Ultrafast optical manipulation of magnetic order

Andrei Kirilyuk, Alexey V. Kimel, and Theo Rasing

Rev. Mod. Phys. 82, 2731 – Published 22 September 2010; Erratum Rev. Mod. Phys. 88, 039904 (2016)

Abstract

The interaction of subpicosecond laser pulses with magnetically ordered materials has developed into a fascinating research topic in modern magnetism. From the discovery of subpicosecond demagnetization over a decade ago to the recent demonstration of magnetization reversal by a single $40 fs$ laser pulse, the manipulation of magnetic order by ultrashort laser pulses has become a fundamentally challenging topic with a potentially high impact for future spintronics, data storage and manipulation, and quantum computation. Understanding the underlying mechanisms implies understanding the interaction of photons with charges, spins, and lattice, and the angular momentum transfer between them. This paper will review the progress in this field of laser manipulation of magnetic order in a systematic way. Starting with a historical introduction, the interaction of light with magnetically ordered matter is discussed. By investigating metals, semiconductors, and dielectrics, the roles of (nearly) free electrons, charge redistributions, and spin-orbit and spin-lattice interactions can partly be separated, and effects due to heating can be distinguished from those that are not. It will be shown that there is a fundamental distinction between processes that involve the actual absorption of photons and those that do not. It turns out that for the latter, the polarization of light plays an essential role in the manipulation of the magnetic moments at the femtosecond time scale. Thus, circularly and linearly polarized pulses are shown to act as strong transient magnetic field pulses originating from the nonabsorptive inverse Faraday and inverse Cotton-Mouton effects, respectively. The recent progress in the understanding of magneto-optical effects on the femtosecond time scale together with the mentioned inverse, optomagnetic effects promises a bright future for this field of ultrafast optical manipulation of magnetic order or femtomagnetism.

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DOI:https://doi.org/10.1103/RevModPhys.82.2731

Erratum

Erratum: Ultrafast optical manipulation of magnetic order [Rev. Mod. Phys. 82, 2731 (2010)]

Andrei Kirilyuk, Alexey V. Kimel, and Theo Rasing

Rev. Mod. Phys. 88, 039904 (2016)

Authors & Affiliations

Andrei Kirilyuk^*, Alexey V. Kimel, and Theo Rasing

Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

^*a.kirilyuk@science.ru.nl

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Vol. 82, Iss. 3 — July - September 2010

