Ultrafast magnetostriction and phonon-mediated stress in a photoexcited ferromagnet

Femtosecond excitation of ${\text{SrRuO}}_3$ nanolayers in a ${\text{SrRuO}}_3/{\text{SrTiO}}_3$ superlattice quenches their ferromagnetism, resulting in magnetostriction. The buildup of mechanical stress is observed in real time by mapping lattice motions via ultrafast x-ray diffraction. A rise time of 500 fs is found for a wide range of excitation wavelengths. In the ferromagnetic phase, phonon-mediated $\left({\sigma }_{\text{ph}}\right)$ and magnetostrictive stress $\left({\sigma }_M\right)$ components display similar strengths but opposite signs. The amplitude of ${\sigma }_M$ follows the temperature dependent magnetization $M^2\left(T\right)$ whereas the strength of ${\sigma }_{\text{ph}}$ is determined by the amount of deposited energy.

Figure 1

(Color online) (a) Measured reciprocal space map of the SL showing pseudomorphic growth of the sample. (b) Thick line: measured x-ray reflectivity of the SL as a function of the diffraction angle $\theta$. Thin line: calculated reflectivity of the sample using dynamical x-ray diffraction theory. (c) Contour plot of the calculated intensity of the (0 0 116) SL Bragg peak as a function of the lattice parameters $c_{\text{STO}}$ and $c_{\text{SRO}}$. The circle and square indicate the initial structure at 300 and 22 K, respectively. The arrow shows the motion of the SL phonon along these coordinates. (d) Density of states (DOS) of majority $(\downarrow )$ and minority $(\uparrow )$ spins in the ferromagnetic and paramagnetic phases according to Ref. 9. Vertical solid arrows: spin-conserving optical transitions; horizontal open arrow: magnon involved in spin-flipping indirect transitions. (e) Frequency dependent absorption coefficient $\alpha \left(\omega \right)$ of ${\text{SrRuO}}_3$ calculated from the experimental data of Ref. 26 (arrows: pump frequencies).

Figure 2

(Color online) (a) Transient change in the x-ray reflectivity $\Delta R/R_0$ after ultrafast optical excitation at ${\lambda }_{\text{ex}}=800\text{nm}$ (circles) and ${\lambda }_{\text{ex}}=2.2\mu \text{m}$ (open diamonds) with the same pump fluence of the SRO layers in the STO/SRO superlattice $\left(T=300\text{K}\right)$. Thin line: (800 nm) pump / (800 nm) probe experiments serve for an exact determination of delay zero. (b) Time evolution of the uniaxial stress in the SRO layers derived from the data in (a) ($T=300\text{K}$, solid circles) and in Fig. 3c ($T=20\text{K}$, solid diamonds).

Figure 3

(Color online) (a) Optical reflectivity change at ${\lambda }_{\text{pr}}=2.2\mu \text{m}$ and (c) transient change in the x-ray reflectivity (symbols) measured with excitation at ${\lambda }_{\text{ex}}=2.2\mu \text{m}$ at various lattice temperatures. Solid lines: fits with ${\tau }_{\text{rise}}={\tau }_{\text{mag}}=500\text{fs}$. Dashed line: simulation with ${\tau }_{\text{mag}}=0$. (b) Temperature dependence of the amplitude $A\left(T\right)$ of the optical $\Delta R/R_0$ (open diamonds) and the SL phonon oscillation (solid diamonds) normalized to the respective value at $T=300\text{K}$. In the ferromagnetic phase $\left(T<T_C=160\text{K}\right)$, the amplitude of the all-optical transients is enhanced, while the SL phonon amplitude is reduced due to the magnetic contractive stress contribution. Both amplitudes follow approximately the temperature dependent magnetization squared $M^2\left(T\right)$ (dashed and solid lines).