The impact of nanoscale compositional variation on the properties of amorphous alloys

The atomic distribution in amorphous FeZr alloys is found to be close to random, nevertheless, the composition can not be viewed as being homogenous at the nm-scale. The spatial variation of the local composition is identified as the root of the unusual magnetic properties in amorphous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {Fe}_{1-x}\hbox {Zr}_{x}$$\end{document}Fe1-xZrx alloys. The findings are discussed and generalised with respect to the physical properties of amorphous and crystalline materials.


Results and discussion
Typical reconstructions of the elemental distribution are shown in Fig. 1. Since the samples were deposited on pre-sharpened Si tips, the interfaces between the layers are curved, reflecting the initial surface geometry as seen in Fig. 1a,b. The red region in Fig. 1b marks the Fe 1−x Zr x -layers, the yellow regions represent the amorphous Al 70 Zr 30 buffer and the blue regions marks the partially oxidised Al 70 Zr 30 capping layers. The measured Zr distribution in Fe 0.81 Zr 0. 19 and Fe 0.91 Zr 0.09 are displayed in Fig. 1c,d, respectively, within which the difference in the Zr-density of the samples is easily seen. When the local concentration of Fe is displayed in a similar way, the (high-) Fe density hinders any meaningful comparison between the samples. Thus, to illustrate the Fe distributions we need to invoke a different approach: We averaged the Fe concentration across 2 nm thick segments, thin enough to avoid severe blurring of the lateral changes in the composition, while providing statistically significant  25 seeding layer (green) is seen, covered by a Fe 81 Zr 19 (red and green) layer. Topmost the presence of oxygen (blue) demonstrates the almost complete oxidation of the capping layer ( Al 75 Zr 25 ). In (d) the distribution of Zr in Fe 81 Zr 19 is illustrated and in (c) corresponding distribution of Zr is shown for the Fe 91 Zr 9 alloy is displayed.  Fig. 2 are all similar. However the distribution in the relative elemental abundance (Fe and Zr) are somewhat different, as e.g. observed in the Fe distribution illustrated in Fig. 3 (right axis). This is possibly reflecting a contribution from a thermodynamic driving force arising from the concentration dependence in the mixing enthalpy of the elements. Let us now consider which effect the spatial variation in concentration can have on the magnetic properties of amorphous Fe 1−x Zr x alloys. When adding a non magnetic element to a ferromagnetic material, the magnetic ordering temperature ( T c ) typically decreases monotonically over a wide concentration range. This effect can be viewed as a consequence of decreased magnetic interactions ( J ) upon dilution as T c ∼ J in a homogenous magnetic system. Fe 1−x Zr x alloys exhibit richer concentration dependence, as illustrated in Fig. 3, in which a maximum in T c is observed, for an Fe concentration of ≃ 0.8. We can use these results to calculate the strength of the local magnetic exchange interaction based upon the concentration maps depicted in Fig. 2. To do so we make an ansatz: T c ∼< J > , where the brackets www.nature.com/scientificreports/ denote a weighted average with respect to concentration. Thus the determined T c is assumed to reflect an average exchange coupling dictated by the average concentration within each voxel. Figure 3 shows both the concentration dependence of T c (left hand y-axis) as well as the determined distribution of Fe concentrations within the samples (right hand y-axis). Although the variance in the distribution is not negligible, we argue the calculations can be used to map the local coupling strength from the average T c values. To ease the comparison, we define the local magnetic interaction, J i , in units of temperature. Based on the above assumptions we calculated the local exchange coupling for both the samples and the results are illustrated in Fig. 4. In these calculations we have used an interpolation and extrapolation for concentrations above 0.93 (see Fig. 3). This is not expected to change the interpretation in any qualitative way, although we can not exclude changes (errors) in the calculated values of J i . As seen in the figure, J i is changing dramatically ( J i ≈ 130 K) over short distances in Fe 0.91 Zr 0.09 , forming twined magnetic regions, resembling the contour maps of the elemental concentrations. The magnetic properties can therefore not be viewed as being homogenous, even on the length scale of few nm. The results obtained from the Fe 0.81 Zr 0.19 sample are illustrated in the right hand part of Fig. 4. The range in J i is much smaller ( J i ≈ 46 K) as compared to Fe 0.91 Zr 0.09 . The change in effective exchange coupling with concentration ( δJ/δc ) is therefore a measure of how corrugated the energy landscape will be. These changes in magnetic interactions must be reflected in e.g. the changes in the spontaneous magnetisation with temperature and we would expect the largest effects to be seen in Fe 1−x Zr x samples when x 0.7 and x 0.9. Let us now test these ideas by comparing the magnetic properties of thin amorphous layers and their single element crystalline counterparts. The ordering temperature of magnetic and structural phase transitions in thin layers are found to