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Figure 1
(Color online) Time scales in magnetism as compared to magnetic field and laser pulses. The short duration of the laser pulses makes them an attractive alternative to manipulate the magnetization.Reuse & Permissions
Figure 2
(Color online) Illustration of stimulated coherent Raman scattering, a possible microscopic mechanism responsible for an ultrafast optically generated magnetic field. Two frequency components of the electromagnetic radiation from the spectrally broad laser pulse take part in the process. The frequency $ω_{1}$ causes a transition into a virtual state with strong spin-orbit coupling. Radiation at the frequency $ω_{2}$ stimulates the relaxation back to the ground state together with the creation of a magnon.Reuse & Permissions
Figure 3
Remanent MO contrast measured for a nickel thin film as a function of time after exciting by a $60 fs$ laser pulse. The results demonstrate ultrafast loss of the magnetic order of the ferromagnetic material within a picosecond after laser excitation. From 19.Reuse & Permissions
Figure 4
Comparison of induced MO ellipticity (open circles) and rotation (filled diamonds) for a $Cu (111) ∕ Ni ∕ Cu$ epitaxial film and Ni thickness and pulse energy as indicated. The inset depicts the polar configuration with pump (1) and probe (2) beams. From 146.Reuse & Permissions
Figure 5
Ultrafast laser-induced dynamics in ${CoPt}_{3}$ . (a) Time-resolved Faraday MO signals, rotation (open circles), and ellipticity (filled circles). The pump-probe cross correlation (dashed line) is displayed for reference. (b) Short-delay relative variations of real and imaginary dielectric tensor components retrieved from the data in (a). For $t ⩽ 100 fs$ , the real and imaginary parts follow different dynamics. From 86.Reuse & Permissions
Figure 6
Laser-induced generation of ${TH}_{2}$ radiation. (a) The THz pulse generated upon ultrafast laser heating of $42 − Å$ -thick in-plane magnetized Ni film. The smooth line is a simulation assuming the time-dependent magnetization of (b) convoluted with a Gaussian instrument response function (full width at half maximum $540 fs$ ). From 20.Reuse & Permissions
Figure 7
(Color online) Interacting reservoirs (carriers, spins, and lattice) in the three-temperature model as suggested by 4b. Some of the possible interaction channels, such as spin lattice and electron-phonon interactions, are considered to be well understood. The direct electron-spin coupling is a subject of current research and active debates.Reuse & Permissions
Figure 8
(Color online) Temporal behavior of electron, lattice, and spin temperatures following excitation with a short laser pulse. The behavior of the spin temperature is shown for both strong coupling (metals) and weak coupling (dielectrics) cases.Reuse & Permissions
Figure 9
(Color online) Time-resolved electron photoemission. Top: Normalized photoelectron spectrum at $300 fs$ (circles) with fit (solid line) and distribution function $f (E; t)$ (dashed line) on a logarithmic scale and divided by $f$ (triangles) on a linear scale at right. The inset sketches the TRPE experiment. Bottom: Photoelectron spectra at different delays are displayed in color (fits in black) and are offset vertically. From 162.Reuse & Permissions
Figure 10
(Color online) Time-resolved XMCD signal with circularly polarized x rays incident at 60° relative to the sample surface vs pump-probe time delay (symbols) measured at the $L_{3}$ edge maximum. As the measured value is proportional to $S + \frac{3}{2} L$ , overall decrease in the signal excludes orbital moments from gaining any significant value at the cost of spins. From 221.Reuse & Permissions
Figure 11
(Color online) Cut through micromagnetic simulation for the Ni film after a partial demagnetization. Left: The evolution of spin-wave emission from the excited area shown in real space. Right: The corresponding Fourier transform shown as a function of spatial frequency. From 58.Reuse & Permissions
Figure 12
Transient magneto-optical Kerr rotation in ${Ga}_{0.974} {Mn}_{0.026} As$ triggered by a $140 fs$ laser pulse with a photon energy of $0.61 eV$ . (a) Magnetic-field dependence of the Kerr rotation. (b) Temperature dependence of the Kerr rotation between 6 and $60 K$ . The signal decreases quickly with increasing temperature and is absent above the Curie temperature $T_{C} = 50 K$ . From 250, 249.Reuse & Permissions
Figure 13
Normalized photoinduced magneto-optical Kerr rotation in ${In}_{0.87} {Mn}_{0.13} As ∕ Ga Sb$ heterostructure with Curie temperature $\sim 60 K$ (a) vs time for different pump fluences and (b) vs pump fluence for different time delays. At high fluences, the signal saturates to $\sim 1$ , suggesting a complete quenching of ferromagnetic order. From 251.Reuse & Permissions
