Nonrelativistic and nonmagnetic terahertz-wave generation via ultrafast current control in anisotropic conductive heterostructures

Full text

Nonrelativistic and nonmagnetic terahertz-wave
generation via ultrafast current control in
anisotropic conductive heterostructures
Sheng Zhang,a,b,†Yongwei Cui ,a,b,c,†Shunjia Wang,a,b,†Haoran Chen,a,b,c Yaxin Liu,a,b Wentao Qin,a,b,c
Tongyang Guan,a,b Chuanshan Tian ,a,b Zhe Yuan,d,e Lei Zhou,a,b Yizheng Wu,a,b,c,*and Zhensheng Taoa,b,*
aFudan University, State Key Laboratory of Surface Physics, Department of Physics, Shanghai, China
bFudan University, Key Laboratory of Micro and Nano Photonic Structures, Shanghai, China
cShanghai Research Center for Quantum Sciences, Shanghai, China
dBeijing Normal University, Center for Advanced Quantum Studies, Department of Physics, Beijing, China
eFudan University, Institute for Nanoelectronic Devices and Quantum Computing, Shanghai, China
Abstract. Precise and ultrafast control over photo-induced charge currents across nanoscale interfaces could
lead to important applications in energy harvesting, ultrafast electronics, and coherent terahertz sources.
Recent studies have shown that several relativistic mechanisms, including inverse spin-Hall effect, inverse
Rashba–Edelstein effect, and inverse spin-orbit-torque effect, can convert longitudinally injected spin-
polarized currents from magnetic materials to transverse charge currents, thereby harnessing these currents
for terahertz generation. However, these mechanisms typically require external magnetic fields and exhibit
limitations in terms of spin-polarization rates and efficiencies of relativistic spin-to-charge conversion. We
present a nonrelativistic and nonmagnetic mechanism that directly utilizes the photoexcited high-density
charge currents across the interface. We demonstrate that the electrical anisotropy of conductive oxides
RuO2and IrO2can effectively deflect injected charge currents to the transverse direction, resulting in efficient
and broadband terahertz radiation. Importantly, this mechanism has the potential to offer much higher
conversion efficiency compared to previous methods, as conductive materials with large electrical anisotropy
are readily available, whereas further increasing the spin-Hall angle of heavy-metal materials would be
challenging. Our findings offer exciting possibilities for directly utilizing these photoexcited high-density
currents across metallic interfaces for ultrafast electronics and terahertz spectroscopy.
Keywords: terahertz optics; ultrafast science; nanophotonics.
Received May 17, 2023; revised manuscript received Jul. 13, 2023; accepted for publication Jul. 31, 2023; published online
Sep. 12, 2023.
© The Authors. Published by SPIE and CLP under a Creative Commons Attribution 4.0 International License. Distribution or
reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.
[DOI: 10.1117/1.AP.5.5.056006]
1 Introduction
Precise control of charge-carrier transport across nanoscale in-
terfaces at ultrafast speeds is essential for the advancement of
various modern technologies, including solar cells,1photosyn-
thesis,2and high-efficiency optoelectronic devices.3Recent
studies have shown that when metallic interfaces are excited
by strong femtosecond laser pulses, enormous current density
exceeding 1010 Acm
−2can be produced,4,5which is several
orders of magnitude higher than those typically used in elec-
tronic devices. If harnessed, these high-frequency and high-
density charge currents could revolutionize the field of ultrafast
electronics6and also lead to the development of bright and co-
herent terahertz sources.7However, due to the nanometer scale
and localization of the generated currents around the buried
interface, collecting their radiation energy poses a significant
challenge.
Recently, Kampfrath et al. demonstrated a promising ap-
proach for utilizing the enormous charge currents for generation
of strong and broadband terahertz radiation.7–9This approach
*Address all correspondence to Yizheng Wu, wuyizheng@fudan.edu.cn;
Zhensheng Tao, ZhenshengTao@fudan.edu.cn
†These authors contributed equally to this work.
Research Article
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involves a heterostructure consisting of a thin heavy-metal (HM)
film, such as Pt, and a thin ferromagnetic (FM) film, where
longitudinal spin-polarized currents injected from the FM layer
can be deflected to transverse charge currents in the HM layer
via the relativistic inverse spin-Hall effect (ISHE). In this
context, longitudinal currents are defined as those flowing
perpendicular to the interface. Recently, metasurface-structured
devices have also been demonstrated for the simultaneous gen-
eration and manipulation of terahertz waveforms.10,11 Moreover,
this concept has attracted great interest because it provides an
all-optical, contact-free method for probing the transient state
of magnetism with subpicosecond time resolution in FM
materials,12–14 antiferromagnetic materials,15 and for reliably
measuring the spin-Hall angle of HM materials.16 Later, other
relativistic mechanisms, including the inverse Rashba–Edelstein
effect17,18 and the inverse spin-orbit-torque effect,19 were also
found capable of terahertz-wave generation, with the former
having comparable efficiency with the ISHE, and with the latter
effect being much weaker.
