Transport properties of Fe60Al40 during the B2 to A2 structural phase transition

The variation of transport behavior in a mesoscopic Fe60Al40 wire, initially possessing the ordered B2 -phase structure, has been observed while inducing a phase transition to the disordered A2 phase. Gradual disordering was achieved using a highly focused beam of Ne+ -ions. Both electrical resistance and anomalous Hall effect were measured simultaneously and in situ during the local ion irradiation. The normal as well as the Hall resistivity show a peak as a function of disorder. The relationship between Hall resistivity and normal resistivity shows the presence of two distinct transport regimes during the phase transition. Ex situ field- and temperature-dependence measurements show that it is necessary to consider the effect of scattering from magnetic clusters to understand these different regimes in transport properties.


Introduction
Applications such as magnetic data storage as well as magnetic sensors and spin-transport devices require a precise control of intrinsic magnetic properties at the nano-and meso-scales [1].An important property is the saturation magnetization, which can be tuned using ion-irradiation induced lattice disordering [2][3][4][5].Typically, modifications using ion irradiation tends to be a destructive process whereby the penetrating ions suppress lattice ordering, leading to a reduced exchange coupling [3,[6][7][8][9].
In contrast to the disorder induced suppression of magnetization, in selected materials such as Fe 60 Al 40 it is possible to generate ferromagnetic order by lattice disordering [10].A drastic increase of the magnetization can occur, for instance through a transition from an ordered B2-phases, possessing a defined site-occupancy to a disordered A2-phase wherein the site-occupancy is random.Corresponding to the structural phase transition, a magnetic transition from para to ferromagnetism is observed.The lattice disordering can be sensitively performed using light-ion irradiation, these materials provide a template for direct writing of magnetic regions at the nano-and meso-scales [11].
The transition from the paramagnetic B2-phase to the ferromagnetic A2-phase can be explained using the local environment model [12], which estimates the magnetic moment of a specific atom related to the number of nearest-neighbor (n-ns) atoms of the same kind.After preparing and annealing, Fe 60 Al 40 orders in a B2-phase [13][14][15].In this state the atomic planes of Fe atoms are separated by Al planes.The Al atoms located in-between impede the exchange interaction of the Fe atoms.Only when there is an Fe atom inside an Al-rich plane (due to unbalanced composition) is a ferromagnetic Fe cluster formed.On average, there are 2.67 Fe-Fe n-ns in the B2-phase [14,15] and the B2 structure thus will have a very small magnetization.
If the material is irradiated with ions of sufficient energy, the introduced atomic displacements lead to the formation of antisite defects, which randomizes the positions of Fe and Al atoms, leading to a disordered A2 structure.In this state, more Fe atoms enter Al planes as compared to the B2 state and on average the amount of Fe-Fe n-ns increases to 4.8 [16].This increase results in a ferromagnetic state with almost 40 times higher magnetization [14, p 436].We will refer to this type of clusters as local magnetic clusters.These clusters are localized to within a couple of atomic cells and typically analyzed theoretically by, for example, DFT calculations such as in [17,18].
The other type of clusters, which in this work are referred to as metaclusters, are localized collections of clusters.Their existence is related to the non-uniform spatial distribution of ions penetrating the material and as a consequence-non-uniform disorder.These clusters can be observed on longer length scales of several to tens of nanometers depending on the ion energy and on the fluence [11,14,15,19].Their influence on the transport properties of the material is more complicated to study theoretically due to the randomness of their positions and distribution of sizes.Therefore, their impact is often ignored in calculations.
In particular, from the simple picture described above it would be expected that with increasing disorder, the density of Fe-Fe clusters will increase, and similar to the change of magnetization [14, figure 4(a)], the resistivity would also be a monotonic function of the ion fluence.However, as shown from first principle calculations [18, figure 4], and experiments [20, figure 4.4], the resistivity as a function of fluence has a peak, approximately when magnetization reaches half of the maximum value for the fully disordered structure.Additionally, it was predicted in [18, figure 6], that the anomalous Hall-effect (AHE) will be a monotonic function of fluence having a sharp decrease around the maximum in resistivity.As is shown later in this work, the results of the measurements made are in disagreement with the predictions of [18].In this work, by measuring both resistance and AHE in parallel with continuous ion irradiation a similar peak was shown in the AHE as was previously reported for resistivity, which might be connected with the presence of metaclusters.

