††thanks: These authors contributed equally to the work.††thanks: These
authors contributed equally to the work.††thanks: email:
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# Ultrafast optical observation of spin-pumping induced dynamic exchange
coupling in ferromagnetic semiconductor/metal bilayer

X. Liu  Department of Applied Science, The College of William and Mary,
Williamsburg, Virginia, 23187, USA  P. Liu  Department of Applied Science, The
College of William and Mary, Williamsburg, Virginia, 23187, USA  H. C. Yuan
Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education),
Shanghai Ultra-precision Optical Manufacturing Engineering Research Center,
Department of Optical Science and Engineering, Fudan University, Shanghai,
200433, China  J. Y. Shi  Key Laboratory of Micro and Nano Photonic Structures
(Ministry of Education), Shanghai Ultra-precision Optical Manufacturing
Engineering Research Center, Department of Optical Science and Engineering,
Fudan University, Shanghai, 200433, China  H. L. Wang  S. H. Nie  State Key
Laboratory of Supperlattices and Microstructures, Institute of Semiconductors,
Chinese Academy of Sciences, Beijing, 100083, China  F. Jin  Z. Zheng  Key
Laboratory of Micro and Nano Photonic Structures (Ministry of Education),
Shanghai Ultra-precision Optical Manufacturing Engineering Research Center,
Department of Optical Science and Engineering, Fudan University, Shanghai,
200433, China  X. Z. Yu  J. H. Zhao  State Key Laboratory of Supperlattices
and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences,
Beijing, 100083, China  H. B. Zhao  Key Laboratory of Micro and Nano Photonic
Structures (Ministry of Education), Shanghai Ultra-precision Optical
Manufacturing Engineering Research Center, Department of Optical Science and
Engineering, Fudan University, Shanghai, 200433, China  G. Lüpke  Department
of Applied Science, The College of William and Mary, Williamsburg, Virginia,
23187, USA

###### Abstract

Spin angular momentum transfer in magnetic bilayers offers the possibility of
ultrafast and low-loss operation for next-generation spintronic devices. We
report the field- and temperature- dependent measurements on the magnetization
precessions in Co2FeAl/(Ga,Mn)As by time-resolved magneto-optical Kerr effect
(TRMOKE). Analysis of the effective Gilbert damping and phase shift indicates
a clear signature of an enhanced dynamic exchange coupling between the two
ferromagnetic (FM) layers due to the reinforced spin pumping at resonance. The
temperature dependence of the dynamic exchange-coupling reveals a primary
contribution from the ferromagnetism in (Ga,Mn)As.

##  I Introduction

There has been growing interest in the ultrafast optical manipulation of
magnetic dynamics in ferromagnetic heterostructures due to its potential
applications in advanced functional spintronic devices. The spin-pumping (SP)
effect, in which a spin-precessing ferromagnetic layer transfers its angular
momentum into another layer by a chargeless spin current, brings a new
mechanism for spin controlling and hence plays an important role in the design
of future spintronic devices.1  Since Heinrich, B. et al first reported the
spin-pumping effect as increased damping of the source layer in ferromagnetic
resonance (FMR) experiments 2  and a few FMR experiments on SP effect have
been performed on transition-metal multilayers 3 ; 4 ; 5 ; 6 , topological
insulators 7 ; 8  and semiconductors 9 ; 10 ; 11 . In addition, Danilov A. et
al. demonstrated that the mutual SP effect modifies the precession dynamics in
a pseudo spin-valve where magnetization precessions are excited simultaneously
in two FM layers by femtosecond laser pulses.12  However, no SP effect has
ever been observed yet for the heterostructure of a Heusler alloy and a
ferromagnetic (FM) semiconductor. Importantly, the hard and soft ferromagnetic
phases in such materials can potentially exhibit a dynamic exchange coupling
that is completely independent of the static exchange coupling due to spin
pumping. This could offer a possibility of ultrafast low-power control of spin
current for next-generation spintronic devices.