All the current-deflection mechanisms described above rely
on a two-step process involving generation of spin-polarized
currents and relativistic spin-to-charge conversion. The spin-
polarized currents are typically extracted from the laser-induced
charge currents through superdiffusive spin scattering,20,21 re-
sulting in a spin polarization rate of 0.2 to 0.4 within the spin
diffusion length.22,23 As a result, an external magnetic field is
usually required to saturate the magnetization of the FM mate-
rials, although field-free emitters have recently been realized by
utilizing exchange bias between antiferromagnetic and FM
nanofilms.24 In the second step, the efficiency of the relativistic
spin-to-charge conversion is characterized by the spin-Hall an-
gle γ. For Pt, which is known for its strong spin–orbit coupling,
γis typically around 0.1,19 while the conversion efficiency of an
AgBi interface is estimated to be between 0.064 and 0.16.18
Consequently, the ability to fully utilize the interface transient
currents is hindered by the low conversion efficiencies in these
two steps. The conversion efficiency could be significantly im-
proved if one could directly and efficiently control the laser-
induced charge currents across the interface, rather than relying
on spin-polarized currents.
In this work, we report a nonrelativistic and nonmagnetic
mechanism for direct conversion of laser-excited high-density
longitudinal charge currents to transverse ones, leading to effi-
cient terahertz-wave generation without the need for external
fields. The generation process is initiated by the superdiffusive
charge current injected from the adjacency of an optically
excited metal thin film, which is then deflected from the longi-
tudinally injected direction to the transverse direction by the
anisotropic electrical conductivity of the conductive rutile
oxides RuO2and IrO2. Notably, RuO2was recently found to
be an itinerant antiferromagnetic material25,26 that has attracted
enormous interest in magneto-electronic research,27–33 whereas
IrO2is nonmagnetic.34 Our results show that the terahertz
emission is highly sensitive to the crystal orientation but not in-
fluenced by the polarization of the excitation laser. This distin-
guishes our mechanism from the aforementioned magnetic near-
infrared (NIR)-to-terahertz conversion mechanisms4,17–19 that
rely on relativistic spin–orbit coupling, as well as from other
nonmagnetic mechanisms, such as optical rectification35,36 or
difference-frequency generation,37,38 which requires coherent
wave mixing of the excitation laser. The conversion efficiency
of the IrO2sample matches that of the ISHE, and this
mechanism can potentially further improve efficiency by imple-
menting conductive materials with stronger electrical anisotropy.
These findings open up possibilities to directly harness interface
high-density charge currents for ultrafast electronics and tera-
hertz spectroscopy.
2 Results
Figure 1(a) illustrates the schematic of the experimental setup.
The device is based on a heterostructure composed of a single-
crystal film of either RuO2or IrO2and a nonmagnetic metal
(NM) thin film, both of which are nanometers thick. Several
different metals (Cu, Pt, W, and Ir) were used for the NM layer.
The RuO2and IrO2films are both conductive rutile oxide
belonging to the space group P42/mnm with unequal lattice
parameters [a¼b>c, see Fig. 1(b)]. As a result, they are both
electrically anisotropic conductors (EACs) with σ∥<σ⊥, where
σ∥and σ⊥are the conductivity along the caxis and that in
the a−bplane, respectively. The single-crystal RuO or IrO2
film was deposited on the TiO2or Al2O3substrates and then
capped by an NM film. See Appendix A and Sec. S1 in the
Supplementary Material for the details of sample preparation
and basic characterizations.
In our experiment, the NM/EAC heterostructure is excited by
femtosecond pulses (duration of ∼25 fs, center wavelength
1030 nm, repetition rate 100 kHz). The excitation laser pulses
are generated through high-quality pulse compression enabled
by solitary beam propagation in periodic layered Kerr media.39,40
The laser beam is incident normally from the substrate side onto
the heterostructure along the −zdirection, and the beam radius
is focused to around 0.7 mm on the sample. The x−y−zco-
ordinates refer to the laboratory frame, while a,b, and care the
crystallographic axes. The polarization of the excitation laser
can be adjusted with a combination of wave plates to be either
linearly polarized with a polarization angle αin the x−yplane
or to be circularly polarized. The sample temperature can be
changed between 77 and 500 K. In the experiment, the orien-
tation of the RuO2or IrO2crystals is varied by growing the
sample on different substrates or by rotating the sample in-plane
around z. Hence, we define the polar angle θbetween the crystal
caxis and the zaxis, and the azimuthal angle φbetween the
projection of the caxis in the x−yplane and the xaxis
[see Figs. 1(a) and 1(b)]. Finally, the emitted terahertz wave-
forms are detected using a polarization- and time-resolved
terahertz spectroscopy setup based on electro-optic sampling
(EOS).41–43 The waveforms of the two orthogonal terahertz
polarizations (Exand Ey) can be resolved (see Appendix A).
