Supplementary Material
Thermal spin injection and accumulation in CoFe/MgO
tunnel contacts to n-type Si through Seebeck spin tunneling
Kun-Rok Jeon1,2, Byoung-Chul Min3, Seung-Young Park4, Kyeong-Dong Lee1,5,
Hyon-Seok Song1, Youn-Ho Park3, and Sung-Chul Shin1,6,*
1
Department of Physics and Center for Nanospinics of Spintronic Materials, Korea
Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Korea
2
National Institute of Advanced Industrial Science and Technology (AIST), Spintronics
Research Center, Tsukuba, Ibaraki 305-8568, Japan
3
Center for Spintronics Research, Korea Institute of Science and Technology (KIST),
Seoul 136-791, Korea
4
Division of Materials Science, Korea Basic Science Institute (KBSI), Daejeon 305-764,
Korea
5
Department of Material Sciences and Engineering, Korea Advanced Institute of
Science and Technology (KAIST), Daejeon 305-701, Korea
6
Department of Emerging Materials Science, Daegu Gyeongbuk Institute of Science and
Technology (DGIST), Daegu 711-873, Korea
Supplementary Note I: Electrical Hanle signals obtained by electrical
spin injection/extraction using the same contact
The sign of thermal spin accumulation (Δμth) has been determined by a direct
1
comparison with that of electrical Hanle signals (ΔVEH, normal, ΔVEH, inverted) obtained in the
same contact a of CoFe/MgO/n-Si (see Fig. 1), using the standard three-terminal Hanle
(TTH) measurements21-23. Instead of applying heating current (Iheating), a non-zero
tunneling current (Itunnel) is applied across the contact a and c while the V is measured using
the contact a and d in applied magnetic fields (Bz, Bx) (see Fig. 1; note that the contact a is
used for electrical injection as well as for the detection of the spin accumulation in the Si).
Figure S1 shows the results obtained from the TTH measurements (up to 5 kOe)
under perpendicular (Bz, closed circles) and in-plane (Bx, open circles) magnetic fields at
300 K. As shown in the ΔVEH–B plots of Figs. S1(a) and S1(b), clear electrical Hanle
signals (ΔVEH, normal in Bz, ΔVEH, inverted in Bx) with a characteristic Lorentzian line shape are
detected for the both polarities of Itunnel of ±3 mA (+, electron spin extraction in Fig. S1(a);
–, electron spin injection in Fig. S1(b)) at 300 K. Figure S1(c) summarizes the magnitude
of electrical Hanle signals (ΔVEH, normal, ΔVEH, inverted) as a function of the Itunnel (up to ±3
mA). Both of the ΔVEH, normal (closed circle) and ΔVEH, inverted (open circle) reveal almost
symmetric behavior with respect to the polarity of Itunnel and their values increase linearly
with increasing the Itunnel, which are consistent with the previous work15.
As shown in Figs. S1(a)-S1(c), the sign of ΔVEH, normal (in Bz) is negative for a
negative Itunnel (or negative electrical voltage (Vel), VCoFe–VSi<0; electron spin injection)
and positive for a positive Itunnel (or positive Vel, VCoFe–VSi>0; electron spin extraction).
Hence, the former ΔVEH, normal (VCoFe–VSi <0) has the same sign with ΔVTH, normal (see Figs.
2(e) and 2(g)), indicating that Δμel induced by the electrical spin injection has the same
sign as Δμth produced by thermal spin injection with the Si heating (TSi>TCoFe).
2
FIG. S1. Three-terminal Hanle measurements (up to 5 kOe) under perpendicular (Bz,
closed circles) and in-plane (Bx, open circles) magnetic fields for the tunneling current
(Itunnel) of (a) +3 mA (electron spin extraction) and (b) -3 mA (electron spin injection) at
300 K. (c) Summary of the magnitude of electrical Hanle signals (ΔVEH, normal, ΔVEH, inverted)
as a function of Itunnel (up to ±3 mA) at 300 K. The electrical voltage (Vel=VCoFe–VGe),
defined as VB=0–ΔVEH, is also shown.
