Ultrafast Quenching of Ferromagnetism in InMnAs \\ Induced by Intense Laser Irradiation
J. Wang
$^{1,\dagger}$ C. Sun
$^1$ J. Kono
$^{1,\ddagger}$ A. Oiwa
$^{2,\sharp}$ H. Munekata
$^3$ \L. Cywi{\'n}ski
$^4$
Time-resolved magneto-optical Kerr spectroscopy of ferromagnetic InMnAs reveals two distinct {\em demagnetization} processes --- fast ($<1$ ps) and slow ($\sim$100 ps). Both components diminish with increasing temperature and are absent above the Curie temperature. The fast component rapidly grows with pump power and saturates at high fluences ($>10$ mJ/cm$^2$); the saturation value indicates a {\em complete quenching} of ferromagnetism on a sub-picosecond time scale. We attribute this fast dynamics to spin heating through $p$-$d$ exchange interaction between photo-carriers and Mn ions while the $\sim$100 ps component is interpreted as spin-lattice relaxation.
quenching-resub-vf.tex
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\begin{document}

\title{Ultrafast Quenching of Ferromagnetism in InMnAs \\ Induced
by Intense Laser Irradiation}

\author{J. Wang,$^{1,\dagger}$ C. Sun,$^1$ J.
Kono,$^{1,\ddagger}$ A. Oiwa,$^{2,\sharp}$ H. Munekata,$^3$
\L. Cywi{\'n}ski,$^4$}\author{L. J. Sham$^4$}
\affiliation{$^1$Department of Electrical and Computer
Engineering, Rice Quantum Institute, and Center for Nanoscale
Science and Technology, Rice University, Houston, Texas 77005,
U.S.A.\\ $^2$PRESTO, Japan Science and Technology Agency, 4-1-8
Honcho, Kawaguchi 332-0012, Japan\\
 $^3$Imaging Science and
Engineering Laboratory, Tokyo Institute of Technology, Yokohama,
Kanagawa 226-8503, Japan\\ $^4$Department of Physics, University
of California, San Diego, La Jolla, California 92093, U.S.A.}

\date{\today}

\begin{abstract}
Time-resolved magneto-optical Kerr spectroscopy of ferromagnetic
InMnAs reveals two distinct {\em demagnetization} processes
--- fast ($<1$ ps) and slow ($\sim$100 ps).  Both components
diminish with increasing temperature and are absent above
the Curie temperature.  The fast component rapidly grows with
pump power and saturates at high fluences ($>10$
mJ/cm$^2$); the saturation value indicates a {\em complete
quenching} of ferromagnetism on a sub-picosecond time scale. We
attribute this fast dynamics to spin heating through $p$-$d$
exchange interaction between photo-carriers and Mn ions while
the $\sim$100 ps component is interpreted as spin-lattice
relaxation.

\end{abstract}
\pacs{78.20.-e, 78.20.Jq, 42.50.Md, 78.30.Fs, 78.47.+p}
\maketitle

%\tableofcontents
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
There is much current interest in dynamical processes in
{\em magnetically-ordered} systems, both from scientific
and technological viewpoints \cite{ZhangetAl02book}. Pumping
a magnetic system with ultrashort laser pulses can strongly
alter the equilibrium among the constituents (carriers, spins,
and the lattice), triggering a variety of dynamical
processes.  Studying these processes can provide estimates for
the time scales / strengths of the various interactions.
Both metallic and insulating magnets have been studied,
%using
%ultrafast optical and magneto-optical spectroscopies,
exhibiting an array of new phenomena.
%\cite{BeaurepaireetAl96PRL,HohlfeldetAl97PRL,ScholletAl97PRL,AeschlimannetAl97PRL,JuetAl98PRB,Beaurepaire1etAl98PRB,GuddeetAl99PRB,KoopmansetAl00PRL,ZhangetAl00PRL,KiseetAl00PRL,BertottietAl01PRL,GuidonietAl02PRL,KimeletAl02PRL,KimeletAl04Nature,DuongetAl04PRL,JuetAl04PRL}.
In particular, the discovery of {\em ultrafast demagnetization}
\cite{BeaurepaireetAl96PRL} suggested an ultrafast scheme for
magneto-optical data writing. At the same time, exactly how a
laser pulse can effectively change the magnetic moment is a
matter of debate
\cite{KoopmansetAl00PRL,GuidonietAl02PRL,ZhangetAl00PRL,Beaurepaire1etAl98PRB}.
%In extreme cases, intense laser pulses were shown to
%increase the
%electron temperature to even above the Curie temperature,
%drive a ferromagnetic to paramagnetic phase transition in the
%femtosecond time scale \cite{Beaurepaire1etAl98PRB}.

