Tuning Magnetic Anisotropy of MnBi Permanent Magnet with Sn*

Abstract

Low-temperature phase (LTP) MnBi has the hexagonal NiAs structure and retains its ferromagnetic phase up to 613 K [1]. Above 613 K, some Mn atoms from the octahedral sites diffuse into the trigonal-bipyramidal sites, resulting in the antiferromagnetic coupling between Mn at the octahedral and Mn at the trigonal-bipyramidal interstitial sites. Therefore, the magnetic moment sharply drops before reaching the Curie temperature (Tc) of 720 K. Spin reorientation of LTP MnBi occurs at about 90 K from ab-plane (0 - 90 K) to c-axis (T > 90 K) [2]. The spin orientation and magnetocrystalline anisotropy of LTP MnBi can be tuned by partially replacing Bi of MnBi with the third element. Sakuma et al. have performed first-principles calculations on Sn-doped MnBi (MnBi1-xSnx) and found that the Ku increases to about 3 MJ/m3 at x = 0.1 from - 0.5 MJ/m3 at x = 0 and then remains unchanged up to x = 0.3, and TC is 580 K for x = 0 [3]. These calculated Ku and TC for x = 0 are much larger and lower than experimental -0.2 MJ/m3 and 720 K, respectively. Sakuma et al. did not relax MnBi1-xSnx (x > 0) to estimate lattice constants, but used the lattice constants (x = 0) for MnBi1-xSnx (x > 0). Therefore, the calculated Ku and magnetic moment for x > 0 would be inaccurate.In this study, hexagonal crystal structures of LTP MnBi and Sn-doped MnBi in Fig. 1 were used. The LTP MnBi unit cell has two Mn atoms at the octahedral 2a sites of (0, 0, 0) and (0, 0, 1/2) and two Bi atoms at the 2c sites of (1/3, 2/3, 1/4) and (2/3, 1/3, 3/4) [4]. We have relaxed MnBi1-xSnx (x = 0, 0.5) unit cell to obtain lattice constants a and c. Doped Sn decreases the a and c from 4.287 and 6.118 Å for x = 0 to 3.954 and 5.456 Å for x =0.5, respectively. Accordingly, the volume and c/a ratio also decrease from 97.37 Å3 and 1.43 (x = 0) to 73.87 Å3 and 1.38 (x = 0.5), respectively. These relaxed lattice constants (x = 0) are in good agreement with the experimental lattice constants [5, 6].The WIEN2k package based on density functional theory (DFT) and using the full-potential linearized augmented plane wave (FPLAPW) method was used to conduct the first-principles calculations [7]. In order to calculate spin-polarization and spin-orbit coupling, we used the DFT within the local-spin-density approximation (LSDA) and 19 × 19 × 27 k-point mesh generating 1400 k-points in the irreducible part of the Brillouin zone.Figure 2 shows density of states for MnBi1-xSnx (x = 0, 0.5). The net magnetic moments per formula unit is 3.613 μB/f.u. for x = 0 and 2.517 μB/f.u. for x = 0.5. The net magnetic moment decreases as the Sn concentration increases. The corresponding saturation magnetization in the unit of Tesla (T) monotonically decreases to 0.794 from 0.865 T as the Sn concentration increases to x = 0.5. Calculated magnetic moment of 3.613 μB/f.u., Ku of -0.2 MJ/m3 and TC of 711 Ku for x = 0 are in good agreement with the previously reported results [8].We will present Ku and magnetic moment as a function of Sn concentration and discuss the discrepancy between Sakuma’s results and this work. **