Figure 1(b) presents the terahertz waveforms generated at
room temperature by a RuO2(10 nm) thin film, Pt (2 nm)/
RuO2(10 nm), and Pt (2 nm)/IrO2(10 nm) heterostructures,
in comparison with a spintronic terahertz emitter composed
of a Pt (2 nm)/Fe (2 nm) heterostructure whose conversion
efficiency has been optimized.9The signal from the spintronic
emitter was measured under an external magnetic field that
magnetizes the FM layer, while those from the RuO2thin film
and from the NM/EAC heterostructures were measured without
any external fields. In this measurement, the RuO2and IrO2
films are both (101)-oriented and are grown on the TiO2ð101Þ
substrates.
First of all, we find that capping RuO2with a 2 nm Pt layer
enhances the emitted terahertz amplitude by a factor of 10,
indicating the strong influence of the heterostructure on the
NIR-to-terahertz conversion. The Pt∕IrO2heterostructure can
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deliver terahertz amplitude about 3 times as strong as Pt∕RuO2.
Remarkably, the terahertz emission from Pt∕IrO2is almost as
strong as that from Pt/Fe, indicating high conversion efficiency.
The strength of this terahertz signal is comparable to those
generated by several commercial terahertz sources based on
nonlinear optical crystals and photoconductive switches.7,9,11
We also find that the terahertz spectra of different samples are
almost identical, as shown in Fig. 1(c).
Previous studies have shown that the ISHE in the NM layer
can cause deflection of spin-polarized currents, leading to sig-
nificant enhancement of terahertz generation in heterostructures,
such as those involving a laser-excited FM layer4,7–9and a ferri-
magnetic yttrium iron garnet layer driven by the spin-Seebeck
effect12 or an antiferromagnetic NiO layer with coherently
excited spin currents.15 The polarity and amplitude of the emit-
ted terahertz field are dependent on the spin-Hall angle (γ) of the
NM material. In Fig. 2(a), we investigate the influence of differ-
ent NM materials on terahertz emission from NM/EAC hetero-
structures. The terahertz-wave amplitudes, the spin-Hall angles
(γ), and the optical absorption coefficients (OACs) of different
NM materials are summarized in Fig. 2(b). Here the most im-
portant observation is that the terahertz-wave polarity from the
W∕RuO2heterostructure is not reversed, despite γof Wbeing of
opposite sign compared to that of Pt.7This behavior contrasts
with the spintronic emitter (see Sec. S2 in the Supplementary
Material). Further, we find that even though Cu has a small
spin-Hall angle, the terahertz amplitude from Cu∕RuO2is com-
parable to that from Pt∕RuO2[Fig. 2(b)]. These results therefore
(b)(a)
(d)
(c1) (c2) (c3) (c4)
Fig. 1 Experimental setup and terahertz signals. (a) Schematic of the experimental setup. The
x−y−zcoordinates are adapted to the laboratory frame and the lattice coordinates are labeled
as a−b−c. The crystal azimuthal angle φ, polar angle θ;and the laser-polarization angle αare
defined. Femtosecond-laser-induced electrons are injected from the NM layer, resulting in tran-
sient electron currents je
zalong z. In the experiment, the excitation pulse is primarily incident from
the EAC layer side. However, for ease of illustration, it is depicted as incident from the NM layer
side. Owing to the electrical anisotropy in the EAC layer, transverse electron currents (je
t) are
generated flowing at an angle of φrelative to the xaxis. Inset: illustration of superdiffusive electron
currents je
zinduced by laser-pulse excitation. (b) Schematic of the ellipsoid of conductivity tensor of
RuO2and IrO2in the laboratory frame, displaying anisotropy in electrical conductivities (σ∥<σ⊥).
The schematic uses the same coordinate and angle definitions as described in panel (a).
(c) Terahertz waveforms generated from (c1) Pt∕IrO2ð101Þ, (c2) Pt∕RuO2ð101Þ, (c3) RuO2ð101Þ,
and (c4) Pt/Fe devices. The signal from the RuO2ð101Þthin film is scaled 10 times for comparison.
(d) Terahertz spectra obtained via fast Fourier transform (FFT) of the waveforms in panel (c).
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clearly distinguish the conversion mechanism of the NM/EAC
heterostructures from ISHE.