Despite the large number of studies performed to date, the
microscopic understanding of effective energy transfer channels
among the subsystems is still elusive.  This is partially due to
the fact that, in the case of metallic ferromagnets, the
distinction between the ``carriers'' and ``spins'' is subtle, as the itinerant electrons contribute both to transport and magnetism.
%In turn
%direct microscopic coupling between the electronic orbital
%degree  of freedom and the collective spins, leading to the
%extremely fast demagnetization on the order of  femtosecond time
%scale, is not well understood.
On the other hand, antiferromagnetic insulators have
shown much slower dynamics, typically on the order of hundreds
of ps \cite{KimeletAl02PRL}, although femtosecond
demagnetization has been predicted \cite{GomezAbaletAl04PRL},
and ultrafast control of magnetism using off-resonance excitation
has been shown experimentally \cite{KimeletAl05Nature}.
%A recent promising experiment \cite{KimeletAl05Nature}, however, demonstrated the possibility of ultrafast control of magnetism in an anti-ferromagnetic insulator using off-resonance excitations.
%Thus, further systematic experimental
%studies exploring the more experimental parameters, e.g., pump
%fluence and lattice temperature, on other more controlled
%environments are strongly desired.
Carrier-mediated ferromagnetism in (III,Mn)V semiconductors
provides an interesting alternative for this type of study.
%, there
%has been intense interest exploring static collective magnetic
%ordering and spin dynamics in semiconductors
%\cite{Awschalometal02book}.
Unlike in ferromagnetic metals, there is a clear distinction
between mobile carriers (holes) and localized spins (Mn ions),
and ferromagnetic order is realized through their strong
coupling ($p$-$d$ exchange interaction). This coupling in turn
makes the magnetic order sensitive to carrier density changes
via external perturbations
\cite{Koshiharaetal97PRL,Oiwaetal01APL,Oiwaetal02PRL,ChibaetAl03Nature}.
%The physical
%situation is illustrated in Fig.~\ref{schemesetup}, where three
%subsystems (collective spins, carriers and lattice) are
%differentiated. The coupling to ferromagnetism (collective spin
%system) can occur via spin-lattice interaction, similar to the
%conventional picture of laser-induced demagnetization, e.g., in
%magneto-optical recording.
%More intriguingly, the coexistence
%and mutual interplay of localized  collective spins and
%delocalized carriers in (III,Mn)Vs provides a unique physical
%scenarios to investigate photoinduced magnetization dynamics,
%whose underlying physics   is rarely addressed on other
%platforms, such as insulating or metallic magnets.

%Untill now, (III,Mn)V ferromagnets have been studied quite
%extentively using static optical or transport methods;
%time-domain magneto-optical spectroscopy has been rarely
%attempted and has not proven  to be a powerful probe.
In this Letter we describe time-dependent magneto-optical studies
of laser-induced demagnetization dynamics in ferromagnetic
semiconductor InMnAs.  We observed a rapid ($<1$ ps) drop of
magnetization along with a slower demagnetization process on the
order of $\sim$100 ps. Both demagnetization components show
strong temperature and pump power dependence.  At high pump
fluences and under external magnetic fields, a complete
quenching of the ferromagnetic phase occurs, which appears as
a saturation of the photoinduced Kerr rotation with pump
fluence.  We attribute the observed fast and slow processes to
the manifestations of hole-localized spin and spin-lattice
interactions, respectively.

The main sample studied was an In$_{0.87}$Mn$_{0.13}$As(25
nm)/GaSb(820 nm) heterostructure with Curie temperature $\sim$60
K, grown by low-temperature molecular beam epitaxy on a
semi-insulating GaAs (100) substrate \cite{SlupinskietAl02JCG}.
Taking into account the electrical  and magnetic influences of
interstitial Mn ions which are  supposed to be double donors and
couple antiferromagnetically  with substitutional Mn ions
\cite{BlinowskietAl03PRB,WangetAl04JAP,EdmondsetAl05PRB}, the
hole density $p$ was extracted analytically from
the saturation magnetization data of the ferromagnetic
component. In the present sample, $p \simeq$ $4 \times 10^{20}$
cm$^{-3}$,
%with  numbers of substitutional and interstitial Mn ions of $1.7 \cdot 10^{20}$ cm$^{-3}$ (73\% of [Mn]) and $6.5 \cdot 10^{20}$ cm$^{-3}$ (27\% of  [Mn]), respectively. This gives the concentration $10^{21}$ cm$^{-3}$ of Mn spins participating in ferromagnetic order.
and the density of Mn spins participating in
ferromagnetic order is $\simeq 10^{21}$ cm$^{-3}$.

The two-color time-resolved magneto-optical Kerr effect
(MOKE) spectroscopy setup used consisted of an
optical parametric amplifier (OPA) pumped by a Ti:Sapphire-based
regenerative amplifier (Model CPA-2010, Clark-MXR, Inc.).
% The OPA was able to produce
%tunable and intense radiation from 522 nm to 20 $\mu$m using different
%mixing crystals.
The OPA pump beam, which was linearly polarized and tuned to 2
$\mu$m, excited transient carriers near the band edge of InMnAs
and a very small fraction ($\sim$10$^{-5}$) of the regenerative
amplifier beam (775 nm) was used as a probe; the high photon
energy of the probe ensured to diminish the ``dichroic
bleaching'' effects \cite{KoopmansetAl00PRL} due to the pump
excited carriers.
%The two beams were made parallel and then focused
%onto the sample mounted inside a cryostat.
%MOKE and reflectivity were monitored simultaneously.
%The MIR pump was modulated by an optical
%chopper with a half harmonic of the laser repetition rate
%($\sim$ 500 Hz). We recorded the intensity difference between
%adjacent reflected NIR probe pulses, both the $s$- and
%$p$-components, as well as as a function of time delay and
%magnetic field.   Two boxcars, locked to the laser reference
%and synchronized with each laser shots, were used to
%simultaneously detect two different polarization states of the
%probe,   namely $s$ and $ p$, with and without pump for the
%adjacent pulses. This scheme has unique advantage capable of
%extracting the transient Kerr rotation angle and differential
%reflectivity from the further computation of same sets of raw
%data.
%More details about the setup can be found elsewhere
%\cite{WangetAl04JMO}.

