1 Introduction

The terahertz (THz) frequency range from 0.1 to 10 THz between the microwave band and the mid-infrared band in the electromagnetic spectrum is often referred to as the “THz gap.” The THz frequency range is intended to be used for biological diagnosis,^[1] objective imaging,^{[2, 3]} and next-generation (6G) wireless communication networks.^{[4, 5]} Recently, developments of new spintronic applications in the THz frequency range have been investigated for spintronic THz emitter,^[6-8] ultrafast spin current,^[9-11] antiferromagnetic materials,^[12-14] and ferromagnetic metal films with large perpendicular magnetic anisotropy (PMA).^[15-18] This newly developed high-speed spintronic technology, THz spintronics,^{[19, 20]} holds promise for the future Internet of Things society.

A leading device in the field of spintronics is nonvolatile magnetoresistive random access memory (MRAM).^{[21, 22]} A macrospin model predicts that the characteristic switching time scale is inverse proportional to the effective PMA field µ₀H_k^eff in the film as long as the magnetic damping constant α is sufficiently small, i.e., α << 1.^[23-25] Therefore, a ferromagnetic layer with large µ₀H_k^eff is required for high-speed spintronic devices and several groups have already demonstrated such high-speed magnetization control in films with large PMA.^{[26, 27]}

Ultrathin films of magnetic materials with large PMA energy, small saturation magnetization M_s, and small α are required for MRAM and other spintronic memory devices. Currently, a CoFeB polycrystalline film is commonly used for MRAM. The PMA energy and M_s for a perpendicularly magnetized CoFeB ultrathin film are less than 0.3 MJ m⁻³ and ≈1000 Ka m⁻¹, respectively, with α of 0.01-0.02.^[28-31]

The use of tetragonal Mn-based magnetic materials and derivatives as the ferromagnetic layer for next-generation spintronic memory devices has attracted much attention because of the large PMA energy in excess of 1.4 MJ m⁻³ and small α of 0.0075–0.015 of these materials.^[32] The growth technique for textured polycrystalline films on thermally oxidized Si substrates is also highly attractive for the mass production of MRAM and various devices with 3D architectures based on conventional Si technology. This encourage the researchers to grow ultrathin films of Mn-based magnetic metals on the Si substrates; however, the PMA energy of the polycrystalline samples prepared in a previous study was degraded.^[33]

Cu₂Sb-type Mn-compounds, such as MnAlGe, are suitable materials for practical application in high-speed spintronic memory devices. In MnAlGe, the Mn atoms occupy the base center 2a position (0,0,0), (1/2,1/2,0), and the magnetic moments of these atoms are ferromagnetically directed along the c-axis in MnAlGe.^{[34, 35]} The distance between the c-planes is relatively large as compared with the nearest neighbor Mn–Mn distance in the c-plane. Therefore, these compounds are considered to be pseudo-2D magnetic materials. The large anomalous Hall effect in a single crystal MnAlGe was discussed by considering the topological feature with a unique 2D Berry curvature distribution, which resembles the 2D Fermi surface obtained in a 2D Mn atomic layer.^[36] Fast magnetization precession was also investigated in a relatively thick (≈100 nm) single crystal thin film of MnAlGe grown on MgO substrate.^{[32, 37]} Although the theoretically predicted value of α of MnAlGe is comparable with that of other tetragonal Mn compounds, the experimentally measured α value was relatively larger as compared with previously reported values for these compounds.

On the other hand, tunnel magnetoresistance (TMR) has not been reported for the Cu₂Sb-type MnAlGe, however, many groups developed TMR ratio for PMA Mn-compounds based MTJs, by using an insertion layer such as Co, CoMn, and CoFe.^{[38, 39]} As discussed in previous studies, the TMR ratio can be controlled by modifying the design of termination atoms at the surface between the MgO barrier layer and ferromagnetic layer in the MTJ.^{[40, 41]} A synthetic antiferromagnetic (SyAF) structure was also developed using a perpendicularly magnetized magnetic layer to increase the PMA while retaining the TMR ratio in the MTJ.^[42] Theoretical calculation also predicted that the SyAF structure is effective for high-speed switching.^[43]