Figure 14
The Faraday rotation at negative (solid circles) and zero (open circles) time delay as a function of the bias temperature with the fit to Eq. (23) (solid and dotted lines, respectively). The difference between the intrinsic magneto-optical signal and that at $500 ps$ is shown by diamonds, together with the calculation based on the fitted parameters (dashed line). The inset shows the transient component of the magnon temperature as a function of the time delay. The solid line is the fit according to Eq. (24). From 130.Reuse & Permissions
Figure 15
(Color online) All-optical excitation of coherent precession. (a) $Δ t < 0$ , the magnetization points in the equilibrium direction, given by the sum of the anisotropy, demagnetizing, and external fields; (b) $0 < Δ t < 1 ps$ , the magnitude of $M$ and/or the anisotropy change due to heating, thereby altering the equilibrium orientation; (c) the magnetization precesses around the new equilibrium direction that is slowly restored due to the heat diffusing away.Reuse & Permissions
Figure 16
Ultrafast laser-induced dynamics in $Ni Fe ∕ Ni O$ exchange-biased bilayer: (a) Easy-axis transient Kerr loops for the photoexcited sample at $t = 1$ and $200 ps$ following pulse photoexcitation at $t = 0$ . The open circles inserted in the bottom trace show expected behavior in the absence of coherent magnetization rotation. (b) Illustration of the trajectory of the magnetization vector in the typical LLG calculation. The initial direction of $M$ is directed along the $z$ axis. $M$ is subject to a damped rotation with a large $y$ component and a finite (out-of-plane) $x$ component indicated schematically. The transient modulation of the $z$ component, measured by experiment, is projected out explicitly in (c). From 110, 107.Reuse & Permissions
Figure 17
(Color online) The dependence of the mode frequency upon the element size is shown for bias field values of (a) $1 kOe$ and (b) $150 Oe$ . The shaded spectra were obtained experimentally while simulated spectra are shown with a solid curve. For each element size, the spatial distribution of the FFT magnitude of the modes in the simulated spectra is shown in the insets. From 121.Reuse & Permissions
Figure 18
Magnetization dynamics of $4 nm$ superparamagnetic cobalt particles in ${Al}_{2} O_{3}$ . (a) Magnetization trajectory in the polar and longitudinal plane. (b) Dynamical polar and longitudinal Kerr signals (10).Reuse & Permissions
Figure 19
(Color online) Light-induced magnetic precession in (Ga,Mn)As slabs. The top panel shows the transient magneto-optical Kerr signal measured in the Voigt geometry (open circles) at $H = 0.17 T$ . The applied field is parallel to [100]. The black curve is the linear prediction fit, which gives two modes of period of 99.7 and $83.9 ps$ . Their contributions to the fitted signal are shown by the curves. The bottom panel shows the Fourier transform of the fit and, in the inset, the calculated $M_{z}$ component for the three lowest eigenmodes. From 246.Reuse & Permissions
Figure 20
(Color online) Temperature dependence of (a) the magnetization precession frequencies $ω_{FMR}$ and $ω_{ex}$ . As temperature decreases from $310 K$ toward $T_{A}$ , the exchange resonance mode $ω_{ex}$ (open circles) softens and mix with the ordinary FMR resonance $ω_{FMR}$ (closed circles). The solid lines are a qualitative representation of the expected trend of the two resonance branches as indicated by Eqs. (25, 27). (b) Temperature dependence of the Gilbert damping parameter $α_{eff}$ . The lines are guides to the eye. From 224.Reuse & Permissions
Figure 21
Excitation and relaxation of the AFM vector moment measured via changes in the magnetic birefringence. Here one can distinguish three processes: (1) electron-phonon thermalization with $0.3 ps$ relaxation time, (2) rotation of the AFM vector with $5 ps$ response time, and (3) oscillations of the AFM vector around its equilibrium direction with an approximate $10 ps$ period. From 128.Reuse & Permissions
Figure 22
(Color online) Minor hysteresis loops of the ${Ga}_{0.98} {Mn}_{0.02} As$ sample, recorded before (open symbols) and after (solid symbols) excitation by single optical pulse with a duration of $100 fs$ , shown together with corresponding magnetization orientations (insets). From 14.Reuse & Permissions
Figure 23
