Giant exchange bias in nanoscale ilmenite-hematite intergrowths: new insights through the application of atomistic Monte Carlo simulations

Giant exchange bias (> 1 T at 10 K) has been observed in a natural hematite sample containing nanoscale exsolution lamellae of ilmenite. The absence of a Morin transition indicates that the bulk hematite spins lie within the (001) basal plane. The bulk ilmenite spins, on the other hand, lie strictly along the c axis. We argue that this perpendicular arrangement of spins cannot yield exchange bias without some local rearrangement of spins close to the ilmenite-hematite interface. Possible interface magnetic structures are explored within the framework of a classical Heisenberg model using Monte Carlo simulations. Simulations were performed using an 8x4x8 supercell of the hematite structure, into which was embedded a 4x4x2 precipitate of ilmenite. Each Fe3+ (hematite) and Fe2+ (ilmenite) spin is modelled as a classical vector, the orientation of which is determined by the sum of three energy contributions: i) the exchange interaction energy due to neighbouring spins; ii) a uniaxial magnetocrystalline anisotropy energy, with anisotropy axis parallel to c; and iii) the magnetostatic energy due to an external applied field. A value for the ilmenite anisotropy constant of -6 K per cation was calculated from the observed susceptibility of pure ilmenite at 4.2 K for fields applied perpendicular to c. The negative value implies that spins prefer to align either parallel or antiparallel to c. The anisotropy constant needed to model hematite below 60 K (in the absence of a Morin transition) is unknown. Simulations were therefore performed for a range of values between 0 and 0.35 K per cation (corresponding to the room-temperature anisotropy value). The positive value means that spins prefer to lie within the basal plane. The results indicate that there is a threshold value of the hematite anisotropy constant below which the hematite spins become tilted out of the basal plane in the vicinity of the interface due to exchange interaction with the highly anisotropic ilmenite spins, thus creating a significant component of magnetisation parallel to c. Tilting is greater for hematite spins adjacent to the (100) interfaces than those adjacent to the (001) interfaces, due to the more favourable configuration for exchange interaction across (100). Tilting appears to persist to temperatures above 60 K (the Néel temperature of ilmenite) due to the presence of anisotropic Fe2+ spins in the contact layers and to the penetration of exchange interactions into the first layer of Fe2+ spins adjacent to the (100) interface. This penetration creates a `ferromagnetic shell' around the perimeter of the ilmenite precipitate, which enhances the net moment. Hysteresis loops at 10 K were simulated for a range of applied field directions and hematite anisotropy constants. Exchange bias is observed whenever there is a significant c component of magnetisation in the hematite phase. A shift of 1 T was obtained with an anisotropy constant of 0.1 K and the equilibrium orientation of hematite spins making an angle of ~ 45° to the basal plane.