipulation and detection of spin-polarized carriers are the key elements of spin-based electronics(1,2). Most practical devices(3-5) use a perpendicular geometry in which the spin currents are accompanied by charge currents. In recent years, new sources of pure spin currents ( that is, transport of spin angular momentum without charge currents) have been demonstrated(6-9) and applied(10-12). Here we demonstrate a conceptually new source of pure spin current driven by the flow of heat across the interface between a ferromagnet and a non-magnetic metal. This spin current is generated because, in a ferromagnet, the Seebeck effect-which describes the generation of a voltage as a result of a temperature gradient-is spin dependent(13,14). We studied this new source of spin currents experimentally in a non-local lateral geometry and developed a three-dimensional model that describes the heat, charge and spin transport in this geometry, enabling us to quantify this process(15). We obtain a spin-dependent Seebeck coefficient for Permalloy of -3.8 mu VK(-1), suggesting that thermally driven spin injection is a feasible alternative for electrical spin injection in, for example, spin-transfer-torque experiments(16)

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   University of GroningenThermally driven spin injection from a ferromagnet into a non-magnetic metalSlachter, A.; Bakker, F. L.; Adam, J-P.; van Wees, B. J.Published in:Nature PhysicsDOI:10.1038/NPHYS1767IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2010Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Slachter, A., Bakker, F. L., Adam, J-P., & van Wees, B. J. (2010). Thermally driven spin injection from aferromagnet into a non-magnetic metal. Nature Physics, 6(11), 879-882.https://doi.org/10.1038/NPHYS1767CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 07-06-2022SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS1767nature PHYSicS | www.nature.com/naturephysics 11I. SUPPLEMENTARY INFORMATION AHere we calculate what happens when heat is sentthrough the FM/NM system in figure 1. We begin bywriting the spin dependent currents:J↑,↓ = −σ↑,↓(1e∇µ↑,↓ + S↑,↓∇T ) (1)here µ↑,↓ is the spin dependent chemical potential. Whena heat current Q is sent through the bulk of a ferromag-net in the absence of a charge current, a spin currentJs = J↑ − J↓ = −σF (1 − P 2)Ss∇T/2 flows, driven bythe spin dependent Seebeck coefficient, which we defineas Ss ≡ S↑ −S↓. Here P is the conductivity polarizationP = (σ↑ − σ↓)/(σ↑ + σ↓) of the FM and σF is the con-ductivity of the ferromagnet. Charge and spin currentconservation1,2 leads to the thermoelectric spin diffusionequation:∇2µs =µsλ2− e(dSsdT(∇T )2 + Ss∇2T ) (2)where µs is the spin accumulation µ↑ − µ↓. In additionto the Valet-Fert spin diffusion equation ∇2µs = µsλ2 twosource terms are present. Both terms can in principleµ↑µ↓Q∆µFM NMλF λNFIG. 1: Thermal spin injection by the spin depen-dent Seebeck coefficient across a FM/NM interface.Schematic figure showing the resulting spin dependent chem-ical potentials µ↑,↓ across a FM/NM interface when a heatcurrent Q = −k∇T crosses it. Heat current is taken to becontinuous across the interface leading to a discontinuity in∇T . No currents are allowed to leave the FM, nevertheless, aspin current proportional to the spin dependent Seebeck co-efficient flows through the bulk FM which needs to becomeunpolarized in the bulk NM. This injects a spin imbalanceµ↑−µ↓ at the boundary which relaxes in the FM and NM withthe length scale of their respective spin relaxation lengths λi.A thermoelectric interface potential ∆µ = Pµs also buildsup1,2. On the left side no spin current is allowed to leaveleading to an opposite spin accumulation.create (albeit small) bulk spin accumulations. We notethat we ignored such terms in deriving the above spincurrent Js = −σF (1 − P 2)Ss∇T/2 flowing through thebulk ferromagnet such that we have µ↑ = µ↓.In figure 1 we sent a heat current Q through theFM/NM interface while we allow no charge or spin cur-rent to leave. The heat current Q = −k∇T needs to becontinuous throughout the system, leading to ∇TFM =kNM/kFM∇TNM at the interface. Since ∇T is constantin both regions individually, and for first order effects wemay assume Ss is constant, the source terms in equation2 are irrelevant. Therefore, we may use the standardValet-Fert spin diffusion equation to solve the bulk spinaccumulation leading to the