%%%%%  FIG. 1  %%%%%
\begin{figure}[floatfix]
\includegraphics [scale=0.6] {fig1.eps}  % 0.65
\caption{(a) The first 3 picoseconds of demagnetization dynamics
in InMnAs/GaSb.  Also shown is the cross-correlation between the
pump and probe pulses.  (b) Demagnetization dynamics convering
the entire time range of the experiment (up to $\sim$1 ns).
There is a slow demagnetization process, which follows the fast
component shown in (a) and completes only after $\sim$100 ps.}
\label{typical}\end{figure}
%%%%%%%%%%%%%%%%%%%%

%Recent demonstrations of voltage-tuned (7) and photoinduced (8-10) alteration
%of ferromagnetism have provided a prototype for building novel photon-spin
%combined devices.


%%%%%%%%%%%% FIG. 1 %%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}
%\includegraphics [scale=0.4] {schemesetup1.eps}
%\caption{Physical pictures showing the path ways leading to
%ultrafast demagnetization in ferromagnetic $p$-InMnAs (a) as
%well as our experimental scheme (b).  It is worth of pointing
%out that, besides the conventional demagnetization mechanism via
% spin-lattice interaction, much faster spin transfer could occur
%through strong ferromagnetic  $p-d$ exchange coupling between
%mobile holes and the localized magnetic moments. In our
%experiment, we selectively pump the sample with 2 $\mu$m
%mid-infrared pulses with photon energy larger than the InMnAs
%band gap but smaller than the GaSb band gap, creating transient
%carriers near the bandedge of the magnetic layer.  Weaker
%near-infrared pulses (775 nm), with photon energy  far above the
%quasi Fermi energy of optical excitation, probe the
%time-dependant ferromagnetism via Kerr rotation. HWP: half
%wavelength plate; WP: Walloston prism; f$_rep$ represents the
%repetition rate from the regenerative amplifier. }
%\label{schemesetup} \end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Using a low repetition-rate laser (50 Hz $-$ 1 kHz) with a short pulse width
%($\sim$150 fs) allowed us to probe the regimes of low average power (minimum
%thermal effect) and high peak fluence (maximum transient carrier density).
%This differentiates our study from previous time-domain magneto-optical
%studies.\cite{zhang,beaurepaire}

% create carriers near the band edge of InMnAs with 0.2 eV extra
%kinetic energy to minimize the effects from the buffer layer and some purely nonlinear optical
%response, such as inter- or intra-valley scattering. A near-infrared (NIR) (775 nm) probe beam
%from a chirped pulse amplifier (Clark CPA-2010) was used to probe the energy
%levels far above the quasi-Fermi level of the optically excited carriers.
%Exploiting the lasers with low-duty cycle (50 - 1K Hz) and ultrashort pulse width ($\sim$ 150 fs) allows us to probe
%the regimes of low average power (minimum
%thermal
%effects) and high peak fluence (maximum transient carrier density $\sim$ 10$^{19}$ cm$^{-3}$, comparable to or larger
%than the background carrier density).
%, which makes our study in strong contrast to previous time-domain magneto-optical studies [1- 4].
%Under our pumping conditions, the maximum density of photocreated carriers are estimated to be comparable
%to or larger than the background carrier density ($\sim$ 10$^{19}$ cm$^{-3}$), and, hence,
%significant modifications in exchange interactions can be expected.

%%%%%%%%%%%% FIG. 2 %%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}
%\includegraphics [scale=0.5] {DR-MOKE.eps}
%\caption{Temporal evolution of differential reflectivity (top)
%and the normalized Kerr rotation (bottom) in InMnAs/GaSb
%ferromagnetic semiconductor heterosructure, plotted in log
%scale.  Inset represents initial decay of  the photo-induced
%Kerr rotation as a function of time delay, in linear scale.  The
%data were  taken 16 K under an external magnetic field of 170 mT.
%The photoinduced Kerr rotation   $\triangle \theta
%_{k}=1/2[\triangle \theta _{k}(-M)-\triangle \theta _{k}(M)]$
%was measured   by changing the sign of external magnetic field.}
%\label{DR-MOKE} \end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Typical data showing the general temporal profile of
the photoinduced Kerr angle change, $\Delta\theta_K$, is shown in
Fig.~\ref{typical}, for the first three ps [in (a)] and the
entire time range [in (b)].
%The transient reflectivity shows a quick
%disappearance of initial negative transients and sign reversal,
%which is due to the trapping of photogenerated carriers as we
%discussed elsewhere \cite{Wangetal03JSC}.  The quick
%disappearance of the negative transient indicates the free
%electron life time of InMnAs $\sim$ 1 ps. One the other hand,
The sign of $\Delta\theta_K$ is always negative, indicating
transient {\em demagnetization}. Distinct temporal
regimes can be identified: an initial
($<$ 1 ps) reduction in magnetization is followed by a slow
and gradual decrease (up to $\sim$100 ps), a
plateau region (up to $\sim$500 ps), and, finally, an
increase (i.e., recovery) toward the equilibrium value.  Also
shown in Fig.~\ref{typical} is the cross-correlation trace
between the pump and probe pulses, showing that the
initial ultrafast demagnetization is occuring even
faster than our time resolution ($\sim$220 fs).

