Ultrafast laser-induced changes of the magnetic anisotropy in a low-symmetry iron garnet film

We explore a thermal mechanism of changing the magnetic anisotropy by using femtosecond laser pulses in a low-symmetry dielectric ferrimagnetic garnet ${\left(\mathrm{YBiPrLu}\right)}_3{\left(\mathrm{FeGa}\right)}_5{\mathrm{O}}_{12}$ film grown on the (210)-type ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ substrate as a model media. Employing spectral magneto-optical pump-probe technique and phenomenological analysis, we demonstrate that the magnetization precession in this film is a result of laser-induced changes of the growth-induced magnetic anisotropy along with the ultrafast inverse Faraday effect. The change of magnetic anisotropy relies on the lattice heating induced by laser pulses of any polarization on a picosecond time scale. We show that the orientation of the external magnetic field with respect to the magnetization easy plane affects the precession noticeably. Importantly, the relative contributions from the ultrafast inverse Faraday effect and the change of different growth-induced anisotropy parameters can be controlled varying the applied magnetic field strength and direction. As a result, the amplitude and the initial phase of the excited magnetization precession can be gradually tuned.

Figure 1

(a) Orientations of the crystallographic axes in the (210)-film, the applied magnetic field ${\mathbf{H}}_{\mathrm{ext}}$, the effective anisotropy field ${\mathbf{H}}_{\mathrm{a}}$, and the net effective field ${\mathbf{H}}_{\mathrm{eff}}$. $x,y,z$ axes are directed along the [001], $\left[1\overline{2}0\right]$, and [210] crystallographic axes, respectively. Effective anisotropy field ${\mathbf{H}}_{\mathrm{a}}$ makes an angle $\gamma ={16}^{\mathrm{o}}$ with the $z$ axis in the $yz$ plane [7], as shown in the inset. The magnetic field direction is described by the polar angle ${\psi }_{\mathrm{H}}={80}^{\mathrm{o}}$ and the azimuthal angle ${\phi }_{\mathrm{H}}$. The direction of magnetization $\mathbf{M}$ is described by the polar ${\psi }_{\text{M}}$ and azimuthal ${\phi }_{\mathrm{M}}$ angles. In a general case the magnetization $\mathbf{M}$ is not collinear with the applied magnetic field and is not in the $yz$ plane. (b) Geometry of the pump-probe experiment (see text for the details).

Figure 2

Static Faraday rotation $\theta$ measured as a function of the external magnetic field applied at the angle (a) ${\psi }_{\mathrm{H}}={80}^{\mathrm{o}}$ and (b) ${\psi }_{\mathrm{H}}=0$ with respect to the sample normal (as shown in the insets). ${\theta }_s$ denotes the Faraday rotation at remanence which is proportional to the samples magnetization $M_s$.

Figure 3

(a) Normalized rotation of the probe polarization induced by the left-handed (${\sigma }^{-}$) circularly polarized pump pulses, measured as a function of the time delay $\mathrm{\Delta }t$ for various magnitudes of the applied magnetic field (symbols). The solid lines represent the best fit in accordance with Eq. (7). (b) Frequency of oscillations in the pump-probe data (a) as a function of the magnetic field magnitude, azimuthal angle ${\phi }_{\mathrm{H}}=0$ (symbols). (c) Frequency of oscillations in the pump-probe data (a) as a function of the magnetic field azimuthal angle ${\phi }_{\mathrm{H}}$ (symbols). $H_{\text{ext}}=0.26$ T. The solid lines in panels (b) and (c) represent the best fit obtained using the analytical expression for magnetic energy [see Appendix pp1].

Figure 4

(a) Normalized probe polarization rotation induced by the left- (${\sigma }^{-}$) and right-handed (${\sigma }^{+}$) circularly polarized pump pulses as a function of the time delay $\mathrm{\Delta }t$ for the various magnetic fields (symbols). (b) Probe polarization rotation induced by the ${\sigma }^{+}$-polarized pump pulses as a function of the time delay $\mathrm{\Delta }t$ measured for the various strengths of positive and negative magnetic field $\pm H_{\mathrm{ext}}$ (symbols). The solid lines on panels (a) and (b) represent the best fit in accordance with Eq. (7). (c), (d) Simulation of laser-induced Faraday rotation of probe pulse based on LLG equation (3) for the same cases as (a) and (b), respectively. Parameters used for the simulation are as follows. $\mathrm{\Delta }{K}_u=\mathrm{\Delta }{K}_i=-1\%;\mathrm{\Delta }{K}_{yz}=-0.5\%$; $|H_{\mathrm{IFE}}|=0.5$ T; ${\tau }_{\mathrm{IFE}}=100\mathrm{fs}$; $\alpha =0.1$.

