PHYSICAL REVIEW B 88, 184407 (2013)

Thermal gradient driven enhancement of pure spin current at room temperature
in nonlocal spin transport devices
S. R. Bakaul,1,3 S. Hu,1 and T. Kimura1,2,*
1Advanced Electronics Research Division, INAMORI Frontier Research Center, Kyushu University, 744 Motooka, Fukuoka 819-0395, Japan
2
CREST, Japan Science and Technology Agency, Sanbancho, Tokyo 102-0075, Japan
3
Japan Society for the Promotion of Science, Tokyo 102-0083, Japan(Received 17 May 2013; revised manuscript received 25 September 2013; published 8 November 2013)
We show that the junction design in the laterally configured ferromagnetic/nonmagnetic (FM/NM) hybrid
structure significantly affects the spin transport under high-bias current. The thermal conductivity mismatch
between FM and NM and the inhomogeneous current distribution at the interface produce a reversed temperature
gradient, which drastically reduces the thermal spin injection efficiency. The homogeneity in the temperature
gradient at the interface is a crucial factor in determining the efficiency of the thermal spin current generation.
The experimental results show excellent agreement with the theoretical model [Y. Takezoe et al., Phys. Rev. B
82, 094451 (2010)] that the spin relaxation is proportional to the second spatial derivative of the temperature.
DOI: 10.1103/PhysRevB.88.184407

PACS number(s): 85.80.−b, 73.50.−h, 85.75.−d

Exploiting electrons’ spin degree of freedom has beensought as one of the most promising ways to meet the futureneed for low-power operated, ultrasmall, and multifunctional
electronic devices.1–5 The advent of laterally patterned, nonlocal spin transport devices (NSTD) is an important milestone
in this regard, as these are capable of generating electronic
charge-free and nondissipative pure spin current.6–8 The mostimperative and primary issue associated with these genericspintronic devices is to enhance the amplitude and generation
efficiency of the pure spin current. Theoretically, the simplest
way to generate large pure spin current in NSTDs is to increase
the excitation charge current density, which enhances the spin
splitting in the nonmagnetic (NM) spin transport channel.
In practice, this technique suffers from a key bottleneckarising from the excitation current-generated Joule heat inboth ferromagnetic (FM) injector and NM channels, as thespin diffusion length (λ) and the spin polarization (P ) strongly
deteriorate with increasing charge current, resulting in a drastic
decrease of the spin generation efficiency.9
Although Joule heating in spin transport devices is naively
considered to be disadvantageous, gradient in spatial temperature (T ) causes several recently discovered spin-related
phenomena, commonly dubbed as spin-caloritronic effects,
such as thermal spin current,10,11 spin-dependent Peltier
effect,12,13 spin Seebeck effect,14 Seebeck spin tunneling,15
and anomalous Nernst-Ettingshausen effect.16,17 These effects
can alter the pure spin current related signals, and dependingon the device geometry and the flow direction of injecting
charge current (Ic ), both deleterious and aiding impacts are
possible to achieve. Thermal spin current, in particular, is
expected to relieve the Joule heat-induced obstacles in purespin generation, although its presence is comparatively weakin typical spin transport devices.
In this work, we show that the junction design in NSTDs
plays a vital role in controlling the temperature gradientlandscape at the interface and thus determining the strength ofthermal spin current. In certain devices, a reversed temperature
gradient is generated that drastically reduces the spin current
generated by the normal temperature gradient. The reversed
temperature gradient is a consequence of thermal conductivity
1098-0121/2013/88(18)/184407(4)mismatch between FM and NM and inhomogeneous current
distribution, which can be minimized by optimizing thejunction design.
Figure 1(a) shows the scanning electron microscopy (SEM)
image of the functional portion of one of the measured devices.
Lateral, nonlocal spin valves with two FM injectors were
fabricated on SiO2 -coated Si substrate by two-step electron
beam lithography, thermal evaporation, and liftoff techniques.
Permalloy (Py) and Cu were used as spin injector and transportchannel materials, respectively. The two Py injectors with
100-nm width and 30-nm thickness, together with a Py detectorof the same width and 10-nm thickness, were fabricated in
the first two steps. The 250-nm-wide and 170-nm-thick Cu
as the transport channel and the voltage measurement probes
were prepared in the next step. Two types of samples were
measured. In type-A samples, the injectors were placed 100 nm
apart from each other, whereas type-B samples’ injectors wereconnected to each other. To create an electronically transparent
interface, prior to the Cu evaporation, a precleaning procedureon the Py layer was performed by using low-dose Ar+ ion
milling.
The pure spin current is mainly generated by a variabledc bias (Idc ) flowing through the injectors labeled as 1 and
2 in Fig. 1(a). A small ac probing current (peak-to-peakdIac = 0.2 mA) was superimposed with Idc , and the amplitudeof the spin current was monitored from the first harmonic
voltage (dVs ) captured between the electrodes 3 and 4, by using
a lock-in amplifier at room temperature. As the charge current
Idc flows from injectors 1 and 2 through terminal 5, purespin is accumulated at the interface, which diffuses towards
the detector FM. When the magnetic field is swept from− ( + )800 Oe to + ( − )800 Oe, dVs /dIac (= Rs ) switchesfrom a high (low) to low (high) value, due to the parallel(antiparallel) and antiparallel (parallel) alignment between theinjector and detector FM. The relative difference between the
Rs in two states is termed as spin signal Rs .
Figures 1(b)–1(d) show field-dependent Rs at 0, + 5, and− 5 mA dc bias, respectively, for type-A devices. For ease ofcomparison, the background signal has been removed fromthese figures. Clearly, Rs is larger at negative bias than that

