Chemical order-disorder transformations in intermetallic alloys^1-10 such as Fe_xAl_100-x and their effects on the physical properties^11-25 attracted steady interest through decades. In particular, the phenomenon of disorder-induced ferromagnetism^11-20 was extensively studied by employing various kinds of treatments that effectively induced the structural transitions from the chemically ordered (B2) to disordered (A2) state. The performed experiments were supported by theoretical studies^21-24 that pointed out the enhancement of magnetic moments in the Fe_xAl_100-x (50 at.% < x < 75 at.%) under the transformation from the B2 to A2 state.

Therefore, the question arises whether the chemically disordered state can survive upon cooling the alloy to temperatures T below the critical temperature T_c for the A2↔B2 transition^{18, 20}. This issue is especially relevant at the nanoscale, when precipitates of a new phase can be still smaller than the critical nucleus for the phase transformation. At a macroscopic scale, writing of nonvolatile ferromagnetism was experimentally demonstrated with Fe₆₀Al₄₀ thin-film specimens under their irradiation by short-pulse laser beam¹⁸. The goal of our study is to produce small nonvolatile magnetic structures^{19, 20} by focusing laser irradiation on the sample surface. In these experiments we employed direct laser interference patterning (DLIP) which allows for fabrication of large-area (up to ~1 cm²) regular structures with periodicities down to λ/2 (λ~500 nm is laser irradiation wavelength)^26-31. The main result we report in this article is demonstration of periodic magnetic nanostructures (PMNS) produced by DLIP. These PMNS are nonvolatile and their formation is associated with laser-induced localized chemical disordering in the alloy. We find that the formed PMNS are clearly detectable with magnetic force microscopy (MFM) at room temperature. Analyzing these findings in terms of chemical order-disorder transitions, we compare the experimental data with our simulations of the disordering/reordering rates. These studies can be useful in a view of a magnetic memory technology which would encode information in regions with different values of the magnetization saturation^{18, 32}. Such an approach would be an alternative to current magnetic memory technology where information bits are domains with opposite orientation of the magnetization vector.

Polycrystalline Fe₆₀Al₄₀ films with a thickness of ~35 nm were sputtered on (100) Si wafers covered by a natural SiO₂ layer from a target of the same composition. For sputtering, the vacuum chamber was pumped out up to a pressure of residual gas of about 10^-9 Pa. The produced samples were post-annealed at 770 K in a vacuum furnace for times ~10³ s and then slowly cooled. After such a treatment, the samples did not have a detectable magnetic response at room temperatures¹⁸. It was also shown with X-ray diffraction¹⁸ that the annealed films were structurally ordered and that the average diameter of crystalline grains in them was about L=15 nm.

In our DLIP experiments, we used nanosecond laser pulses from an injection-seeded Nd:YAG laser (continuum powerlite 9010, λ=532 nm, τ_p=12 ns with a spot in diameter of approximately 0.6 cm on the sample surface). The laser pulse with Gaussian beam profile was split into four beams of the same TE polarization and equal intensity in all beams that impinged on the sample surface at the same angle θ, while the azimuthal angles of the incident beams were φ=π(i-1)/2 (i=1, 2, 3, 4). These beams interfered with each other to yield a two-dimensional pattern of ideally square symmetry with periodicity of Λ=λ/(2sinθ)³³. Figure 1(a, b) shows (a) DLIP geometry and (b) simulated distribution of the light intensity, where yellow and blue colors depict regions of the highest and lowest light intensity, respectively.

The surface of patterned samples was examined with a high-resolution HR-MFM-ML3 probe (Team Nanotec) used basically for MFM. For MFM characterization, we employed a Bruker MultiMode atomic force microscope (AFM) which operated in the tapping/lift mode. Before taking MFM scans, a 0.5 T external magnetic field oriented in the film plane was applied to the sample.