There is no report on the large TMR in MnAlGe, however, it can be grown on amorphous substrates with PMA.^[44] Recently, ultrathin polycrystalline film growth on thermally oxidized Si substrates have been investigated.^{[45, 46]} Because the substitution of Mn sites by Cr atoms enlarges the PMA energy, ^{[47, 48]} (Mn–Cr)AlGe polycrystalline films deposited on thermally oxidized Si substrates were recently systematically investigated and there PMA energy was measured to be 0.7 MJ m⁻³.^{[49, 50]} Although the above-mentioned studies succeeded in investigating the large PMA energy and small M_s of polycrystalline ultrathin films grown on thermally oxidized Si substrates, the magnetization dynamics and α values of these films were not reported.

In this study, we investigated the magnetization dynamics in (Mn–Cr)AlGe and MnAlGe films to clarify the sub-THz magnetization precessional motion and the value of α. Because the films are crystallized by utilizing a MgO template layer, the thickness dependence of α was also systematically investigated. The high-resolution transmission electron microscopy (TEM) study revealed the layered crystal structure of the MnAlGe and (Mn–Cr)AlGe films representing the Cu₂Sb-structure. The partial substitution of Mn sites by Cr atoms in (Mn–Cr)AlGe was also confirmed in the TEM images. Sub-THz magnetization precessional motion with a precession frequency of 0.164 THz and relatively small effective magnetic damping constant α_eff of 0.012 ± 0.001 were obtained in a 5 nm thick (Mn–Cr)AlGe film with large PMA energy of 0.68 MJ m⁻³ and small saturation magnetization of 303 kA m⁻¹. The theoretical calculation inferred that the smaller value of α of (Mn–Cr)AlGe as compared with that of MnAlGe originates from the modulation of the total density of states (DOS) by Cr substitution.

2 Results and Discussion

Figure 1a–k shows the cross-sectional high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) images and corresponding EDS mappings of the MnAlGe and (Mn–Cr)AlGe films with a film thickness of t = 5 nm. Both samples have a layered structure consisting of Mn and Al–Ge layers, which corresponds to the Cu₂Sb-structure as seen in Figure 1e,j. A part of Al atoms diffuses into the top and bottom Mg layers for distance of ≈1 nm. The Cr atoms also form layer structures in the same lines formed by Mn atoms as shown in Figure 1j–k. The EDS mappings clearly demonstrate the partial substitution of Mn sites by Cr atoms that was assumed in previous studies.^{[35, 49, 51]} This is the first experimental observation of the substitution of Mn sites by Cr atoms in a (Mn–Cr)AlGe film, and the substituted and unsubstituted samples do not distinctly differ in terms of their microstructures.

Magnetization curves for the 5 nm thick MnAlGe and (Mn–Cr)AlGe films are shown in Figure 2a,b. The magnetic easy axis of the films was oriented perpendicular to the film plane with an in-plane saturation magnetization field of 3.0 and 4.0 T for MnAlGe and (Mn–Cr)AlGe films, respectively, which indicates that the nanolayer samples maintain the large PMA energy. The M_s and PMA energy (K_u) with various t are shown in Figure 2c,d. The values of M_s and K_u increase as a consequence of Cr substitution and these values are almost constant above t = 5 nm. The significant decrease of M_s and K_u at t = 3 nm is possibly due to the dominant volume of the magnetic dead layers around the MgO interfaces.^{[46, 50]} In a previous study, plasma damage was considered to trigger the formation of the dead layer which consisted of Al-rich oxide composition. The plasma damage is an engineering problem that can be solved in future by modifying the sputtering machine design as well as by optimizing the deposition conditions.

Figure 3a,c shows the typical time-resolved magneto-optical Kerr effect (TRMOKE) signal Δφ_K measured at various magnetic field angles θ_H as a function of the optical delay Δt between the pump and probe laser pulses for the MnAlGe and (Mn–Cr)AlGe films. A damped oscillational signal was observed for all films after the rapid decrease of Δφ_K at Δt = 0 ps, which corresponds to an ultrafast demagnetization induced by pump laser pulse irradiation. The oscillation of Δφ_K corresponds to the magnetization precession induced by the ultrafast demagnetization. The oscillation frequency above 100 GHz and its θ_H dependence is clearly seen in the fast Fourier transform spectra of the experimental results as shown in Figure 3b,d.