general expression for thespin dependent potentials in the bulk:µ↑,↓(x) = A + Bx± C/σ↑,↓e−x/λi ±D/σ↑,↓ex/λi (3)with A-D the parameters to be solved in both regions.At the FM/NM interface we take the chemical poten-tials µ↑,↓ to be continuous as well as the spin dependentcurrents J↑,↓. At the outer interfaces we set the spin de-pendent currents to zero. This leads to a set of equationswhich can be solved. We obtain:B = eσ↑S↑ + σ↓S↓σ↑ + σ↓∇TFM ≡ eSFM∇TFM (4)where we use the definition of the conventional Seebeckcoefficient of a ferromagnet SFM3. The spin accumula-tion at the interface is:B (mT) B (mT)0 100-20-10R 1 (µΩ)0 1008.428.41R2 (µV/mA2)a)c)b)d)12345FIG. 2: Previous device results. a) Coloured SEM figureof the device. The sample consist of the same two ferromag-nets which are now placed 400 nm apart. It is connected bya copper V shape instead of a funnel. b) Non local spin valvesignal by sending current from contact 1 to 3 and measuringthe potential from contact 5 to 4. c,d) Thermal spin injectionresult. The current is now sent from contact 1 to 2 while thepotential was measured between contacts 5 and 4.2 nature PHYSicS | www.nature.com/naturephysicsSUPPLEMENTARY INFORMATION doi: 10.1038/nPHYS17672µs∇TFM= −eλFSsRmis (5)where Rmis = RN/(RN +RF /(1−P 2)) is a conductivitymismatch4 factor in which Ri = λi/σi are the spin resis-tances determined by the relaxation lengths λi and theconductivities σi.For the explanation of the results of Uchida et al.5 asimilar derivation was made6. However, they introducean extra source term for spin accumulation to equation 2which does not decay on the scale of the spin relaxationlength. This allows in their analysis to have a spin accu-mulation in the bulk at interface distances further thanthe spin relaxation length.As a consequence, their experiment is interpreted as aresult of spin accumulation in the bulk which is probedby the inverse spin Hall effect at different locations.In contrast, our effect cannot produce a bulk spin ac-cumulation since we exclude the higher order effects men-tioned before. It can only arise at the interface where itcan inject spins into the NM region.We note that our definition of the spin dependentSeebeck coefficient SS ≡ S↑ − S↓ is in principle thesame as their definition of the spin Seebeck coefficientSS ≡ 1e∂µch↑∂Tn↑−∂µch↓∂Tn↓by virtue of the defi-nition of the Seebeck coefficients (eq. 1).II. SUPPLEMENTARY INFORMATION BIn this section we report on the measurements of aprevious sample. A SEM picture is shown in figure 2 (a).A regular spin valve signal was measured by sending acurrent from contact 1 to 3 and measuring the potentialbetween contact 5 and 4 of which the result is shownin figure 2 (b). In this case a 13.8 mΩ background Rb1is observed on top of a non local spin valve signal Rs1of 3 mΩ. The background is originating from Peltierheating/cooling of the FM/NM interfaces7. Both signalsare close to the calculated 14.1 mΩ and 4.1 mΩ.When the current is sent from contact 1 to 2, we ob-tain the results shown in figure 2 (c,d). A regular spinvalve signal Rs1 of 10 µΩ is observed on top of a small -15µΩ background Rb1. This is somewhat different then thecalculated -100 µΩ background and -4 µΩ spin valve sig-nal. However, these effects are highly dependent on theexact geometry and are due to the small 30 x 30 nm2 sizeof the contact. This makes sure grain size, lithographicprecision and ballistic effects dominate.Thermal spin injection was observed and is shown infigure 2 (d). The background Rb2 is again larger then thecalculated 3.4 µV/mA2. If we compensate for this in themodelling we obtain from the observed ≈ -7 nV/mA2signal a spin dependent Seebeck coefficient for Permalloyof ≈ -5 µV/K.We conclude that also in this device we have goodagreement between observed and calculated thermoelec-tric voltages when we apply a similar correction for theJoule heating. A very similar value for the spin Seebeckcoefficient was found.III. SUPPLEMENTARY INFORMATION CHere we exclude any influence of possible nonlinearbehaviour of the physical effect represented by the Rs1Isignal on our measured thermally driven spin injectionsignal Rs2I2.We start by reasoning what happens if the amount ofcurrent flowing through, or the spin injection efficiencyof, the Py1/Cu interface depends on the temperature.In that case, a Peltier heating/cooling induced changeof the physical effect represented by the Rs1I signal cangive a