ArticlePDF Available

# Charge-to-Spin Conversion and Spin Diffusion in Bi/Ag Bilayers Observed by Spin-Polarized Positron Beam

Authors:

## Abstract and Figures

Charge-to-spin conversion induced by the Rashba-Edelstein effect was directly observed for the first time in samples with no magnetic layer. A spin-polarized positron beam was used to probe the spin polarization of the outermost surface electrons of Bi/Ag/Al_{2}O_{3} and Ag/Bi/Al_{2}O_{3} when charge currents were only associated with the Ag layers. An opposite surface spin polarization was found between Bi/Ag/Al_{2}O_{3} and Ag/Bi/Al_{2}O_{3} samples with the application of a charge current in the same direction. The surface spin polarizations of both systems decreased exponentially with the outermost layer thickness, suggesting the occurrence of spin diffusion from the Bi/Ag interface to the outermost surfaces. This work provides a new technique to measure spin diffusion length.
Content may be subject to copyright.
Charge-to-Spin Conversion and Spin Diffusion in Bi/Ag Bilayers
Observed by Spin-Polarized Positron Beam
H. J. Zhang,1,* S. Yamamoto,2B. Gu,3H. Li,1M. Maekawa,1Y. Fukaya,1and A. Kawasuso1
1Advanced Science Research Center, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
2Quantum Beam Science Directorate, Japan Atomic Energy Agency, 1233 Watanuki, Takasaki, Gunma 370-1292, Japan
3Advanced Science Research Center, Japan Atomic Energy Agency, 2-4 Shirakata Shirane, Tokai-mura, Ibaraki 319-1195, Japan
(Received 22 January 2015; revised manuscript received 12 March 2015; published 22 April 2015)
Charge-to-spin conversion induced by the Rashba-Edelstein effect was directly observed for the first
time in samples with no magnetic layer. A spin-polarized positron beam was used to probe the spin
polarization of the outermost surface electrons of Bi=Ag=Al2O3and Ag=Bi=Al2O3when charge currents
were only associated with the Ag layers. An opposite surface spin polarization was found between
Bi=Ag=Al2O3and Ag=Bi=Al2O3samples with the application of a charge current in the same direction.
The surface spin polarizations of both systems decreased exponentially with the outermost layer thickness,
suggesting the occurrence of spin diffusion from the Bi/Ag interface to the outermost surfaces. This work
provides a new technique to measure spin diffusion length.
DOI: 10.1103/PhysRevLett.114.166602 PACS numbers: 72.25.Ba, 71.70.Ej, 73.20.At, 78.70.Bj
In the last few years, increased attention has been paid to
spintronics due to its potential industrial applications to
data processing and information storage. The charge-
to-spin conversion in nonmagnetic materials, a central
issue in spintronics, is usually realized via the spin Hall
effect (SHE), the Rashba-Edelstein effect (REE), and
topological insulators [1].
The REE is the energy splitting of spin bands induced by
spin-orbit coupling and broken spatial symmetry. In a
two-dimensional (2D) electron gas system, the REE
Hamiltonian is usually expressed as HR¼αRðk×ˆ
zÞ·σ,
where αRis the Rashba parameter, kis the electron
momentum, ˆzis the unit vector of surface normal, and σ
is the vector of the Pauli matrix [2]. Giant REE has been
found in Bi/Ag, Pd/Ag, and Sb/Ag surface alloy systems by
using angle-resolved photoemission spectroscopy [35].
Recently, Rojas Sánchez et al. reported the spin-to-charge
conversion due to the giant REE at the Bi/Ag interface [6].
They used microwave spin pumping to inject a spin current
from a NiFe layer into a Bi/Ag bilayer and detected the
resulting charge current. They proposed that the spin-
to-charge conversion could be ascribed to the REE
coupling at the Bi/Ag interface but not the SHE. Their
findings imply that the REE is more efficient than the SHE
to produce spin-to-charge conversion in spintronics. It is
anticipated that the charge-to-spin conversion is also
possible due to the giant REE at the Bi/Ag interface.
Positronium (Ps), which is the bound state of a positron
and an electron, can only be formed at a local region where
the electron density is low enough (typically, less than
1013 cm2in 2D density) [7]. Therefore, in a metal,
formation of Ps is only possible at the outermost surface
(vacuum side, a few Å away from the first surface layer
[8]). There are two types of Ps: ortho-Ps (spin triplet,
jS; mi¼j1;1i,j1;1i, and j1;0i) and para-Ps (spin
singlet, jS; mi¼j0;0i). Para-Ps decays into two γrays
with energy of 511 keV, and is difficult to distinguish
from free positron-electron two-γannihilation. In contrast,
ortho-Ps, which decays mostly into three γrays (the decay
possibilities into other odd numbers of γrays are negligibly
small) with energy ranging between 0 and 511 keV, is
distinguishable from two-γevents. Inspired by the exciting
progress of spintronics in the last decade, a spin-polarized
positron beam was developed in order to detect the spin
polarization of the outermost surface electrons [9,10].
The change in the ortho-Ps annihilation intensity is
obtained by integrating the intensity over part of the energy
spectrum that is below 511 keV: R¼AL=AP, where ALis
the area under the energy curve in the low energy region
(from 383 to 468 keV), and APis the area under the 2γpeak
(from 494 to 528 keV). When the Ps formation probability
is low, the increment of Rfrom R0(subscript 0means no
Ps formation) is proportional to the ortho-Ps intensity (F3γ
Ps),
ΔR¼RR0F3γ
Ps:ð1Þ
In this study, Rand R0were measured using positron
implantation energies of Eþ¼50 eV and 12 keV,
respectively.