%%%%%%%%%%%%% FIG. 3 %%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}
%\includegraphics [scale=0.4] {power1.eps}
%\caption{Time evolution of photo-induced Kerr rotation as a
%function of pump fluence.  (a)  The curves are vertically
%displaced for clarity, representing the pump fluences of 0.35,
%0.9, 1.8, 3.5, 7  and 10.5 mJ/cm$^2$, respectively (from bottom
%to top).  (b) The temporal profiles of the normalized Kerr
%rotation angle at high pump fluences, 10.5, 12 and 14 mJ/cm$^2$,
%respectively.  (c) MOKE signals vs. power at different time
%delays, corresponding to 5 ps, 20 ps and 80 ps, respectively.
%Lack of slower demagnetization component at high pump fluence
%($>$ 10.5 mJ/cm$^2$) reflects a dynamic ferro- to paramagnetic
%phase transition.  The data were taken at 20K.
%A ferromagnetic loop ``opens up''
%horizontally as soon as the photoinduced signal are gone [shown in (a)].
%}
%\label{power}
%\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%  FIG. 2  %%%%%
\begin{figure}
\includegraphics [scale=0.6] {fig2.eps}  % 0.65
\caption{(a) Steady-state MOKE angle versus magnetic
field, taken with a 775-nm laser diode. (b)
Magnetic field dependence of ultrafast demagnetization dynamics.
 The sign of the MOKE angle change depends on the direction of
the applied magnetic field in a symmetric manner, as expected.
(c) Comparison between MOKE and MCD dynamics, showing no time
lag between them.} \label{mag-dep}\end{figure}
%%%%%%%%%%%%%%%%%%%%

Figure \ref{mag-dep}(a) shows CW MOKE data taken with a 775 nm
laser diode.  The MOKE angle is $\sim$1 mrad and the coercivity
is $\sim$7.5 mT at 10 K.  MOKE dynamics in the first 3 ps is
shown in Fig.~\ref{mag-dep}(b) for different magnetic
fields: +7 mT, 0 mT, and $-$7 mT.  The sign of $\Delta\theta_K$ changes when the direction of the field is reversed, as expected for demagnetization.  In order to eliminate
the possibility that the induced MOKE changes are due to purely
optical effects, we also monitored both MOKE and reflection magnetic
circular dichroism (MCD) at the same time.  The exact
coincidence between MOKE and MCD, shown in
Fig.~\ref{mag-dep}(c), ensures that we are probing magnetic
properties (see, e.g., \cite{KoopmansetAl00PRL}).

%%%%%  FIG. 3  %%%%%
\begin{figure}
\includegraphics [scale=0.5] {fig3.eps}  % 0.55
\caption{Normalized photo-induced MOKE angle change (a)
versus time for different pump fluences and (b) versus pump
fluence for different time delays.  At high fluences, the
signal saturates to $\sim$ 1, suggesting a complete quenching of
ferromagnetic order.} \label{power} \end{figure}
%%%%%%%%%%%%%%%%%%%%

Photoinduced Kerr rotation dynamics, normalized by the MOKE angle
before the arrival of the pump, is plotted for different pump
fluences in Fig.~\ref{power}(a).  At low pump fluences, the fast
($<$ 1 ps) and slow ($\sim$100 ps) demagnetization components
co-exist.  However, as the fluence increases, the fast component
progressively becomes more dominant.  Around $\sim$10 mJ/cm$^2$,
there is no slow demagnetization process any more --- a sharp
initial drop is followed by a completely flat region.  This
``step-function'' like response remains stable both in shape and
magnitude against further increases in pump fluence to 13.4
mJ/cm$^2$, i.e., the demagnetization saturates.  The saturation
value is one, implying that the change in magnetization is
100\% [see also Fig.~\ref{power}(b)].
These results suggest that a {\em complete quenching} of the
ferromagnetic order is occurring on the order of several hundred
femtoseconds.

%%%%%%%%%%%% FIG. 4 %%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}
%\includegraphics [scale=0.40] {temp1.eps}
%\caption{(a) Time evolution of photo-induced Kerr rotation as a
%function of lattice temperature (a).   The curves are vertically
%displaced for clarity.  (b) The extracted Kerr rotation angles
%vs. lattice   temperature at different time delays, i.e., 5 ps,
%20 ps and 80 ps, respectively, are plotted.    The dramatic
%decrease in Kerr rotation as the   temperature approaches the
%critical temperature Tc ($\sim$60 K), indicating that the
%transient   Kerr rotation angle originates from the
%magnetization change of the ferromagnetic state.   (c) The
%photoinduced Kerr rotation at first 3 ps is plotted together
%with the crosscorrelation between pump and probe pulses (the
%shaded area), indicating that the demagnetization is on the
%order of the pulse width, 220 fs. } \label{temp} \end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%  FIG. 4  %%%%%
\begin{figure}
\includegraphics [scale=0.5] {fig4.eps}  % 0.553
\caption{Photo-induced MOKE angle change (a)
versus time for different temperatures and (b)
versus temperature for different time delays.  The photo-induced
change is absent above the Curie temperature ($\sim$60 K).}
\label{temperature}\end{figure}
%%%%%%%%%%%%%%%%%%%%