In this study, we investigate the magnetization precession dynamics of the
Heusler alloy Co2FeAl/FM semiconductor (Ga,Mn)As heterostructure as a function
of applied field and temperature by time-resolved magneto-optical Kerr effect
(TRMOKE). Analysis of the field-dependent effective Gilbert damping indicates
a clear signature of the enhanced dynamic exchange coupling between the two FM
layers due to a reinforced spin pumping. In addition, curvatures of the phase
shift as a function of applied field elucidate the dynamic exchange-coupling
model where the counter-precessing precessions are damped significantly at the
resonant frequency of the two FM layers. The magnetization precession in the
Co2FeAl layer transfers a pure spin current directly into the ferromagnetic
semiconductor (Ga,Mn)As layer without a nonmagnetic metal spacer. On the other
hand, the temperature-dependent results manifest a strong contribution from
the ferromagnetism of (Ga,Mn)As to the dynamic exchange-coupling effect. These
results provide valuable insight into the topic of dynamic exchange coupling
and the detection of spin current. Furthermore, they suggest a new pathway of
ultrafast spin manipulation in metal/semiconductor bilayer systems at low
power and therefore promote the development and design of future spintronic
devices.

##  II Results and Discussion

Figure 1: (a) Schematic of TRMOKE measurement geometry, depicting the
structure of the sample and the magnetization M precessing around the
effective field Heff in Co2FeAl/(Ga,Mn)As bilayer in a canted magnetization
configuration with H applied along hard axis [1-10]. (b) TRMOKE data from
Co2FeAl/(Ga,Mn)As bilayer under the different intensity of the applied field.
(c) FFT analysis for magnetization precession frequency under the different
intensities of the applied field, where the solid lines represent the FFT
peaks fitted by Lorentz functions.

The Co2FeAl/(Ga,Mn)As bilayer sample is grown on GaAs (001) substrates by
molecular-beam epitaxy (MBE). The thickness of Co2FeAl and Ga1-xMnxAs (x=0.07)
layer is 10 nm and 150 nm, respectively. The sample is capped with 2-nm thick
Al layer to avoid oxidation and contamination. The hard FM Co2FeAl exhibits an
in-plane uniaxial magnetic anisotropy with an easy axis along the [110]
direction (Fig. 1(a)), whereas the easy axis of the soft FM (Ga,Mn)As is along
the [1-10] direction below its Curie temperature $T_{c}$ = 50 K.13  Reflection
high-energy electron diffraction (RHEED) patterns, high-resolution double-
crystal x-ray diffraction (DCXRD) measurements, and high-resolution cross-
sectional transmission electron microscopy (HRTEM) reveal high-quality,
single-crystalline, epitaxial growth of the Co2FeAl and (Ga,Mn)As thin
films.13  At low temperatures ($T<T_{c}$), a ferromagnetic alignment of local
Mn moments in the (Ga,Mn)As layer is expected, whereas at high temperatures
($T>T_{c}$) the Mn ions extending a few nanometers from the interface remain
spin-polarized due to the ferromagnetic proximity effect.13

Figure 1(a) shows the experimental geometry of TRMOKE measurements. Field-
dependent TRMOKE measurements are performed on the Co2FeAl/(Ga,Mn)As bilayer
sample from 7 K to 300 K utilizing 100-fs pump and probe pulses at 800 nm
wavelength with a repetition rate of 80 MHz. The external magnetic field is
set along the easy-hard axis [100] of the Co2FeAl layer and the pump fluence
is set at $I$ = 5 $\mu$J/cm2. The probe pulses utilize the balanced detection
technique with a half-wave plate and Wollaston prism to investigate the
transient magnetic state change along longitudinal and polar directions.
Figure 1b displays the TRMOKE data at 10 K with an in-plane magnetic field
scanning from 366 Oe to 550 Oe. The precession signals can be well fitted by a
damped-harmonic function with a linear background:
$\theta_{k}=a_{0}+b_{0}t+A\textrm{ exp}\left(-t/\tau\right)\textrm{
sin}\left(2\pi ft+\varphi_{0}\right)$ , where $a_{0}+b_{0}t$ represents the
linear background, $A$ is the precession amplitude, $\tau$ is the relaxation
time, f is the precession frequency and $\varphi_{0}$ is the phase. The
magnetization precession decays with different relaxation times, with the
fastest decay at 458 Oe. This indicates that a dynamic exchange coupling may
occur between the magnetization precession in the Co2FeAl layer and the
(Ga,Mn)As layer. Here, only one frequency can be extracted from FFT analyses,
as seen in Fig. 1(c), coherent spin precession of (Ga,Mn)As decays fast and
thus vanishes very shortly.

