Bonner-Fisher law

Figure 3 Temperature dependence of the susceptibility, measured by the ESR intensity, of (BCPTTF)2PF6 and (BCPTTF)2AsF6, normalized at room temperature. The solid lines are fittings to a Bonner-Fisher law. (From Ref. 43.)...

From a fitting to the Bonner-Fisher law, a value for /eff/fcB can be estimated to be on the order of 130 K, constant from 300 to 100 K, with enhancement below this temperature. It is interesting to notice that this temperature (100 K) corresponds to the appearance of the 2diffuse lines. The behavior of the susceptibility below 100 K could be attributed to pretransitional spin-Peierls fluctuations, with a depression on the xmiu(j ) as observed in (BCPTTF)2AsF6 (Fig. 3). 

The characteristic behavior described above is particularly well observed with the salts of the last series. For instance, for the representative salt (BCPTTF)2PF6 [46], pretransitional structural fluctuations are found by x-rays to exist on cooling from Tp = 100 K to TsP = 37 K, these fluctuations being almost one-dimensional between 100 and 50 K. The magnetic susceptibility of this salt with regular behavior fits well the Bonner-Fisher law at high T, with J = 165 K, and it starts to deviate appreciably from this law below 100 K, that is, well above Tsp-... 

In this salt (MDT = l-methyl-l,4-dithianium), there is a brick wall stacking arrangement of TCNQ dimers. It is a quasi-one-dimensional semiconductor up to 300 K with an energy gap Ec = 0.22 eV. The magnetic susceptibility follows quite well a Bonner-Fisher law with / = 76 K. At room temperature x = 9.5 x 10-4 emu/mol and there is a maximum = 14.5 x 10 4 emu/mol at Tm = 100 K. There is also a probable spin-Peierls transition at 5.5 K [64]. 

The salts of this series [BEDT-TTF = bis(ethylenedithiolo)tetrathiafulvalene], with X = AuBr2, CuCl2, or Ag(CN)2, are all semiconductors with narrow band widths and strong Coulomb repulsions. For this series the magnetic susceptibility has room-temperature values of = 8 to 9 x 10 4 emu/mol, and maximum values of = 16 to 18 x 10 4 emu/mol, at TM = 60 to 70 K. However, it does not fit well a Bonner-Fisher law in any case. A spin-Peierls transition is found to occur, at 7 K, for the Ag(CN)2 salt only [65]. 

The structure of this salt consists of stacks of twisted dimers. It is a semiconductor with an energy gap Ec = 0.42 eV. At room temperature the electrical conductivity is crM = 0.1 S/cm and the magnetic susceptibility is X = 8 x 10-4 emu/mol. As in the preceding a -(BEDT-TTF)2X series, the magnetic susceptibility does not fit well a Bonner-Fisher law [66]. 

The contribution to the susceptibility due to the perylene chain is enhanced Pauli-like, similar to the Au, Cu, and Co analogs, while the di-thiolate chain contribution pd = Xs"nt(T) is of Bonner-Fisher type. The magnitude of the antiferromagnetic intrachain interactions can be estimated from the 0 value of Curie-Weiss law, which can be adjusted at high temperature [expression (13)] and its value is on the order of 0 = -210 K. 

However, in the case of MEM(TCNQ)2, which is considered as one of the most representative spin-Peierls materials, with TsP = 19 K, the results are quite at variance with the normal behavior described above [46]. For this material, critical fluctuations are also observed correctly, by x-rays, below Tp = 40 K, but they are only of a three-dimensional nature. Moreover, these fluctuations do not produce any detectable effect below TF on the Bonner-Fisher dependence of the magnetic susceptibility. Consequently, this law is perfectly followed, with J = 53 K, down to 19 K [17,18,46]. Some earlier comments on this point have also been given by Schulz [50]. 

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