Methods
The samples were fabricated on 1 cm × 1 cm Si substrates with 270 nm of thermally oxidized layer of SiO 2 on top.For growing FeAl microstructures the substrates were cleaned in acetone in an ultrasonic bath for 5 min.Subsequently, an maN-1420 negative photoresist was applied using spin-coating process.Then, the opening for the Hall-bar of 200 µm × 5 µm was defined using photolithography.The 40 nm Fe 60 Al 40 film was deposited onto this from an alloy target of the same composition using DC magnetron sputtering at room temperature.The sputter deposition was performed in an Ar + atmosphere of 2.9 × 10 −3 mbar at a deposition rate of 0.56 Å s −1 .The base pressure of the chamber was 1.8 × 10 −9 mbar.The deposition was followed by a lift-off process and an annealing step in ultra-high vacuum (9 × 10 −10 mbar) chamber at 500 • C for 1 h.Heating and cooling rates of annealing chamber were 5 • C min −1 and 10 • C min −1 , respectively.The annealing treatment is performed to achieve the B2-phase, confirmed by the presence of the 100 superstructure reflection [see [14,21] for details].The 100 superstructure reflection corresponds to the presence of pure-Fe plane and is gradually suppressed due to atomic site swaps between the Fe and Al atoms, before disappearing with the formation of the A2-phase.The suppression of the 100 superstructure peak is accompanied with a with an increase of the saturation magnetization.Here the atomic displacements have been induced by irradiation of focused Ne + -beams.Precise measurements of the transport properties required the fabrication of Hall-bars.Following the Hall-bar fabrication, by using a similar spin-coating/ photolithography/deposition/lift-off process, Cr (5 nm) Au −1 (100 nm) contacts to the Hall-bar were made.The optical image of the final result is shown in figure 1.The Hall-bars are of 5 µm width with a 50 µm distance between the outer contacts, along the length of the bar.Additional contacts have been placed midway, to enable Hall-voltage measurements.The samples were irradiated using Ne + ions with an energy of 25 keV, while being electrically connected at the same time, as shown in figure 1 The in situ measurements were performed in an Orion NanoFab helium ion microscope (HIM) from Carl Zeiss AG.A Ne + has been used in the gas field ion source which allows reaching a lateral resolution of 1.8 nm under optimal conditions [22,23].A FIBICS NPVE pattern generator is used to raster over the central 50 µm × 5 µm region while keeping a pixel spacing of 7 nm.The beam conditions used are: 25 keV primary energy, 10 µm aperture with a resulting beam current of 0.5 pA at a spot control setting of 4. With the beam current fixed, the Ne + -fluence is a function of the irradiation time.Irradiation and electrical measurements were done in parallel and result in a dose increment between two electrical measurements of 0.005 ions nm −2 .
Irradiation of 25 keV Ne + was performed for fluences up to 10 ions nm −2 .In parallel with ion irradiation a 2-wire resistance, using I + , I − contacts, and a Hall voltage, using V + , V − contacts, were measured for I = 1 mA using separate channels of a 2614B Keithley SourceMeter (see section 3).This current value is an optimization between obtaining a large enough signal-to-noise ratio and avoiding significant resistive heating of the sample during the irradiation step [20, figure 4.6].During the experiment, the sample chips were placed on top of the trapezoidal permanent magnet with the circular top face with area of 2.5 cm 2 in order to tilt magnetization of the sample perpendicularly to the plane and increase the signal from AHE.By using a Teslameter, the magnetic field in the center on the surface of the magnet was measured to be 350 mT.The field of the magnet varies significantly with distance and lateral position, but due to the small Hall-bar dimensions relative to the size of the magnet it was assumed that magnetic field is uniform over the whole area of the Hall-bar.
