1. Introduction

Magneto-dynamics of magnetic nano-materials is of fundamental interest and is essential for various applications in modern magnetic storage technology [1–4]. Recent years, the rapid development of the information society has greatly promoted the demand for fast storage and transmission of information. In this regard, ultra-fast spin dynamics dealing with the magnetization precession on the picosecond timescale is significant. There are many approaches to tailor the spin dynamic properties of thin magnetic layers [5,6], among which the ferromagnetic/nonmagnetic (FM/NM) interfacial spin pumping effect has received the most attention. Based on the spin pumping principle [7,8], the spin current generated by the magnetic moment precession in the ferromagnetic layer is pumped into the nonmagnetic layer across the interface and then dissipates in the nonmagnetic layer. Such a dissipation can increase the relaxation of the magnetic moment precession in the ferromagnetic layer, leading to the increase of magnetic dynamic damping (α) of the ferromagnetic layer. Commonly, the efficient spin pumping effect is related to the spin transparency at the FM/NM interface and the spin-orbit coupling (SOC) of the NM layer. Thus, considerable researches are focused on the spin pumping and spin dynamics of FM/NM, where heavy metals (HM) such as Pt, Ta and W with large SOC attract the most attention [9–12].

It has been previously reported that antiferromagnetic spacers between the FM and HM layers, such as NiO and CoO, benefit the spin current injection and spin transport at the interface [13–15]. Recently, the large domain wall velocity and high switching speed have been obtained in synthetic antiferromagnets [16,17] due to the enhanced magneto-dynamic damping caused by the interlayer antiferromagnetic exchange coupling. Therefore, one would expect that the antiferromagnetic exchange coupling plays an important role in spin dynamics. According to our previous works on transition metal (TM)/rare earth (RE), a large antiferromagnetic exchange coupling between the RE and TM has been found, which has the potential for high tunability in magneto-dynamics [18,19]. Nd is a typical RE metal with large SOC. It shows paramagnetic properties but is antiferromagnetically coupled with TMs at room temperature, resulting in TM/Nd heterostructures, an ideal platform for high efficiency tunable magneto-dynamics.

Previous studies on TM/RE are mainly focused on spin dynamics at few gigahertz frequencies and low magnetic fields, while the modulation of ultrafast spin dynamics remained largely unexplored. Time-resolved magneto-optical Kerr effect (TR-MOKE) is a powerful tool for studying ultrafast spin dynamics due to its high sensitivity and magnetic field dependence. It can observe directly both time domain of spin precession and frequency domain by Fourier transform. It also can provide quantitative information on important ultrafast spin dynamic parameters such as the magneto-dynamic damping and lifetime, in particular, the magnetic field dependence of them. Besides, the excitation energy of TR-MOKE for the magnetic moment is higher compared with other techniques such as microwaves in gigahertz. In this case, the spin transport efficient may be much larger than that observed by conventional techniques, which can be reflected from the larger spin-mixing conductance obtained by TR-MOKE than ferromagnetic resonance (FMR). Such an advantage of ultra-fast spin dynamics facilitates especially to efficiency transport of FM/semiconductor structures [20], where the Schottky barrier may be weakened or overcome. Therefore, ultra-fast spintronics provides an efficient way to inject spin current from ferromagnetic material into the semiconductor layer.

In this letter, we study the ultrafast magnetic response of Nd/Ni₈₀Fe₂₀ (Py) heterostructures on sub-picosecond timescales by time-resolved magneto-optical Kerr effect (TR-MOKE). Effects of the magnetic field and the antiferromagnetically coupled interface on the ultrafast spin dynamics are systemically explored. Results show that the ultrafast spin dynamics of Py is improved by the antiferromagnetic coupling at the Nd/Py interface, which can be further modulated by an external magnetic field.

2. Experiments

The main structure of our sample is Ta (5 nm)/Nd (t nm) /Ni₈₀Fe₂₀ (Py, 6 nm)/Ta (2 nm), where the thickness of Nd (t nm) varies from 0 to 16 nm. Two Ta layers are used as the buffer and capping layer, respectively. Films are deposited on silicon dioxide substrate by DC magnetron sputtering under a base pressure of 1.2 × 10⁻⁵Pa at room temperature. Due to the effective detection depth of TR-MOKE being about 15 nm, Py is located in the upper layer of the Nd. Ar gas pressure is kept at 0.5 Pa during deposition, and a magnetic field of 50 Oe is applied on the substrate to induce a small in-plane uniaxial anisotropy of Py. The structure properties of samples are characterized by X-ray diffraction (XRD) and X-ray reflectivity (XRR). Static and ultrafast spin dynamic magnetic properties of the films are studied by vibrating sampling magnetometer (VSM) and TR-MOKE, respectively. During the TR-MOKE detection [21], laser pulses of ∼50 fs from Ti:sapphire regenerative amplifier with a repetition rate of 1 kHz at a central wavelength of 800 nm is split into a stronger pump (3 mW) and weaker probe (50 µW) beams. The pump pulse is focused on a spot of ∼ 450 µm in diameter on the sample surface, while the probe pulse is focused on a spot of ∼ 250 µm and is located at the center of the pump spot. The polar Kerr rotation of the probe reflected from the sample surface is detected by a balanced optical bridge and measured using a lock-in amplifier, synchronized to an optical chopper that modulates the pump beam. An external magnetic field H generated by an electromagnet is applied at φ = 50° with respect to the surface normal. The strength of H varies from 1726 Oe to 10733 Oe, which is controlled by electrical current and calibrated by a Gauss meter. All measurements are performed at room temperature.