The temperature calculations were performed with a 35-nm-thick Fe₆₀Al₄₀ film on a Si substrate, whose front surface is irradiated by a laser (λ=532 nm) pulse with Gaussian shape and a duration of τ_p=12 ns at the full width at half maximum (FWHM). The temporal evolution of the temperature in the film was retrieved by a finite element heat flow calculations (COMSOL Multiphysics). Effects of melting and resolidification^{18, 20} were not taken into account. The temperature-dependent material constants for Si were taken from the COMSOL Multiphysics Material Library. For the Fe₆₀Al₄₀/Si interfacial thermal conductance with G=9.4×10⁷ W/(m²·K) is used³⁴. As for the parameters of the Fe₆₀Al₄₀ film, we assume that its thermal conductivity, density, and heat capacity are k=20 W/(m·K)³⁵, ρ=6.5 g/cm³³⁶, and C=0.7 J/(g·K)³⁷, respectively.

We find that a single-pulse DLIP treatment provides the formation of the PMNS which consists of alternating bright and dark spots in the MFM images. These patterns are clearly detectable down to an interference pattern periodicity of Λ=0.4 μm (Fig. 1(c)). The periodicity of the magnetic pattern in Fig. 1(c) can be determined in accordance with the distance between adjacent bright or dark spots in the MFM image. Because of the film roughness it is difficult to recognize laser-induced changes in the film topography (Fig. 1(d)).

We remark that the range of laser fluences F which provides the PMNS formation shown in Fig. 1(c) is rather narrow, ±0.2F^* around F^*=0.18 J/cm². Magnetic modifications were not detected after DLIP with F < 0.8F^*, while we observed strongly irregular magnetic patterns at F > 1.2F^*.

We could get a regular and interpretable magnetic pattern more easily by increasing the pattern periodicity from Λ=0.4 μm (Fig. 1(c) or Fig. 2(a)) to larger values, Λ=0.6 μm (Fig. 2(b)) and Λ=2.3 μm (Fig. 2(c)). In PMNS with larger periodicities (Fig. 2(c)), one observes well-separated regions (if Λ > 1.0 μm) of nonzero MFM response, and each such a region contains sub-regions with positive (bright spot) and negative (dark spot) MFM response. One can evaluate the lateral dimensions of these regions that look elongated with the aspect ratio of ≈1:2. It was previously demonstrated^38-40 by numerical simulations of the MFM response and experimentally observed in small magnetic elements that the two-contrast entities in Fig. 2(c) can be attributed to single-domain magnets, whose north and south poles generate stray fields which act on the cantilever by changing both the phase and amplitude of its vibrations. We note, however, that a single domain is not the ground state even for elongated particles which have large enough dimensions⁴¹. The single-domain state we observe in our patterns can result from distortion of the ground magnetization distribution by stray fields of the MFM probe⁴².

It is also interesting that analyzing the correspondences between the topographical relief (Fig. 3(a)) and the MFM image (Fig. 3(b)) allows us to identify the surface features induced by the laser pulse. We see that the topographic peaks are located in those places where the MFM response is neutral between the poles of the patterned entities. Another fact is that the whole area, inside of which the MFM response is nonzero, is significantly larger (~300 nm) than that of the laser-induced bumps in the topographical relief (~100 nm). Presumably, the detected surface features result from local thickening of the film, which is associated with a change in the atomic density of the quenched material of the film after its melting⁴³. It is also highly likely that the magnetic modifications occupy the areas which are much bigger than those of the melted zones within maxima of light intensity.

We now argue that magnetization in the Fe₆₀Al₄₀ thin-film alloy we study can be enhanced upon its chemical disordering. Initially, the phenomenon of disorder- induced ferromagnetism was observed under plastic deformation in bulk alloys, e.g., Ref.^{11, 14}. In the context of our study, it is important to note that different kinds of irradiation such as high-energy ion¹⁷ and short-pulse laser^18-20 beams can be employed for producing the ferromagnetic order via destroying the B2 superstructure in thin-film specimens.