To substantiate the above claim, we performed temperature
dependent meaurements, and the resuts are shown in
Fig.~\ref{temperature}(a).  Here, a strong temperature dependence
of both the fast and slow components is seen. $\Delta\theta_K$
decreases drastically as the temperature approaches the critical
temperature $T_c$ ($\sim$ 60 K), and $\Delta\theta_K$ is {\em
absent above the $T_c$}. These facts further corroborate that the
transient Kerr rotation here measures the magnetization change of
the ferromagnetic state [Fig.~\ref{temperature}(b)].

%Before we discuss the physical picture of subpicosecond quenching of femtosecond phase
%observed in ferromagnetic InMnAs, it is worth of pointing out the
%conventional picture of laser-induced demagnetization, e.g., in
%magneto-optical recording.  The coupling to magnetic (spin)
%system occurs via spin-lattice interaction.  The lattice is
%heated up via phonon emission from the thermalization and
%cooling of excited  hot carriers.  Subsequent energy transfer to
%spins, on the time scale of 1 ns, lead to the demagnetization of
%the sample.  Therefore, the energy transfer mechanism is
%indirect, and the dominating microscopic interaction is the
%spin-lattice coupling.  Such spin-lattice relaxation time has
%been measured in ferromagnetic Gd \cite{vaterlaus} and
%antiferromagnetic FeBo$_3$ \cite{kimel2002} using direct time
%domain MO spectrscopy, indicating a time scale on the order of
%100 ps and 1 ns in ferromagnetic or antiferromagnetic metals,
%respectively.  On the other hand, in the paramagnetic II-VI
%diluted magnetic semiconductors (such as CdMnTe), only indirect
%measurement for the spin-lattice relaxation time have been
%reported, showing that such time exceeds 100 ns \cite{Strutz}.
%Therefore, it is most likely that the slow demagnetization
%process up to 100 ps, visible in the temporal profile of
%transient Kerr rotation in InMnAs, is an indication of
%spin-lattice relaxation time in ferromagnetic semiconductors,
%especially taking into the considerations that the energy scale
%of exchange coupling in III-V ferromagnetic semiconductors is
%similar as that in ferromagnetic metals,  instead of strong
%antiferromagnetic coupling in paramagnetic II-VI materials.
%Therefore, our result provides the first direct   measurement of
%spin-lattice relaxation time in ferromagnetic semiconductors, one
%the order of 100 ps in ferromagnetic InMnAs.


%The more intriguing observation comes from the extremely fast demagnetization component, visible as a non-zero drop
%in transient Kerr signal even within the pulse width, $\sim$ 220
%fs, as shown Fig.~\ref{temp1} (c), where the photoinduced Kerr
%rotation is plotted together with the pump-probe corss
%correlation as function of time delay for the first 3 ps.
%Following scenarios are proposed to explain the ultrfast
%magnetization dynamics observed so far.  Three reservoirs are
%differentiated in p-doped ferromagnetic (III,Mn)Vs: localized Mn
%spins, delocalized hole spins strongly coupled to Mn spins, as
%well  as lattice vibrations, as in Fig.~\ref{schemesetup}.
%After the photoexciation, the processes of energy relaxation and
%trapping of photocarriers are happening on few picoseconds,
%visible in the transient reflectivity of InMnAs, as shown in
%Fig.~\ref{DR-MOKE} (a).  The polarization and energy relaxation
%of holes should happen within the first 1 or 2 ps, leaving hot
%hole  gas behind with relatively long life time due to the
%saturation of hole traps. The transient hole gas and the
%collective   magnetization from the localized spins of Mn ions
%are strongly coupled to each other via ferromagnetic p-d
%exchange interaction. The spin dependent scattering between the
%carriers and Mn spins via p-d exchange can lead to spin-flips,
%providing direct spin transferring channels between the two,
%i.e., the polarization from the collective Mn spins are
%transferred to the hot holes and quickly dissipated in such
%``reservoir'', due to strong spin-orbit scattering and valance
%band mixing.  Furthermore, we can take a closer look at p-d
%exchange Hamiltonian and estimate the time scale for such direct
%spin transfer b considering,

%%%
%\begin{equation}
%H_{p-d}=-\beta \sum
%\limits _{n}\delta (r-R_{n})[S_{n}^{z}\cdot s^{z}+{1\over 2}
%(S_{n}^{+}\cdot s^{-}+S_{n}^{-}\cdot s^{+})],
%\end{equation}
%%%

%where $\beta $ is the $p-d$ exchange coupling constant
%(conventionally denoted by $N_0\beta$ in DMS literature and
%$\sim-$1.0 eV in InMnAs.
%\cite{zudov}).
%$S$ and $s$ and the spin operators of Mn ions and holes,
%respectively.  Spin flip scattering between collective spins and
%hole spins could occur with a characteristic time $\tau_{p-d}$
%$\sim\hbar/ E_{p-d}$ $\sim$ 2 fs,


