Potential High-Performance Magnet: $\mathrm{Fe}$- and $\mathrm{Zr}$-Alloyed ${\mathrm{Ce}}_{2}$${\mathrm{Co}}_{17}$

Potential High-Performance Magnet: $Fe$ - and $Zr$ -Alloyed ${Ce}_{2}$ ${Co}_{17}$

Tribhuwan Pandey and David S. Parker

Phys. Rev. Applied 13, 034039 – Published 16 March 2020

Abstract

By performing comprehensive first-principles calculations, we study the hard magnetic properties of ${Ce}_{2}$ ${Co}_{17}$ and ${Ce}_{2}$ ${Fe}_{17}$ under $Zr$ doping with varying $Co$ concentrations, given the substantial experimental success of $Zr$ in improving the magnetic anisotropy energy (MAE) in ${Ce}_{2}$ ${Co}_{17}$ and ${Sm}_{2}$ ${Co}_{17}$ . We find that the magnetic properties of these alloys become comparable to state-of-the-art magnetic materials by doping with two elements, $Zr$ and $Fe$ , with potential-energy products $B H_{max}$ of 40 MG Oe. The $Zr$ substitution is particularly helpful for improving the MAE, leading to a magnetic hardness parameter $K_{1} / μ_{0} M_{s}^{2}$ that significantly exceeds unity for a substantial range of $Co$ concentrations (between 60% and 100% of the $3 d$ -element concentration). The calculated MAE exhibits a strong dependence on the $Co$ concentration, indicative of a likely valence fluctuation with $Co$ alloying, and shows a maximum value of 7.78 ${MJ / m}^{3}$ for 60% $Co$ doping. Thus, upon experimental verification, these alloys may become competitors to the better-known permanent-magnet materials ${Nd}_{2}$ ${Fe}_{14}$ $B$ and ${Sm Co}_{5}$ .

Received 31 July 2019
Revised 5 January 2020
Accepted 18 February 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.034039

Physics Subject Headings (PhySH)

Ferromagnetism Magnetic anisotropy

Energy applications Ferromagnets Helimagnets Transition-metal rare-earth alloys

Density functional theory First-principles calculations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tribhuwan Pandey and David S. Parker^*

Material Science and Technology Division Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

^*parkerds@ornl.gov

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Vol. 13, Iss. 3 — March 2020

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Figure 1
(a) The rhombohedral crystal structure of the ${Ce}_{2}$ $M_{17}$ ( $M$ = $Co$ or $Fe$ ) unit cell, with all the crystallographic Wyckoff sites denoted by corresponding atomic site colors. (b) The crystal structure of ${Ce}_{2}$ $M_{15} Zr$ after substituting one $Zr$ atom (shown in red) for two dumbbell-site $M$ atoms [the $Fe$ ( $Co$ )- $6 c$ site is shown by the shaded area in (a)]. (c) The nearest-neighbor (NN) $Ce$ - $M$ and $Ce$ - $Zr$ distances in ${Ce}_{2}$ $M_{17}$ and ${Ce}_{2}$ $M_{15} Zr$ . Here, $M$ refers to either $Fe$ or $Co$ . For comparison, the first two $Ce$ NN distances in ${Ce Fe}_{5}$ and ${Ce Co}_{5}$ are 2.806 Å, 3.147 Å and 2.845 Å, 3.179 Å, respectively.
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Figure 2
(a) The total magnetic (spin plus orbital) moment and (b) the MAE in ${Ce}_{2}$ ${Zr Fe}_{15 - x}$ ${Co}_{x}$ as a function of $x$ . Here, the $Co$ doping is performed within the VCA. The symbols correspond to the calculated compositions and the line is a guide to the eye. The blue diamonds represent experimental data from Refs. [10, 12]. Results from calculations both without the Hubbard $U$ (open green diamonds) and with the Hubbard $U_{Ce} = 3$ eV (red filled squares) are compared here.
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Figure 3
The $Ce$ $f$ (black and orange filled lines) and $Co$ plus $Fe$ $d$ , density of states (DOS) (blue lines) and the $Zr$ DOS (red lines) in (a) ${Ce}_{2}$ ${Fe}_{15}$ $Zr$ , (b) ${Ce}_{2}$ ${Fe}_{12}$ ${Co}_{3}$ $Zr$ , (c) ${Ce}_{2}$ ${Fe}_{9}$ ${Co}_{6}$ $Zr$ , (d) ${Ce}_{2}$ ${Fe}_{6}$ ${Co}_{9}$ $Zr$ , and (e) ${Ce}_{2}$ ${Co}_{15}$ $Zr$ , calculated within GGA + SOC + $U$ . The $Zr$ DOS is enlarged by a factor of 15 for clarity. The $Co$ - $Fe$ DOS is averaged over all $Co$ and $Fe$ atoms. The spin-up and spin-down states are shown by the positive and negative values, respectively.
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Figure 4
(a) The modification in $Ce$ spin-down $f$ DOS on going from ${Ce}_{2}$ ${Fe}_{15}$ $Zr$ to ${Ce}_{2}$ ${Co}_{15}$ $Zr$ at various $Co$ concentrations, calculated under GGA + SOC + $U$ . For 40% $Co$ concentration ( ${Ce}_{2}$ ${Fe}_{9}$ ${Co}_{6}$ $Zr$ ) and onward, the valency of $Ce$ switches from tetravalent to trivalent. For clarity, the DOS plots have been shifted vertically with respect to one another. The $Ce$ valency transition is also reflected in the $Ce$ spin ( $M_{SPIN}$ , marked on the left-hand $y$ axis) and orbital ( $M_{ORB}$ , marked on the right-hand $y$ axis) moments shown in (b), where an abrupt increase is observed for 40% $Co$ concentration.
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Figure 5
(a) The orbital magnetic moment $M_{ORB}$ (a) for $Ce$ sites and (b) for $Co$ - $Fe$ sites as a function of x in ${Ce}_{2}$ ${Zr Fe}_{15 - x}$ ${Co}_{x}$ , calculated under GGA + SOC + $U$ . The insets give the anisotropy of the orbital magnetic moment ( $Δ M_{ORB} = M^{c} - M^{a}$ ).
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Figure 6
(a) The configuration used to model 20, 40, 60, and 80% $Co$ doping via the supercell method. (b) The total magnetic (spin plus orbital) moment and (c) the MAE calculated under GGA + SOC + $U$ as a function of x in ${Ce}_{2}$ ${Zr Fe}_{15 - x}$ ${Co}_{x}$ . The symbols correspond to the calculated compositions and the line is a guide to the eye. Results from VCA calculations (red filled squares) are also shown for comparison. The results from calculations without the Hubbard $U$ are shown as green dotted lines with open diamonds.
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Physical Review Applied

Potential High-Performance Magnet: Fe- and Zr-Alloyed Ce2Co17

Tribhuwan Pandey and David S. Parker

Phys. Rev. Applied 13, 034039 – Published 16 March 2020

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Potential High-Performance Magnet: $Fe$ - and $Zr$ -Alloyed ${Ce}_{2}$ ${Co}_{17}$