Coherent Control of the Route of an Ultrafast Magnetic Phase Transition via Low-Amplitude Spin Precession

Time-resolved magneto-optical imaging of laser-excited rare-earth orthoferrite $(\mathrm{SmPr}){\mathrm{FeO}}_3$ demonstrates that a single 60 fs circularly polarized laser pulse is capable of creating a magnetic domain on a picosecond time scale with a magnetization direction determined by the helicity of light. Depending on the light intensity and sample temperature, pulses of the same helicity can create domains with opposite magnetizations. We argue that this phenomenon relies on a twofold effect of light which (i) instantaneously excites coherent low-amplitude spin precession and (ii) triggers a spin reorientation phase transition. The former dynamically breaks the equivalence between two otherwise degenerate states with opposite magnetizations in the high-temperature phase and thus controls the route of the phase transition.

Figure 1

(a) Magnetic structure of RE orthoferrites in the low-temperature (${\Gamma }_2$), intermediate (${\Gamma }_{24}$), and high-temperature (${\Gamma }_4$) phases. (b) Hysteresis of the $z$ component of the weak magnetization in $(\mathrm{SmPr}){\mathrm{FeO}}_3$, probed by means of the Faraday rotation. The measurements show the presence of a phase transition region in which the net magnetic moment gradually rotates by 90° from the $x$ axis to the $z$ axis.

Figure 2

Appearance of an out-of-plane component of the magnetization at a time scale of a few picoseconds due to excitation by a 60 fs laser pulse with energy $10.3\mu \mathrm{J}$. In this case, the initial temperature of the sample was 90 K. The out-of-plane component can point down (black) or up (white). Note that laser pulses with opposite helicities of the polarization create magnetic domains with opposite orientation of the magnetization. Linearly polarized laser pulses produce a multidomain state. Each picture shows an area of approximately $70\times 70\mu {\mathrm{m}}^2$.

Figure 3

Dependence of the laser-induced spin reorientation on temperature (a) and pump pulse energy (b) using pump pulses with right-handed (${\sigma }_{+}$) and left-handed (${\sigma }_{-}$) circular polarization. The magneto-optical images show that, depending on the temperature $T$ and the pump pulse energy $E$, pulses of the same helicity can create domains with opposite magnetization.

Figure 4

(a) Illustration of the mechanism for controlling the path of a laser-induced phase transition. It is based on two effects from the same laser pulse: heating and the excitation of small amplitude spin precession. Because of heating, the effective temperature of the RE $4f$ electrons ($T_{\mathrm{eff}}$) reaches the temperature of the first phase transition ($T_1$) after time $\Delta t$. At that moment, the shape of the potential energy as a function of $M_z$ starts to change dramatically: The minimum of the potential, at $M_z=0$, splits into two minima, which separate further with increasing temperature. The spin precession is instantaneously excited at $t=0$. As the spins oscillate around their equilibrium, the symmetry is dynamically broken. Therefore, $M_z$ will be slightly closer to the left or the right minimum at the moment of the phase transition and will consequently proceed to grow in that direction. (b) The phase diagram, calculated by using a simple model of the mechanism, shows the reorientation direction as a function of sample temperature and pump pulse fluence after excitation with right-handed polarized light. The black and white colors represent a transition to a state in which $M_z$ is negative and positive, respectively. In the gray region, the laser-induced heating is insufficient to trigger the phase transition.