The magnetization precession in the Co2FeAl/(Ga,Mn)As bilayer system is
described by the following modified Landau-Lifshitz-Gilbert(LLG) equation with
an additional spin-torque term:

$\frac{d\mathbf{M}}{dt}=-\gamma\mathbf{M}\times\mathbf{H_{eff}}+\alpha_{0}\mathbf{M}\times\frac{d\mathbf{M}}{dt}+\alpha_{sp}\left(\mathbf{M}\times\frac{d\mathbf{M}}{dt}-\mathbf{M}^{\prime}\times\frac{d\mathbf{M}^{\prime}}{dt}\right)$

where $\mathbf{M}$ is the magnetization direction of the Co2FeAl layer,
$\gamma$ is the gyromagnetic ratio, $\alpha_{0}$ is the intrinsic Gilbert
damping constant, and $\mathbf{H_{eff}}$ is the effective magnetic field in
the Co2FeAl layer including the external magnetic field, the demagnetization
field, the anisotropy field, and the exchange-coupling field. The last term
describes the spin torque which acts on both layers as a bidirectional effect,
in which $\alpha_{sp}$ represents the contribution of spin pumping to the
damping and $\mathbf{M}^{\prime}$ denotes the magnetization of (Ga,Mn)As.
Then, the effective Gilbert damping can be obtained from the relaxation time
$\tau$, using 14 ; 15

$\alpha=2/\left(\tau\gamma\left(H_{a}+H_{b}\right)\right)$

where $H_{a}$ and $H_{b}$ are determined in our previous analysis, which
includes the out-of-plane, in-plane uniaxial, crystalline cubic,
unidirectional and rotatable magnetic anisotropies.15

Figure 2: (a) Effective Gilbert damping constant as a function of externally
applied field at different temperatures from 10 K to 50 K. (b) Red rectangular
solids denote the peak (or strongest if not peak) Gilbert damping from 10 K to
50 K. Blue circle solids are the corresponding fields as a function of
temperature. (c) Illustration of photo-excited exchange-coupling torque and
spin-pumping generated dynamic exchange-coupling mode for damping.

Figure 2(a) shows the temperature-dependent Gilbert damping as a function of
the external field. At $T$ = 10 K, the damping of the magnetization precession
is most pronounced with an external field $H$ = 458 Oe. Below the Curie
temperature ($T_{c}$ = 50 K) of (Ga,Mn)As, the damping peak first shifts from
450 Oe to 650 Oe with the temperature increasing from 10 K to 35 K, as
summarized in Fig. 2(b) insert, and then gradually becomes inconspicuous and
finally disappears at $T=T_{c}$. Such a temperature dependency clearly shows
that the damping peak only exists when the ferromagnetism of (Ga,Mn)As is
well-developed. Meanwhile, the strongest Gilbert damping extracted across all
the fields as a function of temperature (Fig. 2(b)) shows a transition
temperature close to $T_{c}$. This manifests the crucial role of spontaneous
(Ga,Mn)As magnetization in the damping of magnetization precession of Co2FeAl.

The ultrafast pump excitation causes a transient enhancement of exchange
coupling,15  which induces a dynamic exchange-coupling torque acting on both
Fe(Co) spins and Mn spins. In such a case, as shown in Fig. 2(c), the
magnetizations of both FM layers are suddenly pulled towards each other and
start to precess with opposite angular momentum along their own equilibrium
directions. At the resonance, i.e., $f_{CFA}=f_{GMA}$, the precessing
magnetization of Co2FeAl “pumps” a spin current $I_{i}$ directly into the
(Ga,Mn)As layer, which exerts a torque onto the (Ga,Mn)As magnetization and
thereby counteracts its precession. Meanwhile, this spin current $I_{i}$
carries an outflow of angular momentum from the Co2FeAl layer and leads to
damping to its magnetization precession. In other words, the spin current
reinforces the $M$ damping for both FM layers at the resonance. Technically,
there should also be a spin current $I_{j}$ injecting into the Co2FeAl layer
from the magnetization precession of (Ga,Mn)As. 2  However, such a spin
current should be much smaller than that from the Co2FeAl layer.

