Transient quantum isolation and critical behavior in the magnetization dynamics of half-metallic manganites

We combine time-resolved pump-probe magneto-optical Kerr effect and photoelectron spectroscopy experiments supported by theoretical analysis to determine the relaxation dynamics of delocalized electrons in half-metallic ferromagnetic manganite $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Mn}{\mathrm{O}}_3$. We observe that the half-metallic character of $\mathrm{L}{\mathrm{a}}_{1-x}\mathrm{S}{\mathrm{r}}_x\mathrm{Mn}{\mathrm{O}}_3$ determines the timescale of both the electronic phase transition and the quenching of magnetization, revealing a quantum isolation of the spin system in double-exchange ferromagnets extending up to hundreds of picoseconds. We demonstrate the use of time-resolved hard x-ray photoelectron spectroscopy as a unique tool to single out the evolution of strongly correlated electronic states across a second-order phase transition in a complex material.

Figure 1

Time-resolved magneto optical Kerr effect results. (a) Scheme of the pump-probe MOKE experimental setup. (b) Main panel: Scheme of the temperature variation of the three sets of degrees of freedom. In a half-metallic system, the spin system thermalizes last, on timescales much longer than electrons and lattice. Inset: Schematic representation of the three sets of degrees of freedom in a magnetic solid: charges, spins, and lattice. In a half-metallic system, the direct spin-electron demagnetization channel is almost suppressed due to the absence of available spin-flip processes. (c) Main panel: Relative reflectivity variation vs pump-probe delay measured below and above $T_{\mathrm{c}}=335$ K. The dashed curve represents the dynamical reflectivity trace at 400 K scaled to match the amplitude of the initial step in the curve at 200 K. The blue-shaded region highlights the variation of reflectivity induced by the DSWT, as described in the text. DSWT is absent above $T_{\mathrm{c}}$, confirming its magnetic origin. Inset: Finer time-step measurement performed at room temperature, showing the sharp increase and decay of hot-carrier-induced reflectivity. (d) Normalized complex Kerr angle modulus $\left|\mathrm{\Theta }\right|$ vs pump-probe delay, measured at 150 and 300 K. Each curve is obtained as the modulus of the vector sum of independently recorded ellipticity and rotation traces, as sketched in the inset. While in the grayed-out area the signal is still influenced by charge dynamics, a long timescale demagnetization is evident. A minimum is observed for the 150 K curve.

Figure 2

Critical behavior of the magnetic dynamics. Inset: temperature dependence of Kerr ellipticity dynamics. Curves follow the color code (corresponding to different temperatures) depicted in the bar at the right side. A minimum is reached around 250 ps for lowest temperatures. As temperature increases, the minimum shifts to larger delays moving out of the measurable interval. Main panel: critical slow-down modeling. Filled circles are the result of a batch fit of curves in the inset (same color code), representing the characteristic time of ellipticity quench vs temperature. The results of the fit, performed between 10 ps and the absolute minimum of each ellipticity curve, are shown in the inset as gray solid lines for 163 and 305 K. The vertical error bars are given by the standard deviation of the fit, hence error bars for temperatures close to $T_{\mathrm{c}}$ (vertical red line) are larger due to a reduced absolute signal. The dashed line is the fit of the power law, resulting in values of the critical exponent as described in the text.

Figure 3

Decomposition of HAXPES spectra by screening channel. (a) Main panel: Experimental HAXPES Mn 2p spectrum of half-metallic LSMO, measured at $hv=7940$ eV and at $T=85$ K; the presence of well-screened satellite at the low-binding-energy side of the main peaks is indicated by the arrows. The blue line is the Tougaard background used to obtain background-subtracted spectra in Fig. 4. Inset: Intensity variation of the well-screened peak relative to Mn $2p_{3/2}$ vs temperature is shown. (b) Theoretical Mn $2p$ spectrum calculated with $\mathrm{Mn}{3}^{+}$ valence (sum, blue solid line), separated in its initial state components (curves and histograms): the ground state $3d^4$ (yellow, bottom curve), the charge transfer from the ligand hole $3d^5\mathrm{L}$ (orange, middle), and the charge transfer from the well-screened state, $3d^5\mathrm{C}$ (red, top). The energy position of the well-screened satellites is highlighted by the gray-shaded vertical bar.

Figure 4

Dichroism in HAXPES and theoretical analysis. LSMO Mn $2p$ core-level spectra measured at $T=200$ K, i.e., below $T_{\mathrm{c}}$, with left- and right circularly polarized x rays, respectively, labeled LCP and RCP (top spectra, triangles). Differences as measured at $T=200$ K (diamonds, orange) and $T=300$ K (squares, yellow) are shown below. At both temperatures, the largest magnetic signal is located at the energy position of the well-screened satellites. In the bottom part of the panel, calculated spectra with hybridization $V^{*}=1.17$ eV are shown (blue and red solid curves), with differences for $V^{*}=1.17$ eV (orange, solid) and $V^{*}=0$ eV (yellow, solid). Line-shape analysis confirms that hybridization must be taken into account to obtain good agreement with experimental results.

Figure 5

TR-HAXPES line-shape variation. (a) Sketch of the pump-probe HAXPES setup, with main values of the pump-probe scheme and geometric parameters. (b) Evolution of the Mn $2p_{3/2}$ peak in LSMO after optical pumping with 800-nm, 100-fs IR laser at a fluence of $4\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, measured with a 50-ps synchrotron radiation probe at $hv=7940$ eV varying the pump-probe delay. (c) Variation of the line shape of the Mn $2p_{3/2}$ peak. The topmost curve shows the difference between static spectra measured at 150 and at 300 K, highlighting the shifts of spectral weight observable in a quasistatic temperature variation. The other curves are obtained by subtraction of the line-shape “laser off” from the one observed at each delay. At negative delays the absence of significant features confirms the full recovery of the initial state. At time zero, the increase of spectral weight expected from quasistatic temperature changes at high binding energy is not yet present, while the low-binding-energy structure is significantly reduced. On the timescales of the pulse duration (50 ps), the electronic structure is therefore in a long-lived nonequilibrium condition. At positive delays (+100 ps, +300 ps), a higher temperature transient equilibrium is formed: spectral weight changes are analogous to quasistatic line-shape variations. At long delays (1–3 ns) the differences slowly decrease.

Figure 6

Time trace of the low-binding-energy structure evolution. Each point in the graph (filled squares with error bar) corresponds to the area of the difference between the no-pump spectrum and the spectrum recorded at a fixed pump-probe delay, in the range of energies $640.5-638$ eV. To calculate the relative variation, it is divided by the area of the no-pump spectrum in the same range. Spectra in the case of −100ps, +100 ps, and 3.1 ns are shown in top panels, with fitted intensities of the satellites. Blue lines are guides to the eye and the vertical error bars are obtained by the integral of the difference between no-pump and the most negative delays: the absolute value of their deviation from zero gives an estimate of the uncertainty on the integrals due to the measurement noise. The horizontal uncertainty is given by the probe pulse duration of 50 ps and is smaller than the symbol size.