184407-1©2013 American Physical Society

S. R. BAKAUL, S. HU, AND T. KIMURAPHYSICAL REVIEW B 88, 184407 (2013)

FIG. 1. (Color online) (a) Colored SEM image of the fabricateddevice with a gap between two Py spin injectors, and (b)–(d) show
the nonlocal spin signals (dVs /dIac ) of this sample at 0, + 5, and− 5 mA dc bias, respectively. Due to the presence of strong thermal
spin current, the spin signal is higher at negative bias and lower at
positive bias than that at zero bias.

at positive bias. The bias-dependent trend of the normalizedRs is plotted in Fig. 2(a), showing that unlike the positive
bias branch, Rs is not reduced with the increase of negativedc level, rather, it is amplified up to 11% at − 5 mA, comparedto that at zero bias.
Enhancement of spin signal in NSTDs at high bias has
been recently reported by Wang et al. also.18 It was argued that
owing to the nonlinear resistivity at high-bias level, the current
lines become more perpendicular to the interface; therefore,
efficient spin injection becomes possible. However, this ispossible only if an electrically insulating layer is present at
the interface, whereas the typical resistance-area product for
our Py/Cu interface is as low as 0.1 f m2 .19 Furthermore, inthis case the enhancement of spin signal would be independentof the bias polarity, which is unlike our results. Thus, thepossibility of the redistribution of current lines as the origin of
the enhanced spin signal in our devices can be ruled out. Apartfrom this, in a semiconductor-based NSTD Jeon et al. observed
a bias-dependent asymmetric spin signal and attributed it to
the asymmetry in electron tunneling process.20 However, this
scenario is also inapplicable for our case as the devices are all
metallic in nature.
Another phenomenon relevant to our experiments is thePeltier heating-cooling at the Py/Cu interface, which leads
to a dc-bias polarity and amplitude-dependent asymmetrictemperature profile at the interface. Since the spin current

FIG. 2. (Color online) (a) Bias dependence of the normalized spinsignals of (a) type-A and (b) type-B sample. The device schematics
are shown in the insets.

