Direct laser interference patterning of nonvolatile magnetic nanostructures in Fe60Al40 alloy via disorder-induced ferromagnetism
1 Introduction
Chemical order-disorder transformations in intermetallic alloys1-10 such as FexAl100-x and their effects on the physical properties11-25 attracted steady interest through decades. In particular, the phenomenon of disorder-induced ferromagnetism11-20 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 studies21-24 that pointed out the enhancement of magnetic moments in the FexAl100-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 Tc for the A2↔B2 transition18, 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 structures19, 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 saturation18, 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.
2 Methods
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, τp=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.
Fig. 1. (a ) Schematic of the DLIP geometry with four laser beams that impinge on the sample surface and their superposition provides the interference pattern. (b ) Laser intensity distribution simulated for all the beams of TE polarization and equal intensity, which incident at the same angle θ , while the azimuthal angles are φ i=π(i -1)/2, where i=1, 2, 3, 4. Under such parameters, the lattice periodicity is given by Λ =λ /(2sinθ )33. In our experiments, Λ was varied between 0.4 and 2.3 µm. (c ) MFM image of a Fe60Al40 35 nm thick sample treated by DLIP with Λ =0.4 μm and (d ) corresponding topography.
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 τp=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 resolidification18, 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.
3 Results
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 (
We remark that the range of laser fluences F which provides the PMNS formation shown in
We could get a regular and interpretable magnetic pattern more easily by increasing the pattern periodicity from Λ=0.4 μm (
Fig. 2. MFM images of patterned structures that have different periodicities Λ of the interference pattern. (a ) 0.4 μm, (b ), 0.6 μm, and (c ) 2.3 μm.
It is also interesting that analyzing the correspondences between the topographical relief (
Fig. 3. Correspondence between the laser-induced topographical relief (a) and MFM response (b). The bumps on the Fe60Al40 surface, occurring within maxima of light intensity (solid contours), are significantly smaller in their lateral dimensions than the regions in which the MFM response is nonzero. One of the patterned magnetic entities is indicated by dashed contour.
4 Discussion
4.1 Disorder-induced ferromagnetism
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 laser18-20 beams can be employed for producing the ferromagnetic order via destroying the B2 superstructure in thin-film specimens.
Fig. 4. (a ) Fe-based unit cells (top) and the (100) projections (bottom) of the atomic structure in the chemically ordered B2 and disordered A2 states of the Fex Al100-x (x ~50 at.%) alloy. The open boxes are vacancies in the lattice through which the atomic jumps occur for relaxation of the system to its thermodynamic equilibrium. In the A2 state there are magnetic percolation paths (dashed lines). (b ) Simulated change of magnetic moments in Fe under the transformation from the B2 to A2 state21.
4.2 Laser-induced disordering and reordering.
We now present our analysis of how the superstructure (B2 state) is destroyed in FexAl100-x alloys by rasing T above Tc, 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 Tc. First of all, we note that laser fluences, which provide the PMNS (
Fig. 5. (a ) Absorbed fluence F abs as a function of coordinate along the dashed horizontal line in Fig. 1(b) with indications of different positions: 1. maxima of light intensity, where F abs=(1–R )F *>F m (F m is the absorbed fluence required for raising the temperature up to the melting point T m); 2. locations outside the melted zones, in which F c < F abs < F m (F c is the absorbed fluence required for raising the temperature up to T c); 3. local minima of light intensity. (b ) T (t ) dependencies calculated in positions 1, 2, and 3, where the absorbed fluence is respectively F abs=70 mJ/cm2, F abs=65 mJ/cm2, and F abs=35 mJ/cm2. As temperature elevation was calculated with no taking into account effects of melting and resolidification18, 20, the T (t ) dependence calculated at F abs>F m is shown by the dashed curve for t >t m, where t m is the moment of time at which the temperature rise reaches T m. (c ) Unit cell of the interference pattern with the marks for positions in which the T (t ) dependences plotted in (b) are simulated. (d ) Non-equilibrium vacancy concentration cv versus t in zone(s) 2 at T max=T m. The inset shows the asymptotic value cv(∞) at different temperature elevations T max-T c up to T max=T m. (e ) Concentration wave (superstructure) amplitude A (t )/A (0) as a function of time t in zone(s) 2 at different temperature elevations T max-T c up to T max=T m.
The origin of PMNS shown in
where
where ceq(T)=exp(-Ev/kBT) is the equilibrium vacancy concentration, Ev 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) (
As follows from our considerations above, a long enough thermal treatment at T < Tc 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.
Fig. 6. MFM images of the patterned Fe60Al40 surface at the edge of the irradiated zone. The images were taken (a ) before and (b ) after thermal annealing in a furnace at T =770 K for one hour. (c ) Cross section of the MFM image before and after thermal annealing
5 Conclusions
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 Tc for the chemical order (B2) ↔ disorder (A2) transformation. The disordered state occurring in maxima persists in the alloy upon its cooling to temperatures below Tc, 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 Tc (
6 Acknowledgements
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.
7 Competing interests
The authors declare no competing financial interests.
8 Supplementary information
Article Outline
Philipp Graus, Thomas B. Möller, Paul Leiderer, Johannes Boneberg, Nikolay I. Polushkin. Direct laser interference patterning of nonvolatile magnetic nanostructures in Fe60Al40 alloy via disorder-induced ferromagnetism[J]. Opto-Electronic Advances, 2020, 3(1): 01190027.