Bulk and element-specific magnetism of medium-entropy and high-entropy Cantor-Wu alloys

D. Billington, A. D. N. James, E. I. Harris-Lee, D. A. Lagos, D. O'Neill, N. Tsuda, K. Toyoki, Y. Kotani, T. Nakamura, H. Bei, S. Mu, G. D. Samolyuk, G. M. Stocks, J. A. Duffy, J. W. Taylor, S. R. Giblin, and S. B. Dugdale

Phys. Rev. B 102, 174405 – Published 5 November 2020

Abstract

Magnetic Compton scattering, x-ray magnetic circular dichroism spectroscopy, and bulk magnetometry measurements are performed on a set of medium- (NiFeCo and NiFeCoCr) and high-entropy (NiFeCoCrPd and NiFeCoCrMn) Cantor-Wu alloys. The bulk spin momentum densities determined by magnetic Compton scattering are remarkably isotropic, and this is a consequence of the smearing of the electronic structure by disorder scattering of the electron quasiparticles. Nonzero x-ray magnetic circular dichroism signals are observed for every element in every alloy indicating differences in the populations of the majority and minority spin states implying finite magnetic moments. When Cr is included in the solid solution, the Cr spin moment is unambiguously antiparallel to the total magnetic moment, while a vanishingly small magnetic moment is observed for Mn, despite calculations indicating a large moment. Some significant discrepancies are observed between the experimental bulk and surface magnetic moments. Despite the lack of quantitative agreement, the element-specific surface magnetic moments seem to be qualitatively reasonable.

Received 14 August 2020
Accepted 12 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.174405

Physics Subject Headings (PhySH)

Magnetism

Disordered alloys

Compton scattering Korringa-Kohn-Rostoker method X-ray magnetic circular dichroism

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Billington ^1,2,3,*, A. D. N. James ¹, E. I. Harris-Lee ¹, D. A. Lagos ¹, D. O'Neill ⁴, N. Tsuda³, K. Toyoki³, Y. Kotani ³, T. Nakamura³, H. Bei ⁵, S. Mu ⁵, G. D. Samolyuk⁵, G. M. Stocks⁵, J. A. Duffy⁴, J. W. Taylor⁶, S. R. Giblin², and S. B. Dugdale ¹

¹H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
²School of Physics and Astronomy, Cardiff University, Queen's Building, The Parade, Cardiff CF24 3AA, United Kingdom
³Japan Synchrotron Radiation Research Institute, SPring-8, Sayo 679-5198, Japan
⁴Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
⁵Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁶DMSC - European Spallation Source, Universitetsparken 1, Copenhagen 2100, Denmark

^*Present address: School of Physics and Astronomy Cardiff University, Queen's Building, The Parade, Cardiff CF24 3AA, United Kingdom; billingtond1@cardiff.ac.uk

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Vol. 102, Iss. 17 — 1 November 2020

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Images

Figure 1
Experimental (points) and calculated (lines) MCPs, $J_{mag} (p_{z})$ , of (a) NiFeCo, (b) NiFeCoCr, (c) NiFeCoCrPd, and (d) fcc Ni recorded with the scattering vector parallel to the [100] (blue circles, bottom), [110] (red squares, middle), and [111] (black diamonds, top) high-symmetry crystallographic directions. The insets show the directional differences of the MCPs, $Δ J_{mag} (p_{z})$ , between the [100] and [110] (blue circles, bottom), [100] and [111] (orange squares, middle), and [111] and [110] (green diamonds, top) directions. The directional profiles in each panel and directional differences in each inset have been offset by steps of (a) $0.15 μ_{B} {a . u .}^{- 1}$ , (b) $0.025 μ_{B} {a . u .}^{- 1}$ , (c) $0.05 μ_{B} {a . u .}^{- 1}$ , and (d) $0.05 μ_{B} {a . u .}^{- 1}$ for clarity. The experimental and calculated directional profiles have been normalized to their experimentally determined bulk spin moments [from Eq. (9)] along their respective directions. The error bars are statistical errors of one standard deviation. Note that the error bars are larger when the bulk spin magnetic moment is smaller due to the measured signal being proportional to the spin magnetization. The fcc Ni experimental profiles are taken from Ref. [71].
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Figure 2
XAS (top) and XMCD (bottom) spectra of (left to right) Cr, Fe, Co, and Ni in (a) NiFeCo and (b) NiFeCoCr. The multiplication labels indicate the scaling of the XMCD signals. All of the XAS signals have been offset by a constant value of 0.1 for clarity. Note that the incident photon energy is plotted on a logarithmic scale (the 50-eV energy intervals get closer together with increasing energy) for clarity because at lower energies the core-level spin-orbit splitting of species with lower atomic number is smaller.
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Figure 3
XAS (top) and XMCD (bottom) spectra of (left to right) Pd, Cr, Mn, Fe, Co, and Ni in (a) NiFeCoCrPd and (b) NiFeCoCrMn. The multiplication labels indicate the scaling of the XMCD signals. All of the XAS signals have been offset by a constant value of 0.1 for clarity. Note that the incident photon energy is plotted on a logarithmic scale (the 50-eV energy intervals get closer together with increasing energy) for clarity because at lower energies the core-level spin-orbit splitting of species with lower atomic number is smaller.
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Figure 4
Element-specific magnetization curves for (a) NiFeCo, (b) NiFeCoCr, (c) NiFeCoCrPd, and (d) NiFeCoCrMn determined by the XMCD measurements together with their respective magnetization curves determined by the SQUID measurements. The saturated magnetic moments for each atomic species have been scaled to the corresponding total moments determined by the orbital and spin sum rules (except for Pd where it was scaled to the total Pd $d$ -electron moments from the KKR-CPA calculations) listed in Table 2. The inset of (d) shows a close-up of the NiFeCoCrMn magnetization curve from the SQUID measurements together with the Mn magnetization curve from the XMCD measurements. The inset has the same axis labels and units as those of the main panel.
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Figure 5
Species-averaged total moments and spin moments as a function of the relative combined Cr and Mn concentration for NiFeCo (0 at. % $Cr + Mn$ ), NiFeCoCr (25 at. % $Cr + Mn$ ), NiFeCoCrPd (20 at. % $Cr + Mn$ ), and NiFeCoCrMn (40 at. % $Cr + Mn$ ) as determined by KKR-CPA calculations (black), the XMCD orbital and spin sum rules (red), and bulk (SQUID and Compton) measurements (blue). The experimental (SQUID) and calculated (KKR) total moments of NiCoCr (33 at. % $Cr + Mn$ ) from Ref. [27] are also plotted. Solid and dotted lines are guides to the eye for the total moment and the spin moment, respectively. The orbital moment is given by the difference between the total moment and the spin moment. The orbital moment of NiCoCr has not been reported so we have set the calculated $m^{tot} = m^{spin}$ , and magnetic Compton scattering was not performed on NiCoCr or NiFeCoCrMn so is not plotted. The error bars are statistical errors of one standard deviation. The error bars from the bulk measurements are approximately equal to the size of the points.
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