The first term represents the magnetization recovery after the ultrafast demagnetization. A₀ and A₁ are the coefficients corresponding to the amplitudes of the magnetization recovery process, and ν is the recovery rate of the background signal. The second term represents the damped oscillation stemming from the magnetization precession. B₀, τ, f, and δ₀ denote the precession amplitude, lifetime, frequency, and initial phase, respectively. The fitting results well reproduce the oscillational signal as indicated by the solid lines in Figure 3a,c.

The fitting yields µ₀H_k^eff = 3.4, and 4.0 T for the MnAlGe and (Mn–Cr)AlGe films, respectively. These values are well consistent with the values determined via the magnetization curve measurements within the experimental error.

The calculation results of Equation (7) are shown by the solid curves in Figure 3f. The results reveal a large difference between calculated and experimental data at θ_H = 80°. As described in previous reports on magnetic damping in films with large PMA energy,^{[32, 37, 55]} large values of α_eff at higher θ_H are usually observed owing to a strong extrinsic relaxation process, such as two-magnon scattering and magnetic anisotropy distribution. This strong extrinsic relaxation process can also be seen in the α_eff data plot against f as discussed in previous studies^{[56, 57]} (see Section S1, Supporting Information). Therefore, the strong dependence of the α_eff value on θ_H is considered to reflect a certain degree of dependence on the extrinsic relaxation process, then the intrinsic α is lower than the minimum value of α_eff. This led us to conclude that the true α values of the 5 nm thick MnAlGe and (Mn–Cr)AlGe polycrystalline films are no greater than 0.032 and 0.012, respectively. Even though the extrinsic component of the magnetic damping constant is included, the value of the (Mn–Cr)AlGe film is comparable with the values for conventional PMA polycrystalline ultrathin films.

The film thickness dependence of sub-THz magnetization precessional motion was also investigated to optimize the magnetic properties because partial crystallization of MnAlGe and (Mn–Cr)AlGe appears at the MgO interfaces in this fabrication process using the MgO template layer. Figure 4a,b shows the typical TRMOKE signal Δφ_K for the MnAlGe and (Mn–Cr)AlGe films with various t, respectively. Although an oscillational signal with a long decay time was observed for thinner films, faster relaxation was observed in thicker films of both MnAlGe and (Mn–Cr)AlGe. Furthermore, slow demagnetization occurred in the 30 nm thick MnAlGe film, which is resulted from critical slowing down by the thermal heating. This variation in the demagnetization process in the thick film might be attributed to the lower crystallinity and lower Currie temperature (see Section S2, Supporting Information).

The values of f and α_eff are shown in Figure 4c,d for the MnAlGe films, and those for the (Mn–Cr)AlGe films are shown in Figure 4e,f. The sub-THz precession frequency was observed for all the films and slight variation of f is seen in Figure 4c,e. The α_eff values depend on θ_H and reach a minimum value at approximately θ_H = 40°. For the 30 nm thick (Mn–Cr)AlGe film, no clear signal was observed below θ_H = 60°, therefore, the value at θ_H = 60° was used as the minimum value.

Figure 5a shows the thickness dependence of µ₀H_k^eff for the MnAlGe and (Mn–Cr)AlGe films. The value of µ₀H_k^eff, 3.5 and 4.0 T for the MnAlGe and (Mn–Cr)AlGe films, respectively, was evaluated to be almost constant. The value of µ₀H_k^eff slightly decreases at t = 3 nm, which corresponds to the decrease of M_s and K_u as shown in Figure 2c,d. By contrast, the value of α_eff strongly depends on the thickness, as shown in Figure 5b. The lowest values of α_eff for the MnAlGe and (Mn–Cr)AlGe films were 0.024 ± 0.004 and 0.012 ± 0.001, respectively. Optimization of the ferromagnetic layer thickness and partial substitution of Mn sites in MnAlGe with Cr atoms made it possible to obtain the smallest α_eff at t = 5 nm. Because this lowest value is comparable to that of the conventional PMA material, such as CoFeB with α of 0.01–0.02,^[29-31] and its ferromagnetic layer thickness is in the nanometer thickness regime, (Mn–Cr)AlGe is a promising material for future spintronic devices that can be operated in the sub-THz frequency range.