Figure 3: Phase of magnetization precession as a function of externally
applied field at different temperatures from 10 K to 50 K (a), and zoomed
specifically at 10 K (b). (c) TRMOKE data as a function of normalized
precession phase under different applied fields. The red straight line is a
guideline of the phase shift.

In addition to the discussion on damping, the dynamic exchange coupling
between the two FM layers can also be evinced by the field-dependency of the
precession phase. Fig. 3(a) shows that from 10 K to 35 K, the phase drops down
dramatically around certain field windows that correspond to the Gilbert
damping peaks, which move to higher field ranges as temperature increases.
When $T>$ 30 K, the dramatic phase shift becomes less contrastive and then
completely disappears when $T=T_{c}$. We notice that similar features of
phase-shifting are reported in the FMR experiments on similar hard/soft FM
systems.16 ; 17  The observed 30° – 40° phase shift at 10 K, as shown in Fig.
3(c), is comparable with those of the dynamic exchange-coupling spin-valve
structures.7 ; 16 ; 17 ; 18 ; 19

##  III Conclusion

In summary, we have studied the dynamics of the magnetization precession of
Co2FeAl/(Ga,Mn)As heterostructure as a function of applied field and
temperature. The pronounced peaks in effective Gilbert damping of Co2FeAl
magnetization precession reveal the enhanced dynamic exchange coupling between
the two FM layers due to spin pumping. The corresponding field-dependency of
phase shift, which corresponds to that of the Gilbert damping, confirms the
counter-precessing exchange-coupled model where both precessions are damped
significantly at the resonance. In addition, the temperature-dependent results
manifest a strong contribution from the ferromagnetism in (Ga,Mn)As to the
dynamic exchange-coupling effect. These results provide valuable insight into
the topic of dynamic exchange coupling and the detection of spin current.
Mover, they suggest a novel route of ultrafast low-power spin manipulation in
metal/semiconductor bilayer system and hence promote the research of the
future spintronic devices.

##  IV Methods

MOKE experiments. The magnetization of the exchange-coupled Co2FeAl/(Ga,Mn)As
bilayer is measured using a longitudinal MOKE setup. The sample is illuminated
with p-polarized light and the reflected s-polarized light is detected with a
photodiode. The magnetic field is applied along the in-plane [110] or [-110]
crystallographic directions. The measurements are conducted from 5 K to above
room temperature.

TRMOKE experiments. For the pump-probe TRMOKE measurements, a Ti:sapphire
oscillator laser system is employed, which produces 150-fs pulses at 800-nm
wavelength with a repetition rate of 80 MHz. The probe(pump) fluence is fixed
at $\sim$0.5(5) $\mu$J/cm2. The probe pulses ($\lambda=800$ nm) use the
balanced detection approach with a half-wave plate and Wollaston prism to
investigate the transient magnetic state change along longitudinal and polar
directions. The measurements are conducted from 5 K to above room temperature.

##  V Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

##  VI Acknowledgments

The work at the College of William and Mary was sponsored by the DOE through
Grant No. DEFG02-04ER46127. The work at the Department of Optical Science and
Engineering, Fudan University, was supported by the National Natural Science
Foundation of China with Grant No. 11774064, National Key Research and
Development Program of China (Grant No. 2016YFA0300703), and National Key
Basic Research Program (No. 2015CB921403). The work at the State Key
Laboratory of Superlattices and Microstructures, Institute of Semiconductors,
Chinese Academy of Sciences, was supported by National Natural Science
Foundation of China with Grant No. U1632264.