In Figs. 2(c) and 2(d), the dependence of terahertz emission
on the polarization states of the excitation laser is further inves-
tigated. The RuO2crystal used in this measurement is (101)
oriented with its caxis fixed in the x−zplane at φ¼0 deg
[Fig. 1(a)]. The results show that the emitted terahertz wave
maintains a constant field amplitude and linear polarization
along x, when the polarization angle (α) of the linearly polarized
excitation laser is varied [Fig. 2(c)]. Note that this result is ob-
tained after correcting for the birefringent effect of the TiO2sub-
strate. The polarization-independent result is further confirmed
by samples grown on the Al2O3ð1102Þsubstrate, where the
optical birefringent effect is not present (see Sec. S4 in the
Supplementary Material). The Ex−Eyprojections of the tera-
hertz waves under different αare shown in the inset of Fig. 2(c).
Furthermore, there is almost no difference in the amplitudes or
waveforms of the terahertz signals excited by linearly and cir-
cularly polarized laser pulses [Fig. 2(d)]. Similar results can be
obtained from the Pt∕IrO2ð101Þheterostructures (see Sec. S8 in
the Supplementary Material), leading to the conclusion that the
terahertz generation from the NM/EAC emitters is not affected
by the polarization of the excitation laser.
It should be noted that the independence of terahertz
emission on the excitation-laser polarization rules out optical
rectification35,36 in the RuO2or IrO2crystals as the mechanism
for the NIR-to-terahertz conversion. This result is also distinct
from the recent Pt/NiO emitter,15 where the coherent spin-
current generation in NiO depends strongly on the laser polari-
zation. Instead, the polarization independence here is in line
with the spintronic emitters, where the terahertz emission is
initiated by the incoherent conversion of optical energy to
charge/spin currents.4,7This is further supported by the almost
identical terahertz spectra from the two different types of emitters
[see Fig. 1(c)], indicating similar carrier dynamics.
Nonetheless, our results strongly indicate that the efficient
NIR-to-terahertz conversion in the NM/EAC heterostructures
is nonmagnetic in origin. First, ISHE has been excluded. We
also find that the emitted terahertz waves are unaffected by
external magnetic fields (see Sec. S5 in the Supplementary
Material). Second, while RuO2is an itinerant antiferromagnetic
material,25,26 IrO2is known to be nonmagnetic.34 Nonetheless,
the emission properties from the two heterostructures are very
similar (see Sec. S8 in the Supplementary Material). Third,
the temperature-dependent results show that the terahertz-wave
amplitude from Pt∕RuO2ð101Þincreases monotonically up to
500 K (see Sec. S6 in the Supplementary Material), which is
higher than the reported Néel temperature of RuO2thin films.26
Since the OACs of RuO2and IrO2are more than 1 order of
magnitude smaller than that of the NM materials at the wave-
length of ∼1μm,44 we believe that the terahertz emission orig-
inates from the injection of charge currents from the optically
excited NM layer into the RuO2or IrO2crystals [see inset of
Fig. 1(a)]. This is supported by the fact that the general trend
(a) (b)
(c) (d)
Fig. 2 Effect of NM materials and laser polarization states. (a) Terahertz waveforms generated by
NM∕RuO2ð101Þdevices with NM materials of Ir, Cu, W, and Pt. The thickness of the NM layer is
2 nm. (b) Terahertz signal amplitude as a function of the NM materials used for the NM∕RuO2ð101Þ
devices (red bars). For comparison, OACs at the laser wavelength of 1.03 μm (blue bars) and spin-
Hall angles γ(green bars) of the respective NM materials are also shown. (c) Terahertz signal
amplitudes of the Exand Eycomponents from the Pt∕RuO2ð101Þdevice as a function of the
polarization angle αof the linearly polarized excitation laser. Inset: Ex−Eyprojection of the tera-
hertz waves for different values of α. (d) Terahertz waveforms from the Pt∕RuO2ð101Þdevice
excited by excitation pulses with linear, right- and left-circular polarizations.
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of the terahertz amplitude versus NM materials is in semi-
quantitative agreement with the OACs of the NM materials
[Fig. 2(b)]. Here our results also suggest that the thermally
driven Seebeck effect is unlikely to be responsible for the
charge-current injection. This is because the terahertz wave-
forms emitted from devices with different NM materials are
almost identical (see Fig. S2c in the Supplementary Material),
whereas distinctive temperature dynamics would be expected in
these metals after laser-pulse excitation (see Sec. S3 in the
Supplementary Material). Instead, we believe that the dominant
contribution to the interfacial charge currents comes from the
superdiffusive transport of the photoexcited high-energy elec-
trons20,21 prior to the thermalization process.
The observation of the x-polarized terahertz field indicates
the existence of a transverse charge current flowing along the
xdirection in our experimental setup [Fig. 1(a)]. We find that
this can be attributed to the anisotropic electrical conductivity
of single-crystal RuO2and IrO2. Due to the unequal lattice
parameters, the second-rank conductivity tensor is given by
σ⊥00
0σ⊥0
00σ∥!in the crystal coordinate (a−b−c), where
σ∥<σ⊥. By rotating the crystal under the azimuth angle φand
the polar angle θ, off-diagonal tensor components appear in the
laboratory coordinate: σxz ¼ðσ⊥−σ∥Þcos θsin θcos φand
σyz ¼ðσ⊥−σ∥Þcos θsin θsin φ, and the diagonal component
σzz becomes σzz ¼σ⊥sin2θþσ∥cos2θ(see Appendix B).
