Spin susceptibility

ESR can detect unpaired electrons. Therefore, the measurement has been often used for the studies of radicals. It is also useful to study metallic or semiconducting materials since unpaired electrons play an important role in electric conduction. The information from ESR measurements is the spin susceptibility, the spin relaxation time and other electronic states of a sample. It has been well known that the spin susceptibility of the conduction electrons in metallic or semimetallic samples does not depend on temperature (so called Pauli susceptibility), while that of the localised electrons is dependent on temperature as described by Curie law. 

Crude CNTs containing nanoparticles are produced by the arc-discharge method [8]. Although the quantitative value of CNTs cannot be determined because of the unknown amounts of nanoparticles, the whole susceptibility and spin susceptibility of the crude CNTs are reported by a number of researchers. 

It is reported that a CESR peak is observed for the crude CNTs and the spin susceptibility does not depend on temperature [24]. The spin susceptibility is about three times as small as that in the non-particle CNTs. This ratio indicates that the ratio of CNTs and nanoparticles in the crude CNTs is about 1 2. 

CNTs are purified by oxidizing the crude ones as prepared. During the oxidation process, the nanoparticles are removed gradually and eventually only open CNTs remain [9]. An intrinsic CESR was observed from these purified COTs [12]. The temperature dependencies of susceptibility, linewidth and g-value of the CESR are shown in Fig. 2 (open circle). We find a temperature independent spin susceptibility (Pauli) = 4.3 x 10 emu/g. 

Fig. 2. Temperature dependencies of spin susceptibilities, linewidths and g-values of the CESR for the purified CNTs (open circle) and the annealed purified CNTs (solid circle).

Pauli spin susceptibility for the aligned CNTs has been measured and it is reported that the aligned CNTs are also metallic or semimetallic [30]. The temperature dependence of gn and gx s plotted in Fig. 5(a). Both values increase with decreasing temperature down to 40 K. A similar increase is observed for graphite. The g-value dependence on the angle 0 at 300 K is shown in Fig. 5(b) (inset). The g-value varies between gn = 2.0137 and gx= 2.0103 while the direction of magnetic fields changes from parallel to perpendicular to the tubes. These observed data fit well as... 

An ESR study for the K-doped CNTs with a doping level of 1-2% has been reported [35]. The comparison of spin susceptibilities x., between pristine and K-intercalated CNTs is shown in Fig. 7. A significant increase of the susceptibility... 

Temperature dependence of magnetic susceptibility of the PF6 salt was measured from 300 to 4 K at 5 T [35], The spin susceptibility of this salt gradually decreases from 300 to 50 K. Below 50 K, the susceptibility exhibits a rapid decrease accompanied by anisotropic temperature dependence, which is an indication of the long-range antiferromagnetic ordering. A one-dimensional Heisenberg model is... 

It can be shown that the conduction electron net spin susceptibility is proportional to the temperature coefficient of the electronic heat capacity [cf. Eq. (4.42)] and, for free electrons in a single band, having the Fermi energy much lower than any band gap, is given by... 

Some metals are diamagnetic because the conduction electron spin susceptibility is smaller than the induced diamagnetic susceptibility component. On the other hand, various rare earth metals display very strong paramagnetism because of unpaired / electrons that remain associated with individual atoms rather than entering into energy bands. 

This quantity is called the Pauli spin susceptibility. 

Fig. 10.11 Volume spin susceptibility of expanded alkali metals versus reduced volume (Fm—volume at melting point). From Freyland and Hensel (1985).

The solvated electron is responsible for a single, extremely narrow, structureless spin resonance line in the dilute solutions with a g value of 2.0012. Integration of its intensity gives a static spin susceptibility tending towards the... 

Fig. 10.14 Measured static susceptibilities for Na and K solutions in NH3 and the calculated spin susceptibility of a set of independent electrons at 240 K (solid line). The diamagnetic contribution of the NH3 molecules has been eliminated from the measured total susceptibility by using the Wiedemann rule. Since the total susceptibility is quite small in concentrated solutions, the errors may be large. O represent data of Huster (1938) on Na solutions at 238 K represent K-NH3 data of Freed and Sugarman (1943) at the same temperature and + represent data of Suchannek et al. (1967) at room temperature for Na-NH3 solutions. From Cohen and Thompson (1968).

