Interactions Neel temperature

We have described above the evolution of the magnetic properties of the [Cp2M (dmit)]AsFg salts upon isomorphous Mo/W substitution. Another possibility offered by this attractive series is the isomorphous substitution of the counter ion, that is PFg- vs AsF6 vs Sbl- fi. Electrocrystallization experiments conducted with [Cp2Mo(dmit)] and the three different electrolytes afforded an isomorphous series, with a smooth evolution of the unit cell parameters with the anion size [32], This cell expansion with the anion size leads to decreased intermolecular interactions between the [Cp2Mo(dmit)]+ radical cation, as clearly seen in Table 2 from the decreased Curie-Weiss temperatures and Neel temperatures (associated with the transition they all exhibit to an AF ground state). 

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. 

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). 

At room temperature, akaganeite is, like lepidocrocite, paramagnetic. It becomes antiferromagnetic below the Neel temperature of 290 K (Murad, 1988). The value of Tn and the strength of the magnetic interactions are variable and depend upon synthesis conditions (i.e. the temperature and the length of the hydrolysis period). These influence the amount of interstitial water in the compound, which in turn induces spin reduction. Tn decreases linearly to 250 K as the H20/unit cell rises to 0.02 mol mor (Chambaere De Grave, 1984 a). 

In doped semiconductors I is due to direct overlap in transitional-metal oxides the overlap between the d-orbitals is frequentiy via the oxygen ions and is then often called a superexchange interaction. Figure 3.4 shows the kinds of wave function expected. As regards magnitudes, if B 1 eV, 17 10 eV and z=4, kBTN should be 0.01 eV so that 100K, which shows why low Neel temperatures are common. 

In simple cubic compounds like NiO, MnO and CoO the metal ions lie on a face-centred cubic. As pointed out by Ziman (1952), for this structure and for spherical orbitals, antiferromagnetism with a finite Neel temperature must be due to interaction between next-nearest neighbours, because in any antiferromagnetic structure each moment will have as many parallel as antiparallel neighbours. In NiO and CoO the orbitals are not spherical, but in MnO the 3d5 ion is spherical In this compound the Neel temperature is therefore anomalously low, and there remains abnormally strong short-range order above the Neel temperature (Battles 1971). 

In a series of papers on cobalt and other phosphate glasses, Simpson (1970) and Simpson and Lucas (1971) showed that there is no sign of a Neel temperature down to -IK while the corresponding crystals show a Neel temperature near 20 K. In fact the 1//-T curve shows increased slope at low temperatures. Simpson pointed out that the theorem of Ziman (1952) (see Section 2)—that nearest-neighbour interaction cannot give antiferromagnetism for spherical orbitals— may be applicable here the orbitals are not spherical but are oriented at random. 

There is no adequate theory of the Neel temperature of a random distribution of centres in a dilute alloy, of indeed one exists. For higher concentrations of the magnetic matrix, with the assumption that only nearest neighbours interact, there is considerable theoretical work, giving a percolation limit , the concentration c0 at which long-range order disappears. The behaviour of TN is as (c —c0)12. For details see Brout (1965), Elliott and Heap (1962) and Klein and Brout (1963). 

The ideal ID Heisenberg anhferromagnet becomes increasingly correlated within the chain as the temperature cools but will remain disordered even at T = 0 (see Section 2.8). Long-range order arises from the presence of weaker interactions J between the chains. The ratio of the Neel temperature r v to the exchange strength Tiq/ 2J ) is a... 

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