An overview of the first principles studies of doped RE-TM5 systems for the development of hard magnetic properties

doi:10.1016/j.jmmm.2019.165902

Journal of Magnetism and Magnetic Materials

Volume 496, 15 February 2020, 165902

https://doi.org/10.1016/j.jmmm.2019.165902 Get rights and content

Abstract

In this study, we compiled all the first principles calculations performed on RE-TM₅ (RE: rare earth, TM: transition metal) system to address the following question: Has everything been tried to improve the hard magnetic properties of this special intermetallic compound, and are there any venues that are worth pursuing? As it is the case with the first principles studies in any field, they are driven mainly by experimental work: (i) to validate their results, and (ii) to extend our understanding of the underlying physical phenomena so that the theory in hand can be used as a predictive tool to shed light on certain what-if scenarios. Our analysis indicates that three major compounds are investigated more than others: (1) YCo₅, because it can potentially be an intermediate-performance hard magnet, and the presence of yttrium with no localized 4f electrons simplifies calculations significantly, (2) SmCo₅, because it has the largest magnetic anisotropy energy among all RE hard magnets as well as very impressive high temperature performance, (3) CeCo₅, because Ce is the most abundant rare earth element with a curious 4f electron behavior that gives rise to pronounced deviations in its structural and magnetic properties across the lanthanides series. This is followed by a brief analysis of several ab initio approaches that were developed to treat these rather complicated systems both at 0 K and at finite temperatures. Towards the end, we elucidate the role of exchange-correlation approximations such as local density approximations (LDA) and generalized gradient approximation (GGA) formulation in determining the MAE and M_s by analyzing their corresponding density of states (DOS), and providing our results on a rather overlooked hard-magnetic material: LaCo₅.

Introduction

Permanent magnets have been the “movers and shakers” of the modern technology as they are the key components of traction motors, loudspeakers, wind turbines and several other mass market consumer goods. Their vital role has been the main driving force for the research and development efforts in the last 60 years with a goal of making them lighter, more energy efficient and cheaper. The fundamental properties that are of interest in permanent magnet materials are the Curie temperature, T_C, magnetic anisotropy, K, and saturation magnetization, M_s. T_C is the temperature at which ferromagnetism is lost. In the mean-field approximation, T_C is estimated to be proportional to the magnetic exchange interactions between adjacent spins [1]. In rare earth based hard magnets such as SmCo₅, T_C is mainly the result of the exchange interactions between transition metals as it is much larger than those between rare earth elements. K represents the energy per unit volume required for changing the orientation of the magnetic moments under the application of a magnetic field which is essential for achieving high coercivity in permanent magnets. Magnetic anisotropy can be a result of the shape and/or crystalline nature. While shape anisotropy is the main reason that AlNiCo type magnets have their hard magnetic properties [2], it cannot provide a substantial improvement in the anisotropy of a magnet [3]. The second kind is the magnetocrystalline anisotropy energy (MAE) which is intrinsic to a material i.e., insensitive to changes in the microstructure. It is the result of spin–orbit (SO) coupling and its interaction with the crystal electric field (CEF) created by the surrounding charges which produces an energetically favored alignment of magnetic moments along a specific crystalline direction. This second source of anisotropy has potential for further improvement upon doping and inducing slight changes in the lattice parameters. Saturation magnetization, M_s, is the magnetic moment per unit volume which is a result of both spin and orbital motion of electrons in a magnetic material. M_s is particularly important when one considers that the maximum energy product, (BH)_max is roughly proportional to the square of the M_s, ${(B H)}_{\max} \approx M_{s}^{2}$ [4].

This review article is devoted to the RE-TM₅ system mainly because of its crystal structure and how it creates a unique TM network to favor a large MAE value. The structure of RE-TM₅ is that of a CaCu₅ as the prototype (P6/mmm, No.191). This structure can be described as alternating layers of hexagonal nets formed by the TM atoms (2c) with the RE sitting at the center of the net (Fig. 1a-b and d), and planes of TM atoms (3 g) arranged in a Kagome network as shown in Fig. 1c.

The favorable arrangement of this TM₅ network is possibly driving the formation of a large orbital magnetic moment of TM atoms that couples with the spin moment via SO coupling which leads to large MAE and M_s values [5], [6], [7]. This was proven by first principles studies that compare the MAE value of YCo₅ with a hypothetical compound Co₅ having the same CaCu₅ structure with yttrium replaced by a vacancy. It was found that the MAE of Co₅ per Co atom is comparable to that of YCo₅ proving that MAE is mainly fueled by the special Co₅ network in this structure [8]. What is more interesting is that, when the vacant yttrium sites are occupied by an additional cobalt atom producing the Co₆ compound, there is a substantial drop in the MAE value which indicates that the itinerant electrons at the RE site distort the CEF responsible for large MAE values [5]. While SO interactions couple the orbital and spin components of magnetic moments, a strong CEF pins the aspherical 4f electron cloud at the RE site according to the crystal lattice giving rise to large MAE values in these compounds [9]. These results underpin an important feature of the RE-TM₅ crystal structure: the special arrangement of TM₅ network decorated with a RE atom with few itinerant electrons appears to be the fundamental building bricks or “motifs” that gives rise to extraordinary hard magnetic properties.

