Magnetic states of iron in metastable fcc Fe–Cu alloys

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Abstract

X-ray magnetic circular dicroism at the K absorption edge of iron is exploited to elucidate the local spin structure of Fe in metastable, ferromagnetic fcc Fe–Cu alloys. At Fe concentrations as high as 50 at.%, Fe–Cu alloys are particularly suitable for studying the magnetic state of iron in an fcc environment, because of the negligible contribution of copper to the alloy magnetic moment. The experimental spectra are consistent with the picture of iron atoms coexisting in two different magnetic moment states and point out at the negative sign associated with the low magnetic moment state. This result brings in more evidence on multiple magnetic states, simultaneously present in 3d alloys with competing ferromagnetic and antiferromagnetic interactions, and offers a common explanation to the Invar effects recently reported for the Fe–Cu system.

Introduction

The capability to describe and predict the magnetic properties of binary transition metal alloys, or even the phase diagram of pure metals, still represents a challenge for advanced first-principles theories of electron states in solids. In spite of the development of computation techniques, which enable to efficiently carry out local spin density, and beyond, calculations of the electronic structure in magnetic systems, first-principle studies remain mostly confined to structurally simple and possibly ordered phases of crystalline solids. Theoretical investigations of model magnetic systems have, however, the merit of pointing out at the mutual links of electronic structure with magnetic properties, structural phase and stability. On the experimental side, the magnetic behaviour of binary transition metal alloys is summarized in the popular Slater–Pauling curve [1], which emphasizes the connection between electronic state and crystallographic phase when the average magnetic moment per atom is plotted versus the number of outer electrons. Most of body-centered-cubic (bcc) and face-centered-cubic (fcc) alloys follow the main branch of the Slater–Pauling curve, although some exceptions exist for those systems whose magnetic state is affected by local environment effects which bring in competing interactions. The most notable examples are the fcc Fe–Ni alloys which, at Ni concentrations close to 35%, show also the Invar effect. Competing ferromagnetic–antiferromagnetic interactions are at the origin of the complex behaviour which Fe–Ni alloys exhibit as to crystallographic structure, magnetic phase and Invar anomalies.

A deeper understanding of the microscopic nature of magnetism in solids can be accomplished by both theoretical and experimental investigations of the structure-, lattice parameter- and chemical order-dependencies of the magnetic properties in transition metal alloys. Properly tailored binary alloys of transition metals represent a suitable mean to produce a controlled variation of the atomic volume of the components, thus making ordinarily unstable bulk magnetic phases stable at unusual volumes and crystallographic structures. While no a priori constraint applies to the computational treatment of metastable phases, the ordinary and natural solid solubility limits can be overcome by exploiting modern preparation techniques, like mechanical alloying, to produce unusual metastable alloy phases. Binary alloys with one non-magnetic component turn out to be artificial systems of special interest, which enable the study of the magnetic element as frozen in an exotic, genuinely bulk phase. Alternatively, the volume dependence of the magnetic state could be investigated by applying an external pressure to the pure transition metal, which has the advantage of a continuous change of the atomic volume, although through a volume reduction only, and, hence, of the 3d band width.

Among ferromagnetic transition metals, iron continues to be a challenging subject and one of the most investigated materials. The knowledge of the iron phase diagram, especially the high pressure and high temperature behaviour [2], is considered of primary importance in Earth science. Also a superconducting phase of iron has been reported [3] to develop at low temperatures (¡2 K) and moderately high pressures (15–30 GPa). Since Fe is a weak ferromagnet, its magnetic moment is not stable and can change considerably with the structure. Under normal conditions, Fe is bcc ferromagnetic (α phase), with an fcc (γ) phase developing above the temperature T0=1183  K. The magnetic state of the fcc phase of metallic iron at temperatures lower than T0 is still under debate [4]. One of the first and most popular models, originally introduced to explain the Invar behaviour observed in the fcc alloy Fe34Ni66at room temperature is the so-called two-state model [5]. According to this model, two states are possible for fcc Fe, namely a high spin (HS) and a low spin (LS) state. The original conjecture of Weiss [5] was later on supported by modern first principle calculations of collinear magnetic structures of fcc iron [6], which point out at the stability of only two magnetic states: the low-spin state, stable at low atomic volume, associated to a magnetic moment of 1 μB, and favoring antiferromagnetic coupling, and the high-spin state stable at large atomic volume, associated with a magnetic moment ranging from 2.5 to 3 μB and favoring strong ferromagnetism. More recently, a theoretical investigation [7] of fcc Fe–Ni explained the Invar anomaly as originating from a non-collinear structure of the iron magnetic moments, which is also coupled to a volume dependence of the magnetic moment amplitude. The emerging picture suggests that non-collinear spin alignments, some of them more stable than the collinear configuration, could be associated to the ground state of fcc iron and extensive calculations of the Invar anomalies in Fe-based alloys have been recently carried out in ref. [8].

