Magnetoelastic coupling to coherent acoustic phonon modes in the ferrimagnetic insulator $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$

In this work we investigate single crystal $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$, a promising candidate material for Floquet engineering and magnetic control, using ultrafast optical pump-probe reflectivity and magneto-optical Kerr spectroscopy. $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$ is a Mott-Hubbard insulator with a ferrimagnetic and orbitally ordered ground state ($T_C$ = 32 K). We observe multiple signatures of the magnetic phase transition in the photoinduced reflectivity signal, in response to above band-gap 660-nm excitation. Magnetic dynamics measured via Kerr spectroscopy reveal optical perturbation of the ferrimagnetic order on spin-lattice coupling timescales, highlighting the competition between the ${\mathrm{Gd}}^{3+}$ and ${\mathrm{Ti}}^{3+}$ magnetic sub-lattices. Furthermore, a strong coherent oscillation is present in the reflection and Kerr dynamics, attributable to an acoustic strain wave launched by the pump pulse. The amplitude of this acoustic mode is highly dependent on the magnetic order of the system, growing sharply in magnitude at $T_C$, indicative of strong magneto-elastic coupling. The driving mechanism, involving strain-induced modification of the magnetic exchange interaction, implies an indirect method of coupling light to the magnetic degrees of freedom and emphasizes the potential of $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$ as a tunable quantum material.

Figure 1

(a) Optical conductivity and (b) index of refraction of GTO/LSAT thin film as a function of photon energy and temperature. Red arrows indicate the 1.88 eV pump/probe energy. The weak feature in ${\sigma }_1$ at 2 eV corresponds to the MH gap, while the steep feature near 5 eV arises from ${\mathrm{O}}_{2p}$ to ${\mathrm{Ti}}_{3d}$ and ${\mathrm{Gd}}_{4f}$ charge transfer transitions. (c) Depiction of 1.88 eV laser excitation, corresponding to intersite Ti 3d-3d transition across the MH gap.

Figure 2

(a) Photoinduced differential reflectivity signal $\mathrm{\Delta }R/R$ at all measured temperatures, from 10 to 295 K, taken on a single crystal $\mathrm{Gd}\mathrm{Ti}{\mathrm{O}}_3$ sample. The black curves are exponential fits to the data, of the form given in Eq. (1). The blue star indicates the data curve taken at $T_C$. (b) $\mathrm{\Delta }R/R$ values at 500 ps, an approximation of the peak signal at all temperatures. The red line is a power law fit, commonly seen in systems undergoing a second-order magnetic phase transition. (c) Representative pump-probe scans at 10 and 100 K, indicating the various timescales involved in the recovery process [see Eq. (1)].

Figure 3

(a) Time constant (black) and amplitude (red) of the spin-lattice coupling term, extracted from exponential fits to the $\mathrm{\Delta }R/R$ data. The vertical gray section indicates the fM transition region $T_C=32$ K, where the lifetime is too long to measure [see 30 K curve marked by a blue star in Fig. 2]. The red dashed line depicts zero amplitude and clarifies the crossover region. (b) Coherent acoustic phonon response, isolated by subtracting the exponential fits from the $\mathrm{\Delta }R/R$ data. The inset shows the $\mathrm{\Delta }R/R$ residual to a longer delay time of 150 ps, where higher frequency components emerge.

Figure 4

Time-resolved Kerr dynamics at various magnetic fields, recorded as the difference between the MOKE signal in opposing field directions $\mathrm{\Delta }\theta =\mathrm{\Delta }\theta (+H)-\mathrm{\Delta }\theta (-H)$. This is a measure of the photoinduced change in the out-of-plane magnetization $\mathrm{\Delta }{M}_z$. Red arrows indicate the crossover to negative values of $\mathrm{\Delta }\theta$.

Figure 5

(a) Schematic depiction of the spin dynamics. Photoexcitation directly perturbs the Ti spins, which fluctuate and decrease their projection along the applied field H (parallel to the $a$ axis, $+z$) in $t<{\tau }_{s-l}$ ps, increasing the MOKE signal. At longer times: if H and/or magnetic order is weak, induced spin fluctuations and the AFM exchange coupling lowers the projection of Gd spins along $z$. Conversely, if H is larger than the exchange field, at 1 T, Gd does not reorient and no negative component of the signal is observed. (b) Coherent acoustic phonon response, isolated by subtracting the exponential fits from the time-resolved Kerr data (at 1 T applied field). The dynamics appear similar to the $\mathrm{\Delta }R/R$ residual, implying a common origin which we attribute to a coherent strain wave launched by the pump pulse. The appearance of this signal in the Kerr response indicates coherent acoustic phonon manipulation of the magnetic order, presumably from exchange modulation.

Figure 6

FFT amplitude of the $\mathrm{\Delta }R/R$ residual, taken at pump/probe wavelength of 660 nm (a) and 800 nm (b). The red dashed lines indicate the approximate peak positions of the 660 nm FFT. Note the redshift to lower frequency at higher wavelength. (c) The integrated FFT amplitudes at various frequencies as a function of temperature, normalized. (d) The FFT limited to the first 40 ps and (e) 60 ps of the $\mathrm{\Delta }R/R$ data. The higher frequency mode emerges only after 40 ps.