Supplementary Note II: Hanle measurements in larger perpendicular
magnetic fields
We performed a decisive test10 using the Hanle measurements in larger
perpendicular magnetic fields (Bz) (see Fig. 1) to rule out any possibility that the observed
spin accumulation is induced by the origin of the spin caloric effect (e.g., the spin Nernst
effect)4 in Si. It is possible that the spin Nernst effect4 produces a spin current (along the
z-axis) transverse to a thermal gradient (in the x- or y-axis direction) via the spin orbit
interaction of Si (see Fig. 1). This would cause spin accumulation at the Si interface with
3
the spins pointing parallel to the film plane (note that the direction of the accumulated
spins is transverse to the thermal gradient and to the spin current). Figure S2(a) illustrates
the expected characteristic behavior10 of the Δμth signal as a function of Bz for two
different origins ((i) and (ii)) of Δμth. (i) If the spins were accumulated by origin of the
spin Nernst effect in Si without thermal spin injection from FM to Si, they would be
unrelated to the magnetization (M) of FM10. This gives rise to a simple reduction of Δμth
signal in small values of Bz (the blue line in Fig. S2(a)) because the direction of the
induced spins is always orthogonal to Bz irrespective of the M of FM. (ii) In contrast, if
the spins induced in Si were thermally injected from FM, their direction would coincide
with that of the M of FM10,19,20 even with larger values of Bz. This results in distinctly
different behavior of the Δμth signal with larger Bz values (the red line in Fig. S2(a)) as
compared to the case (i). As Bz is increased, the Δμth value is sharply reduced due to the
Hanle effect; thereafter, it gradually increases when the M of FM rotates out of the film
plane. When the M and the induced spins in the Si are fully aligned with Bz higher than
μ0Ms of FM (where μ0 is the permeability of the free space and Ms is the saturation
magnetization), the Δμth signal eventually becomes saturated.
Figure S2(b) shows the obtained thermal Hanle signals (ΔVTH, normal, ΔVTH, inverted;
normalized) under applied magnetic fields (Bz, Bx) up to 50 kOe with an Iheating value of
±10 mA (note that each Hanle curve is the average of two curves measured with positive
and negative Iheating values). The ΔVTH, normal signal (closed symbol) clearly reveals the
distinctive behavior with Bz; the Hanle effect in a small Bz (<2 kOe), the increase of ΔVTH,
normal
due to the rotation of M in an intermediate Bz (2-22 kOe), and the saturation of ΔVTH,
normal
in a large Bz (>22 kOe). This result excludes any possible origin for thermal spin
accumulation in our system that does not involve spin injection from CoFe to Si. It was
4
noted earlier that the difference of the ΔVTH, normal value in the saturation region from the
peak value at zero Bz is associated with the initial spin precession and dephasing effect
caused by the local magnetostatic fields due to the finite roughness of the CoFe/MgO
interface, as proven by the inverted Hanle signal (ΔVTH, inverted, open symbol) under an inplane magnetic field (Bx)19,20.
FIG. S2. (Color online) (a) Expected characteristic behavior of the thermal spin
accumulation (Δμth) signal as a function of the perpendicular magnetic field (Bz) for two
different origins ((i) and (ii)) of Δμth: (i) Δμth by thermal spin injection from CoFe to Si
(red line) and (ii) Δμth without thermal spin injection from FM to Si (blue line). (b)
Obtained thermal Hanle signals (ΔVTH,
normal,
ΔVTH,
inverted;
normalized) under applied
magnetic fields (Bz, Bx) up to 50 kOe with the heating current (Iheating) of ±10 mA. Note
that each Hanle curve is the average of two curves measured with positive and negative
Iheating values.