contribution to the Rs2I2 signal. However, from themodeling we know that at the typical current of 1 mA weused, the effective Joule heating is ≈10 times larger. TheRs3I3 signal, then representing the Joule heating inducedchange, should therefore be ≈10 times larger than theRs2I2 signal. However, R3I3 was simultaneously mea-sured and found absent. This excludes any thermallyrelated contributions to our measured Rs2I2 signal.Our contacts are highly ohmic, causing the Rs1I signalin the first place. In the case of tunnel contacts, electricalspin injection can depend on the bias voltage applied. Wecan reason that if our contacts are slightly tunnelling,the effect represented by the Rs1I signal can still havean influence on our thermally driven spin injection signalRs2I2 without being present in the R3I3 signal.By checking the magnitude of such effects in previoussamples7 which have been prepared in an identical way,we can also rule out such effects. We note that at a typi-cal current of 1 mA Rs1I ≈ 20 nV, while Rs2I2 ≈ -15.6 nV.We see from previous measurements7 that at these cur-rents the change in electrical spin injection visible in theRs2I2 signal is less then 5%. Any signal in the Rs2I2 shouldthen be less then 1 nV. On top of that, it should also beof different sign then our observed thermally driven spininjection signal.Finally, we note that the Rs1I signal for our deviceis of different sign then that observed in a previous de-vice reported on in the previous section. However, thethermally driven spin injection signal is of identical sign,showing the fact that there are no spurious contributions.1 van Son, P.C., van Kempen, H. & Wyder, P. Boundary Re-sistance of the Ferromagnetic-Nonferromagnetic Metal In-terface. Phys. Rev. Lett. 58, 2271-2273 (1987)nature PHYSicS | www.nature.com/naturephysics 3SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS176732 Valet, T. & Fert, A. Theory of the perpendicular mag-netoresistance in magnetic multilayers. Phys. Rev. B. 48,7099-7113 (1993)3 Barnard R.D. Thermoelectricity in metals and alloys. (Tay-lor and Francis LTD., London, 1972)4 Schmidt, G., Ferrand, D., Molenkamp, L.W., Filip, A.T.& van Wees, B.J. Fundamental obstacle for electrical spininjection from a ferromagnetic metal into a diffusive semi-conductor. Phys. Rev. B 62, R4790 (2000)5 Uchida, K. et al. Observation of the Spin Seebeck effect.Nature 455, 778-781 (2008)6 Uchida, K. et al. Phenomenological analysis for spin-Seebeck effect in metallic magnets. J. Appl. Phys. 105,07C908 (2009)7 Bakker, F.l., Slachter, A., Adam, J.-P. & van Wees, B.J.Interplay of Peltier and Seebeck effects in nanoscale nonlo-cal spin valves, arXiv:1004.0118v1 (submitted to Phys. Rev.Lett.)

   University of GroningenThermally driven spin injection from a ferromagnet into a non-magnetic metalSlachter, A.; Bakker, F. L.; Adam, J-P.; van Wees, B. J.Published in:Nature PhysicsDOI:10.1038/NPHYS1767IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2010Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Slachter, A., Bakker, F. L., Adam, J-P., & van Wees, B. J. (2010). Thermally driven spin injection from aferromagnet into a non-magnetic metal. Nature Physics, 6(11), 879-882.https://doi.org/10.1038/NPHYS1767CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 26-04-2023SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS1767nature PHYSicS | www.nature.com/naturephysics 11I. SUPPLEMENTARY INFORMATION AHere we calculate what happens when heat is sentthrough the FM/NM system in figure 1. We begin bywriting the spin dependent currents:J↑,↓ = −σ↑,↓(1e∇µ↑,↓ + S↑,↓∇T ) (1)here µ↑,↓ is the spin dependent chemical potential. Whena heat current Q is sent through the bulk of a ferromag-net in the absence of a charge current, a spin currentJs = J↑ − J↓ = −σF (1 − P 2)Ss∇T/2 flows, driven bythe spin dependent Seebeck coefficient, which we defineas Ss ≡ S↑ −S↓. Here P is the conductivity polarizationP = (σ↑ − σ↓)/(σ↑ + σ↓) of the FM and σF is the con-ductivity of the ferromagnet. Charge and spin currentconservation1,2 leads to the thermoelectric spin diffusionequation:∇2µs =µsλ2− e(dSsdT(∇T )2 + Ss∇2T ) (2)where µs is the spin accumulation µ↑ − µ↓. In additionto the Valet-Fert spin diffusion equation ∇2µs = µsλ2 twosource terms are present. Both terms can in principleµ↑µ↓Q∆µFM NMλF λNFIG. 