generation efficiency depends on the temperature of the device,
the Peltier effect often modifies the detected spin voltage.21
However, according to our current flow direction notation [seethe inset of Fig. 2(a)], due to Peltier heating, a negative current
would increase the temperature of the interface; therefore, a
reduction in spin signal is expected in this case. Therefore,
the Peltier effect cannot account for the enhanced spin signal
observed in our experiments.
We argue that the enhancement of spin signal at negative
dc bias is a manifestation of the thermal spin injection.10 As
the resistivity of Py (ρPy = 18 μ cm) is one order higher
than that of Cu (ρCu = 1.7 μ cm) and the heating power is2, Py is hotter than Cu. As a result of the
proportional to ρIdc
generated temperature gradient (∇T ) at the interface, Seebeck
voltage is developed, which injects extra spin-polarized current
into Cu. Since ∇T is uncorrelated to the bias current direction,
at both positive and negative polarity, it provides same amountof excess up (↑) spin accumulation at the interface. On the other
hand, negative and positive dc biases create ↑ and ↓ (down)
spin accumulation, respectively. Therefore, total accumulated
spin is enhanced at negative bias and attenuated at positive
bias, causing a bias-dependent asymmetry in the detected spinsignal. At low temperature, Erekhinsky et al. also reported
asymmetric bias dependence of spin signal originating fromthe thermal spin current.11 We emphasize that in our sample
such thermal spin not only creates asymmetric bias dependence
but also counteracts the Joule-heating-mediated degradationof spin signal at room temperature and assists the purespin generation efficiency to transcend the value at zero dc
level.
To understand the effect of removing the gap between
spin injectors on the thermally generated spin current, westudied the bias-dependent response of nonlocal spin current in
type-B samples [Fig. 2(b)]. Interestingly, the spin signal in thiskind of devices reduces with increasing dc bias, irrespectiveof the current polarity. This suggests that the contribution
from the thermal spin current is insignificant and the bias
dependence of Rs is mainly dominated by the Joule heatingin this case. The slight asymmetry in it can be understood as
an effect of the bias-dependent asymmetric temperature profileon the spin signal, caused by the Peltier heating (at negative
dc bias) and cooling (at positive dc bias) at the interface.
Since temperature gradient generates the thermal spin current, we use the finite element program Comsol Multiphysics22
to simulate the temperature landscape generated by the bias
current Idc = 5 × 1011 A/m2 at the interfaces of both types ofdevices, which are shown in Figs. 3(a) and 3(b). The substrate
is modeled as a 1-μm-thick Si coated by 300-nm-thick SiO2
layer. The temperature at the bottom of the Si layer is fixed at
300 K. The thermal conductivities of Cu, Py, Si, and SiO2 are
400, 46, 130, and 1.4 W m−1 K−1 , respectively. For simplicity,
we do not include any thermal resistance between Cu and
Py. We note that such thermal resistance affects only themagnitude of the temperature gradient, not the sign of it. An
interesting feature in type-B sample’s temperature landscapeis that near the interface, the sign of the temperature gradientsat Y = 150 and Y = 300 nm are opposite to each other, which
can be noticed from the Z dependence of temperature shownin Figs. 3(c) and 3(d). This can be understood if we look at
the Fourier’s heat equation, which governs the temperature

184407-2

THERMAL GRADIENT DRIVEN ENHANCEMENT OF PURE . . .

FIG. 3. (Color online) Temperature profile of the Y Z plane along
the center of the Py/Cu interface of (a) type-A and (b) type-B
devices. The white lines define the positions of the Py electrodes. The
black lines indicate places where line profiles of temperature were
evaluated, and (c) and (d) show the Z dependence of the temperatureof type-B sample at Y = 150 nm and Y = 300 nm, respectively.
Unlike type A, type-B samples have a large Py/Cu interface areawith reversed temperature gradient, which causes the minority spin
injection and reduction of overall spin signal amplitude. (e) and (f)show the cross-sectional profiles of the temperature gradient along Z
direction at Z = 30 nm of type-A and type-B samples, respectively.

profile:23
k


 2
d T
d 2T
d 2T
+ ġ = 0.
+
+
dx 2
dy 2
dz2

(2)

