We study the effects of the local lattice structure around magnetic ions, on the uniaxial magnetic anisotropy (MA) in transition metal oxides, particularly ferrites, using the electron theory. We address M-type hexagonal ferrites, tetragonally distorted spinel ferrites, and an ilmenite (CoMnO3). The tight-binding scheme with spin–orbit interaction (LS coupling) is applied to calculate the electronic structure and MA energy of small clusters composed of a transition metal (TM) ion and surrounding oxygen ions. The results of uniaxial MA for M-type ferrites agree with those calculated using the first principles as well as those obtained experimentally, indicating the validity of the present scheme. The high numerical accuracy enables us to conclude that the p − d mixing between Fe3+ and O2− ions is crucial for the uniaxial MA of M-type ferrites and that a change in the local lattice structure around TM ions may cause a sign change in the local uniaxial MA of Fe2+ or Co2+ doped in M-type ferrites. The results of the uniaxial MA in tetragonally distorted spinel ferrites agree well with the experimental ones. These observations may indicate a feasible method to enhance the magnitude of the uniaxial MA in ferrites.

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Strain Engineering of Magnetic Anisotropy In article number 2101034, Hiroshige Onoda, Hideto Yanagihara, and co‐workers demonstrate that the strain engineering technique is a promising way to induce large magnetic anisotropy without using heavy metals or rare earth elements. The spins (red arrows) of Co ions (light blue) on the octahedral sublattice of the spinel structure change their preferred direction in response to the epitaxial stress of the cobalt ferrite thin film due to the change in the orbital moment.

crucial for application in functional spintronic devices and high-density magnetic recording technology. [3][4][5][6][7] To explore or synthesize magnetic materials with high coercivity, materials with large MAs are required for obtaining high-performance permanent magnets. Because MA is indirectly proportional to the symmetry of the crystal, materials with lower crystal symmetry are promising for application as high-MA compounds. Generally, the physical origin of large MAs is spin-orbit interaction (SOI), calculated as the inner product of orbital (L ) and spin angular momenta (S) with an interaction constant λ. For a given spin moment, the magnitude of SOI is determined by λ and the expected value of the orbital angular momentum. Magnetic materials composed of noble metals often exhibit large MAs, attributed to the large λ values of noble metals. In contrast, the large MAs of permanent magnets composed of rare-earth elements are attributed to their large values of λ and orbital angular momenta. [3,[8][9][10][11][12][13] In transition metal alloys or compounds that do not contain heavy or rare-earth elements, L is often quenched in a crystal field. Consequently, magnetic materials with large MAs are rare. In contrast, a certain amount of orbital angular momentum is sometimes retained in oxides, owing to the localized character of the wave functions of transition metal ions in the crystal field. The magnitude of the orbital angular momentum is influenced by the electronic configurations of the magnetic ions; therefore, the MAs of magnetic oxides can be induced/enhanced by introducing asymmetry, such as lattice deformations. This phenomenon can be considered to be magneto-elastic in nature because the change in magnetic state is induced by lattice deformation. Furthermore, a large uniaxial MA can be realized by uniaxial lattice deformation. The epitaxial distortion arising from the lattice mismatch between oxide thin films and their substrates can be employed to effectively induce lattice distortion.Co x Fe 3−x O 4 (CFO) has a cubic lattice, as shown in Figure 1a, and exhibits a large cubic MA with a Néel temperature of 769 K for x = 1.0 and has been reportedly used as permanent magnets. [14] Extensive magneto-elastic effects have been reported, along with the existence of a large orbital moment in Co 2+ . [15][16][17][18][19][20][21][22][23][24][25][26] The large cubic MA of bulk CFO has been elucidated theoretically using a single-ion model; the cubic and local trigonal lattice symmetries split the down-spin t 2g state into a singly Perpendicular magnetic anisotropy (PMA) energy up to K u = 6.1 ± 0.8 MJm −3 is demonstrated in this study by inducing large lattice distortion exceeding 3% at room temperature in epitaxially distorted cobalt ferrite Co 0.73 Fe 2.18 O 4 (001) thin films. Although the thin film materials include no rare-earth elements or noble metals, the observed K u is larger than that of the neodymium-iron-boron compounds for high-performance permanent magnets. The large PMA is attributed to the sig...