After each irradiation cycle the Hall-bar was optionally annealed with a higher current of I = 20 mA, if inducing reverse A2 to B2 structural phase transition was necessary.According to [20, p 50] a current of 20 mA can lead to annealing of the sample at ambient temperature.Under vacuum conditions of the HIM microscope chamber, the Joule heating of the sample is expected to yield higher temperatures due to the absence of air side cooling.By modeling using the COMSOL-software it was found, that at this current the Hall-bar will be at about 215 • C-235 • C for ambient pressure and 486 • C-507 • C at a pressure of 1 × 10 −5 mbar.This temperature is sufficient to reliably anneal the sample [13][14][15], but is still below the temperature of the dewetting of the film [15, figure 1].
Subsequent ex situ experiments were made on samples that were irradiated to selected states of disorder: 1. non-irradiated: it is annealed at I = 20 mA, which returned the sample into the ordered B2-phase; 2. 0.7 ions nm −2 : the sample was irradiated to the fluence value, where the maximum resistivity was observed.This state is an intermediate partly disordered state; 3. 10 ions nm −2 : the sample was irradiated up to the state where there is a saturation in resistivity, which corresponds to the fully disordered state.
Additional transport measurements were done using an electrical characterization insert of the Multifunction Measurement System from Cryogenic Ltd Au contacts of the Hall-bar were wedge bonded to Au-plated pads of the insert holder using a 40 µm Al wire on the F&S BONDTEC Series 56i wire bonder.Magnetoresistance MR measurements were done with magnetic field applied out-of-plane of the sample and swept in the range from −5 to 5 T. The magnetic field sweeps were conducted at 4 K, to minimize the thermal noise contribution, and a current of I = 100 µA to avoid unwanted heating.The dependence of resistance on temperature were recorded in the range of 4-300 K.

Results
In figure 2(a) magnetometry loops are shown, measured on extended thin films from the same deposition series at 300 K, but without any fabrication steps.The films were irradiated with different fluences using Ne + broad-beam irradiation prior to the magnetometry measurement.The external magnetic field was applied in the film-plane.The obtained saturation magnetizations are 30 kA m −1 , 190 kA m −1 and 710 kA m −1 for non-, partially-and fully-irradiated samples, respectively, which is consistent with previous reports [14,20].Consequently, it was concluded that the initial non-irradiated state is indeed a non-ferromagnetic B2-phase.
In figures 2(b)-(d) the temperature dependence is shown of the average magnetization of the film irradiated at different fluences.During the measurement the sample was first cooled down from 350 K to 10 K in a zero magnetic field.Then, the magnetic moment was recorded at the applied field of 5 mT while sweeping the temperature from 10 K to 350 K (black, ZFC lines in figures 2(b)-(d).The FC data were recorded in the presence of same applied magnetic field by cooling the sample from 350 K to 10 K. Both, non-irradiated and 0.7 ions nm −2 irradiated samples show a bifurcation in magnetic moment between FC and ZFC sweeps at low temperatures.This suggests that at these fluences decoupled magnetic clusters are present in the film.The corresponding blocking temperatures amount to 100 K (non-irradiated) and 138 K (partly-disordered, 0.7 ions nm −2 ).The peak of the magnetic moment in the case of ZFC curve for partly irradiated sample is considerably wider, than that of the non-irradiated sample, which might indicate a broader distribution of magnetic clusters sizes.However, for the fully disordered 10 ions nm −2 the ZFC and FC curves coincide and the sample exhibits a typical ferromagnetic-like dependence of magnetization as a function of temperature, which is consistent with the magnetometry presented in figure 2(a).
In figure 3 In figures 4(a) and (b) the dependence is shown of the normalized resistance and AHE as a function of magnetic field applied perpendicularly to the surface of the Hall-bar.For the non-irradiated B2-phase (red curve) there is a quadratic change in the magnetoresistance for low magnetic fields (below 4 T).Typically a quadratic behavior of the resistivity in low-fields can be explained by the ordinary (positive) magnetoresistance effect (OMR) [24, p 84].The measurements on the present mesoscopic wire are consistent with the results on continuous thin films reported in [25, figure 4].The sign of magnetoresistance is negative, since the resistance decreases as the amplitude of the applied field increases.