1: Thermal spin injection by the spin depen-dent Seebeck coefficient across a FM/NM interface.Schematic figure showing the resulting spin dependent chem-ical potentials µ↑,↓ across a FM/NM interface when a heatcurrent Q = −k∇T crosses it. Heat current is taken to becontinuous across the interface leading to a discontinuity in∇T . No currents are allowed to leave the FM, nevertheless, aspin current proportional to the spin dependent Seebeck co-efficient flows through the bulk FM which needs to becomeunpolarized in the bulk NM. This injects a spin imbalanceµ↑−µ↓ at the boundary which relaxes in the FM and NM withthe length scale of their respective spin relaxation lengths λi.A thermoelectric interface potential ∆µ = Pµs also buildsup1,2. On the left side no spin current is allowed to leaveleading to an opposite spin accumulation.create (albeit small) bulk spin accumulations. We notethat we ignored such terms in deriving the above spincurrent Js = −σF (1 − P 2)Ss∇T/2 flowing through thebulk ferromagnet such that we have µ↑ = µ↓.In figure 1 we sent a heat current Q through theFM/NM interface while we allow no charge or spin cur-rent to leave. The heat current Q = −k∇T needs to becontinuous throughout the system, leading to ∇TFM =kNM/kFM∇TNM at the interface. Since ∇T is constantin both regions individually, and for first order effects wemay assume Ss is constant, the source terms in equation2 are irrelevant. Therefore, we may use the standardValet-Fert spin diffusion equation to solve the bulk spinaccumulation leading to the general expression for thespin dependent potentials in the bulk:µ↑,↓(x) = A + Bx± C/σ↑,↓e−x/λi ±D/σ↑,↓ex/λi (3)with A-D the parameters to be solved in both regions.At the FM/NM interface we take the chemical poten-tials µ↑,↓ to be continuous as well as the spin dependentcurrents J↑,↓. At the outer interfaces we set the spin de-pendent currents to zero. This leads to a set of equationswhich can be solved. We obtain:B = eσ↑S↑ + σ↓S↓σ↑ + σ↓∇TFM ≡ eSFM∇TFM (4)where we use the definition of the conventional Seebeckcoefficient of a ferromagnet SFM3. The spin accumula-tion at the interface is:B (mT) B (mT)0 100-20-10R 1 (µΩ)0 1008.428.41R2 (µV/mA2)a)c)b)d)12345FIG. 2: Previous device results. a) Coloured SEM figureof the device. The sample consist of the same two ferromag-nets which are now placed 400 nm apart. It is connected bya copper V shape instead of a funnel. b) Non local spin valvesignal by sending current from contact 1 to 3 and measuringthe potential from contact 5 to 4. c,d) Thermal spin injectionresult. The current is now sent from contact 1 to 2 while thepotential was measured between contacts 5 and 4.2 nature PHYSicS | www.nature.com/naturephysicsSUPPLEMENTARY INFORMATION doi: 10.1038/nPHYS17672µs∇TFM= −eλFSsRmis (5)where Rmis = RN/(RN +RF /(1−P 2)) is a conductivitymismatch4 factor in which Ri = λi/σi are the spin resis-tances determined by the relaxation lengths λi and theconductivities σi.For the explanation of the results of Uchida et al.5 asimilar derivation was made6. However, they introducean extra source term for spin accumulation to equation 2which does not decay on the scale of the spin relaxationlength. This allows in their analysis to have a spin accu-mulation in the bulk at interface distances further thanthe spin relaxation length.As a consequence, their experiment is interpreted as aresult of spin accumulation in the bulk which is probedby the inverse spin Hall effect at different locations.In contrast, our effect cannot produce a bulk spin ac-cumulation since we exclude the higher order effects men-tioned before. It can only arise at the interface where itcan inject spins into the NM region.We note that our definition of the spin dependentSeebeck coefficient SS ≡ S↑ − S↓ is in principle thesame as their definition of the spin Seebeck coefficientSS ≡ 1e∂µch↑∂Tn↑−∂µch↓∂Tn↓by virtue of the defi-nition of the Seebeck coefficients (eq. 1).II. SUPPLEMENTARY INFORMATION BIn this section we report on the measurements of aprevious sample. A SEM picture is shown in figure 2 (a).A regular spin valve signal was measured by sending acurrent from contact 1 to 3 and measuring the potentialbetween contact 5 and 4 of which the result is shownin figure 2 (b). In this case a 13.8 mΩ background Rb1is observed on top of a non local spin valve signal Rs1of 3 mΩ. The background is originating from Peltierheating/cooling of the FM/NM interfaces7. Both signalsare close to the calculated 14.1 mΩ and 4.1 mΩ.When the current is sent from contact 1 to 2, we ob-tain