Direct measurement of the three-dimensional magnetization vector trajectory in GaMnAs by a magneto-optical pump-and-probe method
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(Color online) Schematic illustration of two magneto-optical effects in (Ga,Mn)As, which are responsible for a rotation of the polarization plane Δβ of reflected light at normal incidence. (a) Polar Kerr effect (PKE) that is due to the different index of refraction for σ + and σ − circularly polarized light propagating parallel to the direction of magnetization M. (b) Magnetic linear dichroism (MLD) that is due to the different absorption (reflection) coefficient for light linearly polarized parallel and perpendicular to M if the light propagates perpendicular to the direction of M. Ex and Ey are the projections of the light amplitude to the crystallographic directions  and , respectively.
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(Color online) Magneto-optical signals (polarization rotations) measured in (Ga,Mn)As. (a) Dynamics of the MO signal induced by an impact of pump pulse on the sample that was measured by probe pulses with different polarization orientations β (points); lines are fit by Eq. (1) with parameters ωMn = 20.2 GHz, τG = 360 ps, and τp = 1050 ps. (b) Spectral dependence of static PKE and MLD, the arrow indicates the spectral position of the laser pulses used in the time-resolved experiment shown in part (a); note that the data for MLD are multiplied by 5 for clarity. (c) and (d) Polarization dependence of the oscillation amplitude A (c) and of the pulse function amplitude C (d) at time delay of 200 ps that was obtained by fitting the dynamics shown in (a) (points). Lines are results of simultaneous fits of A(β) by Eq. (2) and C(β) by Eq. (3) with parameters: δϕqe = +1.1°, δθqe = 0°, δMs /M 0 = −1% (Ref. 9). The deduced position of the easy axis in the sample without the pump pulse ϕ 0 = 119° is depicted by the vertical arrow in (c).
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(Color online) Direct experimental reconstruction of the magnetization real-space trajectory. An impact of the pump pulse induces a change of the magnetization magnitude and orientation relative to the corresponding equilibrium values (see inset in part (a) for a definition of the polar, ϕ, and azimuthal, θ, angles). (a) Time evolution of δϕ(t), δθ(t), and δMs (t)/M 0; the dotted line depicts the in-plane evolution of the easy axis position around which the magnetization precesses. (b) Orientation of magnetization at different times after the impact of the pump pulse; the sample plane is represented by the vertical line and the equilibrium position of the easy axis is depicted by the grey spot.
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