The fully disordered A2-phase (10 ions nm −2 , green curve), in contrast to the non-irradiated samples, shows two distinct linear slopes in a the magnetoresistance with a transition at the saturation point.Although less visible, a similar change in slope is also present for the 0.7 ions nm −2 sample.Since this additional effect disappears after saturation it can not be attributed to the OMR or related effects, but must be connected with the direction of the magnetization such as anisotropic magnetoresistance (AMR).The AHE data in figure 4(b) exhibits also two distinct linear slopes as a function of applied field for all samples.For the case of AHE the change in slope is more pronounced for the irradiated samples as the contribution from AHE greatly exceeds that of the normal Hall effect, that keeps contributing to R AHE after the AHE effect has saturated.For the non-irradiated B2 sample, the contributions from normal Hall effect and AHE are comparable as shown in the inset of figure 4(b).This is again consistent with measurement of other groups, where increase in the anomalous Hall angle is reported as a function of fluence (see [25, figure 5]).In addition, the sign of the slopes of R AHE for the non-irradiated sample is positive and opposite to that of the fully disordered one, which additionally hints to the dominant role of the normal Hall effect for the non-irradiated sample.The magnetic field for which a change in slope for the resistance dependence is observed for the irradiated samples (for both 0.7 ions nm −2 and 10 ions nm −2 samples) coincides with the saturation fields in AHE.
As can be seen in figure 2(a) for 0.7 ions nm −2 , which is close to the maximum in resistivity in figure 3(a), the magnetization is about 27% of the maximum achievable for 10 ions nm −2 .
In figures 5(a)-(c) magnetic field sweeps of the normalized resistance are shown at different temperatures for the non-irradiated (a), 0.7 ions nm −2 (b) and 10 ions nm −2 (c) samples.There is a noticeable change in slope of the magnetoresistance for different temperatures for the non-irradiated and the 0.7 ions nm −2 samples.In the non-irradiated case close to room temperature the magnetoresistance practically vanishes.The same trend was observed for 0.7 ions nm −2 , but even at room temperature NMR was observed.However, for 10 ions nm −2 the results for different temperatures look practically the same.
The dependence of the resistivity and AHE effect on temperature is shown in the supplementary material.

Dependence of transport on disorder
There are several potential contributions to resistivity that will change as a function of ion fluence.First, the most obvious one, are structural changes.As shown by [21, pp 56-58] and [26], magnetization change is induced by both lattice expansion and an antisite disorder.By x-ray diffraction it has been shown that for disorder values above 1 − S = 0.6 the 100 superstructure reflection of B2-phase vanishes [21, figure 3.10].This value of disorder corresponds to about 60% of the saturation magnetization of the A2 structure.This loss of the B2 long-range order could contribute both to an increase and to a decrease in resistivity.As argued by [17, p 1198], above an atomic composition of 30% of Al, disorder in the structure leads to an addition of the Al 3p electrons to the Fermi level, which decreases the resistivity.In contrast, from simulations conducted in [18, p 5] it is expected, that increased scattering due to the larger number of defects leads to an increase in resistivity for small disorder, which is proportional to the fluence.Unfortunately, a conversion from the order parameter S to the fluence is not straight forward, therefore qualitative arguments are used in the following.
As can be seen in figure 3(a) the latter contribution seems to dominate in experiments for low fluences (>0.6 ions nm −2 ).
In addition to the effects mentioned above, there are magnetism related effects of different origins.As the resistance is measured at non-zero temperatures thermal fluctuations of magnetic moments within the Fe-clusters exist.Since the temperature is not varied during the experiment, these fluctuations should lead to a constant offset of the resistivity.However, due to ion irradiation, magnetic moments of local clusters are varied as sketched in figure 6.In the figure a qualitative magnetic moment distribution is shown, which is assumed to be proportional to the amount of n-ns.
For non-irradiated 0 ions nm −2 sample being in the crystalline B2-phase, there is about 1 Fe atom per 4 Al atoms in the Al planes due to the stoichiometry.This corresponds to evenly spaced magnetic clusters of 8 Fe-Fe n-ns separated by about a lattice constant.This results in a spatial distribution of magnetic moments, as sketched in the upper image of figure 6.The fact that clusters are indeed similar in magnetic moment is further confirmed by a relatively sharp peak in the moment around the blocking temperature for the non-irradiated case in figure 2(b).