the results shown in figure 2 (c,d). A regular spinvalve signal Rs1 of 10 µΩ is observed on top of a small -15µΩ background Rb1. This is somewhat different then thecalculated -100 µΩ background and -4 µΩ spin valve sig-nal. However, these effects are highly dependent on theexact geometry and are due to the small 30 x 30 nm2 sizeof the contact. This makes sure grain size, lithographicprecision and ballistic effects dominate.Thermal spin injection was observed and is shown infigure 2 (d). The background Rb2 is again larger then thecalculated 3.4 µV/mA2. If we compensate for this in themodelling we obtain from the observed ≈ -7 nV/mA2signal a spin dependent Seebeck coefficient for Permalloyof ≈ -5 µV/K.We conclude that also in this device we have goodagreement between observed and calculated thermoelec-tric voltages when we apply a similar correction for theJoule heating. A very similar value for the spin Seebeckcoefficient was found.III. SUPPLEMENTARY INFORMATION CHere we exclude any influence of possible nonlinearbehaviour of the physical effect represented by the Rs1Isignal on our measured thermally driven spin injectionsignal Rs2I2.We start by reasoning what happens if the amount ofcurrent flowing through, or the spin injection efficiencyof, the Py1/Cu interface depends on the temperature.In that case, a Peltier heating/cooling induced changeof the physical effect represented by the Rs1I signal cangive a contribution to the Rs2I2 signal. However, from themodeling we know that at the typical current of 1 mA weused, the effective Joule heating is ≈10 times larger. TheRs3I3 signal, then representing the Joule heating inducedchange, should therefore be ≈10 times larger than theRs2I2 signal. However, R3I3 was simultaneously mea-sured and found absent. This excludes any thermallyrelated contributions to our measured Rs2I2 signal.Our contacts are highly ohmic, causing the Rs1I signalin the first place. In the case of tunnel contacts, electricalspin injection can depend on the bias voltage applied. Wecan reason that if our contacts are slightly tunnelling,the effect represented by the Rs1I signal can still havean influence on our thermally driven spin injection signalRs2I2 without being present in the R3I3 signal.By checking the magnitude of such effects in previoussamples7 which have been prepared in an identical way,we can also rule out such effects. We note that at a typi-cal current of 1 mA Rs1I ≈ 20 nV, while Rs2I2 ≈ -15.6 nV.We see from previous measurements7 that at these cur-rents the change in electrical spin injection visible in theRs2I2 signal is less then 5%. Any signal in the Rs2I2 shouldthen be less then 1 nV. On top of that, it should also beof different sign then our observed thermally driven spininjection signal.Finally, we note that the Rs1I signal for our deviceis of different sign then that observed in a previous de-vice reported on in the previous section. However, thethermally driven spin injection signal is of identical sign,showing the fact that there are no spurious contributions.1 van Son, P.C., van Kempen, H. & Wyder, P. Boundary Re-sistance of the Ferromagnetic-Nonferromagnetic Metal In-terface. Phys. Rev. Lett. 58, 2271-2273 (1987)nature PHYSicS | www.nature.com/naturephysics 3SUPPLEMENTARY INFORMATIONdoi: 10.1038/nPHYS176732 Valet, T. & Fert, A. Theory of the perpendicular mag-netoresistance in magnetic multilayers. Phys. Rev. B. 48,7099-7113 (1993)3 Barnard R.D. Thermoelectricity in metals and alloys. (Tay-lor and Francis LTD., London, 1972)4 Schmidt, G., Ferrand, D., Molenkamp, L.W., Filip, A.T.& van Wees, B.J. Fundamental obstacle for electrical spininjection from a ferromagnetic metal into a diffusive semi-conductor. Phys. Rev. B 62, R4790 (2000)5 Uchida, K. et al. Observation of the Spin Seebeck effect.Nature 455, 778-781 (2008)6 Uchida, K. et al. Phenomenological analysis for spin-Seebeck effect in metallic magnets. J. Appl. Phys. 105,07C908 (2009)7 Bakker, F.l., Slachter, A., Adam, J.-P. & van Wees, B.J.Interplay of Peltier and Seebeck effects in nanoscale nonlo-cal spin valves, arXiv:1004.0118v1 (submitted to Phys. Rev.Lett.)

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Thermally driven spin injection from a ferromagnet into a non-magnetic
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Thermally driven spin injection from a ferromagnet into a non-magnetic metal

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