The asymmetry of ΔRthat is induced by the spin flip of
the outermost electrons (þPP) can be written
as [11]
ΔRðþPÞΔRðPÞ
ΔRðþPÞþΔRðPÞ¼2ϵð1Þϵð0Þ
2ϵð1Þþϵð0ÞPþPy
;ð2Þ
where ϵð1Þand ϵð0Þare the detection efficiencies of
annihilation γrays from j1;1iplus j1;1iand j1;0i,
PRL 114, 166602 (2015) PHYSICAL REVIEW LETTERS week ending
24 APRIL 2015
0031-9007=15=114(16)=166602(5) 166602-1 © 2015 American Physical Society
respectively. From the known values of Pþ,ϵ, and the
experimental asymmetry, the transverse spin polarization
(Py
) can be determined. For our detector alignment
(perpendicular to the positron beam), the factor
½2ϵð1Þϵð0Þ=½2ϵð1Þþϵð0Þ equates to a constant of 0.6.
A schematic of the spin-polarized Ps annihilation experi-
ment is shown in Fig. 1(a). A transversely spin-polarized
positron beam was generated by a 22Na source
(370 MBq) and an electrostatic beam apparatus. The
base pressure of the positron beam apparatus was
6×108Pa. The final beam diameter was 1 mm. The
spin polarization of the positron beam, Pþ, was measured
to be 0.3 [12]. The beam was guided to inject into the center
of a sample. A reversible direct current (jc), which was
perpendicular to Pþ, was applied to the two sample ends
through two electrodes. The beam energy Eþwas adjusted
to 50 eV by a deceleration tube from the initial value of
12 keV. The center of the sample was electrically grounded.
The Ps annihilation γrays were detected by using a high-
purity Ge detector.
The component of the surface spin polarization (P)
along the yaxis was obtained from
Py
¼Pcos ϕ¼ΔRþjcΔRjc
0.18ðΔRþjcþΔRjcÞ;ð3Þ
where ϕis the relative angle of Pto Pþ(yaxis), ΔRþjc
and ΔRjcare the three-γannihilation intensities that
correspond to an input charge current density of þjc
and jc, respectively. In this experiment, the charge current
was repeatedly reversed between þjcand jc. To deter-
mine Py
, the averages of all ΔRþjcand ΔRjcwere
calculated. The positive (negative) sign of Py
corresponds
to the direction of surface spin polarization in the yaxis (y
axis) with an input charge current of þjcin the zdirection.
Two types of Bi/Ag bilayer structures, Bið05Þ=
Agð25Þ=Al2O3and Agð25500Þ=Bið8Þ=Al2O3(numbers
in round parenthesis denote film thickness in nm), were
prepared on α-Al2O3½0001substrates. As shown in
Figs. 1(b) and 1(c), both samples have the Ag layer connected
to the two electrodes of the dc power supply. To determine
the resistivity of Bi films, three Bi films (100, 200, and
500 nm) were deposited on α-Al2O3½0001substrates [13].
Consequently, the resistivity of the present Bi films was
determined to be 300 μΩcm, which was approximately
60 times larger than that of Ag films (5μΩcm). Thus, the
charge currents mainly flow in the Ag layers.
The square-shaped substrates with length of 20 mm and
width of 57mm, were cut from α-Al2O3½0001wafers
(mean roughness <0.1nm). All film depositions were
carried out at a substrate temperature of 300 K. The
substrates were annealed at 873 K for 30 min in a vacuum
chamber (with a base pressure of 3×107Pa), which was
separated from the beam apparatus. The preparation of each
Ag=Bi=Al2O3sample was completed in this chamber. First,
the Bi layer was deposited onto the substrate by thermal
deposition with Bi granules (99.9999%). Subsequently,
using rf magnetron sputtering with an Ag target (99.99%),
the Ag layer was deposited onto the Bi layer in a pure Ar
(99.999%) ambient at a pressure of 0.3 Pa. The growth rates
of Bi and Ag in this chamber were 0.1 and 1.9nm=min,
respectively. During the Bi deposition process, the Bi
thickness was monitored by using a quartz crystal thickness
monitor (SQM-160, Sigma instruments, measurement error
of 0.1nm) that was positioned close to the substrate. The
Ag=Bi=Al2O3sample was then transferred to another
chamber that was connected to the beam apparatus. The
transfer took place through air and took approximately 20
minutes. To remove any oxide layer from the sample
surface, a 1 keV Arþsputtering was utilized.
Each Bi=Ag=Al2O3sample was prepared as follows:
The Ag film was deposited onto the substrate in the
above separated chamber. Subsequently, the Ag=Al2O3
sample was transferred to the chamber that was
connected to the beam apparatus through air within 20
minutes. After cleaning the Ag surface with a 1 keV Arþ
sputtering, the Bi film was deposited at a growth rate of
0.05 nm=min.
The crystallinity and surface roughness of samples were
characterized by XRD patterns (SmartLab, Rigaku) and
atomic force microscopy (AFM) observation (AFM5300E,
FIG. 1 (color online). The positron beam and the samples.