As the material is irradiated, the average amount of Fe-Fe n-ns in the local clusters increases from 2.67 to 4.8 [14,16].Since this is done by disordering the lattice, it can no longer be assumed that almost every Fe-cluster will have 8 Fe-Fe n-ns.Spatially distributed clusters with different amounts of Fe-Fe n-ns exist.This situation corresponds to the magnetic moment distribution sketched in the central panel of figure 6, where the magnetic moment varies spatially in amplitude and is no longer periodic.This interpretation is supported by the much wider and gradual peak in ZFC-FC curves for 0.7 ions nm −2 in figure 2(b) around the blocking temperature compared to that of non-irradiated sample.
For the moving conduction electron, this increase in random spatial variation of the magnetic moments of neighboring clusters is similar to the temperature fluctuations of magnetic moments within a cluster itself.Therefore, this can be viewed as an additional scattering mechanism, which leads to the resistance increase shown in figure 3(a) in the range of 0-0.6 ions nm −2 .
Above a critical fluence, further randomization of the crystal lattice will provide a more uniform spatial magnetic moment distribution.The limit is the fully randomized lattice with close to 4.8 Fe-Fe n-ns in a the cluster as shown in the bottom image of figure 6.This effect decreases the additional scattering contribution from spatial magnetic moment variations present at low fluences.Therefore, it can be assumed that there exists a critical fluence, at which the spatial fluctuations of the magnetic moment within several local clusters are maximized, which qualitatively is in agreement with the results presented in figure 3(a).For high fluences (>6 ions nm −2 ) the magnetic moments become even more uniform than in the non-irradiated case, and therefore the observed resistivity is even lower for the fully disordered A2-phase, than for the ordered B2-phase.
In addition demagnetization effects have to be taken into account.The demagnetizing field depends on the magnetization of the sample and in the infinite thin film approximation can be defined as [27,28]: where⃗ z is the unit-vector perpendicular to the Hall-bar plane, and M s is the saturation magnetization of the sample.For this work the use of the thin film approximation is well justified as the width and the length of the irradiated region exceed the thickness more than 100 times [27].Due to the fact that M s of the sample does not remain fixed with fluence, the demagnetization field also depends on the fluence.Changes in the demagnetization field will change the perpendicular component of the magnetization, which leads to changes in the resistivity via the anisotropic magnetoresistance (AMR) effect.From the AMR point of view, a higher fluence corresponds to a higher demagnetization field and an increase in the in-plane component of the magnetization.From figure 4(a), it is known that Fe 60 Al 40 shows a positive anisotropic magnetoresistance.This means, that the in-plane magnetization state, namely when the magnetization is parallel to the current direction in the Hall-bar, corresponds the highest resistivity.At low-fluences (<0.6 ions nm −2 ), the field of the permanent magnet is sufficiently high to saturate the magnetization out-of-plane (perpendicular to the current), and the resistivity contribution from the AMR is lowest.Therefore, if AMR would be a dominant cause of the resistivity versus fluence dependence, it would be reasonable to expect the resistivity to steadily grow and saturate.However, the resistivity of the 10 ions nm −2 sample is actually lower than that of the non-irradiated one (figure 3(a)).
In addition to local clusters, metaclusters also give an indirect contribution to resistivity.Just as the moment of the local clusters undergoes thermal fluctuations, the same is happening for the moment of the metaclusters.Similar to the local clusters, at low-to-moderate fluence the metaclusters grow in size but staying practically isolated from one another.This creates an additional random modulation of the spatial magnetic moment distribution, which similar to local clusters leads to a resistivity increase.At the high fluences, as disordered magnetic clusters percolate more and more into the lattice, the density of metaclusters becomes such that neighboring clusters start to overlap and percolation network of exchange coupled metaclusters is formed.This average exchange interaction over the whole film partly stabilizes the moments of the individual metaclusters against thermal fluctuations.Evidence of this effect is the observed decreased splitting in magnetic moment between ZFC and FC curves at low-temperatures as the fluence increases and the complete absence of the splitting for the 10 ions nm −2 case, indicating exchange coupled ferromagnetic-like behavior (figures 2(b)-(d)).A decrease of thermal fluctuations related to exchange, leads to a decrease in resistivity, which is consistent with the fact, that the non-irradiated sample shows higher resistivity than that of the 10 ions nm −2 .