As a result, when the charge current (jz) is injected along −z
(electron current along z), the conductivity anisotropy leads
to the transverse charge current density of jx¼jzβ0cos φ
and jy¼jzβ0sin φ, where the coefficient of conductivity
anisotropy β0is given by β0≈ðσ⊥−σ∥Þcos θsin θ
σ⊥sin2θþσ∥cos2θwhen
ðσ⊥−σ∥Þcos θsin θ≪σ⊥sin2θþσ∥cos2θ. The amplitude
of the xðyÞ-polarized terahertz field ExðyÞis proportional to
the transverse currents jxðyÞ.
The above theory is confirmed by the experimental measure-
ments under different crystal orientations [(101), (110), (100),
and (001)], as shown in Fig. 3(a). We find that only when
the crystal orientation is (101) with θ¼34.7 deg can strong
terahertz emission be observed, and for φ¼0 deg, only the
x-polarized terahertz field is observed, because β0cos φ≠0
and β0sin φ¼0. On the other hand, when the caxis is either
aligned with z[(001) with θ¼0 deg] or in the x−yplane
[(100) or (110) with θ¼90 deg], the terahertz emission in both
polarizations is strongly suppressed, because β0¼0under these
conditions. Our results also show that when the crystal orienta-
tion is (101), the polarization of the emitted terahertz field
rotates following the azimuthal angle φ[Fig. 3(b)]. The peak
amplitudes are summarized in Fig. 3(c), and the sinusoidal
behaviors of the Exand Eyamplitudes are in excellent agree-
ment with β0cos φand β0sin φ, respectively.
The ability to convert jzto jx;y is characterized by β0of dif-
ferent materials, which is analogous in position to the spin-Hall
angle γwithin the ISHE formalism.4,45,46 In Table 1, we list the
experimentally measured σ∥and σ⊥of RuO2and IrO2, respec-
tively (see Appendix A). When the crystal orientation is (101),
we find that β0of IrO2is ∼5times that of RuO2. In Fig. 4(a),we
show that terahertz amplitudes from the Pt∕IrO2and Pt∕RuO2
structures both grow linearly as a function of the incident pump
(a)
(c)
(b)
Fig. 3 Effect of crystal orientations. (a) Exand Eycomponents of terahertz waveforms generated
by NM∕RuO2devices with different crystal orientations and polar angles θ. (b) Exand Eycom-
ponents of terahertz waveforms generated by Pt∕RuO2ð101Þat different azimuthal angles φwhile
keeping θfixed at 34.7 deg. (c) Terahertz signal amplitude of Exand Eycomponents from the
Pt∕RuO2ð101Þdevice at different azimuthal angles φ. The solid lines represent the sine and cosine
fitting to the results.
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fluence (F) when F<0.4mJcm
−2. Remarkably, the slope of
the linear increase of Pt∕IrO2is ∼4.8times that of Pt∕RuO2,
in excellent agreement with the ratio of β0between the two
materials. We note that, due to the low conductivity of RuO2
and IrO2, the impedance shunt effect only contributes ∼15%
of the difference in terahertz amplitudes (see Appendix C).
The NIR-to-terahertz conversion efficiency of the Pt∕IrO2het-
erostructure almost reaches that of Pt/Fe heterostructure. More
interestingly, the signal increases of these two structures both
deviate from a linear increase at F≈0.4mJcm
−2, while that
from the Pt∕RuO2structure continues to increase linearly at
high pump fluence. This behavior may be attributed to the con-
trasting temperature-dependent behaviors of the three structures:
when the laser excitation increases the sample temperature, the
terahertz signal from Pt∕RuO2increases monotonically with
the rising sample temperature up to 500 K, whereas those from
Pt∕IrO2and Pt/Fe structures both decrease (see Sec. S6 in the
Supplementary Material).
In Figs. 4(b) and 4(c), we plot the dependence of the terahertz
amplitudes as a function of the thickness of the EAC layer
(dEAC) and the NM layer (dNM ), respectively. Here we take
the Pt∕RuO2device as an example. Importantly, we find that
the terahertz amplitude gradually increases as dNM increases
from 0 and peaks at ∼2nm. This indicates that the deflection
of the charge currents is not caused by the interface effect. In
contrast, the terahertz amplitude as a function of dEAC exhibits
much slower variation, and the maximum terahertz signal is
generated when dEAC ≈7.5nm.
