Magnetic anisotropy modified by strain effects in Y$_2$Fe$_{14}$B*

In exhibiting the coercivity of permanent magnets, magnetocrystalline anisotropy plays an important role. Since itinerant magnetic states are responsible to direct interactions among magnetic sites, d states are expected to be sensitive to lattice strain. In this work, we report strain effects on magnetic properties theoretically studied by first-principles calculations for Y$_2$Fe$_{14}$B, where Y is a prototypical $f^0$ rare-earth element [1]. To analyze the local magnetic anisotropy, we developed a method to decompose the magnetic-anisotropy energy into contribution from each atomic site as well as from couplings among specific atomic orbitals, where the sum rule is satisfied by including indirect off-site contributions in the second-order perturbation. The OpenMX code is used for first-principles calculations. The lattice constants of Y$_2$Fe$_{14}$B are changed from the equilibrium values independently, where we found the uniform compression enhances the perpendicular magnetic anisotropy. Our magnetic-anisotropy decomposition identified dominant magnetic site and orbital couplings. Our method will enable us to study the anisotropy at microstructure interfaces. [1] Z. Torbatian, T. Ozaki, S. Tsuneyuki, and Y. Gohda, Appl. Phys. Lett. 104, 242403 (2014).