Measurements were made over multiple irradiation-annealing cycles, undergoing phase transitions between the A2 ↔ B2 phases.The resistivity of the B2-phase was higher than that of A2 for all the cases.This highlights the dominant role of the magnetic local clusters and metacluster formation over structural and demagnetizing field/AMR effects in the transport properties for the B2 → A2 phase transition in Fe 60 Al 40 .
The increase in exchange with fluence adds an additional contribution to the decreasing resistivity [24, section 5] The more Fe clusters couple to the neighboring ones-the higher the average exchange interaction throughout the sample, and consequently, the stronger the exchange splitting.This should lead to a steady decrease in resistivity due to irradiation.This increase in splitting is again confirmed by the increasing saturation magnetization in figure 2(a) and a transition from cluster-like to ferromagnet-like behavior of ZFC-FC curves for high-fluences.
In the following the evolution is considered of the AHE in figure 3(a), where ρ xy , measured in parallel with ρ xx , is plotted as a function of fluence.As can be seen for low fluences ρ xy is increasing similar to resistivity ρ xx .At a slightly lower fluence (0.42 ions nm −2 ) compared to that of the resistivity it reaches a maximum and then monotonically saturates.
Since the magnetic field is fixed by a permanent magnet, the contribution related to the ordinary Hall-effect only leads to an offset and does not change with fluence.However, the AHE is proportional to the magnetization component perpendicular the film plane: where R AHE is the AHE constant, I is the amplitude of the electric current and M ⊥ is the perpendicular component of the magnetization.The R AHE can depend on several factors [29].Broadly, these factors can be separated into intrinsic, which are related to the band structure of the material and extrinsic, related to the defects.Considering that the films were prepared using magnetron sputtering and due to different types of defects created by ion irradiation it is expected that the intrinsic contribution is smaller compared to the extrinsic contribution.Moreover, as can be seen from figure 3 Although ρ xy qualitatively follows the evolution of ρ xx as is expected in the extrinsic regime, the fact that the peaks in ρ xx and ρ xy are observed at different fluences indicates that other effects may be involved.An effect that contributes to the decrease of the AHE resistivity is the demagnetizing field.As in the case of resistivity, changes in the demagnetization field will decrease the perpendicular component of the magnetization, which in turn reduces the AHE voltage.We attribute the discrepancy between maxima in ρ xx and ρ xy in figure 3(a) to this effect.To reliably eliminate the influence of this effect one would need to saturate the magnetization perpendicularly for all possible M s values.This requires a perpendicular external field higher than the maximum possible ⃗ B dem , which, considering the value of saturation magnetization for Fe 60 Al 40 of 710 kA m −1 in A2-phase (figure 2 The resistivity and AHE during a reverse A2 to B2 phase transition are shown in the supplementary.At an annealing current of I = 20 mA the reverse transition happens during the 42 s.

Magnetic field dependence of resistivity
The qualitative model of local and metaclusters can also be applied to understand the magnetotransport properties shown in figure 4. The observed negative MR of the non-irradiated sample can be attributed to the s − d scattering of conduction electrons on fluctuating magnetic moments of Fe atoms in the local Fe-clusters [30, p 1836].Although the measurements were conducted at 4 K, still some thermal fluctuations in the direction of magnetic moments of local clusters remain.Under external magnetic field the increased Zeeman term suppresses the thermal fluctuations, thereby lowering the probability of thermal spin-flips, thus reducing the scattering of the s-electrons.
As the sample magnetization increases during irradiation, other effects that depend on the average magnetization direction such as AMR also play a role.Therefore, it is only possible to compare the NMR effects for irradiated and non-irradiated samples after the applied field exceeds the saturation field.As was mentioned in section 3, this point occurs at the change in slope of magnetoresistance [R(µ 0 H)] and saturation of AHE (figure 4).