Ultrafast laser-induced dynamics in RhFe: (a) Schematic of the ultrafast generation of ferromagnetic order by inducing an AM-FM transformation in FeRh when excited with femtosecond optical pulses. Time evolution of (b) the transient Kerr effect $Δ θ_{K} (t)$ and (c) the transient reflectivity $Δ R (t)$ as a function of pump fluences (labeled for each curve in $mJ ∕ {cm}^{2}$ ). The curves are vertically displaced for clarity. From 108.Reuse & Permissions
Figure 24
(Color online) Transient magnetization reversal dynamics measured for a pump fluence of $6.29 mJ ∕ {cm}^{2}$ . Insets show hysteresis loops measured at distinct pump-probe delays. The loops demonstrate the magnetization reversal after about $700 fs$ . From 222.Reuse & Permissions
Figure 25
(Color online) Coherent precession of the magnetization triggered by linearly polarized laser pulses. (a) Time dependence of the precession for different planes of pump polarization $θ$ , with an applied field of $| H_{ext} | = 350 Oe$ in the plane of the sample. Circles represent measurements and solid lines simulations based on the Landau-Lifshitz equation. (b) Precessional amplitude as a function of the plane of pump polarization. Round and square symbols represent amplitudes extracted from measurements at $\pm H_{ext}$ . The solid line is a best fit. From 91.Reuse & Permissions
Figure 26
(Color online) Dependence of the precessional amplitude on the applied in-plane magnetic field $H_{ext}$ . Round and square symbols represent amplitudes extracted from measurements at $\pm H_{ext}$ . From 91.Reuse & Permissions
Figure 27
(Color online) Graphical illustration of the process of photoinduced magnetic anisotropy caused by linearly polarized laser excitation and the subsequent precessional dynamics. From 91.Reuse & Permissions
Figure 28
(Color online) Illustration of the photoexcitation of electrons between iron ions in different crystallographic sites. A laser pulse induces electron transfer from a ${Fe}^{3 +}$ ion in the octahedral site (denoted by [a]) to a ${Fe}^{4 +}$ ion in the tetrahedral site [denoted by (d)]. The dodecahedral site with the divalent lead impurity is denoted by {c}.Reuse & Permissions
Figure 29
Temporal behavior of second-harmonic generation (SHG) and third-harmonic generation (THG) measured in reflection from single crystal NiO (111) at $6 K$ . (b) Fourier transform of the SHG data after subtraction of the steplike decrease at $t = 0$ . Dashed and straight lines: fitted spectral contributions and envelope. (c) THG signal from (a). From 60.Reuse & Permissions
Figure 30
(Color online) Laser-induced magnetic anisotropy and subsequent spin precession in ${Ga}_{0.8} {Mn}_{0.2} As$ . (a) Temporal profiles of the angle of tilt of the effective magnetic field $H_{eff}$ experienced by the spins. The time dependence originates from transient photoinduced magnetic anisotropy in the material, (b) temporal evolution of the $x$ component of magnetization, and (c) $y$ and $z$ as function of time. All profiles are extracted on the basis of experimental curves. (d) Precessional motion of magnetization in $M_{y} - M_{z}$ parameter space (92).Reuse & Permissions
Figure 31
(Color online) Laser-induced magnetism in GaMnAs: (a) Illustration of hole-density-tuning effects via external stimuli in III-V FMSs seen in the static experiments (147). FM: ferromagnetism. $4 p$ is hole density change. (b) Schematic diagram of the spin-dependent density of states in GaMnAs. Femtosecond pump pulses create a transient population of holes in the valence band. (c) Time-resolved magneto-optical Kerr effect dynamics at $70 K$ and under $1.0 T$ field. Transient enhancement of magnetization, with $\sim 100 ps$ rise time, is clearly seen after initial fast demagnetization. From 248.Reuse & Permissions
Figure 32
Changes in Hall resistance and sheet resistance at $4.2 K$ for a $Ga Mn As ∕ Ga As$ sample under cw light irradiation, the polarization state of which is controlled by a quarter waveplate. The inset shows the magnetization curve extracted from the anomalous Hall effect measurements, indicating in-plane magnetic anisotropy of the current sample. From 188.Reuse & Permissions
Figure 33
(Color online) Precession following excitation with circularly polarized light. The two helicities $σ^{+}$ and $σ^{-}$ give rise to precession with an opposite phase and a different amplitude. During the $100 fs$ presence of the laser pulse the magnetization precesses in the dominating axial magnetic field $H_{F}$ created by the circularly pump pulse. Subsequent precession takes place in the effective magnetic field $H_{eff}^{'}$ , possibly modified by the photomagnetic effects, see Sec. 5A. From 90, 91.Reuse & Permissions
Figure 34
