Magnetic Ordering of MnO, FeO, CoO and NiO

In the paramagnetic high-temperature state, MnO, FeO, CoO, and NiO all have a rocksalt or NaCl crystallographic structure. Below the Neel point, these 3d TM ´ monoxides order  antiferromagnetically into magnetic superstructures, which can be determined using neutron diffraction. From the classic papers by Shull, Strauser, and Wollan [16], the magnetic unit cell is found to be close to cubic with a doubled lattice parameter in order to accommodate the AF spin arrangement. In fact, the spins were found to be parallel on cubic {111} planes (so-called F sheets) but antiparallel on neighboring {111} planes (see Figure 4.4). The relative orientation of the spins with respect to each other is determined by exchange interactions. The main factor responsible for this particular (so-called type 2) AF arrangement is the 180◦ superexchange interaction. It couples next nearest-neighbor (nnn) spins. The nearest-neighbor (nn) interaction is much weaker and frustrated. This frustration is lifted by exchange striction. Assuming a collinear spin structure, a trigonal distortion restricts the number of possible spin structures to the four experimentally observed T-domains.

The absolute orientation of the spins within the {111} sheets, on the other hand, is determined by interactions coupling the spin to the lattice. Possible contributions to this magnetic anisotropy are the dipole–dipole interaction and the single ion anisotropy. In the latter case, the spin is coupled to the lattice in two steps, the spin–orbit interaction couples the spin to the orbital momentum, and the crystal-field couples the orbital to the lattice. For closed shell configurations in cubic symmetry, the orbital momentum is quenched and spin–orbit interaction is small in contrast to open shell t2g configurations. For the TM monoxides considered in this chapter, single ion anisotropy is small for Mn2+ (d5) and Ni2+ (d8), but it is large for Co2+ (d7) and Fe2+ (d6).

 MnO and NiO

 In both MnO and NiO, the trigonal distortion stabilized by exchange is the main distortion. It leads to an elongated rhombohedral unit cell with α < 60◦ . The orientation of the spins with respect to the lattice is determined by a detailed interplay between dipole–dipole interactions and single ion anisotropy. There is a relatively large force, both from dipole–dipole interactions and SOC, that restricts the spins to a direction in the {111} planes. The precise direction within these planes is a subtle and quite involved problem. Experimentally, a further reduction of the crystal symmetry to monoclinic is observed for both NiO [17] and MnO [18] and the spins are found to be oriented in one of the three possible {112} directions perpendicular to the rhombohedral axis, thus generating 24 domains in total, namely 6 possible S domains (including spin reversed domains) for each of the 4 T domains.

 FeO and CoO

 In the paramagnetic phase, both CoO and FeO have a nearly cubic structure, but below the Neel temperature ( ´ TN) the spin orientation induces a noncubic charge density, which distorts the crystal structure. For instance, for spins being oriented in the [001] direction one would expect a charge density as depicted in Figure 4.3a. For electrons (FeO, d6) this would lead to a tetragonal elongation (c > a), and for holes (CoO, d7) to a tetragonal contraction (c < a). For CoO, there is still some debate about the precise spin direction. It is clear, however, that there is a relatively large tetragonal distortion, with (c < a) in accordance with the above example, accompanied by a smaller rhombohedral elongation lowering the total symmetry to monoclinic. The general consensus on the spin direction is that it is slightly tilted away from the tetragonal axis. [19–21]. For FeO, one finds the spin to be in the [111] direction. An accompanying orbital momentum can be associated with a √1/3(√1/2(ı − 1)dyz + √1/2(−ı − 1)dxz + dxy) orbital, which has a larger charge density perpendicular to the [111] direction than parallel to it. Therefore, FeO shows a trigonal elongation. There are no other distortions found in FeO, which might be related to the fact that both the magnetostriction and the local single ion anisotropy are optimized by the same trigonal elongation.

Reference: http://bookzz.org/dl/928264/eff92d