For increasing fluence metaclusters related to ion irradiation are formed.Since Fe atoms are exchange coupled within one metacluster, a cumulative effect can be considered of the magnetic fluctuations of separate Fe moments as fluctuations of the average moment of the metacluster.Since the total moment of the metaclusters is much higher, than that of the local Fe clusters, the Zeeman effect due to it will be much higher and the stabilization effect from external magnetic field is also stronger.This means that the decrease in resistivity as a function of field should be steeper for the 0.7 ions nm −2 sample and, indeed, this increase in slope is observed if the red and blue curves are compared in figure 4(a).
Extending the same line of argument further, one could assume, that for even higher fluences (10 ions nm −2 ) the effect should be even more pronounced.However, on the contrary, for the fully disordered case, the slope of the R(µ 0 H) is smaller after the saturation (above 1.1 T), than that of 0.7 ions nm −2 .In case of 10 ions nm −2 the metaclusters are overlapping, in contrast to lower fluences.The exchange interaction established in this regime additionally stabilizes the directions of the magnetic moments against thermal fluctuations.Since the direction of magnetic moments within the clusters is already stabilized by exchange, the effect of the applied magnetic field is lowered, which is reflected in the smaller slope of R(µ 0 H) for the fully disordered 10 ions nm −2 case in high fields.For lower fields, below 1.1 T, the change in slope for the 10 ions nm −2 sample is related to the AMR effect.
In order to further prove the considerations above, in figures 5(a)-(c) the R(µ 0 H) dependence is plotted for non-irradiated (a), 0.7 ions nm −2 (b) and 10 ions nm −2 (c) for different temperatures.As can be seen in figures 5(a) and (b) an increase in temperature increases fluctuations of the magnetic moments and reduces the relative impact of the external field.As a consequence the slope of the R(µ 0 H) dependence decreases as a function of temperature for both non-irradiated and 0.7 ions nm −2 .This effect is negligible for 10 ions nm −2 , where additional exchange coupling still plays a dominant role.
Onoda et al [31] used the Green's Function approach to calculate the Hall effect in ferromagnets in different defect concentration regimes.Comparing the range of ρ xy vs. ρ xx observed in figure 3 during the disordering, with the model in [31], the scattering mechanism in Fe 60 Al 40 falls well within the intrinsic 'moderately dirty' regime, throughout the disordering process.The increasing ρ xy vs. ρ xx during the initial stages of disordering (figure 3, lower panel), is consistent with an increase in defect concentration and the subsequent decrease of the ρ xy /ρ xx reverses the trend towards the modeled behavior for a clean material, suggesting increased homogeneity due to merging of the metaclusters.Thus the defect scattering in the Fe 60 Al 40 occurs within an intermediate regime where both intrinsic as well as extrinsic AHE mechanisms may co-exist.Furthermore, DFT calculations in literature [18,26,32] on the B2 and A2 phases show that along with the increased spin-splitting of the DOS, there is a tendency towards a reversal in the spin-polarization at the Fermi level, consistent with the AHE sign-reversal.
The observed shift in the transport regime at a critical degree of disordering (figure 3) is consistent with the calculations of [18], except for the increasing ρ xy vs. ρ xx during the initial disordering, where theory predicts a vanishing AHE.The unambiguous peak in AHE observed during the initial disordering process points toward a significant contribution of the scattering from metaclusters, which is a practical aspect of the phase transition, and provides an applications relevant regime where transport properties are observed to depend sensitively on the lattice disorder.

Conclusions
Based on fluence-, field-and temperature-dependent resistance and anomalous Hall effect measurements it is concluded that, although both structural and magnetic effects can have influence on transport properties in Fe 60 Al 40 , the magnetic effects provide the dominant contribution.Upon a transition from ordered B2-phase to disordered A2-phase it was found that two effects occur.First, with irradiation and the associated disorder the amount of nearest-neighbors within the local Fe-clusters increases from 2.67 to 4.8.Simultaneously, due to the non-uniform distribution of disordered regions, larger magnetic regions are formed.Their influence on the transport properties is clearly visible in the negative MR effect, when compared to the non-irradiated sample.As the density of these magnetic metaclusters increases to a degree when they start to overlap, additional 'inter-cluster' exchange interaction reduces the thermal fluctuations of the magnetic moments within the clusters.As a consequence this leads to there being two distinct regimes in transport properties, which manifest as a peak in both resistivity and AHE as a function of disorder, providing a sensitive degree of control over the magnetotransport.