(Color online) Magnetic excitations in $Dy Fe O_{3}$ probed by the magneto-optical Faraday effect. Two processes can be distinguished: (1) instantaneous changes of the Faraday effect due to the photoexcitation of Fe ions and relaxation back to the high spin ground state $S = 5 ∕ 2$ and (2) oscillations of the Fe spins around their equilibrium direction with an approximately $5 ps$ period. The circularly polarized pump pulses of opposite helicities excite oscillations of opposite phase. Inset shows the geometry of the experiment. Vectors $δ H^{+}$ and $δ H^{-}$ represent the effective magnetic fields induced by right-handed $σ^{+}$ and left-handed $σ^{+}$ circularly polarized pump pulses, respectively. From 129.Reuse & Permissions
Figure 35
The amplitude of the spin oscillations as a function of pump fluence. From 129.Reuse & Permissions
Figure 36
(Color online) Suppression of heat-driven oscillations of the net magnetization in a multidomain sample: (a) At $Δ t < 0$ , the magnetizations $M_{1}$ and $M_{2}$ of oppositely magnetized domains are tilted due to the balance among magnetocrystalline anisotropy field $H_{a}$ , shape anisotropy field $H_{s}$ , and external field $H_{e}$ . (b) After photoexcitation, $Δ t > 0$ , heating induces out-of-phase oscillations of the $z$ components of $M_{1}$ and $M_{2}$ .Reuse & Permissions
Figure 37
(Color online) Precession of the magnetization excited by circularly polarized pump pulses in GdFeCo, probed via the magneto-optical Faraday effect. For certain values of the external field $H_{e}$ , the two helicities $σ^{+}$ and $σ^{-}$ give rise to precession with different phase. The lines are guides to the eye.Reuse & Permissions
Figure 38
Double-pump experiment in magnetic garnet with circularly polarized laser pulses of opposite helicity. Shown is how amplification and complete stopping of the magnetization precession can be achieved depending on the phase of the precession when the second laser pulse arrives. The time delay between the two pump pulses is fixed at approximately $0.6 ns$ , and the precession frequency is controlled by varying the external field. From 91.Reuse & Permissions
Figure 39
(Color online) Illustration of the double-pump experiment for circularly polarized pump pulses of opposite helicity arriving at an (a) odd number of half precessional periods and (b) an integer number of full precessional periods. The magnetization is either rotated further away from the effective field direction causing subsequent precession to take place with almost twice the original amplitude or the magnetization is rotated back into the effective field direction and no further precession takes place. From 91.Reuse & Permissions
Figure 40
(Color online) Coherent control of spins in $Dy Fe O_{3}$ with two circularly polarized laser pulses. (a) Precession triggered by the first laser pulse, (b) amplification of spin precession by the second laser pulse that comes after an even number of full periods, and (c) stopping of the spin oscillations by the second pump that comes after an odd number of half periods.Reuse & Permissions
Figure 41
(Color online) Precession of the magnetization triggered by left- and right-handed circularly polarized laser pulses at different values of the in-plane applied magnetic field. For the $σ^{-}$ helicity, at an applied field of $\sim \pm 150 Oe$ , no precession is observed due to a perfect balance of the two photomagnetic effects $δ H^{a}$ and $H^{F}$ . From 90.Reuse & Permissions
Figure 42
(Color online) Illustration of the switching process. Initially at $t < 0$ the magnetization is along $H_{eff}$ . During the presence of the laser pulse $0 < t < 100 fs$ photoinduced modification of the anisotropy fields leads to a new long-lived equilibrium along $H_{eff}^{'}$ . Simultaneously, the strong optomagnetically generated field $H^{F}$ causes the magnetization to precess into the new state. After $t > 100 fs$ the optical pulse is gone and the approximately 0.6° switching of $M$ is complete. From 90.Reuse & Permissions
Figure 43
(Color online) Noninertial and inertial scenarios to transfer a point mass over a potential. The noninertial mechanism (above) requires a continuous driving force that pulls the mass over the potential barrier. A similar scenario is realized in magnetization reversal via precessional motion in ferromagnets. In contrast, in the inertial mechanism (below), during the action of the driving force the coordinate of the particle is hardly changed, but the particle acquires enough momentum to overcome the barrier afterwards. From 126.Reuse & Permissions
Figure 44