Quantitatively, when we fix the crystal orientation with
θ¼34.7 deg and φ¼0 deg, the amplitude of the x-polarized
terahertz field (Ex) is directly related to the z-integration of the
transverse charge current density (β0jz)by
7
ExðωÞ¼ZðωÞeZdEAC
0
dzβ0jzðz; ωÞ;(1)
where eis the elementary charge. Here ZðωÞis the effective
impedance of the heterostructure in the transverse direction
shunted by the adjacent substrate and air spaces, which is related
to the thickness of the EAC layer (dEAC) and the NM layer
(dNM) (see Appendix C). The longitudinal current density jz
is proportional to the density of the absorbed photons:
jz∝Fabs
dNMℏω0, where Fabs is the absorbed laser fluence of the
NM layer and ℏω0is the excitation photon energy. In addition,
the spatial distribution of jzthat contributes to the terahertz ra-
diation is localized near the heterostructure interface, due to the
finite hot-electron velocity-relaxation lengths in the EAC layer
(a) (b)
(c)
Fig. 4 Optimizing the conversion efficiency. (a) Terahertz signal amplitude as a function of inci-
dent laser fluence from the Pt∕RuO2ð101Þ,Pt∕IrO2ð101Þ, and Pt/Fe samples. The red and blue
dashed lines represent the linear fits to the low-fluence experimental results of Pt∕IrO2ð101Þand
Pt∕RuO2ð101Þ, respectively. The slope of the red dashed line is ∼4.8 times of that of the blue
dashed line. (b) Terahertz signal amplitude as a function of thickness of the RuO2layer (dEAC)
of the Pt∕RuO2ð101Þdevice. (c) Terahertz signal amplitude as a function of thickness of the
Pt layer (dNM) of the Pt∕RuO2ð101Þdevice. The solid lines in (b) and (c) represent a global fit
using the thickness-dependent model (see Appendix C).
Table 1 Longitudinal (σ∥) and transverse (σ⊥) conductivities,
crystal polar angles θ, and the coefficients of electrical anisotropy
β0of RuO2ð101Þand IrO2ð101Þ.
σ∥(×105Ω−1m−1)σ⊥(×105Ω−1m−1)θβ
0
RuO2ð101Þ8.13 8.63 34.7 0.028
IrO2ð101Þ3.18 4.22 35.0 0.139
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(λEAC) and the NM layer (λNM)(seeAppendix C). The best fits to
the experimental results are shown in Figs. 4(b) and 4(c) (solid
lines), which yield λRuO2≈3.2nmand λPt ≈1nmfor RuO2and
Pt, respectively. The latter is consistent with previous work.7
3 Discussion
Our study has demonstrated a nonmagnetic and nonrelativistic
mechanism for generating strong terahertz-wave emission by
directly harnessing laser-excited charge currents across nano-
scale interfaces. This approach utilizes the anisotropic electrical
conductivity of materials and eliminates the need for conversion
of charge currents to spin-polarized currents. Our results also
highlight the importance of using conductive materials to enable
efficient injection of laser-induced currents into the EAC layer.
This is supported by the fact that the Pt∕TiO2ð101Þheterostruc-
ture does not generate terahertz radiation [Fig. 4(c)], although
TiO2ð101Þis an insulator exhibiting similar crystal anisotropy.
Compared to the ISHE mechanism, this mechanism could
offer much higher conversion efficiency by selecting conductive
materials with large electrical anisotropy, whereas further
increasing the spin-Hall angle γof HM materials would be
difficult. For example, the conductivity in the basal plane of a
graphite thin layer is σ⊥≈106Ω−1m−1, while that normal to the
plane is σ∥≈50 Ω−1m−1.47 When charge currents are injected
with an angle of θ¼0.5 deg to 2 deg relative to the material
normal axis, the significant difference in conductivity could pos-
sibly lead to terahertz emission with an order of magnitude of
higher intensity compared to that from the Pt∕IrO2ð101Þdevice
in this study (see Sec. S7 in the Supplementary Material). This
could potentially be achieved by implementing a spatially
varying chemical vapor deposition method to create nanoscale
thickness gradients48,49 in the layered materials, thereby enabling
precise control over the current-injection angle θ. However,
special care must be taken to achieve a high-quality interface
between the NM and layered materials with thickness gradients
to suppress interfacial scattering.50
4 Appendix A: Experimental Details
Single-crystal RuO2and IrO2films were epitaxially grown on
the double-polished TiO2or Al2O3substrates by dc magnetron
sputtering at 500°C in a chamber with the base pressure better
than 2×10−8Torr. Both TiO2and Al2O3substrates were pre-
annealed at 500°C for 1 h before sample growth. Both RuO2and
IrO2films were grown by reaction sputtering in the mixed
atmosphere of Ar and O2with the ratio of 4:1. The normal
metals Pt, W, and Cu were deposited by dc magnetron sputtering
at room temperature.