%\section*{Interpretation of experiments and side-points}
%\begin{itemize}
%\item \textit{What is being measured by MOKE.}  In MOKE experiment the difference of optical properties for two circular polarizations of light is being probed. Such a difference may arise from the spin-splitting of bands (caused by the magnetic order influencing the band-structure through sp-d interaction), or from the presence of transient population of carriers of either spin created by the pump (named ``dichroic bleaching'' in \cite{Koopmans}). The two-color setup is used to diminish the latter
%effect and extract the Kerr rotation component that depends on the band splitting, which in turn is proportional to the magnetization of Mn spin system.
%\item \textit{Pump-polarization dependent transient.} Despite the two-color setup, strong pump-polarization dependent transient apperars in the results, showing that the effects of  ``dichroic bleaching'' are not negligible within first 2 ps. The decay time of this transient is very close to the decay time of  the negative peak in differential reflectivity, supporting the view that the initial MOKE signal is dominated by the carrier effects. This breakdown of a two-color approach can be explained by the
%combination of disorder effects and two-photon absorption (TPA).
%\item \textit{Disorder and absorption} Disorder has a big influence on properties of ferromagnetic semiconductors \cite{Timm}. In the context of optical properties, the need for including the disorder effects has been recognized, either by using a phenomenological breaking of k-selection rule \cite{Szczytko} or by using a broadening parameter $\gamma\approx 100$ meV \cite{Jungwirth,Sinova_optics}. Breaking of wave-vector selection rule has a big impact on photoexcitation process in these materials. In
%the perfect crystal, the energy width of the initial
%distribution of photocarriers is connected with the laser
%linewidth, whereas in the disordered material, this energy
%spread is governed by the disorder broadening. This can be
%read out from the structure of absorption coefficient
%formula \cite{Mahan,DasSarma}
%%%
%\begin{equation}
%\alpha(\hbar\omega) \sim  \int d^{3}k \int dE A_{v}
%(\mathbf{k},E) A_{c}(\mathbf{k},E+\hbar\omega)
%\Big( f(E) - f(E+\hbar\omega) \Big)
%\end{equation}
%%%
%where $A_{n}(\mathbf{k},E)$ is a spectral density for
%band $n$ and $f(E)$ is the occupation factor.
%\item \textit {Two-photon absorption} Even for the lowest
%pump fluence used, the linear absorption is saturated (the
%number of photocarriers estimated using the linear absorption
%formulas exceeds the number of states available in the
%$\Gamma$ valley of conduction band by orders of magnitude).
%The value of the TPA absorption coefficient $\beta$ for
%photon energy of 0.62 eV was calculated in the 8 band Kane's
%model for InAs (without the exchange splitting), giving the
%value of 200 $\frac{GW}{cm}$, which is
%a sensible value (through the $\beta \sim n^{-2}E_{g}^{-3}$
%scaling \cite{TPA_scaling} we can estimate the TPA coefficient
%for InAs from experimental and theoretical data for other
%semiconductors, see e.g. \cite{Hutchings}). The number of
%carriers excited in TPA process is estimated to be
%$3\times 10^{19} cm^{-3}$, which is quite close to the estimate
%made using a disorder-broadened distribution of excited
%electrons (about $10^{19}$ cm$^{-3}$).
%\item \textit{Estimate of the concentration of photocarriers} As a result of the above, the concentration of photocarriers is of the order of $10^{19}$ cm$^{-3}$ for the lowest fluences. Most of these carriers are created in TPA transition, putting them closer in the phase space to the region which is directly felt by the probe (the thermalization of excited electron population creates a high-energy tail, which further increases the phase-space filling effect influencing the probe). It has been shown
%that the optical orientation for TPA process is nearly the same as in SPA \cite{TPA_polarized}, which explains the presence of the polarization-dependent transient, reflecting the high degree of polarization of photoexcited carriers.
%\item \textit{The concentration of holes}
%\item \textit{Higher pump fluences}
%The above estimates were performed for the lowest pump fluence used in the experiments. Much higher fluences are also used, and total demagnetization is finally observed for fluence of $\sim 40 \frac{mJ}{cm^{2}}$. This regime of light intensities rests outside the realm of applicability of the above approach.  The peak intensity  corresponding to the pulse of such a fluence is about $ I \approx 200 \frac{GW}{cm^{2}}$, which is of the same order of magnitude as the intensity at which all the multi-photon
%absorption processes become comparable in strength \cite{TPA_scaling}: $ I_{critical} = \frac{n E_{g}^{4}}{\hbar P^{2}} \frac{\hbar c}{e^{2}} \approx 300 \frac{GW}{cm^{2}} $.
%So fluences causing the complete demagnetization correspond to the regime where higher order nonlinear absorption processes come into play.
%\item \textit{What happens to the energy absorbed by the sample.} Because of the difference of masses, most of the energy carried by absorbed photons is taken by excited electrons. In the process of electron trapping the carrier kinetic energy is transferred to the lattice \cite{Yassievich} - this leads to very fast heating of the lattice. Part of the energy imparted to the electrons may be transferred to the holes by the Auger process \cite{Gelmont}, in which low-energy hole is annihilated and
%high-energy one (in a split-off band) is created. Below we are going to argue that holes can effectively transfer their energy to the localized spin system through p-d interaction.
%\item \textit{ A remark on the density of holes}
%The experimental $p$ is $10^{19}$ cm$^{-3}$, which is very unreliable, the Hall effect measurement being probably influenced by a small population of holes of higher mobility in GaSb. Such a possibility has been put forward \cite{Furdyna}, as all the other samples of InMnAs (grown on InAs or AlSb) having similar $T_{c}$ have at least an order of magnitude higher concentration than that measured by the Hall effect. Such an order of magnitude is in agreement with the predictions of the popular mean-field
%theory \cite{Dietl} of ferromagnetic transition (for critical temperatures between 30 and 50 K in InMnAs $p$ between 2 and $5\times10^{20}$ cm$^{-3}$ is needed \cite{Tc}). In the model of ultrafast demagnetization below we use $p\sim 10^{20}$ cm$^{-3}$.

