Susceptibility external fields

If 5 aj(r) is slowly varying in space, tire long-wavelength limit x-j(k —> 0) reduces to a set of static susceptibilities or thennodynamic derivatives. Now, since for t > 0 the external fields are zero, it is useful to evaluate the one-sided transfomi... 

Figure 10.2 Arrhenius plot of the natural logarithm of the relaxation time extracted from the ac susceptibility data as a function of the inverse temperature for 1 at different external fields as indicated. (Reprinted from Ref. [6]. Copyright (2009) American Chemical Society.)...

Fig. 7 Temperature dependence of the static magnetic susceptibility of (a) (EDT-TTFBr2)2 FeBr4 (b) (EDO-TTFBr2)2FeCl4 (c) (EDO-TTFBr2)2FeBr4 measured at an external field of B = 1 T after the core diamagnetic contributions are subtracted...

The effect of an external field on the glassy dynamics can be studied by recording the ac susceptibility as a function of time for different bias fields, x" normalized by its value just after the quench, is shown in Figure 3.25 for... 

Response to external field is used to determine magnetic susceptibility and electronic ground state of spin system Nuclear magnetic resonance (NMR) sjjectra Observe some atoms from protein and solvent, report on protein and, indirectly, the iron center. 

It is implied in Eq. (38) that, at temperature 0, the value of susceptibility becomes infinite and that there is a finite value of the magnetic moment per unit volume (see Eq. 36), even in the absence of an external field (H = 0) at temperatures lower than 0. Below 0 (a characteristic temperature for a given substance), atom and dipoles (spins) of magnetic materials are ordered. 

Let us consider an optical system with two modes at the frequencies oo and 2oo interacting through a nonlinear crystal with second-order susceptibility placed within a Fabry-Perot interferometer. In a general case, both modes are damped and driven with external phase-locked driving fields. The input external fields have the frequencies (0/, and 2(0/,. The classical equations describing second-harmonic generation are [104,105] ... 

Let us consider a quantum optical system with two interacting modes at the frequencies coi and ff>2 = respectively, interacting by way of a nonlinear crystal with second-order susceptibility. Moreover, let us assume that the nonlinear crystal is placed within a Fabry-Perot interferometer. Both modes are damped via a reservoir. The fundamental mode is driven by an external field with the frequency (0/ and amplitude F. The Hamiltonian for our system is given by [169,178] ... 

A comparison of magnetic properties Property Effect of external field Specific susceptibility (x) at. 20 C, (cgs units) g 1 Temperature dependence of X Field dependence of X... 

Magnetic Shielding.—A magnetic field H induces intramolecular currents which depend on the susceptibility. These induced currents produce an induced field Hina which modifies the external field. The effective local field at a nucleus A is therefore... 

In the first period, which ended with a review [18], the complex susceptibility x (0)) was expressed through the law of motion of the particles perturbed by a.c. external field E(t). The results of these calculations rigorously coincide with those obtained, for example, in Refs. 22 and 23, respectively, for the planar and spatial extended diffusion model (compare with our Ref. 18, pp. 65 and 68). The most important results of this period are (i) the planar confined rotator model [ 17, p. 70 20], which has found a number of applications in our and other [24—31] works (ii) the composite so-called confined rotator-extended diffusion model. However, this approach had no perspectives because of troublesome calculations of the susceptibility x ( )-... 

Measured moments can also be obtained at fixed external field with varying temperature, converted to M in emu/mol, and then to the intrinsic property of magnetic susceptibility from M at a low applied external field H, well below the saturation region the susceptibility x = Mj II. The present lack of standardized magnetic units is a frequent cause of frustration to those comparing magnetic measurement reports in the literature.45 Many X measurements are reported in units of emu/(Oe mol) or cm3/mol, which are (perhaps surprisingly) equivalent. 

Fig. 24 Magnetic susceptibility for BABI at 10,000 Oe external field. A-D represent fits to the experimental data (A) square planar AFM system with J/k = — 1.6 K (B) square planar bilayer AFM system with J2olk = —1.4 K and interlayer Jik = —1.3 K (C) AFM spin pairing with Jjk = —3.8 K C is same model as C, with Jik = — 2.4 K D is same model as B, with J2T>lk = — 1.2K and interlayer Jik = — 1.9K (from calorimetric analysis).

Many of the different susceptibilities in Equations (2.165)-(2.167) correspond to important experiments in linear and nonlinear optics. x<(>> describes a possible zero-order (permanent) polarization of the medium j(1)(0 0) is the first-order static susceptibility which is related to the permittivity at zero frequency, e(0), while ft> o>) is the linear optical susceptibility related to the refractive index n" at frequency to. Turning to nonlinear effects, the Pockels susceptibility j(2)(- to, 0) and the Kerr susceptibility X(3 —to to, 0,0) describe the change of the refractive index induced by an externally applied static field. The susceptibility j(2)(—2to to, to) describes frequency doubling usually called second harmonic generation (SHG) and j(3)(-2 to, to, 0) describes the influence of an external field on the SHG process which is of great importance for the characterization of second-order NLO properties in solution in electric field second harmonic generation (EFISHG). 

From FPE (4.27) it follows that in the absence of internal and external fields (U = 0) the parameter Tp exhaustively determines the response time of the system to a weak external excitation. For example, it is only xD that determines the dispersion of the magnetic susceptibility in a magnetically isotropic particle. 

In the framework of statistical thermodynamics, the initial (equilibrium) susceptibilities are obtained as the even derivatives (2nd, 4th,. ..) of the free energy F with respect to the external field at // - 0. Expanding F in the power... 

In principle, the electric fields to be inserted in Eq.(7) are the electric fields at the location of the molecule. Instead of the local electric fields oc the external fields E are usually used. Therefore, local field correction factors have to account for the electric field screening of the surrounding material when going from the macroscopic susceptibilities to the molecular hyperpolarizabilities as shown below. 

It is customary to relate the polarization to the external field by defining a susceptibility x(t) tensor via the relation... 

Fig. 33. Plot of isothermal magnetization and differential susceptibility of a weakly anisotropic antiferromagnet versus the applied external field (Ms = saturation magnetization of a sublattice)...

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