Section snippets

Literature survey

In this section, we report what has been done in the past, from a first principles approach perspective, to improve the hard-magnetic properties of RE-TM₅ compounds. The efforts can be summarized as doping the TM site with impurities such as Fe, Ni, Cu etc., as well as distorting the structural parameters of the unit cell. Both efforts are geared towards manipulating the density of states (DOS) of electrons at the Fermi level with the hopes of improvements in the areas of: (i) MAE due to

0 K: Density functional theory (DFT)

Density functional theory (DFT) is an important theoretical tool of computations. The basic idea behind the DFT is to use electron density as the main variable to describe any property of a many-body system. The goal of DFT is to solve the unmanageable many-body problems with many-electron wavefunctions with simple electronic density approach. This goal can be achieved by solving Kohn-Sham equation: $[- \frac{h^{2}}{2 m} \nabla^{2} + V (r) + V_{H} (r) + V_{XC} (r)] Ψ_{i} (r) = ∊_{i} Ψ_{i} (r)$ where first term is the kinetic energy of the electrons, $V (r)$ =

A case study: LaCo₅

In this section, we analyze an important member of the RE-TM₅ compound: LaCo₅. This compound has lanthanum at the RE sites with no 4f electrons. Nonetheless, it still has respectable MAE of ≈5 meV/fu [20] due to the contributions from the cobalt network. Our goal is to show that Coulomb U, and exchange J corrections may not be essential in predicting the MAE of these compounds. In addition, we attempt to elucidate the role of the choice of exchange correlations in determining the MAE of these

Conclusions & outlook

In this review article, we attempted to treat the important RE(TM)₅ compound system which is known for its high magnetic anisotropic properties due to its unique arrangement in space. Our analysis comprised mainly of first principles (DFT) approaches rather than experimental results. A few key points that can be extracted from this study are as follows:

i.
1:5 system has a special network of TM atoms which can provide remarkable magnetic anisotropies when the TM sites are occupied atoms with

Acknowledgments

This research is supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office. The authors would like to acknowledge Ed Moxley for providing technical support and maintaining/updating computational facilities and software packages including the Raman cluster and the WIEN2K program at Ames Laboratory. H. U. would like to acknowledge Son V. Phan for providing

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A Hubbard U correlation parameter was not introduced neither at the lanthanum, as it does not possess any 4f electrons, nor at the cobalt sublattice. In an earlier study, our claim was that a Coulomb-U, and an exchange-J correction parameter at the cobalt site may not be absolutely necessary to predict reasonable MAE values within an error margin that allows one to draw meaningful conclusions [4]. This approach makes the electronic structure calculations free from any empirical corrections that artificially increases the MAE of these compounds.
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Review ArticlesAn overview of the first principles studies of doped RE-TM5 systems for the development of hard magnetic properties

Abstract

Introduction

Section snippets

Literature survey

0 K: Density functional theory (DFT)

A case study: LaCo5

Conclusions & outlook

Acknowledgments

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

Scripta Mater.

Comput. Mater. Sci.

Comput. Mater. Sci.

Comput. Mater. Sci.

J. Alloys Compd.

J. Alloys Compd.

J. Magn. Magn. Mater.

J. Magn. Magn. Mater.

J. Solid State Chem.

J. Magn. Magn. Mater.

J. Solid State Chem.

Phys. Rev. Applied

The structure and properties of alnico permanent magnets

J. Phys. Soc. Jpn.

Magnetism and Magnetic Materials

J. Appl. Phys.

J. Phys. F: Met. Phys.

PHYSICAL REVIEW B

J. Appl. Phys.

IEEE Trans. Magn.

J. Magn. Magn. Mater.

Phys. Rev. B

Phys. Rev. X

Phys. Rev. B

Phys. Rev. B

Phys. Rev. Materials

J. Appl. Phys.

Matter Phys.

Matter Phys.

Phys. Rev. B

J. Appl. Phys.

Review Articles
An overview of the first principles studies of doped RE-TM₅ systems for the development of hard magnetic properties

0 K: Density functional theory (DFT)

A case study: LaCo₅