3. Results and discussion

Figure 1(a) shows the XRD spectrum of Ta (5 nm)/Nd (16 nm)/Py (6 nm)/Ta (2 nm). The Nd (100), Nd (004) and Py (111) diffraction peaks are clearly observed, indicating the high texture of the Py layer and the perfect polycrystalline structure of Nd when the thickness of the Nd layer is 16 nm. The XRD figures with 0 nm Nd, 8 nm Nd and 12 nm Nd layers are presented in the inset of Fig. 1(a). The XRD data shows, at a thinner Nd thickness of 8 nm, the diffraction peak of Nd (100) disappears, which means that Nd is either in an amorphous state or too thin to detect. With the increase of Nd thickness, Nd changes the texture to (100) and (004) from (100). And Py always shows a (111) texture. X-ray reflectivity (XRR) measurements are also performed to detect the thickness and interface quality, and the spectrum is shown in Fig. 1(b). The well-periodic oscillation pattern indicates that the interface of the Nd/Py bilayer is well-controlled. The period of the XRR pattern is about 27.8 nm, close to the total thickness of the detected sample. Figure 1(c) presents the magnetic hysteresis loops of Nd (t nm)/Py measured by VSM, with the magnetic field along the easy axis in the film plane. With the increase of the Nd thickness, the saturation magnetization (M_s) of Nd/Py bilayers decreases while its coercive field (H_c) increases with increasing thickness of the Nd layer, as shown in Fig. 1(d). M_s of Nd/Py bilayers shows a descending trend the thickness of Nd changes from 0 to 8 nm, then turns to be stable with the increasing Nd thickness. The stable M_s value of Nd/Py is much smaller than that of naked Py films, which may be attributed to the proximity effect at the Nd/Py interface. Due to the magnetic proximity effect, magnetic moments of Nd around the Nd/Py interface are induced by the adjacent Py layer, which is antiparallel to the magnetization of Py. Such an antiferromagnetically coupled interface has been demonstrated by X-ray magnetic circular dichroism (XMCD) at room temperature in previous studies [5,18,19]. Therefore, an antiferromagnetically coupled configuration at the Nd/Py interface is formed and the antiferromagnetic coupling is within 8 nm. Besides, with the increase of the Nd thickness, the antiferromagnetic coupling effect becomes larger, by which Hc is enhanced with the antiferromagnetic exchange coupling between Py and Nd [22].

 

Fig. 1. (a) XRD pattern and (b) XRR result of Ta (5 nm)/Nd (16 nm)/Py (6 nm)/Ta (2 nm). The XRD pattern of Ta (5 nm)/Nd (t nm)/Py (6 nm)/Ta (2 nm), where t = 0, 8 and 12 in the upside of inset. (c) Magnetic hysteresis loops of Nd (t nm)/Py at the in-plane easy axis. (d) Variation of the saturation magnetization (Ms) and coercive field (Hc) versus Nd thickness for Nd (t nm)/Py (6 nm). Dash lines are guided to the eye.

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The schematic structure of the sample for TR-MOKE measurement is illustrated in Fig. 2(a). After a pump laser pulse excitation, an ultrafast demagnetization is triggered, and the anisotropy field suddenly changed, which forced the magnetization to precess around a new equilibrium direction. After the anisotropy field recovers, the initial equilibrium angle gradually restores and the magnetization continues to oscillate for several hundred picoseconds [23–25]. In Fig. 2(b), the dots show the measured transient Kerr signal (θ_k) representing the time evolution of the magnetization in Ta (5 nm)/Nd (12 nm)/Py (6 nm)/Ta (2 nm) thin film under different external magnetic fields. From Fig. 2(b), we see that the θ_k (magnetization) exhibits the damped oscillation behavior in a fixed magnetic field. Both of the oscillation period and the relaxation time of the samples are decreased when the external magnetic field increases.

