Figure 1 shows the dependency of the reflectivity normalized to the equilibrium value on the delay between the pump and the probe pulses of the four studied samples and its variation with temperature in the range of 5–300 K. In general, the responses of the pure palladium film change very slightly with temperature. The addition of the iron dopant leads to a development of a temperature dependence of ΔR/R(Δt) responses, both qualitative (the appearance of new relaxation components) and quantitative (changes in their amplitudes and time constants). While two decaying exponents are sufficient to describe the relaxation of the reflection coefficient of the Pd and Pd0.962Fe0.038 films at the lowest temperature, a minimum of four is required for the Pd0.94Fe0.06 film and only three for Pd0.92Fe0.08. Thus, with an increase in the iron concentration x in a Pd1−xFex system, the photoinduced dynamics of the electronic subsystem changes from a relatively simple to a much more complex one; subsequently, the character partially simplifies again.

Figure 1: Temperature evolutions of the reflectivity transients of Pd1−xFex alloy thin epitaxial films for compositions with x = 0 (a), 0.038 (b), 0.062 (c), and 0.080 (d).

In quantitative terms, in the general case, the relaxation response can be described by the sum of four decaying exponents, two fast and two relatively slow ones, with one positive and one negative amplitude in each pair:

(1)

A significant difference in the values of the characteristic times for the fast and slow components makes it possible to fit them separately, which improves the accuracy of the parameter determination.

To describe the relaxation of the reflectivity of a palladium film, Figure 1a, the first two terms in Equation 1 are sufficient. The fast component with an amplitude Af has a decay time = 0.24 ± 0.02 ps. The lifetime of the second, slow component with the amplitude As is = 410 ± 10 ps. Figure 1b–d shows similar dynamics of the reflectance for three films with iron contents of 3.8, 6.2 and 8.0 atom %. At room temperature, the behavior of the responses for the films with 3.8 and 6.2 atom % of iron is similar to the responses obtained from the pure Pd film. The abovementioned fast component for these films has approximately the same lifetime, ≈0.3 ps. The lifetime of the slow component in the samples with 3.8, 6.2, and 8.0 atom % of iron is 240 ± 10, 210 ± 10, and 290 ± 10 ps, respectively. However, with an increase in the iron concentration, at times up to ca. 10 ps, an additional fast exponential decaying component appears. This component is opposite in sign to those given above. The main feature of these responses is their strong temperature dependence. At temperatures above the Curie temperature of the samples, they are not detectable. However, on cooling, starting from the Curie temperature, the ΔR/R(Δt) responses increase sharply. The amplitude of the fast negative component increases in absolute value. Also, both the amplitude and the relaxation time of the slow positive component decrease. At temperatures of 90 and 160 K, another slow negative component appears in the samples with 6 and 8 atom % of iron, respectively. Its relaxation time is about 1 ns. The amplitude of this component is one order of magnitude smaller than the amplitudes of the other components.

Figure 2 shows temperature dependency of the ultrafast dynamics of magnetization. The data are presented here for the films with x = 0.038 and x = 0.080; for the sample with x = 0.062, the responses can be found in [37]. Photoinduced demagnetization and the recovery are observed only at T < TC. One can readily recognize two demagnetization processes that reveal themselves as the rising components and occur at time scales of subpicoseconds and tens of picoseconds. Therefore, the responses in the general case are described by the expression:

(2)

where components with amplitudes and describe the rise (demagnetization), while the factor following the square brackets describes the decay of the signal (magnetization recovery).

Figure 2: Temperature evolution of the time-resolved magneto-optical Kerr angle transients for the Pd0.962Fe0.038 (a) and Pd0.92Fe0.08 (b) epitaxial thin films at T < TC; red solid lines are the results of fits with Equation 2.

Temperature dependences of the amplitudes and the lifetimes of the selected components, obtained from the fit of the experimental data with Equation 1 and Equation 2, are presented in Figure 3 and Figure 4 for the reflectivity and time-resolved MOKE, respectively. We note here the invariance of the amplitude As (Figure 3a) and relaxation time (Figure 3b) at T ≥ TC, and a kink in their dependences at T = TC for the films with x = 0.038 and 0.062. The evolution of this component is not so obvious for the film with x = 0.080: The kink in its temperature dependence and the onset of its suppression take place at a temperature slightly above TC. Below TC, all three samples reveal a decrease of As and a shortening of In the samples with 3.8 and 6.2 atom % of iron, the drop of As with the temperature decrease slows down and ceases reaching values of ≈15% and ≈30% of its maximum, respectively, at 5 K.

Figure 3: Temperature dependences of the amplitudes (a) and the lifetimes (b) of the slow relaxation components of the reflectivity transients shown in Figure 1. In panel (a) the amplitude As for each sample is normalized to its magnitude at room temperature.

Figure 4: Temperature dependences of the amplitudes of the fast (squares/solid lines) (a) and the slow (circles/dashed lines) (c) photoinduced demagnetization components; characteristic times (b) of the magnetization recovery (squares/solid lines) and (d) of the slow demagnetization (circles/dashed lines) of the Pd0.962Fe0.038 (blue), Pd0.938Fe0.062 (black), and Pd0.92Fe0.08 (red) epitaxial films.

Other characteristics, that is, the amplitudes Af and Bs and the relaxation times and , do not reveal any anomalies in their temperature dependences and therefore are not presented. The amplitude of the fast component Bf for each Pd1−xFex alloy film has a nonzero value practically over the entire temperature range of 5–300 K. It gradually increases with decreasing temperature for samples with 6.2 and 8.0 atom % of iron. For the sample with 3.8 atom % of iron, it has the same behavior down to 150 K, and then decreases to zero at the lowest temperatures. The relaxation time of this component is practically independent of the temperature and is = 0.80 ± 0.10 ps.

Figure 4a shows the temperature dependences of the amplitudes of the fast demagnetization process. It is observed in the entire temperature range below the Curie temperature of the samples. The average rise time of the fast component of demagnetization for all three samples is ≈0.3 ps and depends only slightly on the temperature. The variation with temperature of the amplitude of the slow demagnetization component of the Pd0.962Fe0.038 sample, Figure 4c, is similar in character to that of the fast component. In contrast, in the Pd0.938Fe0.062 sample, starting from TC, the amplitude increases with lowering the temperature and reaches a maximum at ≈160 K. On further cooling, the amplitude decreases with a tendency to saturate at a small, but still detectable value at the lowest temperatures. In the Pd0.92Fe0.08 sample, the slow component is observed only in the range 120 K < T < TC. Here, it also appears at TC, reaches a maximum at ≈180 K, and drops to zero value at ≈125 K.

Temperature dependences of the characteristic time of the slow demagnetization component are shown in Figure 4d. It has a minimum value for all films at the lowest temperatures of the range of its observation. For the samples with an iron content of 3.8 and 6.2 atom %, the minimum is ≈10 ps, and for a film with 8 atom % of iron, it is ≈20 ps. However, on warming of a sample, the slow demagnetization time increases and becomes several times longer on approaching the Curie temperature.

The magnetization recovery time reveals a similar behavior (see Figure 4b) demonstrating a kind of a critical slowing down characteristic for second-order phase transitions. Starting from a value of ≈0.5 ns at the lowest temperatures, grows rapidly on approaching TC of the samples, where it gets two to three times longer.