(a) Schematic of the spin-polarized positron beam. The sample
layer stack of (b) Bi=Agð25Þ=Al2O3and (c) Ag=Bið8Þ=Al2O3.
The yellow blocks represent the Mo electrodes.
PRL 114, 166602 (2015) PHYSICAL REVIEW LETTERS week ending
24 APRIL 2015
166602-2
Hitachi). Figure 2shows the XRD θ2θcurves: The Ag
film in the Agð25Þ=Al2O3sample is a polycrystal with the
(111), (200), (220), and (311) planes. The Bi layer of the
Agð25Þ=Bið8Þ=Al2O3is also polycrystalline with the (012)
and (003) planes. The Ag layer of the Agð25Þ=Bið8Þ=
Al2O3exists mainly in the (220) orientation [14]. From
AFM images, the mean roughnesses of Agð25Þ=Al2O3and
Bið8Þ=Al2O3were determined to be approximately 1.1 and
2.5 nm, respectively. Additionally, the mean grain diam-
eters of Ag in Agð25Þ=Al2O3and Bi in Bið8Þ=Al2O3were
found to be 40 nm from AFM measurements.
Various thicknesses of Bi layers (dBi ¼0.1, 0.2, 0.3, 0.6,
1, 2, 3, and 5 nm) were deposited on Agð25Þ=Al2O3. The
same charge current of 0.1 A (corresponding to the 2D
current density of jc¼1419 A=m) was applied. For the
Agð25Þ=Al2O3sample, the difference of ΔRjcwas rather
small at jc15 A=m and could only be observed at much
higher jc. Figure 3(a) shows ΔRjcfor Agð25Þ=Al2O3at
jc¼89.3A=m. The surface spin polarization of 3.2% that
is estimated from Fig. 3(a), which corresponds to 0.5% at
jc¼15 A=m, is probably induced by the spin Hall effect
in Ag film. Figure 3(b) shows that the difference of ΔRjc
of Bið0.3Þ=Agð25Þ=Al2O3is larger than that of the
Agð25Þ=Al2O3sample, even though jcis much lower.
Figure 4shows the Bi thickness dependence of the
surface spin polarizations that normalized to the values at
jc¼15 A=m. The surface spin polarization increases from
0.5 to 0.9% with increasing dBi from 0 to 0.2 nm, reaches
4.1% at dBi ¼0.3nm, and subsequently decreases gradu-
ally for dBi >0.3nm. Considering the Bi atomic radius
(0.15 nm), dBi ¼0.3nm is approximately one monolayer.
As shown by the solid line in Fig. 4, the above Bi thickness
dependence of the surface spin polarization can be fitted by
an exponential function:
FIG. 2 (color online). XRD patterns of (a) α-Al2O3substrate,
(b) Agð25Þ=Al2O3, (c) Bið8Þ=Al2O3, and (d) Agð25Þ=Bið8Þ=
Al2O3. The filled diamondmarks represent the imperfections
in the α-Al2O3substrates.
FIG. 3. Variation of ΔRas a function of input charge current
of þjcand jcfor (a) Agð25Þ=Al2O3at jc¼89.3A=m,
(b) Bið0.3Þ=Agð25Þ=Al2O3at jc¼18.9A=m, and (c) Agð25Þ=
Bið8Þ=Al2O3at jc¼17.5A=m.
FIG. 4. The surface spin polarization of Bi=Agð25Þ=Al2O3
samples as a function of Bi thickness. The six data points of
Bið0.3Þ=Agð25Þ=Al2O3were fitted to an exponential function
of Eq. (4).
PRL 114, 166602 (2015) PHYSICAL REVIEW LETTERS week ending
24 APRIL 2015
166602-3
Py
ðdBiÞ¼Py
ð0.3Þexp½0.48ðdBi 0.3Þ:ð4Þ
Similarly to the Bi=Agð25Þ=Al2O3samples, Ag layers of
different thicknesses (dAg ¼25, 100, 200, 300, 400,
500 nm) were deposited on Bið8Þ=Al2O3. The input charge
current was also regulated to 0.1 A for each sample, and the
surface spin polarization was normalized to the value at
jc¼15 A=m. As shown in Fig. 3(c), the difference of
ΔRjcis observed at dAg ¼25 nm. More importantly, its
magnitude and sign are comparable and opposite, respec-
tively, to those of Agð25Þ=Al2O3and Bi=Agð25Þ=Al2O3.
polarization. Figure 5shows that the surface spin polari-
zation decreases with increasing dAg. Again, this can be
fitted by an exponential function:
Py
ðdAgÞ¼Py
ð25Þexp½0.0028ðdAg 25Þ:ð5Þ
zation and the thickness dependencies for Bi=Agð25Þ=
Al2O3and Ag=Bið8Þ=Al2O3suggest that excess electron
spins generated at the Bi/Ag interface diffuse into both Bi
and Ag layers and eventually appear at the outermost
surfaces. Also, the current-induced spin polarization within
the Ag layers of Ag=Bið8Þ=Al2O3samples is overcompen-
sated by excess and opposite spins supplied from the Bi/Ag
interface.