 

Fig. 2. (a) Schematic structure of the sample and TR-MOKE measurement geometry. (b) Kerr signal (θ_k) for Ta (5 nm)/Nd (12 nm)/Py (6 nm)/Ta (2 nm) at the different external magnetic fields. The solid lines are the best fittings. (c) FFT spectrum for the oscillatory components in (b).

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To quantitatively analyze the precession process of the magnetic moment, a phenomenological equation can be used to fit the oscillation curves [25]:

 

Fig. 3. Field dependent (a) precession frequency, (b) relaxation time and (c) effective magnetic damping (αeƒƒ) of Ta (5 nm)/Nd (12 nm)/Py (6 nm)/Ta (2 nm). Dash lines are guided to the eye.

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Here, the effective damping (α_eƒƒ) includes the contribution for single layer of Py and the contribution from interface effect for the Nd/Py bilayer.

From Eq. (2), we obtain the effective magnetic damping of Nd (12 nm)/Py (6 nm) bilayer at different external magnetic fields as shown in Fig. 3(c). With the increase of the external magnetic field, the effective magnetic damping decreases from 0.053 to 0.044, then turns to be stable when H > 6000 Oe. Commonly, α_eƒƒ consists of two components: intrinsic damping and extrinsic damping. The intrinsic damping is determined by the internal magnetic property of the material, and the extrinsic component usually comes from the nonuniform spin precession [26]. The latter can be excluded due to the single frequency peak in the FFT spectrum. According to the VSM results, the saturation magnetization Ms decreases with increasing the thickness of Nd, which implies an antiferromagnetic coupling at the interface between Py and Nd. Our previous studies demonstrate that the anti-ferromagnetically coupled interface facilitates the spin pumping effect, which can increase the effective magnetic damping of the magnetic layer [22,27]. Therefore, we suspect that the magnetic field-dependent behavior of α_eƒƒ may be caused by the suppression of the antiferromagnetically coupled interface, which weakens the spin pumping effect in the Nd/Py structure, especially at the high-field region.

In order to clarify the interfacial effect on ultrafast spin dynamics of Nd/Py structures, we perform the thickness-dependent investigation at different external magnetic field conditions. Figure 4(a) shows the Kerr signal of different samples at 10733 Oe. With the increases of Nd thickness, at an external field of 10733 Oe, the damped oscillation periods for all samples are similar. The relaxation time decreases first then tends to a stable value, while the effective magnetic damping changes in the opposite way, as shown in Fig. 4(b) and (c) respectively. For different intensity of external field, these thickness dependent behaviors are similar, which implies the interfacial spin pumping effect. It is more obvious at lower magnetic fields than higher magnetic fields, denoting that the spin pumping effect can be suppressed by a high magnetic field.

 

Fig. 4. (a) The transient Kerr signal of Nd (t nm)/Py detected at 10733 Oe. Thickness dependences of (b) the relaxation time and (c) the effective magnetic damping of Nd (t nm)/Py at different external fields. (d) Variations of the effective spin-mixing conductance and the effective magnetic damping of Nd (16 nm)/Py as functions of the external field. Solid lines are fitting curves, and dashed lines are guided to the eye.

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We further investigate the spin transmission mechanism in Nd/Py structures by analyzing the ultrafast spin dynamics based on spin pumping theory. The spin pumping theory describes the damping enhancement in terms of a spin current pumped through the interface. The precession magnetization of Py gives rise to an accumulation of spins in the diffusive Nd material, and a spin current backflow is induced by the spin accumulation. In this way, spin relaxation in Nd/Py structures is enhanced, improving the damping of Py. According to the spin pumping theory, the enhancement of effective magnetic damping is derived by using the following equation [28]:

4. Conclusions

To summarize, ultrafast spin dynamics of Nd/Py structures have been systematically investigated by TR-MOKE. The saturation magnetization of Nd/Py shows a descending trend with the Nd thickness, implying the antiferromagnetically coupled interface in this structure. With the increase of Nd thickness in Nd/Py structures, the spin relaxation time detected by TR-MOKE decreases first and then tends to a stable value, while the effective damping changes in opposite way. These thickness dependent behaviors are more obvious at lower magnetic fields than at higher magnetic fields, demonstrating the interface contribution to spin dynamic modulation, which can be suppressed by the external magnetic field. On the other hand, with the increasing external magnetic field, the effective interfacial spin-mixing conductance is decreased from 19.35${\times} $10¹⁵cm^-2 to 11.73${\times} $10¹⁵cm^-2, proving that the external field can also modulate the spin current transmission at the Nd/Py interface. This research reveals the important role of the magnetic field on ultrafast spin dynamics in RE-based magnetic heterostructures.