scale with the thickness (n) 28 and can be described as: where n is the extension of a "dead" layer at each interface, is an exponent and T c (∞) is the ordering temperature of bulk (infinitely large) sample. Typical results obtained from crystalline single element layers and alloys of amorphous materials are illustrated in Fig. 5. The results obtained from crystalline Co and Ni on Cu 29 , as well as Fe 0.68 Co 0.24 Zr 0.08 30 layers are reasonably linearised over a wide range in this representation (1/n). The changes obtained from Fe 0.90 Zr 0.10 31 layers, exhibit completely different behaviour, with = 0.16 ± 0.04 as compared to ≃ 1 for the other layers. This is not surprising when considering the extreme variation of the effective coupling strength within the Fe 0.91 Zr 0.09 samples. Extrapolating the thickness dependence of T c for the Fe 0.68 Co 0.24 Zr 0.08 layers 30 , results in a T c = 1025 ± 7 K which is an order of magnitude higher than that of Fe 0.90 Zr 0.10 . Hence although the concentration dependence of T c is not known, we can safely conclude that [δJ/δc]/J is at least an order of magnitude larger in Fe 0.90 Zr 0.10 as compared to Fe 0.68 Co 0.24 Zr 0.08 . This observation provides the basis for the obtained differences and consequently Fe 0.90 Zr 0.10 can only been regarded as magnetically continuous well below its ordering temperature.
The extension of the "dead" layers, n , is significantly different in crystalline and amorphous samples as seen in Fig. 5. While crystalline single-element samples typically exhibit a ferromagnetic behaviour to the monolayer limit, amorphous layers loose their spontaneous magnetisation at thicknesses which are almost an order of www.nature.com/scientificreports/ magnitude larger. The large n in amorphous alloys is readily rationalised when considering the changes in the effective exchange coupling, reflected in the variation of J within the samples (see Fig. 4). Above the apparent T c , the amorphous layers will not be paramagnetic: there will be regions with substantial moments, albeit fluctuating, and thereby not contributing to the spontaneous magnetisation. These are separated by sections with a weaker exchange coupling, effectively decoupling the intrinsically ferromagnetic regions. This interpretation is confirmed by the field dependence of the magnetisation of Fe 0.90 Zr 0.10 , which resembles a super-paramagnetic like behaviour well above the as determined T c 30-32 . The effect is illustrated in the inset in Fig. 5, in which a field   29 , the FeCoZr from Ahlberg et al. 30 and Fe 0.90 Zr 0.10 from reference Korelis et al. 31 . The inset illustrates the the temperature and field dependence of the magnetisation in a 1.5 nm Fe 0.89 Zr 0.11 at fields between 0 and 6 mT adapted from Liebig et al. 32  www.nature.com/scientificreports/ of 1 mT is seen to induce a moment which is approximately one half of what is obtained at 80 K. The range of the magnetic correlation in these layers, was estimated to be of the order of 100 nm 31 at T = T c + 20 K , which is substantially larger than the length scales of the compositional contours observed here. Thus, well above the ordering temperature there are large regions within which the variations in J are partially suppressed by magnetic proximity effects 13 . Furthermore, the large magnetic susceptibility observed in a wide temperature range below T c , reflects at least partially the distribution in J i (T c,i ) 30,31 . Finally, when the thickness of the amorphous layers is smaller or equal to 2 n , a superparamagnetic behaviour is observed at 5 K. 31 Similar effects are observed in Fe 0.68 Co 0.24 Zr 0.08 layers 30 . The results presented here provide therefore a base for the understanding of the ordering and phase transitions in amorphous alloys, including finite size effects on magnetic ordering.

conclusions
The randomness in the local chemical composition has a large impact on the magnetic properties of amorphous alloys. Its effect is clearly seen in both finite size scaling of the ordering temperature as well as the extension of interface regions in e.g. Fe 1−x Zr x amorphous alloys. The extraordinary mechanical properties of amorphous alloys 11,33 can be argued to stem from the same roots. The analogy to magnetic properties is straight forward: Replacing the magnetic interactions with chemical binding, results in spatial variation of atomic interactions and thereby changes in local mechanical properties. Recently, it was noted that atomic arrangements and the related probability distributions for particle displacements can be correlated with string-like excitations. These have a significant impact on the structural relaxation, atomic rearrangement and mechanical properties of metallic glasses 34 . Thus, having access to direct information on the atomic arrangements, such as obtained when using APT, can therefore shed light on a series of open questions concerning the physical properties of amorphous alloys 35 . We also note the lack of a theoretical framework for both the effect of non-homogenous interactions and www.nature.com/scientificreports/ its influence on the emergent magnetic order in finite size systems. Finally, to implement realistic descriptions of amorphous alloys we need to recognise that random compositions are intrinsically inhomogeneous in nature.