We assume a simple exponential form of expðd=λsd Þ
for spin diffusion, where λsd is the spin diffusion length and
the prefactors in the exponentials of Eqs. (4) and (5)
correspond to 1=λsd. Thus, we determine a spin diffusion
length of λsdðBiÞ¼1=0.48 2.1nm for the Bi layer and
λsdðAgÞ¼1=0.0028 357 nm for the Ag layer. The spin
diffusion length in Bi is comparable to a recent value of
λsdðBiÞ¼1.2nm that was obtained from the inverse SHE
of a Py/Bi bilayer [15]. Also, the above λsdðAgÞof 357 nm
does not conflict with the previous reports of 132, 152, 700,
and 300 nm [1618].
The spin diffusion length is a critical parameter in
spintronics. The present study demonstrates that it has
the potential to quantitatively characterize the spin diffu-
sion length by detecting the surface spin polarization of
samples with different thicknesses of material upon the
same film with a known value of spin polarization [such
as Agð25Þ=Bið8Þ=Al2O3].
In the study of spin-to-charge conversion in Bi/Ag
bilayers, the authors attributed the spin-to-charge conver-
sion to the inverse REE but not the inverse SHE since the
spin Hall angle of a BiAg alloy (2.3%) has the opposite
sign to their observation [19]. Considering the fact that the
above-obtained spin diffusion lengths agree with those
reported so far, the spin polarizations on the outermost
surfaces of the Bi/Ag system observed here may be a
consequence of the REE, which is the inverse mechanism
of the one observed by Rojas Sánchez et al. with the spin
pumping method.
The charge-to-spin conversion in a sample that contains
a magnetic layer has been observed before. In 2010, Miron
et al. detected a current-driven spin torque induced by the
REE in Ptð3Þ=Coð0.6Þ=Alð1.6Þ=SiO2[20]. In 2011, they
observed the perpendicular switching of a single Co
ferromagnetic layer in the same sample [21]. Our previous
report on current-induced spin polarization of six transition
metals (Pt, Pd, Au, Cu, Ta, and W) was tentatively
explained as the surface spin accumulation due to the
REE [10]. These samples were also associated with the
magnetic layer due to the ferromagnetic property of
the nanoscaled Pt and Pd. The validity of the explanation
still remains a problem that needs to be experimentally
addressed. In this sense, the present observation of opposite
spin polarizations at opposite surfaces in Bi/Ag bilayers, as
far as we know, is the first direct observation of the REE in
a sample with no magnetic layer inside.
The spin density hδsiresulting from the REE and a
charge current is given by [22]
hδsm
eαR
eEF
jc;ð6Þ
where m
eis the effective electron mass, eis the elementary
charge, and EFis the Fermi energy. For the Bi/Ag[111]
system, m
e¼0.35 m0(m0is the electron rest mass),
αR¼3.05 ×1010 eVm, and EF¼0.18 eV is calculated
from the Fermi wavelength kF¼0.13 Å1and m
e[3].
Thus, at the Bi/Ag interface, hδsi5×1010 cm2for
jc¼15 A=m. On a metal surface, Ps is formed at the
vacuum side where the electron density (n2D)islow
enough, typically, less than 1013 cm2. For the Bi surface,
n2D¼ð0.54Þ×1013 cm2at the first surface layer
[2325], which may nearly fulfill the above Ps formation
condition. For the Ag surface, such a low electron density is
available at a vacuum region, a few Å away from the first
surface layer [8]. Therefore, an observable spin polarization
FIG. 5. The surface spin polarization of Ag=Bið8Þ=Al2O3
samples as a function of Ag thickness. The data were fitted to
an exponential function of Eq. (5).
PRL 114, 166602 (2015) PHYSICAL REVIEW LETTERS week ending
24 APRIL 2015
166602-4
Py
is estimated to be at least ð0.11Þ%. Thus, the order of
magnitude of the spin polarization observed here,
Py
¼ð45Þ%, could be explained by the REE.
In conclusion, we demonstrate charge-to-spin conversion
in Bi/Ag bilayers by using spin-polarized Ps annihilation
spectroscopy. Direct evidence of spin diffusion is found by
analyzing the outermost layer thickness dependence of
surface spin polarization of Bi=Ag=Al2O3and Ag=Bi=
Al2O3samples.
We are grateful to J. Ieda and S. Maekawa of JAEA, T.
Seki, K. Takanashi, and E. Saitoh of Tohoku University for
their valuable suggestions and discussions. This work was
financially supported by JSPS KAKENHI under Grant
No. 24310072 and the NSFC under Grant No. 11475130.
*zhang.hongjun@jaea.go.jp
[1] S. Maekawa, S. O. Valenzuela, E. Saitoh, and T. Kimura,
Spin Current (Oxford University Press, Oxford, 2012).
[2] Y. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984).
[3] C. R. Ast, J. Henk, A. Ernst, L. Moreschini, M. C. Falub, D.
Pacilé, P. Bruno, K. Kern, and M. Grioni, Phys. Rev. Lett.
98, 186807 (2007).
[4] C. R. Ast, G. Wittich, P. Wahl, R. Vogelgesang, D. Pacilé,
M. C. Falub, L. Moreschini, M. Papagno, M. Grioni, and
K. Kern, Phys. Rev. B 75, 201401 (2007).
[5] L. Moreschini, A. Bendounan, I. Gierz, C. R. Ast,
H. Mirhosseini, H. Höchst, K. Kern, J. Henk, A. Ernst,
S. Ostanin et al.,Phys. Rev. B 79, 075424 (2009).
[6] J. C. Rojas Sánchez, L. Vila, G. Desfonds, S. Gambarelli,
J. P. Attané, J. M. De Teresa, C. Magén, and A. Fert, Nat.
Commun. 4, 2944 (2013).