Here, the first three terms are mainly related to the heatdiffusion and governed by the thermal conductivity k, whereas
the last term takes care of generated Joule heat and depends onρ Py and ρ Cu . The one-order difference between ρ Py and ρ Cu
leads to an inhomogeneous current distribution at the interface.
At the edge of the interface, all the current enters through Py
first and then spreads in Cu. Therefore, here the current density
and generated heat are higher in Py than those in Cu, whereas
the situation is reversed at the interface far from the edge.
In addition, since Cu has a larger thermal conductivity thanPy, heat generated in Py at the edge of the interface is more
effectively transported in Cu than Py. Therefore, sign reversalof ∇T takes place at some part of the interface, especially indevices with large interface area.
Now the strong and weak presence of thermal spin currents
in type-A and type-B devices can be understood as aneffect of the reversed ∇T at the Py/Cu interface. The ∇T
induced electric field is calculated according to the relation:
Ez = −S∇Z T and cross-sectional profiles (at Z = 30 nm)
are plotted in Figs. 3(e) and 3(f) respectively. Here S =−20 μV/m is the Seebeck coefficient for Py.24 Unlike thetype-A sample, the negative electric field is generated in alarge portion of the interface area of type-B sample. As aconsequence, thermal spins accumulated in such area is ↓ type,

PHYSICAL REVIEW B 88, 184407 (2013)

which counterbalances the effect of the ↑-type thermal spin
accumulated near the edge. Therefore, in this case, the overall
contribution of the thermal spin injection on the detected spinsignal is negligible. On the contrary, the effect of the reversed∇T is diminished if the Py/Cu interfacial area is small, andthere is a gap between the injectors, which causes strong
presence of thermal spin in the detected spin signal.
The thermal spin current in a homogeneous ∇T landscape can be calculated by Eq. (1) of Ref. 10. However,in reality and as the Comsol simulation suggests, ∇T ishighly inhomogeneous at the FM/NM interface of NSTD.
The inhomogeneity in ∇T can increase the spin relaxation
rate in FM and thus randomizes electrons’ spin and reduces
the effectively generated thermal spin current.25 The theory
suggests that the spin relaxation rate is proportional to thespatial double derivative of temperature (∇Z2 T ). This is plottedin Figs. 4(a) and 4(b), showing that the spin relaxation effectis lowest at the center of the interface and highest at theedge. On the other hand, ∇Z T is stronger at the edge thanthat at the center. Therefore, the magnitude of the effective
thermally generated spin injection at the edge and centerof the interface could be comparable. Thus, to obtain aquantitative comparison between the effective thermal spin
injections at these places, ∇Z2 T should be included as ascaling factor in Eq. (1) of Ref. 10. Accordingly, we calculate
the generated thermal spin current density in every unit cell
(1 nm × 1 nm) of the interface by using the modified formula:2)Ss ∇Z T. |∇ 2 T | . Taking spin polarization P = 0.3 andJs(T h) = −(1−P
2ρFZ
spin-dependent Seebeck coefficient Ss = −3.8 μV/K fromthe literature,10 we estimate Js(T h) at the interfaces of bothtypes of devices. As shown by the cross-sectional profiles ofFig. 4(d), in type-B sample’s interface both ↑ and ↓ types ofspin current are present, and their magnitudes are of similarorder. Summing the contributions from all unit cells, we findthat the total Js(T h) in the type-A sample is 3.6 times larger
than that in the type-B sample. This corroborates with our

FIG. 4. (Color online) |∇ 2 T | landscape in Py under the Py/Cu
interfaces of the (a) type-A and (b) type-B devices, and (c) crosssectional profile along the dotted line of the interface area. Spinrelaxation torque is large at the places where |∇ 2 T | Value is high,and (d) shows the calculated thermal spin current for both types ofdevices, taking spin relaxation torque into consideration.