##  VII Author Contributions

X. L., P. L., H. C. Y, J. H. Z., H. B. Z., and G. L. designed and analyzed the
experiments. H. L. W., S. H. N., J. Y. S., and X. Z. Y. prepared the samples
and carried out characterizations using MOKE, RHEED, and SQUID measurements.
H. C. Y., J. Y. S., X. L., P. L., and F. J. performed the TRMOKE experiments.
X. L., P. L., H. C. Y. and J. Y. S. conducted the data analysis and
simulations. All authors discussed the results. X. L., P. L., J. H. Z., H. B.
Z., and G. L. wrote the manuscript with contributions from all authors.

##  VIII Competing Interests

The authors declare no competing financial interests.

## References

  * (1) Tserkovnyak, Y. _et al._ Enhanced Gilbert damping in thin ferromagnetic film.  _Phys. Rev. Lett._ 88, 117601 (2002).
  * (2) Heinrich, B. _et al._ Dynamic exchange coupling in magnetic bilayers.  _Phys. Rev. Lett._ 90, 187601 (2003).
  * (3) Stenning, G. B. G. _et al._ Magnetization dynamics in an exchange-coupled NiFe/CoFe bilayer studied by x-ray detected ferromagnetic resonance.  _New J. Phys._ 17, 013019 (2015).
  * (4) van der Laan, G. _et al._ Time-resolved X-ray detected ferromagnetic resonance of spin currents.  _J. Electron Spectrosc._ 220, 137-146 (2017).
  * (5) Saitoh, E. _et al._ Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect.  _Appl. Phys. Lett._ 88, 182509 (2006).
  * (6) Costache, M. V. _et al._ Electrical detection of spin pumping due to the precessing magnetization of a single ferromagnet.  _Phys. Rev. Lett._ 97, 216603 (2006).
  * (7) Figueroa, A. I. _et al._ Spin pumping through a topological insulator probed by x-ray detected ferromagnetic resonance.  _J. Magn. Magn. Mater._ 400, 178-183 (2016).
  * (8) Shiomi, Y. _et al._ Spin-electricity conversion induced by spin injection into topological insulators.  _Phys. Rev. Lett._ 113, 196601 (2014).
  * (9) Shikoh, E. _et al._ Spin-pump-induced spin transport in p-type Si at room temperature.  _Phys. Rev. Lett._ 110, 127201 (2013).
  * (10) Žutić, I. & Dery, H.  Spintronics: Taming spin currents.  _Nat. Mater._ 10, 647 (2011).
  * (11) Ando, K. _et al._ Electrically tunable spin injector free from the impedance mismatch problem.  _Nat. Mater._ 10, 655 (2011).
  * (12) Danilov, A. P. _et al._ Optically excited spin pumping mediating collective magnetization dynamics in a spin valve structure.  _Phys. Rev. B_ 98, 060406 (2018).
  * (13) Nie, S. H. _et al._ Ferromagnetic interfacial interaction and the proximity effect in a Co2FeAl/(Ga,Mn)As bilaye.  _Phys. Rev. Lett._ 111, 027203 (2013).
  * (14) Zhao, H. B. _et al._ Ultrafast magnetization dynamics of epitaxial Fe films on AlGaAs (001).  _Appl. Phys. Lett._ 86, 152512 (2005).
  * (15) Liu, X. _et al._ Ultrafast enhancement of interfacial exchange coupling in ferromagnetic bilayer.  __, arXiv:2203.00293 ().
  * (16) Marcham, M. K. _et al._ Phase-resolved x-ray ferromagnetic resonance measurements of spin pumping in spin valve structures.  _Phys. Rev. B_ 87, 180403 (2013).
  * (17) Baker, A. A. _et al._ Anisotropic absorption of pure spin currents.  _Phys. Rev. Lett_ 116, 047201 (2016).
  * (18) Li, J. _et al._ Direct detection of pure ac spin current by x-ray pump-probe measurements.  _Phys. Rev. Lett_ 117, 076602 (2016).
  * (19) Baker, A. A. _et al._ Spin pumping in magnetic trilayer structures with an MgO barrier.  _Sci. Rep._ 6, 35582 (2016).