[7] A. Held and S. Kahana, Can. J. Phys. 42, 1908 (1964).
[8] N. D. Lang and W. Kohn, Phys. Rev. B 1, 4555 (1970).
[9] A. Kawasuso, Y. Fukaya, M. Maekawa, H. J. Zhang,
T. Seki, T. Yoshino, E. Saitoh, and K. Takanashi, J. Magn.
Magn. Mater. 342, 139 (2013).
[10] H. J. Zhang, S. Yamamoto, Y. Fukaya, M. Maekawa, H. Li,
A. Kawasuso, T. Seki, E. Saitoh, and K. Takanashi, Sci.
Rep. 4, 4844 (2014).
[11] D. W. Gidley, A.R. Köymen, and T. W. Capehart, Phys.
Rev. Lett. 49, 1779 (1982).
[12] A. Kawasuso and M. Maekawa, Appl. Surf. Sci. 255, 108
(2008).
[13] C. Yang, Research Project (on the Internet) in Research
Experiences for Undergraduates, Materials Physics, Florida
University, 2008 (unpublished).
[14] M. A. Majeed Khan, S. Kumar, M. Ahamed, S. A.
Alrokayan, and M. S. AlSalhi, Nanoscale Res. Lett. 6,
434 (2011).
[15] D. Hou, Z. Qiu, K. Harii, Y. Kajiwara, K. Uchida,
Y. Fujikawa, H. Nakayama, T. Yoshino, T. An, K. Ando
et al.,Appl. Phys. Lett. 101, 042403 (2012).
[16] R. Godfrey and M. Johnson, Phys. Rev. Lett. 96, 136601
(2006).
[17] T. Kimura and Y. Otani, Phys. Rev. Lett. 99, 196604
(2007).
[18] Y. Fukuma, L. Wang, H. Idzuchi, S. Takahashi,
S. Maekawa, and Y. Otani, Nat. Mater. 10, 527 (2011).
[19] Y. Niimi, H. Suzuki, Y. Kawanishi, Y. Omori, T. Valet,
A. Fert, and Y. Otani, Phys. Rev. B 89, 054401 (2014).
[20] I. M. Miron, G. Gaudin, S. Auffret, B. Rodmacq, A. Schuhl,
S. Pizzini, J. Vogel, and P. Gambardella, Nat. Mater. 9, 230
(2010).
[21] I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V.
Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl,
and P. Gambardella, Nature (London) 476, 189 (2011).
[22] P. Gambardella and I. M. Miron, Phil. Trans. R. Soc. A 369,
3175 (2011).
[23] C. R. Ast and H. Höchst, Phys. Rev. Lett. 87, 177602
(2001).
[24] T. Hirahara, I. Matsuda, S. Yamazaki, N. Miyata, S.
Hasegawa, and T. Nagao, Appl. Phys. Lett. 91, 202106
(2007).
[25] N. Marcano, S. Sangiao, C. Magen, L. Morellon, M. R.
Ibarra, M. Plaza, L. Perez, and J. M. De Teresa, Phys. Rev. B
82, 125326 (2010).
PRL 114, 166602 (2015) PHYSICAL REVIEW LETTERS week ending
24 APRIL 2015
166602-5
... Since bismuth is a semimetal with the electrical conductivity being much lower than that of platinum [20], one would expect bismuth to have a very large spin Hall angle (Θ sH ) (the ratio of the spin current to the longitudinal charge current, i.e., charge-spin conversion efficiency). Therefore, many investigations on spin current phenomena in Bi semimetal systems have been carried [29][30][31][32][33][34] and indeed large spin Hall angles of about 10 % have been reported in some of these experiments [29]. ...
... Nevertheless, we do notice that our calculated SHC values for fcc Pt and β-Ta (Table II) agree very well with the previous independent calculations using the different methods [53,54], and thus we are confident that our calculated SHC values are reliable. As mentioned before, the magnitude of the reported Θ sH values varies from zero (negligibly small) to 24 %, depending on the spin current detection method and also the magnetic material used to inject spin current in the experiments [29][30][31][32][33][34]. Since the spin Hall angle also depends on the electric conductivity, it would be better to compare the experimentally determined and theoretically calculated SHC. ...
Preprint
Full-text available
Bismuth is an archetypal semimetal with gigantic spin-orbit coupling and it has been a major source material for the discovery of seminal phenomena in solid state physics for more than a century. In recent years, spin current transports in bismuth have also attracted considerable attention. In this paper, we theoretically study both spin Hall effect (SHE) and spin Nernst effect (SNE) in bismuth, based on relativistic band structure calculations. First, we find that there are three independent tensor elements of spin Hall conductivity (SHC) and spin Nernst conductivity (SNC), namely, $Z_{yx}^z$, $Z_{xz}^y$, and $Z_{zy}^x$. We calculate all the elements as a function of the Fermi energy. Second, we find that all SHC tensor elements are large, being $\sim$1000 ($\hbar$/e)(S/cm) and comparable to that of platinum. Furthermore, because of its low electrical conductivity, the corresponding spin Hall angles are gigantic, being $\sim$20%. Third, all the calculated SNC tensor elements are also pronounced, being comparable to that [$\sim$0.13 ($\hbar$/e)(A/m-K)] of gold, although they are several times smaller than platinum and $\beta$-Ta. Finally, in contrast to Pt and Au where $Z_{yx}^z = Z_{xz}^y = Z_{zy}^x$, the SHE and SNE in bismuth are strongly anisotropic, i.e., $Z_{yx}^z$, $Z_{xz}^y$ and $Z_{zy}^x$ differ significantly. Consequently, the Hall voltages due to the inverse SHE and SNE from the different conductivity elements could cancel each other and thus result in a small spin Hall angle if polycrystalline samples are used, which may explain why the measured spin Hall angles ranging from nearly 0 to 25% have been reported. We hope that these interesting findings would stimulate further spin current experiments on bismuth using highly oriented single crystal specimens.