It is clear from eqs (7) and (8) that Fs[M] monotonously increases with M, so that — as expected — the minimum of Fs[Af] corresponds to M = 0, for which the spin entropy attains the highest value. It is convenient to introduce the spin susceptibility xs related to... 

Fig. 25. Curie temperature as a function of the hole concentration for Gao.95Mno.os As computed from the 6 x 6 Luttinger model (solid line). Straight dashed lines represent results obtained assuming large and small values of the spin-orbit splitting A0, respectively. The dotted line is calculated neglecting the effect of the spin-orbit interaction on the hole spin susceptibility (Dietl et al. 2001c).

Another important issue requiring further studies is the role of carrier-carrier correlation. It is known that the effect of disorder on carrier-carrier interactions controls the localization and enhances the spin susceptibility (Altshuler and Aronov 1985), and thus the tendency towards ferromagnetism. However, spin-disorder scattering may limit the efficiency of this process (Altshuler and Aronov 1985). If this is the case, LSDA (Jungwirth et al. 1999 Lee et al. 2000) can provide a reasonable evaluation of the relevant Fermi-liquid parameter. 

Iodine oxidation of Ni(OEP) and Cu(OEP) yields polycrystalline materials with a range of stoichiometries.108 Resonance Raman studies indicate the presence of I5- in contrast to the I3 observed for larger ring macrocycles. Single crystal studies of Ni(TMP)I indicate a metal-over-metal stack arrangement but with the Ni(TMP) unit puckered. The iodine superlattice is incommensurate with the Bragg lattice.107 The room temperature conductivity is 10 Q-1 cm-1 and increases on lowering the temperature to reach a rounded maximum at 115 K. The spin susceptibility is temperature independent down to a transition temperature of 28 K, well below the conductivity maximum. Below 28 K the susceptibility decreases in an activated fashion with Ajk 60 K.108... 

Theory (1) The effective energy barrier between the two harmonic oscillators, AE (oo IT), which determines the probability of electron transfer along the conjugated chain decreases with increasing temperature thus, conductivity is semiconductor-like. (2) The spin susceptibility is due only to the unpaired Ji-electrons from TTF (all the 7i-electrons on TCNQ are in the paired state). Thus, the susceptibility is weak. (3) The spin-paired n-electrons on TCNQ resonate between the two harmonic oscillator states at frequency, . Such oscillation can perturb the g-factor of (TTF)+. As the increases with the temperature rise, the perturbation becomes greater, and the g-factor deviates more from that of the pure (TTF)+. 

Experiment (1) A sharp drop occurs in anomalously high conductivity just above 60 °K [38-41], (2) Conductivity has a negative temperature coefficient [37-42], (3) Spin susceptibility, on the other hand, increases with the temperature rise [45,47], (4) The EPR line width decreases nearly in the same manner as conductivity with the temperature rise and becomes relatively constant at about 300 °K [46], (5) The single EPR g-factor remains essentially constant throughout the temperature range [46]. 

By substituting Eqs. (2) and (3) into Eq.(l) and dividing it by Vu, the unit molecular volume of [TCNQ-TTF], Pauli spin susceptibility is reduced to... 

Magnetic Susceptibility of TiNi has been previously observed [39] to be temperature independent and interpreted as due to Pauli spin susceptibility. This categorizes the magnetic property as one that is insensitive to the atomic arrangement. The magnetic susceptibility has the constant values, 2.1 x 10 6 (emu/g) below the Ms and 3.0 x 10"6 (emu/g) above the As temperature. Between these two temperatures a plot of the data has a triangular form but as predicted, no difference is observed between those obtained from complete and incomplete cycles. 

Fig. 4. The concentration dependence of various electronic properties of metal-ammonia solutions, (a) The ratio of electrical conductivity to the concentration of metal-equivalent conductance, as a function of metal concentration (240 K). [Data from Kraus (111).] (b) The molar spin (O) and static ( ) susceptibilities of sodium-ammonia solutions at 240 K. Data of Hutchison and Pastor (spin, Ref. 98) and Huster (static, Ref. 97), as given in Cohen and Thompson (37). The spin susceptibility is calculated at 240 K for an assembly of noninteracting electrons, including degeneracy when required (37).

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