Origin of the spin reorientation transitions in (Fe1–xCox)2B alloys

Abstract

Low-temperature measurements of the magnetocrystalline anisotropy energy K in (Fe 1−x Co x ) 2 B alloys are reported, and the origin of this anisotropy is elucidated using a first-principles electronic structure analysis. The calculated concentration dependence K(x) with a maximum near x = 0.3 and a minimum near x = 0.8 is in excellent agreement with experiment. This dependence is traced down to spin-orbital selection rules and the filling of electronic bands with increasing electronic concentration. At the optimal Co concentration, K depends strongly on the tetragonality and doubles under a modest 3% increase of the c/a ratio, suggesting that the magnetocrystalline anisotropy can be further enhanced using epitaxial or chemical strain.Magnetocrystalline anisotropy (MCA) of a magnetic material is one of its key properties for practical applications, large easy-axis anisotropy being favorable for permanent magnets.1 Intelligent search for new materials requires understanding of the underlying mechanisms of MCA. This can be particularly fruitful for substitutional alloys whose properties can be tuned by varying the concentrations of their components. The analysis is often relatively simple in insulators, where MCA is dominated by single-ion terms which can be deduced from crystalfield splittings and spin-orbital (SO) selection rules. In contrast, in typical metallic alloys the band width sets the largest energy scale, and MCA depends on the details of the electronic structure.The (Fe 1−x Co x ) 2 B solid solution 2-6 (space group I4/mcm 7 ) is a remarkable case in point. Fe 2 B has a fairly strong easy-plane MCA, and Co 2 B, at low temperatures, a small easy-axis MCA. However, the alloy has a substantial easy-axis MCA around x = 0.3, 2 making it a potentially useful rare-earth-free 8 permanent magnet. At x ≈ 0.5 the MCA again turns easy-plane, peaks at x = 0.8, and then turns easy-axis close to x = 1. These three spin reorientation transitions must be related to the continuous evolution of the electronic structure with concentration. The goal of this Letter is to elucidate the origin of this rare phenomenon.First, we report the results of experimental measurements at low temperatures.Single crystals of (Fe 1−x Co x ) 2 B were grown from solution growth out of an excess of (Fe,Co) which was decanted in a centrifuge. 9The single crystals were grown as tetragonal rods which were cut using a wire saw to give them the shape of a rectangular prism. The demagnetization factor was calcua) This article has been accepted by Applied Physics Letters.After it is published, it will be found at http://scitation.aip.org/content/aip/journal/apl . lated using Ref. 10. Field-dependent magnetization measurements were performed in a Quantum Design MPMS at 2 K in fields up to 5.5 T. The MCA energy K was determined as the area between the two magnetization curves, with the field parallel and perpendicular to the c axis, taken at the same temperature.6 The results shown in Fig. 1 Density-functional calculations using several different m...

Magnetic properties of(Fe1−xCox)2Balloys and the effect of doping byEdström1, Werwiński2, Iuşan3 et al. 2015Phys. Rev. B

“…This failure is most likely due to the atomic sphere approximation (ASA), which approximates the potential as being spherically symmetric around each atom, in contrast to the VCA calculations presented in the previous section, which included full potential (FP) effects. This is in contrast with a recent publication [49], where authors suggest that the qualitatively wrong behavior in the MAE predicted for the Co-rich side is a failure of the exchangecorrelation functional itself, yielding too high magnetization. Nevertheless, the CPA description in ASA coincides with experiments on the Fe-rich side.…”

“…In Ref. [49] the filling of states with alloy concentration was investigated and related to the variation of the MAE. It was suggested [49] that the spin-diagonal part of the spin-orbit operator is most important with rather strong and nearly constant, positive MAE contributions coming from the coupling between majority spin states while coupling between minority spin states yields the variation in the MAE.…”

Tunable dimensional crossover and magnetocrystalline anisotropy in Fe2P -based alloys

“…To identify the mechanisms of MCA and its dependence on band filling, we first consider the site and spin decomposition of the anisotropy of the SOC energy [19,31]. We have verified that, as expected, this quantity closely follows the concentration dependence of K in these alloys.…”

“…We now examine the contributions to K coming from different regions in the Brillouin zone [19]. Figure 5 shows the difference of the minority-spin single-particle energies for magnetization along the x and z axes in pure Fe 2 P, resolved by k. We see that the MCA accumulates over a fairly large part of the Brillouin zone, with the most important contribution coming from the region with k z ≈ k 1/3 = | A|/3 (bright red area in Fig.…”

“…Substitutional disorder was treated using our implementation of the coherent potential approximation (CPA) [17] with spin-orbit coupling (SOC) included and the MCA energy K calculated following Refs. [18][19][20]. The atomic sphere radii were carefully chosen to reproduce the full-potential band structure.…”