In the terahertz experiment, we excited the sample with fem-
tosecond pulses (duration, 25 fs; center wavelength, 1030 nm;
pulse energy, 15 μJ; repetition rate, 100 kHz; and beam radius at
the sample, 0.7 mm) under normal incidence from the substrate
side. The terahertz electric field was subsequently detected by
EOS using a 300 μm-thick (110)-oriented GaP crystal, with the
two orthogonal components (Exand Ey) resolved using a broad-
band wire-grid polarizer. All the measurements were performed
in a dry air atmosphere. The details of the polarization-resolved
EOS setup can be found elsewhere.11
For the electrical measurements, the single-crystal RuO2ð100Þ
and IrO2ð100Þfilms were patterned into devices with two
orthogonal Hall bars through standard photolithography and
Ar-ion etching. The current can flow through either the crystal
aaxis or baxis. The width and the distance between the two
electrodes of the Hall bars are 150 and 600 μm, respectively.
The electrical measurements were carried out on a cryogenic
probe station (LakeShore EMPX-HF) at room temperature.
A dc current of 1 mA was injected into the longitudinal bar, and
the voltage was detected by a Keithley 2182A nanovoltmeter.
5 Appendix B: Electrical Anisotropic
Conductivity Tensor
Both RuO2and IrO2are rutile oxides with the P42/mnm space
group, where Ru/Ir atoms occupy the center of stretched oxygen
octahedrons. The conductivity tensor in the crystal coordinate that
satisfies the requirements of symmetric transformation is given by
σ
↔¼2
4
σ⊥00
0σ⊥0
00σ∥3
5:(2)
In the laboratory frame (x−y−z), the crystal orientation is
defined by the azimuthal angle φand the polar angle θ. The
conductivity tensor in the x−y−zcoordinate is given by
σ
↔0
xyzðθ;φÞ¼2
4
cos φ−sin φ0
sin φcos φ0
001
3
52
4
cos θ0−sin θ
01 0
sin θ0 cos θ3
52
4
σ⊥00
0σ⊥0
00σ∥
3
52
4
cos θ0 sin θ
010
−sin θ0 cos θ3
52
4
cos φsin φ0
−sin φcos φ0
001
3
5
¼2
6
4
ðσ⊥cos2θþσ∥sin2θÞcos2φþσ⊥sin2φðσ⊥cos2θþσ∥sin2θ−σ⊥Þsin φcos φðσ⊥−σ∥Þcos θsin θcos φ
ðσ⊥cos2θþσ∥sin2θ−σ⊥Þcos φsin φðσ⊥cos2θþσ∥sin2θÞsin2φþσ⊥cos2φðσ⊥−σ∥Þcos θsin θsin φ
ðσ⊥−σ∥Þcos θsin θcos φðσ⊥−σ∥Þcos θsin θsin φσ
⊥sin2θþσ∥cos2θ
3
7
5:
(3)
As a result, when charge currents are injected along
the −zdirection [electron currents je
zalong zin Fig. 1(a)],
transverse currents along the x- and y-directions can be
induced, with the conversion efficiency characterized by β0¼
ðσ⊥−σ∥Þcos θsin θ
σ⊥sin2θþσ∥cos2θþðσ⊥−σ∥Þcos θsin θ. When ðσ⊥−σ∥Þcos θsin θ≪
σ⊥sin2θþσ∥cos2θ, we obtain β0≈ðσ⊥−σ∥Þcos θsin θ
σ⊥sin2θþσ∥cos2θ.
6 Appendix C: Model for Thickness
Dependence of Terahertz Amplitude
To model the terahertz emission amplitude of the NM/EAC
bilayer, we make use of Eq. (1). The impedance of the bilayer
is given by
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ZðωÞ¼ Z0
nairðωÞþnTiO2ðωÞþZ0·Rd
0dzσðz; ωÞ;(4)
where ωis the terahertz frequency, Z0¼377 Ωis the vacuum
impedance, d¼dNM þdEAC is the total thickness of the heter-
ostructure, σðz; ωÞis the space-dependent sample conductivity,
and nair and nTiO2are the refractive indices at the terahertz fre-
quency of air and TiO2, respectively. As noted in Ref. 7, after
excitation by the pump pulse, the terahertz signal is only con-
tributed by the hot electrons injected from the NM layer that fall
within the electron diffusion length of the EAC layer, λEAC.
Similarly, only excited electrons within the diffusion length of
the NM layer, λNM, are able to propagate through the interface
without scattering. As a result, the terahertz radiation is caused
by the charge currents localized near the interface of the hetero-
structure.
