Antiferromagnetic states

Figure 1 Energy difference between the possible antiferromagnetic states and the ferromagnetic one as the function of Au concentration in the substrate. and J, refer to the orientation of the magnetic moments in a layer. The substrate is assumed to be on the left hand side.

A three-dimensional set of intermolecular interactions is further confirmed by the observation of a transition to an antiferromagnetic ground state in both radical complexes, at a Neel temperatures of 8 (Mo) and 4.5 K (W), in accordance with the difference of Curie-Weiss temperatures between both complexes. Note also the spin-flop field in the antiferromagnetic state, found at 5.5 kG in [Cp M(dmit)2] and at 8 kG in [Cp W(dmit)2] , a consequence of the stronger spin orbit coupling in the latter. 

Figure 8.9 Schematic illustrations of spin states in a two dimensional periodic material. Circles indicate individual atoms and the dotted lines show a single supercell. In (a), all electrons are paired on each atom. In the remaining examples, a single unpaired electron exists on each atom. Examples of a ferromagnetic state, an antiferromagnetic state and a more complex mag netic state are shown in (b), (c), and (d), respectively.

Lepidocrocite is paramagnetic at room temperature. The Neel temperature of 77 K is much lower than that of the other iron oxides and is the result of the layer-like structure of this mineral. The sheets of Fe(0,0H)6 octahedra are linked by weak hydrogen bonds, hence magnetic interactions are relatively weak. The saturation hyperfine field is also lower than for any other iron oxide (Tab. 6.2). In the antiferromagnetic state, the spins are ordered parallel to the c-axis with spins in alternate layers having opposite signs. A decrease of T by 5 K was observed for Al-lepidocrocites with an Al/(Fe-i-Al) ratio of 0.1 (De Grave et al., 1995). 

In the antiferromagnetic state, the spins are oriented parallel to the c-axis. Moss-bauer studies have indicated that the number and type of subsites in the magnetic structure may be influenced by the halide concentration, the nature of the halide and the level of excess protons vhich balance the halide charge. When chloride is present in the structure, there are tv o different Fe " sites, vhereas for fluoride-containing akaganeite, the number of non-equivalent cation sites may be greater. 

Hematite is paramagnetic above 956 K (Tc). At room temperature it is weakly ferromagnetic and at 260 K (the Morin temperature, Tm), it undergoes a phase transition to an antiferromagnetic state. Particles smaller than about 8 nm display superpara-magnetic relaxation at room temperature. A plot of the dependence of the B f (Hi) of hematite on temperature is shown in Figure 6.7 the plot follows an approximate Brillouin curve. 

Fig. 6.7 Temperature dependence of the magnetic properties of hematite. Tc = Curie temperature,Tm = Morin temperature, pm = paramagnetic region, wfm = weakly ferromagnetic region afm = antiferromagnetic region. The insets show simulated Mossbauer spectra of hematite in the paramagnetic, weakly ferromagnetic and antiferromagnetic states (Murad, 1988, with permission).

Fe(OH)2 is difficult to investigate because it is so readily oxidized. At room temperature it is paramagnetic and is antiferromagnetic below 33 K (Miyamoto, 1976). Fe(OH)2 has a layer structure. In the antiferromagnetic state all spin moments within a layer are parallel and also parallel to the c-axis spins between adjacent... 

The antiferromagnetic state described by the occupation of the lower Hubbard band is stabilized by inclusion of such electron correlation, but the ferromagnetic analog is not. This is a result exactly analogous to the stabilization of the lowest singlet state in cyclobutadiene below the triplet. For the simple density of states used by Hubbard in his treatment he showed in fact that the condition for ferromagnetism was... 

Fig. 8.12 The rectangular d band model of the (a) nonmagnetic, (b) ferromagnetic, and (c) antiferromagnetic states. (From Pettifor (1980).)...

These g-tensor site matrices gA and gB are subsequently employed for the computation of the total molecular g-tensor of the antiferromagnetic state by multiplication with the respective... 

In this book we treat the discontinuous nature of the transition using an analysis introduced by Brinkman and Rice (1970a, b). This applies to bandcrossing transitions and transitions in an array of one-electron centres. We term the latter Mott transitions when the centres have a moment we do not limit the term to cases when the moment is that of a single spin, and indeed such cases are rare (Chapter 3). The insulating antiferromagnetic state is sometimes called a Mott insulator . A Mott transition can be accompanied by a change of structure (see Section 3 below). 

Results of a first principles calculation shows that the antiferromagnetic state is more stable than the ferromagnetic state, and that the energy gap decreases with the Mn composition (Zhao, Y.-J. et al. 2001b). The reason for the discrepancies between theoretical expectations and experimental results is not clear it may stem from the substitution of Ge for Mn in surface-doped samples. More recent plane-wave pseudopotential and KKR-CPA calculations show that the intrinsic defects are responsible for the stabilization of the ferromagnetic state (Mahadevan and Zunger 2002 Kamatani and Akai 2001b). 

Ac-susceptibility measurements by Morellon et al. (2000) showed, that (on heating) Gdj(Sio.iGeo.9)4 undergoes a first-order transition from a ferromagnetic to an antiferromagnetic state at 7c = 81 K, followed by a second-order transition to the paramagnetic state at 7n = 127 K. Measurements of the thermal dependence of the lattice parameters... 

---