Figure 5

(a) Initial phase ${\xi }_0$ of the probe polarization oscillations excited by ${\sigma }^{\pm }$-pump pulses as a function of the applied field, as extracted from the experimental data in Fig. 4. (b) Amplitude of the polarization- and field-dependent contributions to the probe polarization oscillations shown in Figs. 4 and 4 as a function of the applied magnetic field strength.

Figure 6

(a) Normalized probe polarization rotation induced by the left-handed circularly ${\sigma }^{-}$-polarized pump pulses of different photon energy measured as a function of the time delay $\mathrm{\Delta }t$ at $H_{\mathrm{ext}}=0.26$ T applied along the hard axis (symbols). (b) Normalized magnetization precession amplitude (solid symbols) and transmission change (open symbols) of the probe beam as a function of absorption coefficient $\beta$ at the pump photon energy $E_p$. The inset depicts the absorption coefficient as a function of photon energy of the pump. Apparent oscillations in the inset result from the interference of the light in the garnet film. Arrows show the pump photon energies $E_p$ used to obtain the results in panel (a). (c) Normalized probe polarization rotation induced by the linearly polarized pump pulses for different azimuthal angles of pump polarization plane $\varphi$ with respect to the (001) crystallographic direction of the film measured as a function of the time delay $\mathrm{\Delta }t$ at $H_{\mathrm{ext}}=0.28$ T directed along the hard axis (symbols). The solid lines on panels (a) and (c) represent the best fit in accordance with Eq. (7).

Figure 7

(a) Normalized probe polarization rotation induced by the left-circularly ${\sigma }^{-}$-polarized pump pulses of different azimuthal angles $\phi$ measured as a function of the time delay $\mathrm{\Delta }t$ (symbols). The solid lines represent the best fit in accordance with Eq. (7). (b) Initial phase ${\xi }_0$ (solid symbols) and amplitude (open symbols) $\mathrm{\Delta }{\theta }_0/{\theta }_S$ of the laser-induced precession as a a function of ${\phi }_{\text{H}}$ measured for an external magnetic field of $H_{\mathrm{ext}}=0.26$ T. (c) $z$ component of the torque ${\mathbf{T}}_0$ (4) calculated as a function of ${\phi }_{\text{H}}$ for the case when $\mathrm{\Delta }{K}_i=2\mathrm{\Delta }{K}_{yz}$. Note that the abrupt change of the initial phase ${\xi }_0$ observed at ${\phi }_{\text{H}}={180}^{\circ }$ occurs because the effective anisotropy field $H_a$ jumps to another equilibrium position when ${\phi }_{\text{H}}>{180}^{\mathrm{o}}$.

Figure 8

Graphical illustration of the process of pulse-induced magnetic anisotropy change with the following precessional dynamics for (a), (c) ${\phi }_{\text{H}}=0$ and (b), (d) ${\phi }_{\text{H}}={90}^{\circ }$. Cases (c) and (d) depict magnetization trajectory after the excitation calculated using parameters as in Fig. 4. Note that in the case (b), (d), the effective anisotropy field and the applied field both lie in the $yz$ plane. As a result, induced change of the anisotropy parameters does not deflect the net effective field away from this plane. This prevents the appearance of the $z$ component of the induced torque ${\mathbf{T}}_0$. By contrast, when the applied field is perpendicular to the $yz$ plane, the same change of the anisotropy modifies both deflection of ${\mathbf{H}}_{\mathrm{eff}}$ from the $yz$ plane and its orientation in the plane. As a result, all three components of the induced torque ${\mathbf{T}}_{\mathbf{0}}$ should be finite.

Figure 9

Static Faraday rotation as a function of the external magnetic field in the film with strong anisotropy with external field applied at (a) ${\psi }_{\mathrm{H}}={80}^{\circ }$ and (b) ${\psi }_{\mathrm{H}}=0$. ${\theta }_s$ denotes the Faraday rotation at remanence, which is proportional to the samples magnetization $M_S$. Insets show the experimental geometries used for measuring the static Faraday rotation in the samples.

Figure 10

(a) Normalized rotation of the probe polarization induced by the linearly polarized laser pulse as a function of the pump-probe time delay $\mathrm{\Delta }t$ measured for positive and negative magnetic field of $\pm 0.63$ T in the film with strong anisotropy. (b) Field-dependent contribution to the laser-induced dynamics, extracted using Eq. (6) from the data shown in the panel (a) (symbols). Solid line is a fit using Eq. (B1). (c) Normalized change of the sample transmission as a function of pump-probe time delay $\mathrm{\Delta }t$.