184407-3

S. R. BAKAUL, S. HU, AND T. KIMURAPHYSICAL REVIEW B 88, 184407 (2013)

experimental observation that the thermal spin generation isstronger in type-A samples than those in type-B samples.
To summarize, we show that in lateral NSTDs owing to
the large difference between the FM and the NM’s thermal
conductivity and inhomogeneous current distribution in thejunction, a reversed temperature gradient is developed, which
reduces the generation efficiency of the thermal spin current.

Such reversed temperature gradient can be diminished bycreating a gap between the two spin injectors. Our results
and simulation support the theoretical prediction25 that the
spatial double derivative of temperature causes spin relaxation
effect, which should be considered in analyzing the thermally generated spin current and designing the structures of
NSTDs.

*

14

kimura@ifrc.kyushu-u.ac.jp
G. E. W. Bauer, E. Saitoh, and B. J. Van Wees, Nat. Mater. 11, 391(2012).
2
R. Jansen, Nat. Mater. 11, 400 (2012).
3
I. Zutic, J. Fabian, and D. S. Sarma, Rev. Mod. Phys. 76, 323 (2004).
4
C. Chappert, A. Fert, and F. Nguyen, Nat. Mater. 6, 813 (2007).
5
S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton,
S. von Molnár, M. L. Roukes, A. Y. Chtchelkanova, and D. M.
Treger, Science 294, 1488 (2001).
6
M. Johnson and R. H. Silsbee, Phys. Rev. Lett. 55, 1790 (1985).
7
F. J. Jedema, A. T. Filip, and B. J. van Wees, Nature 410, 345 (2001).
8
M. Johnson and R. H. Silsbee, Phys. Rev. B 37, 5312 (1988).
9
F. Casanova, A. Sharoni, M. Erekhinsky, and I. K. Schuller, Phys.
Rev. B 79, 184415 (2009).
10
A. Slachter, F. L. Bakker, J.-P. Adam, and B. J. van Wees, Nat.
Phys. 6, 879 (2010).
11
M. Erekhinsky, F. Casanova, I. Schuller, and A. Sharoni, Appl.
Phys. Lett. 100, 212401 (2012).
12
J. Flipse, F. L. Bakker, A. Slachter, F. K. Dejene, and B. J. vanWees, Nat. Nanotechnol. 7, 166 (2012).
13
F. L. Bakker, A. Slachter, J.-P. Adam, and B. J. van Wees, Phys.
Rev. Lett. 105, 136601 (2010).
1

K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae,
K. Ando, S. Maekawa, and E. Saitoh, Nature (London) 455, 778(2008).
15
J.-C. Breton, S. Sharma, H. Saito, S. Yuasa, and R. Jansen, Nature(London) 475, 82 (2011).
16
T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose,
N. Nagaosa, and Y. Tokura, Phys. Rev. Lett. 99, 086602 (2007).
17
S. Y. Huang, W. G. Wang, S. F. Lee, J. Kwo, and C. L. Chien, Phys.
Rev. Lett. 107, 216604 (2011).
18
X. J. Wang, H. Zou, and Y. Ji, Phys. Rev. B 81, 104409 (2010).
19
T. Kimura, N. Hashimoto, S. Yamada, M. Miyao, and K. Hamaya,
NPG Asia Mater, 4, e9 (2012).
20
K. Jeon, B. Min, Y. Jo, H. Lee, I. Shin, C. Park, S. Park, andS. Shin, Phys. Rev. B 84, 165315 (2011).
21
S. Hu and T. Kimura, Phys. Rev. B 87, 014424 (2013).
22
http://www.comsol.com.
23
Y. A. Cengel, Heat Transfer: A Practical Approach, 2nd ed.
(McGraw-Hill, New York, 2003).
24
A. Slachter, F. L. Bakker, and B. J. van Wees, Phys. Rev. B 84,
020412(R) (2011).
25
Y. Takezoe, K. Hosono, A. Takeuchi, and G. Tatara, Phys. Rev. B
82, 094451 (2010).

184407-4