Role of spin-lattice coupling in the ultrafast demagnetization of ${\mathrm{Gd}}_{1-x}{\mathrm{Tb}}_x$ alloys

After excitation by femtosecond laser pulses, Gd and Tb exhibit ultrafast demagnetization in two steps, with the time constant of the second step linked to the coupling strength of the $4f$ magnetic moments to the lattice. In time-resolved magneto-optical Kerr effect measurements of ${\mathrm{Gd}}_{1-x}{\mathrm{Tb}}_x$ alloys, we observe a decrease in this time constant from 33 to 9 ps with Tb content $x$ increasing from 0 to 0.7. We explain this behavior by the stronger spin-lattice coupling of Tb compared to Gd, which increases the effective spin-lattice coupling in ${\mathrm{Gd}}_{1-x}{\mathrm{Tb}}_x$ with $x$. In contrast, the faster time constant of the first demagnetization step exhibits no dependence on $x$. Additional time- and element-resolved x-ray magnetic circular dichroism measurements show a two-step demagnetization of Gd and Tb in ${\mathrm{Gd}}_{0.6}{\mathrm{Tb}}_{0.4}$ with an equivalent time scale of the second step but a different magnitude of demagnetization which persists for 15 ps. We explain this by an increased coupling of the Gd $4f$ magnetic moments to the lattice compared to pure Gd, via interatomic exchange coupling to the neighboring Tb $4f$ moments mediated by $5d$ electrons, which has limited efficiency and allows an estimation of a characteristic time scale of the interatomic exchange coupling. We assign the first demagnetization step to the dynamics of the laser-excited $5d$ electrons, while the second demagnetization step is dominated by the strength of spin-lattice coupling of the $4f$ electrons.

Figure 1

(a) Schematic electronic density of states for rare earth elements Gd and Tb. 1.5 eV pump pulses excite predominantly $5d$ electrons in the vicinity of the Fermi level $E_{\mathrm{F}}$, which are probed by time-resolved MOKE at the same photon energy. XMCD at the $M_5$-edge probes the $4f$ magnetic moments directly and element selectively by resonantly exciting the $3d_{5/2}$ core level electrons to the unoccupied $4f_{\downarrow }$ states. $\uparrow$ and $\downarrow$ denote majority and minority spins, while $H$ and $M$ refer to the external magnetic field and magnetization, respectively. (b) The coupling between Gd and Tb $4f$ and $5d$ magnetic moments and the lattice in ${\mathrm{Gd}}_{1-x}{\mathrm{Tb}}_x$ alloy is shown schematically.

Figure 2

Characterization of the magnetic properties of epitaxial ${\mathrm{Gd}}_{1-x}{\mathrm{Tb}}_x$ films on W(110) by static MOKE. (a) Magnetization $M$, normalized to the saturation magnetization $M_S$, depending on the external magnetic field $H$, measured at a base temperature $T_0$ of 220 K. Increasing coercivity and/or changing shape of the hysteresis loops with increasing Tb content point to the influence of the strong Tb spin-lattice coupling. (b) Temperature-dependent magnetization $M$, normalized to its value $M_0$ at 220 K. The inset shows the linear concentration dependence of the Curie temperature $T_{\mathrm{C}}$. The line is a guide to the eye.

Figure 3

Dependence of ultrafast magnetization dynamics on the Tb concentration $x$ in ${\mathrm{Gd}}_{1-x}{\mathrm{Tb}}_x$ alloy measured with time-resolved MOKE at a base temperature of 220 K and in an external magnetic field of $\pm 0.04$ T. (a) The transient change of the magnetization, as measured by the change in Kerr rotation $\Delta \theta$ normalized to the value ${\theta }_0$ for the unexcited sample, is displayed for five different Tb concentrations ranging from 0 (uppermost curve) to 0.7 (lowermost curve). (b) The resulting rate of the quasiequilibrium process $\gamma =1/{\tau }_2$, with ${\tau }_2$ being the time constant of the second step of demagnetization as derived from double exponential fits to the time-resolved MOKE data [plotted as black lines in (a)], shows an increase towards larger Tb concentration. This behavior is well described by a linear fit to the data (solid line). $\gamma$ for pure Tb is taken from [19]. Inset: In the time constant ${\tau }_1$ of the first step of demagnetization, no clear trend with increasing Tb concentration can be observed.

Figure 4

X-ray absorption spectra of ${\mathrm{Gd}}_{0.6}{\mathrm{Tb}}_{0.4}$ at the Gd and Tb $M_{5,4}$ edges measured with circularly polarized x rays, with the sample's magnetization oriented parallel (A${}_{+})$ and antiparallel (A${}_{-})$ to the x-ray propagation direction by applying an external magnetic field $H=\pm 0.5$ T, are displayed in the upper panel. The absorption spectra are normalized to the continuum step after the Tb $M$ edges. The lower panel shows the XMCD, which is proportional to A${}_{-}$-A${}_{+}$, with the proportionality factor [32] given by the angle of ${35}^{\circ }$ to the surface normal under which $H$ is applied and the x-ray polarization degree of 90%. The shaded areas mark the photon energies where the time-resolved XMCD measurements were performed. The inset depicts element-resolved hysteresis loops of Gd and Tb, taken at the respective $M_5$ edges.

Figure 5

Time- and element-resolved ultrafast demagnetization of Gd (squares) and Tb (circles) in ${\mathrm{Gd}}_{0.6}{\mathrm{Tb}}_{0.4}$. The temporal evolution of the XMCD signal, which corresponds to the transient, element-resolved $4f$ magnetic moment $\mu$, normalized to its value ${\mu }_0$ before laser excitation, is shown for a pump-probe delay of up to 50 ps. XMCD acquired with 10 ps long x-ray pulses is displayed in the inset. All XMCD measurements were performed at base temperature 82 K and in an external magnetic field of $\pm 0.5$ T.