%\end{itemize}

%\section*{Demagnetization mechanism}
In the standard picture of laser-induced demagnetization, the
heat deposited in the lattice is transferred into the spin
system through spin-lattice interaction (for microscopic model see e.g.  \cite{HubneretAl96PRB}).
%(phonon-localized spin or phonon-magnon scattering mediated by spin orbit interaction \cite{HubneretAl96PRB}).
The heating up of the spin system
then results in demagnetization, occurring at the time scale of
spin-lattice relaxation, $\tau_{sl}$, which is at least of the
order of 100 ps ($\approx 80$ ps in Gd
\cite{VaterlausetAl91PRL} and over ns in
paramagnetic CdMnTe \cite{StrutzetAl92PRL}). Much faster
demagnetization is expected when the process of direct
carrier-spin interaction is taken into account. Such an
interaction has been identified as the source of possible fast
demagnetization in metals \cite{BeaurepaireetAl96PRL}, and the
importance of the spin-orbit scattering of carriers has been
stressed \cite{Beaurepaire1etAl98PRB}.

Here, we can put these ideas on a stronger footing, exploiting
the simplicity of carrier-``spin'' coupling in diluted magnetic
semiconductors (DMS). The $p$-$d$ exchange interaction $H_{p-d}$
$\sim$$\beta\mathbf{S}\mathbf{s}$ (see, e.g.,
\cite{Furdyna88JAP}) couples the spins of delocalized holes with
localized Mn moments; the latter are the main source of the
macroscopic magnetization $\mathbf{M}$ (the carrier contribution
to $\mathbf{M}$ is very small). The mean-field part of this
interaction causes a spin-splitting of bands proportional to the
average value of Mn spin, which is exactly what is measured in
magneto-optical experiments. Photoexcitation creates a
nonequilibrium population of hot holes, with a blurred Fermi
surface. This strongly increases the number of states available
for spin-flip scattering, coming from the off-diagonal part of
$H_{p-d}$, allowing the flow of energy and angular momentum
between carriers and localized spins.  Demagnetization is caused
by this flow of polarization from Mn to holes, which is
sustained by efficient hole spin relaxation. The whole process
can be envisioned as the reverse of the Overhauser effect: the
excited carriers are becoming dynamically polarized at the
expense of the localized spins, and the dissipation of
magnetization occurs through spin relaxation in the carrier
system.

Spin-flip scattering has been used to describe the cw heating of
Mn by electrons in a paramagnetic DMS \cite{KonigetAl00PRB}, and the idea of
magnetization relaxation through spin-flips with carriers with
subsequent spin-relaxation by spin-orbit interaction can be
traced as far as the fifties \cite{Mitchell57PR} (recently
rejuvenated for DMS
\cite{TserkovnyaketAl04APL,SinovaetAl04PRB}).

At lowest pump fluences the demagnetization is $\sim20\%$
after 200 fs, and using the estimate of
$p \simeq 4 \cdot 10^{20}$ cm$^{-3}$ we see that every hole has to
participate in $\sim$1 spin-flip
($0.2\cdot{5 \over 2}\cdot10^{21}/(4\cdot10^{20}$))
%(based on ratio of the number of spin flips to the number of holes)
to achieve such
an effect. This leads to an upper bound  for spin-relaxation time
$\tau_{s}\leq 200$ fs, which is reasonable: the momentum
scattering time in disordered III-V DMS is of the order of 10 fs
\cite{JungwirthetAl02APL}, and furthermore, in the excited
population other scattering mechanisms (carrier-carrier and
phonon scattering) play a significant role. Strong spin-orbit
interaction in the valence band leads to close correlation
between the momentum scattering and spin relaxation times.

