Some rare-earth intermetallic compounds are superior in magnetic properties such as saturation magnetization and magnetocrystalline anisotropy, and are suitable for permanent magnetic materials. This is due, at least in part, to the orbital magnetic moment of the 4f shell, and also to its interaction with the crystal field. Thus it is important to know the 4f orbital magnetic moment of rare-earth ions in those compounds in order to theoretically search for novel permanent magnets. However, first-principles calculations based on density functional theory (DFT) still have a problem with the treatment of 4f orbital magnetic moments: even for 3d transition metals, they are often underestimated in DFT calculations. Therefore some additional corrections such as the so-called DFT+U method [1] [2] or the self-interaction correction (SIC) are necessary to describe the strongly correlated 4f electronic states adequately. Of course, comparison with experimental inputs is inevitable to validate these corrections. A suitable material to study the 4f orbital magnetic moment with reference to experimental information is SmFe12 with ThMn12 structure [3] [4]. This is due to its relatively simple crystal structure, and also the abundance of recent detailed experimental results, as it has received renewed attention as a promising candidate for new permanent magnet materials in the last few years. Of course it is well known that this system is thermodynamically unstable, but also that Ti substitution for Fe can stabilize the crystal structure. In the resulting crystal structure, the volume of the so-called interstitial region is larger than in other well-known rare-earth intermetallics such as Nd2Fe14B or SmCo5. Thus we can expect that the 4f electrons of Sm ions are well localized enough to form the well-defined 4f orbital magnetic moment. We calculate the electronic structure of SmFe12 and orbital moment of the Sm ions with the DFT+U method (GGA+U). In the frame work of the first-principles method, we have to investigate ground state properties, however, the DFT+U method sometimes might converge to metastable states [5]. Therefore, we examine several initial conditions and investigate the properties of a possible ground state. In present study, we use three initial conditions to approach the true ground state. The initial conditions are reflected in the orbital potential for 4f states of the Sm ions, the matrix elements of which are specified by the magnetic quantum number m. First one is set so that m=3,2,1,0,-1 states are occupied (Condition 1). Second one is set so that m=3,2,1,0,-2 states are occupied (Condition 2). The final one is set so that mainly m=3,2,1,0,-2 states are occupied, however, these states include the hybridization between different m reflecting four-fold symmetry (Condition3). We tested these conditions and search the true ground states. According to the calculated U dependence of the orbital moment and total energy shown in Figure 1, the third one (Condition 3) yields the lowest energy regardless of the U value. The calculated orbital moment of the Sm ions is about 3.0μB which is smaller than the maximum value expected from 4f5 configuration regardless of the U value. This implies that the orbital moment of the Sm ions is partially quenched due to the crystal field. The calculated 4f charge density has the four-fold symmetry which reflects the symmetry of the crystal. The calculated total, f-partial, and m-resolved f-partial density of states (DOS) are shown in Figure 2 (a) and (b). In Figure 2 (a), DOS is mainly composed by the Fe states and the down spin Sm f-states are well localized below the fermi level. Increasing U value, the gap between upper and lower Hubbard part of Sm f states becomes larger. In our calculation, we have confirmed that the anti-parallel spin configuration between Fe and Sm becomes stable. From the calculated f-partial density of states in Figure 2 (b), m=3,2,1,0,-2 states are mainly occupied. It yields the orbital moment roughly 4.0μB. In addition, hybridized states between m=3 and m=-1, m=2 and m=-2, and m=1 and m=-3 are also realized according to the initial condition. These states cause the reduction of the orbital moment from 4.0μB to 3.0μB due to the partial quenching of the orbital moment. In our DFT+U calculation, the quenching of the orbital moment is predicted, the comparison with the experimental data such as XMCD is expected. For future work, we are going to investigate the effect of the quenching of the orbital moment to magnetocystalline anisotropy energy.

**References:**

[1] V. I. Anisimov, J. Zaanen, and O. K. Andersen, Phys. Rev. B., Vol. 44, p. 943 (1991). [2] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B., Vol. 52, p. 5467 (1995). [3] Y. Hirayama et al., Scripta Mater., Vol. 138 p.62-65 (2017). [4] Y. Harashima et al., JPS Conf., Proc. 5 011021 (2015). [5] P. Larson, I. I. Mazin, D. A. Papaconstantopoulos, Phys. Rev. B., Vol. 67, p. 214405 (2003).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b5996e56e128ba38c565fd1cb782b50a.jpg)
The U dependence of the calculated (a) orbital moment and (b) total energy including spin-orbit coupling. Bule, red and black plots correspond to the initial conditions Condition1, Conditon2 and Condition3 (see text). The magnetization axis is set (001) direction.

![](https://assets.underline.io/uploads/markdown_image/1/image/90fadae7780a3329e44ab8a1e7d70d88.jpg)
The calculated density of states (DOS) of SmFe12 with U=0.8 Ryd and J=0.0615 Ryd. (a) Black line corresponds to total DOS and red line corresponds to Sm f-partial DOS. (b)Sm f-partial DOS and m-resolved Sm f-partial DOS. The magnetization axis is set the (001) direction with spin-orbit coupling.

 Theoretical investigation of the orbital moment of the Sm ions in SmFe12 with the GGA+U method.

*Session Chair: Hossein Sepehri-Amin, Busshitsu Zairyo Kenkyu Kiko*

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JC: RE-based Permanent Magnets

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Theoretical investigation of the orbital moment of the Sm ions in SmFe12 with the GGA+U method.

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