... The current-induced spin polarization (CISP), also known as the Edelstein effect [9] or the charge-to-spin conversion [10,11], is that a charge current driven through a 2D system with Rashba spin-orbit coupling (RSOC) generates a spatially homogeneous spin polarization perpendicular to the applied bias. Thus a nonzero spin polarization is generated in nonmagnetic systems purely electrically. ...
... This phenomenon also offers us a new way to manipulate the direction of the in-plane spin polarization by tuning the PEF. Since the spin polarization is a central issue in spintronics [10,11,19,[21][22][23], the CISP sign change in monolayer InSe may be used to construct extremely thin spintronic devices. ...
Article
We find that perpendicular electric fields can give rise to a tunable current-induced spin polarization in monolayer InSe. The interplay between the Rashba and the intrinsic Dresselhaus spin-orbit coupling leads to several Lifshitz transitions near the valence band maxima. Interestingly, the sign of the spin polarization changes with increasing perpendicular electric fields. We propose a spin potentiometric device to measure current-induced spin polarization.
... The control and manipulation of the spin-charge interconversion plays a critical role in modern spintronics [1,2]. In the two-dimensional system, the (inverse) Edelstein effect has gained much attention since its potential application in spintronics devices [3][4][5][6][7][8][9][10][11][12][13][14][15]. In the direction of inverse Edelstein effect (IEE), a pure spin current j s through the system generates a transverse charge current j c , and the Edelstein effect (EE) describes the inverse process. ...
... The microscopic mechanism of both EE and IEE requires the presence of the spin-orbit coupling (SOC), which results in the specific spin-momentum locked electronic band structures. Thus, the usual candidate physical systems include the metallic heterostructure [4][5][6][7][8][9][10][11] and the topological insulators [15][16][17][18][19][20][21]. In the metallic heterostructure, the spacial inversion asymmetry lifts the spin degeneracy and gives rise to the Rashba SOC [22]. ...
Article
Full-text available
We propose that the hybridization between two sets of Rashba bands can lead to the unconventional Rashba band structures where the two Fermi circles from different bands own in-plane helical spin textures with the same chiralities, and possess group velocities with the same directions. Through the first-principles calculations, we predict that monolayer OsBi2 hosts such simple and pure unconventional Rashba bands near Fermi energy. Under the weak spin injection, we show that the two Fermi circles from the unconventional Rashba bands both give the positive contributions to the spin-to-charge conversion and thus induce the giant inverse Rashba-Edelstein Effect with large conversion efficiency, which is very different from the conventional Rashba-Edelstein Effect. Our studies not only provide a promising material of monolayer OsBi2 to possess unconventional Rashba bands, but also demonstrate its potential application to achieve highly efficient spin-to-charge conversion in spintronics.
... Also, the emission energy of Ps from surfaces brings about the information of the electronic band of the materials [1,5]. Focusing on the spin of the electron in Ps, it is possible to study spin-polarized surface electronic states and spin currents in solids [6][7][8][9]. ...
Article
Full-text available
Positronium is a bound state of one electron and one positron. It can be seen as the lightest neutral “atom”. It can also be seen as a neutralized electron or a neutralized positron. Since positronium is electrically neutral, special techniques are required to generate a variable energy beam of positronium. In recent years, it has become possible to efficiently generate positronium negative ions in which another electron is bound to positronium. It is possible to generate an energy-tunable positronium beam by accelerating positronium negative ions with an electric field and irradiating them with laser light to photodetach one electron. Generation of such a positronium beam has actually been realized, and applied research has begun. Here, we describe the energy-variable positronium beam generation, its applied research including the observation of the motion-induced resonance of positronium and the first measurement of the binding energy of positronium to one electron.
... However, since it is difficult to distinguish the interfacial REE from the bulk SHE [19] and there are some parasitic effects in most REE spin-charge conversion measurements [20], one should be very careful about the existence of interfacial REE. For instance, the latest experimental evidences suggest that there is no large REE at the Bi/Ag interface [20,21], which was previously considered a typical interfacial REE system [12,22]. ...
Article
Full-text available
Previous studies have shown that Rashba-Edelstein effect may exist at the permalloy (Py)/Al2O3 interface due to inversion symmetry breaking. We systematically investigated the magnetoresistance and spin-torque ferromagnetic resonance (ST-FMR) in a series of Py/δPt/Al2O3 structures, where the Py/Al2O3 interface is decorated with or without ultra-thin Pt. The magnetoresistance measurements show that the original Py/Al2O3 exhibits an ordinary anisotropic magnetoresistance, while Pt decoration introduces an additional spin–orbit magnetoresistance. The ST-FMR measurements show that a damping-like torque does exist in Py/Al2O3 but are relatively small compared with the Pt decorated samples, and the previously observed field-like torque in Py/Al2O3 may be contributed mainly by the Oersted field caused by the current inhomogeneity. Our results suggest that the strength of spin–orbit coupling at the Py/Al2O3 interface is relatively weak and can be enhanced by Pt decoration.