5
Supplementary Note III: Characteristic feature of thermal Hanle signal
depending on host semiconductor
It was very recently argued that the Hanle-type signals observed in metal-based
tunnel contacts [Ni80Fe20/Al2O3/non-magnetic metals (NMs)]30 using TTH measurements
might come from the oxide tunnel barrier itself rather than from the spin accumulation
(Δμ) in the NM electrodes. In order to investigate this possibility in our system, we
performed an important test through the comparison analysis of the line shape of thermal
Hanle signal (ΔVTH) obtained in Si system with that of different SC (Ge) system16, in
which fundamentally the same CoFe/MgO tunnel contact was used for the thermal spin
injection experiment. If the ΔVTH originates from the tunnel oxide (MgO) itself, it does
not depend on the type of the host SC, and thus the almost similar line-shape of the signal
should be observed in both Si and Ge systems. In contrast, if the ΔVTH arises from the Δμ
in the SC, it depends obviously on the host SC, and thereby the different characteristic
feature of the signal should be observed in the Si and Ge systems.
Figures S3(a) and S3(b) show the obtained thermal Hanle signals [ΔVTH,
normal
(closed symbol), ΔVTH, inverted (open symbol); normalized] under applied magnetic fields
(Bz, Bx) up to 4.5 kOe, respectively, for the Si [CoFe/MgO(2 nm)/Si] and Ge
[CoFe/MgO(2 nm)/Ge] systems, with the Iheating values of –10 and +10 mA. The results
are for the case of SC heating (ΔT>0). It is noteworthy that, taking into account the similar
depletion width, roughness, and magnetization, it is likely that the properties of
CoFe/MgO tunnel contacts to Si and Ge are not fundamentally different20. In Figs. S3(a)
and S3(b), albeit using almost the same CoFe/MgO tunnel contacts, we can witness the
clearly different features of ΔVTH (i.e., the ratio of ΔVTH, inverted to ΔVTH, normal and the width
of ΔVTH, normal) depending on the host SC. The Si system [Fig. S3(a)] with effective values
6
of spin lifetime (τeff) 97-102 ps, as extracted from the simple Lorentzian fit (black line) of
the normal Hanle curve [note that the extracted τeff value should be considered as the
lower bound for the real spin lifetime (τsf) due to the artificial broadening of the Hanle
curve caused by the local magnetostatic fields]19, shows a pronounced inverted Hanle
effect. On the other hand, the inverted Hanle effect is relatively weaker for the Ge system
[Fig. S3(b)] having τeff values of 82-83 ps. The different characteristic feature of ΔVTH in
the Si and Ge systems can be seen unambiguously in Fig. S3(c), where the |ΔVTH, inverted/
ΔVTH, normal| and τeff values (obtained in the Si and Ge systems) are plotted as function of
Iheating (–10 to +10 mA). These results are well consistent with the previous our reports20
that the different characteristic features of the electrical Hanle signals in CoFe/MgO/Si
and CoFe/MgO/Ge contacts are mainly ascribed to the different τsf values relying on the
host SC. As a consequence, we can conclude that the ΔVTH obtained in our system does
not originate from the tunnel oxide (MgO) itself.
It should be finally mentioned that, as discussed in Refs. 7, 8, and 31, the magnitude
of spin signal obtained in TTH measurements cannot be explained by any existing
theories9,28,32 including the direct tunneling into SC and/or the two-step tunneling via
localized states (LSs) at oxide/SC interface or within oxide, and thus the quantitative
deviation of the obtained spin signal from the predicted value by the theory (in the TTH
measurements) does not directly indicate the Δμ in the LSs. The origins of this discrepancy,
i. e., other enhancement factors not yet incorporated in the existing theory9,28,32, are still
under investigation.
7
FIG. S3. Obtained thermal Hanle signals [ΔVTH, normal (closed symbol), ΔVTH, inverted (open
symbol); normalized] under applied magnetic fields (Bz, Bx) up to 4.5 kOe, respectively,
for (a) the Si [CoFe/MgO(2 nm)/Si] and (b) Ge [CoFe/MgO(2 nm)/Ge] systems16, with
the Iheating values of –10 and +10 mA. The results are for the case of SC heating (ΔT>0).
(c) Summary of |ΔVTH, inverted/ ΔVTH, normal| and τeff values obtained in the Si and Ge systems
for various Iheating (–10 to +10 mA).
8
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Yuasa, and R. Jansen, arXiv:1211.4460 (2012).
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R. Jansen, A. M. Deac, H. Saito, and S. Yuasa, Phys. Rev. B 85, 134420 (2012).
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