The effect of single $40 fs$ circular polarized laser pulses on the magnetic domains in ${Gd}_{22} {Fe}_{74.6} {Co}_{3.4}$ . The domain pattern was obtained by sweeping at high-speed $(\sim 50 mm ∕ s)$ circularly polarized beams across the surface so that every single laser pulse landed at a different spot. The laser fluence was about $2.9 mJ ∕ {cm}^{2}$ . The small size variation in the written domains is caused by the pulse-to-pulse fluctuation of the laser intensity. From 223.Reuse & Permissions
Figure 45
(Color online) Demonstration of compact all-optical recording of magnetic bits. This was achieved by scanning a circularly polarized laser beam across the sample and simultaneously modulating the polarization of the beam between left and right circular. From 223.Reuse & Permissions
Figure 46
(Color online) The magnetization evolution in ${Gd}_{24} {Fe}_{66.5} {Co}_{9.5}$ after the excitation with right- $(σ^{+})$ and left-handed $(σ^{+})$ circularly polarized pulses at room temperature. The domain is initially magnetized “up” (white domain) and “down” (black domain). The last column shows the final state of the domains after a few seconds. The circles show areas actually affected by pump pulses. From 235.Reuse & Permissions
Figure 47
(Color online) Magnetization reversal triggered by a combined action of a short magnetic field pulse $H_{eff}$ and ultrafast heating of electrons to a temperature of $T_{el}^{*}$ . (a) Phase diagram showing the magnetic state of the ${(30 nm)}^{3}$ volume achieved within $10 ps$ after the action of the optomagnetic pulse with parameters $H_{eff} = 20 T$ , $Δ t_{eff}$ , and $T_{el}^{*}$ . (b) The averaged $z$ component of the magnetization vs delay time as calculated for $250 fs$ magnetic field pulses $H_{eff} = 20 T$ and $T_{el}^{*} = 1130 K$ . (c) Switchability vs the pump intensity for ${Gd}_{22} {Fe}_{68.2} {Co}_{9.8}$ at room temperature. Peak electron temperature $T_{el}^{*}$ is calculated using $C_{e}$ . Note that in this range of intensities the amplitude of the effective light-induced magnetic field varies within $19.2 - 20.8 T$ . From 235.Reuse & Permissions
Figure 48
(Color online) Excitation and detection of the ferromagnetic mode of spin precession by linearly polarized pump pulses. (a) Experimental geometry. (b) Pump-induced rotation of the probe polarization $ϕ$ as a function of time delay between linearly polarized pump and probe pulses for different values of the applied magnetic field. (c) The frequency $Ω_{0}$ of the observed oscillations as a function of the applied field strength $H$ . (d) The frequency $Ω_{0}$ of the oscillations as a function of temperature $T$ . The results were obtained for a pump intensity of $10 mJ ∕ {cm}^{2}$ . Pump pulses were linearly polarized with azimuthal angle $θ = 45 °$ . Results in (b) and (c) are obtained at a temperature $T = 10 K$ . From 116.Reuse & Permissions
Figure 49
(Color online) Laser-induced magneto-optical response from ${FeBO}_{3}$ : (a) Oscillations of the probe polarization as a function of the time delay between linearly polarized pump and probe pulses for different orientations of the pump polarization. The pump pulses propagate along the $z$ axis shown in (b). The probe pulse is not shown in (b) for simplicity. (c) The amplitude of oscillations as a function of the pump polarization azimuthal angle (symbols) and its fit using Eq. (71) (line). The results are obtained at $T = 10 K$ , $H = 1.75 kOe$ , and $I = 10 mJ ∕ {cm}^{2}$ . From 116.Reuse & Permissions
Figure 50
(Color online) Spin precession excited by circularly polarized pump pulses propagating along (a) the $z$ axis and along (b) the $y$ axis. $σ^{+} - σ^{-}$ is the difference between the spin precession amplitude excited by right- and left-handed circularly polarized pump pulses. In both cases the magnetic field is applied along the $x$ axis and the probe is at 10° from the pump propagation direction. The results are obtained at $T = 10 K$ and $I = 10 mJ ∕ {cm}^{2}$ . From 116.Reuse & Permissions
Figure 51
(Color online) Experimental dependencies of the oscillations amplitude $ϕ_{0}$ (dots) on (a) the magnetic field $H$ and (b) pump intensity $I_{0}$ . Solid lines in (a) and (b) represent the dependencies described by Eq. (71). (c) Initial phase $ζ$ of the pump-induced oscillations as a function of the magnetic field $H$ when described by $ϕ (Δ t) = ϕ_{0} \sin (Ω_{0} Δ t + ζ)$ . A typical experimental curve $ϕ (Δ t)$ is shown (circles) in (d). For reference, the curves $ϕ (Δ t) = ϕ_{0} \sin (Ω_{0} Δ t + 0)$ (solid line) and $ϕ (Δ t) = ϕ_{0} \sin (Ω_{0} Δ t + π ∕ 2)$ (dashed line) are shown. The experimental results shown in (a)–(d) are obtained for the pump polarization $θ = 45 °$ and temperature $T = 10 K$ . From 116.Reuse & Permissions

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