Methods
Amorphous FeZr thin films have been deposited by DC magnetron sputtering from elemental targets at room temperature. The base pressure was below 5 × 10 −10 mbar and the (purified) Ar pressure during growth was 4 × 10 −3 mbar. Since FeZr thin films on Si substrates grow partly crystalline at room temperature 36 an amorphous AlZr seed layer was deposited from an Al 75 Zr 25 compound target. The same target was used to deposit a capping layer to avoid oxidation of the magnetic layers. For APT, layers were deposited directly on pre-sharpened Si micro-tips with two different Fe and Zr target power ratios, resulting in compositions of Fe 91 Zr 9 and Fe 81 Zr 19 . The chemical compositions were confirmed by energy dispersive X-rays as well as atom probe analysis.
APT analyses were carried out on LEAP 4000 XHR (Cameca) in laser pulsing mode using a laser wavelength of 355 nm, a laser energy of 70 pJ, a pulse repetition rate of 200 kHz, with a detection rate of 0.003 ions per pulse. Three different samples were successfully analyzed. These contained 2.3 × 10 5 atoms in a volume of 20 nm × 20 nm × 20 nm and 7.4 × 10 4 atoms in a volume of 14 nm × 14 nm × 14 nm. These were analyzed by two different slices each and in more than six slice volumes, confirming the presented result. The sample temperature was set to 70 K in these measurements. As the pulse method always removes the particular uppermost surface atoms, the depth resolution of this APT analysis is one atomic layer. The lateral resolution within the layer is about 0.5 nm 37 .
The 3-D reconstruction of the ion positions was performed using IVAS 3.6.6 (Cameca). The initial radius of curvature r 0 and the specimen's shank half angle θ were determined by scanning electron microscope (SEM) (Helios, FEI) before the analysis and later applied in the reconstruction process. In both the amorphous alloys typical values of r 0 and θ were found to be r 0 = 30 nm and θ = 16 • , respectively. After the reconstruction, the 1st FeZr layer was chosen for evaluation of the chemical homogeneity by studying the concentration histogram, www.nature.com/scientificreports/ by using the 'cluster search' and the 'concentration mapping' provided by IVAS 3.6.6. In the voltage curve and detection rate curve of analysis, no burst was detected in the FeZr layer. Nevertheless, we cropped a volume of FeZr layer away from AlZr/FeZr interfaces for data evaluation to avoid possible impact of bursts at the proximity of interfaces. Impacts by orientation-dependent differences in resolution on the results could be excluded by using the cluster search. To allow for undoubtedly atomic classification, the signal at m/e = 27 is removed in the data evaluation processes because of the mass overlap of Fe and Al ( 54 Fe 2+ and 27 Al + ) in the seeding and capping layers. This approach was not implemented in the analyses of the Fe-Zr layers. A random FeZr alloy with the same volume and nominal composition was simulated and investigated for comparison, by using Region of Interest (ROI) simulation tool of the same software. The simulation of the volume assumed a bcc lattice. We, therefore, included a 0.5 nm smearing of the data to better mimic the amorphous alloys. The detection efficiency was set to 0.36, which is a typical value for the LEAP 4000 with reflectron. The detection efficiency has pure geometrical reasons and is therefore assumed to be insensitive to the detected elements 37 . The chosen density ρ in atoms per nm 3 was adjusted to the best match value in a respective volume to that of the measured counterpart. The density is ρ = 77.82 atoms nm −3 for Fe 91 Zr 9 , ρ = 79.86 atoms nm −3 for Fe 81 Zr 19 , respectively. Typical depth profiles are shown in Fig. 6 for a) Fe 0.91 Zr 0.09 and c) Fe 0.81 Zr 0.19 samples. The Zr depth profiles shown in Fig. 6a) provide the matching average concentration of 9 at% Zr for the alloy, as given by the dashed black line. Some local concentration values exceed the doubled standard deviation (2 σ -value, marked with the red dotted lines) of the average Zr concentration. This is also observed for the simulated alloys illustrate in Fig. 6b,d. Figure 7 shows a typical frequency distribution analysis of the measured (left side, a,c) and the simulated random (right side, b,d) alloy yielding the same average composition. Each block contains 100 atoms. The majority of blocks in the frequency distributions follow the binomial distribution, given by the black dashed envelope. For the measured 19 at.% Zr alloy shown in Fig. 7c, Zr-rich regions are observed (marked with red arrows) that exceed the binomial envelope and that are not visible for the simulated random alloy. This observation is consistent with a slight thermodynamically driven composition variations in the alloy.