Contrary to the theoretical achievements on the fcc phase of bulk Fe, a well-founded experiment-versus-theory comparison is still lacking, mostly because of the difficulties to obtain clear and unambiguous experimental data on multiple magnetic states of fcc iron. Experimental data on the bulk fcc phase of iron, practically, come only from fcc alloys and solid solutions or thick Fe films grown on fcc substrates, where Fe is found in an fcc environment, and in many cases the experimental technique does not clearly distinguish between the different magnetic structures at microscopic level. One of the most known examples are the Fe–Ni alloys, where several neutron scattering measurements which represent the most straightforward technique for the determination of the atomic magnetic moment distribution, although not atom-specific, have been carried out [9]. In this case, neutron diffraction experiments are not sufficient to unambiguously define the magnetic state of iron because of the non-negligible nickel contribution and local order effects. The active role played by Ni in setting up the magnetic properties of the alloys, prevents from obtaining the localized magnetic moments at the iron sites by neutron scattering data only.

Considering the complexity of the calculated magnetic ground state of fcc iron, experimental investigations aimed at disclosing the relationship between multiple coexisting magnetic configurations, fcc phase and Invar behaviour are mandatory. Among the possible systems, the solid solutions of Fe–Cu at Cu-rich concentrations, synthesized by the mechanical alloying technique of high-energy ball milling, represent an extremely favorable system which stabilizes a bulk phase of fcc Fe at low temperature. The processing technique of high-energy ball milling has proved to be quite effective in producing solid solutions of components which ordinarily have little or no miscibility at room temperature. Solid solutions of Fe–Cu have been extensively studied over the whole concentration range [10] for both their technological potential and theoretical description, which tackles fundamental concepts in thermodynamics. Recently, magnetization measurements have been repeated [11] over an extended set of Cu concentrations for a mapping of the Fe–Cu system against the Slater–Pauling curve. An even more recent investigation [12] on three fcc Fe–Cu alloys, namely 16, 44 and 65 at.% Fe, exploited temperature-dependent neutron diffraction, coupled to low temperature magnetometry, to provide some experimental evidence of the Invar behaviour of these alloys [12]. This feature, as in Fe–Ni alloys, can be related to competing ferromagnetic–antiferromagnetic interactions arising from the different local arrangements of the atomic magnetic moments which Fe can assume when in an fcc environment.

In this paper, we report on X-ray Magnetic Circular Dichroism (XMCD) measurements at the Fe K edge of two fcc Fe–Cu alloys, namely Fe50Cu50and Fe40Cu60, aimed at getting experimental evidence on the local magnetic state of Fe in the high-volume fcc environment of the Fe–Cu system. The results, which a probe sensible to the local spin structure like XMCD can provide, would also complement the first studies carried out by non polarized X-ray absorption techniques at the Fe K edge, namely Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near-Edge Structure (XANES), in the fcc Fe50Cu50 solid solution [13].

Section snippets

Experimental

A set of already well characterized powder samples, produced by high energy ball milling, with compositions 20, 40, 50 and 60 at.% Fe and in quantities as large as several grams, was available. The samples of the present XMCD experiment were prepared out of this powder production. Characterization measurements were carried out on the powders for every composition, namely bulk magnetization and X-ray diffraction measurements, which showed all the alloys to be ferromagnetic and fcc single phase.

Data analysis and discussion

A detailed interpretation of the XMCD signal is quite a complex task and it has been accurately performed within an atomic model [22]. Such an approach is not completely appropriate to treat the case of the p-like empty states sampled in the present experiment. Indeed, these states are largely delocalized and belong to an electronic band which spans several electron volts. Presently, the theoretical interpretation of the XMCD signal at the K edge of 3d transition metals has not reached the same

Conclusions

The investigation of the magnetic state of fcc Fe remains a central issue for first-principle theories of electronic states in solids, which attains a special relevance when the theoretical models of the double magnetic and volume state are invoked as a possible explanation of the Invar anomalies. Although the Invar behaviour is reported for some well-known iron compounds, the explanation of the microscopic mechanisms driving this behaviour cannot be considered complete, and certainly it is not

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