Chapter
The Rashba effect has been intensively investigated since it plays a crucial role in the field of spintronics. However, the conventional Rashba model often fails to explain the complex behavior of the spin polarization and the magnitude of spin-splitting in real materials. In this chapter, we discuss the role of the wavefunctions of the Rashba states in films using orbital-selective SARPES and high-resolution SARPES. First, the spin-textures of Bi-based surface alloys beyond the Rashba model were investigated, and the orbital-coupled spin texture was found to be the origin of the complex spin structure. Second, the magnitudes of the spin-splittings in quantum-well films were investigated by varying the film thicknesses. It was demonstrated that the spin-splitting depends on the film thicknesses and the quantum numbers of the well states, leading to a universal scaling of the Rashba parameters determined by the charge densities at the interface.
Article
Nontrivial momentum-space spin texture of electrons can be induced by spin-orbit coupling and underpins various spin transport phenomena, such as current-induced spin polarization and the spin Hall effect. In this work, we find a nontrivial spin texture, spin antivortex, can appear at certain momenta on the Γ-K line in a 2D monolayer Pb on top of SiC. Different from spin vortex due to the band degeneracy in the Rashba model, the existence of this spin antivortex is guaranteed by the Poincaré-Hopf theorem and thus topologically stable. Accompanied with this spin antivortex, a Lifshitz transition of Fermi surfaces occurs at certain momenta on the K-M line, and both phenomena are originated from the anticrossing between the j=1/2 and j=3/2 bands. A rapid variation of the response coefficients for both the current-induced spin polarization and spin Hall conductivity is found when the Fermi energy is tuned around the spin antivortex. Our work demonstrates the monolayer Pb as a potentially appealing platform for spintronic applications.
Article
We employ Onsager’s irreversible thermodynamics (IrTh) to study the Inverse Edelstein effect (IEE) for a non-magnetic material (NM) adjacent to a topological insulator (TI) with a strong spin-orbit interaction. The TI surface state region is treated as quasi two-dimensional (2d). For the IEE, the source is a 3d spin flux incident from the NM that converts, at the NM/TI interface, to a quasi-2d charge current in the TI. For the Edelstein Effect (EE), the source is a quasi-2d charge flux incident from the TI that converts, at the interface, to a three-dimensional (3d) spin flux in the NM. For strong spin-orbit coupling, as considered here, when the 3d spin flux crosses to the 2d TI, the quasi-2d charge current is produced along with a quasi-2d spin accumulation. (For weak spin-orbit coupling, production of charge current and of spin accumulation are distinct processes.) We compute the associated rates of heating.
Preprint
Full-text available
Non-trivial momentum-space spin texture of electrons can be induced by spin-orbit coupling and underpins various spin transport phenomena, such as current-induced spin polarization and spin Hall effect. In this work, we find a non-trivial spin texture, spin anti-vortex, can appear at certain momenta on the $\Gamma-\text K$ line in 2D monolayer Pb on top of SiC. Different from spin vortex due to the band degeneracy in the Rashba model, the existence of this spin anti-vortex is guaranteed by Poincare-Hopf theorem and thus topologically stable. Accompanied with this spin anti-vortex, a Lifshtiz transition of Fermi surfaces occur at certain momenta on the $\text K- \text M$ line, and both phenomena are originated from the anti-crossing between the $j=1/2$ and $j=3/2$ bands. A rapid variation of the response coefficients for both the current-induced spin polarization and spin Hall conductivity is found when the Fermi energy is tuned around the spin anti-vortex. Our work demonstrates the monolayer Pb as a potentially appealing platform for spintronic applications.
Article
Full-text available
Current-induced spin polarization (CISP) on the outermost surfaces of Au, Cu, Pt, Pd, Ta, and W nanoscaled films were studied using a spin-polarized positron beam. The Au and Cu surfaces showed no significant CISP. In contrast, the Pt, Pd, Ta, and W films exhibited large CISP (3~15% per input charge current of 10(5) A/cm(2)) and the CISP of Ta and W were opposite to those of Pt and Pd. The sign of the CISP obeys the same rule in spin Hall effect suggesting that the spin-orbit coupling is mainly responsible for the CISP. The magnitude of the CISP is explained by the Rashba-Edelstein mechanism rather than the diffusive spin Hall effect. This settles a controversy, that which of these two mechanisms dominates the large CISP on metal surfaces.
Article
Full-text available
The spin Hall effect (SHE), induced by spin-orbit interaction in nonmagnetic materials, is one of the promising phenomena for conversion between charge and spin currents in spintronic devices. The spin Hall (SH) angle is the characteristic parameter of this conversion. We have performed experiments of the conversion from spin into charge currents by the SHE in lateral spin valve structures. We present experimental results on the extrinsic SHEs induced by doping nonmagnetic metals, Cu or Ag, with impurities having a large spin-orbit coupling, Bi or Pb, as well as results on the intrinsic SHE of Au. The SH angle induced by Bi in Cu or Ag is negative and particularly large for Bi in Cu, 10 times larger than the intrinsic SH angle in Au. We also observed a large SH angle for CuPb but the SHE signal disappeared in a few days. Such an aging effect could be related to a fast mobility of Pb in Cu and has not been observed in CuBi alloys.