In order to substantiate the above physical picture we used a single heavy-hole spin-split band to calculate the spin-flip scattering rates \cite{KonigetAl00PRB}: \begin{eqnarray*}
W_{m,m'} = \frac{2\pi}{\hbar}
\frac{\beta^{2}}{4}\sum_{\sigma}  \int
\frac{d^{3}k}{(2\pi)^{3}}  \int \frac{d^{3}q}{(2\pi)^{3}}
f_{\sigma}(\mathbf{k}) \Big( 1 - f_{-\sigma}(\mathbf{q}) \Big)
\\ \delta \Big( \epsilon_{-\sigma}(\mathbf{q}) -
\epsilon_{\sigma}(\mathbf{k}) + \delta \Big) | \langle m |
S_{\pm} | m' \rangle |^{2} \end{eqnarray*} where
$m=-\frac{5}{2},..., \frac{5}{2}$,
%the choice of upper or lower signs in ladder operators depends on whether $m=m'+1$ or $m=m'-1$,
$\delta$ is the mean-field splitting of the Mn spin
levels, and $\sigma$ is the hole spin. The
occupation functions $f_{\sigma}(\mathbf{k})$ are thermal, with
a high effective temperature $T_{h}$ mimicking the highly
nonequilibrium state of holes, and with possible different Fermi
levels for two spin directions. The  dynamics of Mn spins is
described by a simple rate equation for diagonal elements of the
localized spin density matrix $ \dot{N}_{m} = \sum_{m'} (
W_{mm'}N_{m'} - W_{m'm}N_{m})$,
% the value of $W_{mm'}$ does not depend crucially on the intricacies of the
% valence band structure, it is mostly determined by the thermal
% spread of carriers' distribution functions and the overall
% density of states with spins up and down available for spin-flip scattering.
and the dynamics of the average hole spin $s$ is given by $ \dot{s} = -\gamma\dot{M} -
\frac{1}{\tau_{s}}(s-s_{eq}(M,T_{h}))$, where $M$ is the average Mn spin, $\gamma$ is the ratio of Mn to hole density, and $s_{eq}$ is the instantaneous equilibrium value of the average hole spin.

The results of calculations show a demagnetization of 10\%
within 200 fs for $T_{h}=1000$ K, $\tau_{s}=10$ fs,  and
$p=4\cdot 10^{20}$ cm$^{-3}$, which compares well with the
experiment. For much less favorable value of hole spin-relaxation time $\tau_{s}=100$ fs we get  $\Delta M/M \approx 5$ \%. More theoretical work on strong photoexcitation
of disordered III-V DMS and spin relaxation of hot holes is
needed to verify the parameters used above. However, it is clear
that even our simple model shows that ultrafast demagnetization
is possible in these materials.
%Higher temperatures or (more importantly) faster spin relaxation times will give stronger
%demagnetization. The more effective demagnetization at higher $p$ comes from growing density of states available in scattering events.

% The papagraph below is optional:
%It should also be noted, that the demagnetization process demands
%the existence of minority spins (flipping them into the majority
%direction demagnetizes the Mn population). In the situation
%where the material is a half-metallic ferromagnet, as it was
%proposed in the case of GaMnAs \cite{KojimaetAl03PRB}, the
%demagnetization process will be highly suppressed.

% this one is a repeat, can probably be left out:
%The observed long-time dynamics is connected with the
%``traditional'' pathway of heat transfer (with the intervention
%of the lattice). The results are similar to the ones seen by
%Kojima \cite{KojimaetAl03PRB} in GaMnAs, which were modeled by
% 3-temperature
%model \cite{BeaurepaireetAl96PRL,HerouxetAl05unpub}.
%In contrast to
%this model, in our simple treatment we emphasize
%the role of polarization transfer between the systems (with
%possibility of  ``bottleneck'' when carrier spin relaxation is
%not fast enough), not only the heat exchange. We also do not use
%the concept of localized spin temperature, which might not be
%applicable on such a short time scale.
%The basic requirements
%for efficient demagnetization are: spin relaxation time of
%carriers $\tau_{s} \leq 100$ fs, large density of states at the
%Fermi level, presence of both minority and majority spin
%carriers and strong carrier-Mn coupling (but not so strong as to
%render the system half-metallic).
The observed long-time dynamics is connected with the
``traditional'' pathway of heat transfer (with the intervention
of the lattice). The results are similar to those seen by
Kojima \cite{KojimaetAl03PRB} in GaMnAs, which were modeled by
the 3-temperature model
\cite{BeaurepaireetAl96PRL,HerouxetAl05unpub}. Our model
concentrates on the subpicosecond time-scale, where we
emphasize the role of polarization transfer between the systems
(with the possibility of ``bottleneck'' when $\tau_{s}$ is not
small enough), not only the heat exchange.
%We also do not use the concept of localized spin temperature, which might not be applicable in this regime.

In conclusion, we have made the first observation of two distinct
demagnetization regimes in the dynamics of laser-excited InMnAs.
We interpret the novel demagnetization dynamics as a
result of ferromagnetic exchange couplings and spin-lattice
interactions, manifesting themselves as a fast ($<$1 ps)
and relatively slow ($\sim$100 ps) components, respectively.
The fast component completely quenches ferromagnetism at high
pump fluences. Systematic power and temperature dependence of
this ultrafast demagnetization provides convincing evidence
supporting the proposed physical picture.

\smallskip

This work was supported by DARPA (MDA972-00-1-0034), NSF
(DMR-0134058, DMR-0325474, DMR-0325599, INT-0221704), ONR
(N000140410657), and MEXT (No.14076210).

\medskip

\noindent$^{\dagger}$Present address: Lawrence Berkeley National
Laboratory, Berkeley, California.

\noindent$^{\ddagger}$To whom correspondence should be addressed.
Electronic address: kono@rice.edu.

\noindent$^{\sharp}$Present address: Department of Applied Physics,
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656,
Japan.

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%\bibliography{jun}

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\end{thebibliography}



\end{document}

cond-mat0504611.extracted_bib
\begin{thebibliography}{10}
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

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\end{thebibliography}