Following the above assumptions and the formalism in
Ref. 51, we obtain the spatial distribution of the ballistic charge
current density inside the EAC layer by
jzðzÞ¼jiðdNMÞ
sinhz−dEAC
λEAC 
sinhdEAC
λEAC ;(5)
and the injected charge current density jiðdNM Þis proportional
to the zintegration of the photoexcited hot electron density over
the NM layer by considering λNM ,
jiðdNMÞ∝Fabs
dNMℏω0
tanhdNM
2λNM:(6)
By inserting Eqs. (4)–(6) into Eq. (1), we obtain
ExðωÞ∝Fabs
dNMℏω0
·Z0
nairðωÞþnTiO2ðωÞþZ0·ðσEACdEAC þσNM dNM Þ
·tanhdNM
2λNM·tanhdEAC
2λEAC;(7)
with the two diffusion lengths (λNM and λEAC) and a global
amplitude being the only free parameters. Here Fabs considers
only the absorbed fluence by the NM layer, which is also thick-
ness-dependent by considering the reflection and absorption
loss on the EAC layer and the NM layer,
Fabs ¼F·ð1−R1Þ·ð1−R2Þ·e−αNMdNM ·ð1−e−αEAC dEAC Þ;(8)
where R1and R2are the reflectivity of the EAC–air interface
and the EAC–NM interface, respectively. αNM and αEAC are the
OACs of the NM and the EAC materials, respectively. Most of
the optical and electrical parameters in the model can be deter-
mined by the literature values (see Sec. S3 in the Supplementary
Material) or by experimental measurements, leaving the hot-
electron velocity relaxation lengths7(λNM and λEAC) and a global
amplitude as the only free parameters. The fitting to the exper-
imental results in Figs. 4(b) and 4(c) yields λNM ≈1nm for
Pt and λEAC ≈3.2nmfor RuO2. The former is consistent with
previous work.7
Code, Data, and Materials Availability
All data in support of the findings of this paper are available
within the article or as Supplementary Material.
Acknowledgments
This work was accomplished at Fudan University. L.Z. and
Z.T. would like to acknowledge the support from the National
Key Research and Development Program of China (Grant
No. 2022YFA1404700). C.T. and Z.T. would also like to
acknowledge the support from the National Key Research and
Development Program of China (Grant No. 2021YFA1400200).
L.Z., C.T., Y.W., and Z.T. would like to acknowledge the
support from the National Natural Science Foundation of
China (Grant No. 12221004). Y.W. and Z.T. would also like
to acknowledge the support from the Shanghai Municipal
Science and Technology Basic Research Project (Grant
No. 22JC1400200). Y.W. would like to acknowledge the
support from the National Key Research Program of China
(Grant No. 2022YFA1403300), the National Natural Science
Foundation of China (Grant Nos. 11974079 and 12274083), and
the Shanghai Municipal Science and Technology Major Project
(Grant No. 2019SHZDZX01). L.Z. would like to acknowledge
the support from the Natural Science Foundation of Shanghai
(Grant No. 20JC1414601). Z.Y. would like to acknowledge
the support from the National Natural Science Foundation of
China (Grant No. 12174028). Z.T. would like to acknowledge
the support from the National Natural Science Foundation of
China (Grant No. 12274091). The authors declare no competing
interests.
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Chuanshan Tian is a professor in the Department of Physics and State
Key Laboratory of Surface Physics, Fudan University. His research group
has long been committed to the experimental exploration of surface and
interface physical and chemical phenomena, with a special focus on de-
veloping advanced nonlinear spectroscopy techniques to solve molecular
and electronic structures at interfaces related to renewable energy and
environmental issues.
Zhe Yuan is a professor in the Institute for Nanoelectronic Devices and
Quantum Computing, Fudan University. His research interests are mainly
focused on spintronics theory and first-principles calculations, including
spin transport and dynamics, magnetic materials, and the neuromorphic
computing algorithms implemented using spintronic devices.
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Lei Zhou is “XiDe”chair professor and head of the Department of
Physics at Fudan University. His main research focuses on the field of
nano-optics. In 2019, he was elected as a fellow of the Optical Society of
America, and won the second prize of Chinese National Natural Science
Award. He is the founding editor-in-chief of Photonics Insights, managing
editor of Nanophotonics, and serves on editorial boards for Physical
Review Materials and Opto-Electronic Science.
Yizheng Wu has been a professor in the Department of Physics and
State Key Laboratory of Surface Physics, Fudan University, since
2005. His research interests span multiple branches of magnetism and
spintronics, including thin film magnetism, antiferromagnetic spintronics,
spintronics terahertz emission, and spin-correlated transport in single
crystal systems.
Zhensheng Tao has been a professor in the Department of Physics and
State Key Laboratory of Surface Physics, Fudan University since 2018.
His research activities are devoted to the experimental study of ultrafast
optics and condensed matter physics, with a particular focus on the study
of ultrafast non-equilibrium light-matter interactions and the development
of ultrafast optical technologies.
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