Article
Full-text available
The Rashba effect is an interaction between the spin and the momentum of electrons induced by the spin-orbit coupling (SOC) in surface or interface states. Its potential for conversion between charge and spin currents has been theoretically predicted but never clearly demonstrated for surfaces or interfaces of metals. Here we present experiments evidencing a large spin-charge conversion by the Bi/Ag Rashba interface. We use spin pumping to inject a spin current from a NiFe layer into a Bi/Ag bilayer and we detect the resulting charge current. As the charge signal is much smaller (negligible) with only Bi (only Ag), the spin-to-charge conversion can be unambiguously ascribed to the Rashba coupling at the Bi/Ag interface. This result demonstrates that the Rashba effect at interfaces can be used for efficient charge-spin conversion in spintronics.
Article
Full-text available
Inverse spin Hall effect has been investigated in bismuth(Bi)/permalloy(Py) bilayer films by using the spin pumping at room temperature. From the ferromagnetic-resonance-spectrum linewidth data, Bi is proved to be a good spin sink in our structure. We measured inverse spin Hall voltage and conductance of the Bi/Py bilayer and found that the inverse spin Hall current, Ic, decreases with increasing the Bi thickness, which is in contrast to the former understanding in similar bilayer systems, e.g., Pt/Py. We constructed a model to explain the thickness dependence of Ic quantitatively, in which spin transport modulation near Bi/Py interface is considered.
Article
Full-text available
The surface of a magnetic solid is a different physical system from the underlying bulk, and may have different magnetic properties. The manner in which the magnetism of the surface differs from the bulk depends on the mechanism of magnetic coupling in general, and has recently become a topic of active theoretical and experimental interest. This thesis presents the first use of a spin-polarized low-energy positron beam to investigate surface magnetism. For different crystallographic faces of Ni, the magnetization is deduced from the asymmetry in formation of the triplet spin state of positronium when either the Ni magnetization or the positron-beam polarization is reversed. The measured asymmetries in the triplet positronium formation can be directly related to the polarization, P(,e)-, of those electrons participating in positronium formation. By measuring the temperature dependence of P(,e)-on Ni (110) we show, consistent with other experimental results, that the surface magnetization in the range 0.46 < T/T(,c) < 1.0 differs markedly from the bulk magnetization. Rapid quenching of the ferromagnetic order is observed for submonolayer coverages of oxygen, demonstrating the extreme surface sensitivity of this technique. The deduced polarization changes sign from majority on Ni(110) to minority on Ni(100) and is smaller than the bulk electron spin polarization. This is inconsistent with recent self-consistent calculations of surface magnetization which predict an enhancement of the local moment near the surface. A comparison of the sign and magnitude of results for these surfaces from spin -polarized field emission to the present measured asymmetries in triplet positronium formation reveals a correspondence between these techniques. A qualitative understanding of the results of the present experiment can be obtained by viewing the positronium formation process as the tunneling of a metal electron through the surface to the bound state on a bare positron. Details of the detection of surface defects using positronium formation and of room temperature thermal desorption of "cold" positronium from alkali covered Ni surfaces in discussed in the appendices.
Article
Full-text available
In situ microscopic-four-point probe conductivity measurements were performed for ultrathin Bi films on Si(111)-7×7. From the extrapolation of thickness-dependent conductivity and decrease in conductivity through surface oxidization, we found clear evidence of large surface-state conductivity (σSS ∼ 1.5×10−3 Ω−1/◻ at room temperature) in Bi(001) films. For the thinnest films ( ∼ 25 Å), the transport properties are dominated by the highly inert surface states that are Rashba spin-split, and this suggests the possibility of using these Bi surface states for spintronics device application.
Article
A variational search is made for a quasi-bound state of an electron–positron pair in a metal. The basic equation used is the effective Schrödinger equation derived from the electron–positron propagator in an approximation which accurately accounts for the two-body correlations. It is found that no such state exists in metals and hence it can have no influence on the positron annihilation rates. However, the state appears for electron gases of sufficiently low density, ,* and thus determines the low-density annihilation rates.
Article
The first part of this paper deals with the jellium model of a metal surface. The theory of the inhomogeneous electron gas, with local exchange and correlation energies, is used. Self-consistent electron density distributions are obtained. The surface energy is found to be negative for high densities (rs≤2.5). In the second part, two corrections to the surface energy are calculated which arise when the positive background model is replaced by a pseudopotential model of the ions. One correction is a cleavage energy of a classical neutralized lattice, the other an interaction energy of the pseudopotentials with the electrons. Both of these corrections are essential at higher densities (rs≤4). The resulting surface energy is in semiquantitative agreement with surface-tension measurements for eight simple metals (Li, Na, K, Rb, Cs, Mg, Zn, Al), typical errors being about 25%. For Pb there is a serious disagreement.
Oscillatory effects in a strong magnetic field B and magnetic susceptibility are investigated, as applied to 2D systems, in which the twofold spin degeneracy is lifted by the spin-orbit-interaction Hamiltonian HSO= alpha ( sigma *k). nu . The term HSO is shown to change greatly the usual patterns of B-1-periodic oscillations; some oscillations are strongly suppressed due to the diminishing of the gaps between adjacent levels, and new oscillations appear due to intersections of levels.