Figure 4(a) illustrates how the B2 state is destroyed via atomic diffusion jumps through vacancies (boxes) in the Fe_xAl_100-x lattice where x~50 at.%. As a result, magnetic Fe atoms appear in the centers of the Fe-based unit cells (antisite defects) instead of Al atoms. This reconfiguration leads to percolation between adjacent Fe planes, thus yielding the transformation from the superparamagnetic to ferromagnetic state^{11, 15}. Note that the appearance of the antisite defects results in shortening the minimal distance between Fe atoms from a to $a\sqrt 3 /2$, wherea is the atomic lattice constant. Qualitatively, this leads to the enhancement of exhange interactions because of the bigger overlap of d-orbitals between Fe neighbors. Figure 4(b) illustrates the calculation results performed at x=50 at. % and x=75 at.%²¹, which indicate the enhancement of the magnetic moment per Fe atom (μ_Fe) upon the transformation from the B2 to A2 state. Based on a linear interpolation, we conclude that μ_Fe in the B2 and A2 state at x=60 at. % is respectively 0.8 μ_B and 1.8 μ_B.

We now present our analysis of how the superstructure (B2 state) is destroyed in Fe_xAl_100-x alloys by rasing T above T_c, which is driven by nanosecond laser irradiation. The question is how the disordered (A2) state (and thus ferromagnetism) can be trapped upon cooling the sample below T_c. First of all, we note that laser fluences, which provide the PMNS (Figs. 1-3), are not only sufficient for temperature elevation in the maxima of light intensity significantly above T_c=1563 K⁴⁴, but even above the melting point T_m=1662 K⁴⁴. This conclusion is based on our experimental observations of the bumps formed in the maxima of light intensity (Fig. 3(a))⁴³ and is supported by our calculations of temperature elevation induced by laser irradiation. In order to evaluate the temperature rise, we had to get the relationship between the incident and absorbed fluence by measuring the optical reflectivity of our samples (R=0.6) in the continuous-wave mode.

Figure 5(a-c) shows (a) the distribution of the absorbed fluence F_abs in units of (1-R)F^* along the dashed horizontal line in Fig. 1(b) and (b)T(t) dependencies at different locations through (c) a pattern of square symmetry with Λ=0.4 μm. The specific locations, inside of which we calculate T(t), are as follows: 1) Maxima of light intensity [bumps (Fig. 3(a))], 2) The regions which are located outside the melted zones but in which the maximal temperature T_max exceeds T_c, and 3) Local minima of laser intensity along the dashed horizontal line in Fig. 1(b).

The origin of PMNS shown in Figs. 1-3 can be associated with chemical disordering in the Fe₆₀Al₄₀ atomic lattice at T > T_c. Based on theoretical considerations given in Supplementary Information, we calculate the disordering rates, which depend on the non-equlibrium concentration of vacancies generated by laser. As we do not take into account effects of melting and resolidification^{18, 20} in our calculations of T(t) (Fig. 5(b)), we can account for the disordering rates only if T_maх < T_m. Obviously, we should perform these calculations in zones where T_c < T_max < T_m, i.e., in zone(s) 2, as indicated in Fig. 5(a-c). Figure 5(d, e) shows (d) the vacancy concentration c_v(t) as a function of time t and (e) changes in the concentration wave amplitude A(t)/A(0) for different temperature elevations in zone(s) 2 up to T_max=T_m. As seen from Fig. 5(e), chemical disordering, i.e., decrease of A(t)/A(0), becomes dominating at T_max-T_c > 60 K. At lower temperature elevations above T_c, the disordering occurring at T > T_c has a lower rate than the reordering does, which occurs at T < T_c. Therefore, erasing of the ferromagnetism in the Fe₆₀Al₄₀ is feasible with a train of laser pulses²⁰. The concentration wave amplitude A[T(t)] was found in accordance with the following equation:

1 $ A\left[ {T\left( t \right)} \right] = A\left( 0 \right)\exp \left[ {\int {_{{t_1}}^{{t_2}}\alpha \left( t \right){\rm{d}}t} } \right], $

where $\alpha \left( t \right) = \frac{{32D\left( t \right)\left[ {({T_{\rm{c}}} - T\left( t \right)} \right]{c_{\rm{v}}}\left( t \right)}}{{T\left( t \right){a^2}\left( {1 - x} \right)}}, $

$D\left( t \right) = {D_0}\exp \left( { - {E_{\rm{m}}}/{k_{\rm{B}}}T} \right)$ is the diffusion coefficient, D₀ the pre-exponential factor, E_m the activation energy for the atomic diffusion (or enthalpy of vacancy migration), and t₁, t₂ are the starting and finishing moments of a relaxation process; see Supplementary Information. The non-equilibrium vacancy concentration shown in Fig. 5(d) is retrievable from the relaxation equation of the Bloch type

2 $ \frac{{{\rm{d}}{c_v}}}{{{\rm{d}}t}} = \frac{{{c_{{\rm{eq}}}}\left( T \right) - {c_{\rm{v}}}}}{\tau }, $

where c_eq(T)=exp(-E_v/k_BT) is the equilibrium vacancy concentration, E_v the enthalpy of vacancy formation, τ=L²/D the relaxation time, which is the characteristic time of vacancy life between its formation and annihilation at crystallite boundaries; see also Supplementary Information. In order to account for A(t) (Fig. 5(e)), we have chosen the following parameters: D₀=2.6×10^-3 m²/s^{7, 8}, E_v=0.9 eV and E_m=1.7 eV^{8, 9}, and L=15 nm¹⁸.

As follows from our considerations above, a long enough thermal treatment at T < T_c should provide extensive formation of the B2 phase and thus reducing the magnetization¹⁷. It was shown previously¹⁸ with Kerr magnetometry that the magnetic response of the Fe₆₀Al₄₀ alloy after its irradiation by nanosecond laser becomes comparable to that of a ferromagnetic material like Fe. However, such a strong response practically vanishes after standard thermal annealing of the sample at T=770 K for times t~10³ s. In our work, we used the same kind of treatment to test our explanations for the PMNS origin. Figure 6 shows MFM images of a Fe₆₀Al₄₀ sample (a) after DLIP at the very edge of the irradiated zone and (b) after thermal annealing of this sample. We see that the PMNS becomes much less pronounced after annealing. It is seen from the cross sections (Fig. 6(c)) of the MFM images that the degradation of the MFM pattern occurs via rather a decrease of the MFM response but not via shrinking the patterned entities. Such a behavior can be explained in terms of homogeneous nucleation of the B2 phase⁶, which occurs inside the chemically disordered regions of the magnetic A2 phase.

Using magnetic force microscopy (MFM), we have studied the conditions for the formation of periodic magnetic nanostructures (PMNS) in the Fe₆₀Al₄₀ alloy under direct laser interference patterning (DLIP). The PMNS formation is associated with the effect of chemical-disorder-induced ferromagnetism when the alloy is heated in maxima of light intensity up to temperatures above the critical temperature T_c for the chemical order (B2) ↔ disorder (A2) transformation. The disordered state occurring in maxima persists in the alloy upon its cooling to temperatures below T_c, and so, these regions are nonvolatile and appear to be ferromagnetic at room temperature. As our simulations show, the disordering rate can be significant below the melting threshold at sufficient temperature elevation above T_c (Fig. 5(e)). Therefore, there can be no need to melt the film to modify the magnetism by laser in the system under study. The findings we report here are believed to have a potential for developing a magnetic memory technology^{18, 32} which would be alternative to current magnetic memories.

N. I. Polushkin acknowledges the support by the Russian Foundation for Basic Research (grant #18-02-00827_a) and by the Program of Fundamental Research of the Presidium of the Russian Academy of Sciences "Nanostructures: Physics, Chemistry, Biology, Technology, Basics". P. Graus, T. B. Möller, P. Leiderer and J. Boneberg acknowledge the support by the DFG through the SFB 767 at the University of Konstanz.

The authors declare no competing financial interests.