Figure 1 .
Figure 1.Sketch on top of an optical image of the Hall-bar of the Helium Ion Microscope experiment.Trapezoidal structure represents a permanent magnet that produces a 350 mT magnetic field, oriented perpendicular to the sample plane.Ne + ion beam is scanned across the central part of the Hall-bar.The energy of the beam was 25 keV with the maximum fluence of 10 ions nm −2 .In parallel, 2-wire resistance (contacts I + , I − ) and anomalous Hall effect (contacts V + , V − ) were measured at I = 1 mA.

Figure 2 .
Figure 2. (a) In-plane magnetometry results of thin films for different fluences.Field-cooled (FC) (at 5 mT) and zero-field cooled (ZFC) magnetic moments of the same films as a function of temperature for (b) 0 ions nm −2 ; (c) 10 ions nm −2 ; (d) 0.7 ions nm −2 .The FC and ZFC parts are depicted with different colors for clarity.
(a) the dependence is shown of the resistivity (ρ xx ) and Hall resistivity (ρ xy ) as a function of ion fluence.Resistance, Hall voltage and fluence were measured in-parallel, but not synchronous as a function of time.Fluence was then interpolated and evaluated at the time points when resistance and Hall voltage readings were taken.In figure 3(b) the dependence of the ρ xy as a function of ρ xx is shown.As is clear in figure 3(a) the resistivity behaves similarly to that of Fe 60 Al 40 Hall-bar measured in [20, figure 4.4].Starting from low fluences the resistivity increases with increasing fluence and peaks at a fluence of 0.6 ions nm −2 .For higher fluences, the resistivity gradually decreases and eventually saturates.The fluence at which the loss of the long-range order occurs is expected to take place around the peak in resistivity, according to the magnetization vs fluence dependence for similar films presented in [14, figure 4(a)].The AHE resistivity ρ xy behaves similarly to ρ xx , having a peak at an intermediate fluence and saturating for higher fluences.Although the dependencies of ρ xx and ρ xy on ion fluence are qualitatively similar, however, the peak in the AHE occurs at a lower fluence of 0.42 ions nm −2 .

Figure 3 .
Figure 3. (a) Resistivity (ρxx) and AHE (ρxy) of Fe60Al40 as a function of Ne + ion fluence during B2 to A2 phase transition.The maximum in ρxx was observed at 0.6 ions nm −2 , whereas the maximum in ρxy was observed at 0.42 ions nm −2 .In (b) ρxy is plotted as a function of ρxx.The dependence is linear with different slopes for points before and after the peak in ρxx.

Figure 4 .
Figure 4. Resistance (a) and AHE (b) as a function of magnetic field applied perpendicular to the plane of the Hall-bar.Measurements were performed at T = 4 K. Every curve (for non-irradiated, 0.7 ions nm −2 and 10 ions nm −2 ) is normalized by its corresponding maximum absolute value.In (b) results for non-irradiated and 0.7 ions nm −2 are vertically shifted to RAHE/RAHE_max = 0 for better comparison.In the inset of (b) a small AHE present in the non-irradiated samples is depicted.

Figure 5 .
Figure 5. Dependence of the resistance as a function of magnetic field applied perpendicular to the surface of the Hall-bar at different temperatures for (a) non-irradiated, (b) 0.7 ions nm −2 and (c) 10 ions nm −2 .Every curve is normalized to its corresponding maximum absolute value.

Figure 6 .
Figure 6.Sketch of a spatial distributions of Fe-Fe n-ns in Fe60Al40 that are proportional to cluster magnetic moment for different fluences.Note, that this is a qualitative representation and not the measured one.In insets an examples of possible atomic arrangements are shown.The insets were reproduced from [14, figure 1] with the permission from the authors.
(b), ρ xy is linearly changing as a function of ρ xx in both low-and high-fluence regimes, indicating that AHE is dominated by skew-scattering [29, pp 2-5].