Figure 6a shows the values of α as a function of δ for bulk MnAlGe and (Mn_0.8Cr_0.2)AlGe. For (Mn_0.8Cr_0.2)AlGe, α is smaller for all δ as compared with MnAlGe. Note that an increase in δ reinforces the scattering strength, which is the inverse of the relaxation time τ, of electrons (δ ∝ 1/τ). The calculated values of α significantly depend on δ. In MnAlGe, the value of α increases as δ approaches the limits δ→0 and δ→∞, reflecting the conductivity-like contribution (α ∝ τ) and the resistivity-like contribution (α ∝ 1/τ), respectively. However, in (Mn_0.8Cr_0.2)AlGe, the conductivity-like contribution of α is suppressed at δ→0 owing to the residual scattering by the Mn–Cr disorder. An appropriate δ value was determined for MnAlGe and (Mn_0.8Cr_0.2)AlGe by comparing the resistivities obtained experimentally at low temperature with those that were calculated theoretically based on the Kubo–Greenwood formula.^{[63, 64]} In the low temperature measurements, the resistivity was evaluated to 100 µΩ cm at 10 K for both the MnAlGe and (Mn–Cr)AlGe films. The theoretical calculation reproduces this resistivity with δ of 86.9 and 67.3 meV for MnAlGe and (Mn_0.8Cr_0.2)AlGe, respectively. The open circle and triangle in Figure 6a indicate the value of α that corresponds to the value of δ in each compound: the values that were obtained for α are 1.18 × 10⁻³ and 6.84 × 10⁻⁴ for MnAlGe and (Mn_0.8Cr_0.2)AlGe, respectively. As in previous reports on the theoretical calculation of α for Co₂MnSi and Mn–Ga,^{[16, 65, 66]} these values of α are less than ten times as small as the experimentally measured values. These differences in α between the theoretical calculations and experiments would be caused by factors such as the off-stoichiometric composition, site-disordering, and crystallization. However, in this study, these α values are qualitatively consistent from the perspective of the magnitude relationship, i.e., α of (Mn–Cr)AlGe is smaller than α of MnAlGe.

The contribution of extrinsic factors on α could be different in the MnAlGe and (Mn–Cr)AlGe films; therefore, experimental investigations on the intrinsic damping constant are required to conclude the DOS modulation effect. Detailed understanding of the effect of Cr substitution on the magnetic damping would require further theoretical and experimental investigations by sufficiently varying the Cr composition of (Mn–Cr)AlGe in future studies. We also want to comment on the future prospects of increasing the TMR ratio. As discussed in the previous reports, appropriate stacking layer design is important to increase the TMR ratio of the MTJ.^{[38-40, 42]} The stacking layer design of the MTJ is also possible for (Mn–Cr)AlGe because (Mn–Cr)AlGe shows highly (001)-textured growth using the (001)-textured MgO interfaces as demonstrated in our TEM study and a previous report.^[50] TMR ratio investigation in the MTJs with (Mn–Cr)AlGe layer is a future study for the high-speed spintronic device development.

3 Conclusion

In conclusion, the sub-terahertz magnetization dynamics in the MnAlGe and (Mn–Cr)AlGe films was systematically investigated by means of an all-optical time-resolved magneto-optical Kerr effect. The TEM study clearly showed the pseudo-2D crystal structures and partial substitution of the Mn sites of MnAlGe by Cr atoms in films representing the Cu₂Sb-structure. The 5 nm thick (Mn–Cr)AlGe thin film exhibits the smallest effective magnetic damping constant α_eff of 0.012 ± 0.001 with a magnetization precession frequency of 0.164 THz. The theoretical calculation infers that the DOS modulation at the Fermi level as a result of Cr substitution decreases the intrinsic α. The thickness and partial substitution of Mn sites in the MnAlGe film by Cr enabled the large PMA energy of 0.68 MJ m⁻³, small saturation magnetization of 303 kA m⁻¹, and small α to be realized by depositing highly textured polycrystalline films with a thickness of a few nanometers on thermally oxidized Si substrates.

4 Experimental Section

Conflict of Interest

The authors declare no conflict of interest.