Revealing the Nature of the Ultrafast Magnetic Phase Transition in Ni by Correlating Extreme Ultraviolet Magneto-Optic and Photoemission Spectroscopies

By correlating time- and angle-resolved photoemission and time-resolved transverse magneto-optical Kerr effect measurements, both at extreme ultraviolet wavelengths, we uncover the universal nature of the ultrafast photoinduced magnetic phase transition in Ni. This allows us to explain the ultrafast magnetic response of Ni at all laser fluences—from a small reduction of the magnetization at low laser fluences, to complete quenching at high laser fluences. Both probe methods exhibit the same demagnetization and recovery timescales. The spin system absorbs the energy required to proceed through a magnetic phase transition within 20 fs after the peak of the pump pulse. However, the spectroscopic signatures of demagnetization of the material appear only after $\approx 200\mathrm{fs}$ and the subsequent recovery of magnetization on timescales ranging from 500 fs to $>70\mathrm{ps}$. We also provide evidence of two competing channels with two distinct timescales in the recovery process that suggest the presence of coexisting phases in the material.

Figure 1

(a) Schematic of EUV ARPES and TMOKE measurements on Ni(111). The fluence profile of the laser excitation below the sample surface separates the magnetization response into two different regions (i) and (ii), depending on whether the in situ fluence is above the critical fluence $F_c$. Using TR ARPES, the probed depth is on the order of a monolayer, while TR-TMOKE probes the entire laser-heated depth of $\approx 10\mathrm{nm}$. (b) Schematic of the excitation present in the laser-induced phase transition in Ni when critical phenomena are taken into consideration [27]. When the laser fluence exceeds the critical fluence $F_c$, the electron temperature exceeds $T_c$ and the sample rapidly undergoes a magnetic phase transition, as evidenced by multiple critical phenomena.

Figure 2

Change in the exchange splitting ($\mathrm{\Delta }{E}_{\mathrm{ex}}$) in Ni measured using TR ARPES, for the absorbed laser fluence below ($0.21\mathrm{mJ}/{\mathrm{cm}}^2$, grey) and above ($1.7\mathrm{mJ}/{\mathrm{cm}}^2$, red) the critical fluence $F_c$. The solid lines are the fits to Eq. (1). Inset: Static ARPES spectrum plot along the $\overline{\mathrm{\Gamma }}-\overline{K}$ direction recorded using He ${\mathrm{I}}_{\alpha }$ photons.

Figure 3

Magnetization dynamics in Ni measured using TR TMOKE over a full range of laser fluences. The highest fluence is sufficient to fully suppress the sample magnetization. The data are offset for clarity. Red curves: Fits to our microscopic model which considers the critical behavior, as well as the depth-average effects in the TR-TMOKE measurements. Inset: Fluence-dependent amplitudes of the demagnetization and recovery processes directly extracted from the TR-TMOKE results. In the TR-TMOKE results, the magnetization $⟨M⟩$ and the extracted amplitudes $⟨A_1⟩$, $⟨A_2⟩$, and $⟨A_3⟩$ are averaged over the entire probed depth (see text). The dashed yellow line highlights the linear relation of the amplitude $⟨A_3⟩$ to the absorbed fluence when the fluence is above the critical fluence.

Figure 4

(a) Top panel: Schematic magnetization of a ferromagnet as a function of temperature under thermal equilibrium with a single critical point ($T_c$). Bottom panel: Extracted amplitudes of the change of magnetization in a monolayer of Ni as a function of in situ fluence and heat source. The correspondence of $T_c$ to the two critical fluences ($F_c$ and $F_c^{\prime }$) is highlighted. (b) The laser-induced magnetization variation in Ni as a function of time and depth. The black dashed lines represent the contours of equal magnetization. The white dashed lines separate different regions for the in situ fluence relative to the two critical fluences $F_c$ and $F_c^{\prime }$. (c) The relative contributions of the fast ($⟨A_2⟩$) and slow ($⟨A_3⟩$) recovery processes directly extracted from the TR-TMOKE results in Fig. 3. Inset: Potential scenarios for the coexistence of ferromagnetic and paramagnetic phases in different fluence regions.