Susceptibility Chi Research Articles

The resistive susceptibility of random diode-insulator networks

The authors consider regular crystal lattices in which the bonds are either diodes (probability p) or insulators. The mean number of backbone bonds LBB(p) when averaged over lattice points is found to be related to the mean size of clusters S(p) by LBB(p)=zpS(p) where z is the number of bonds directed away from any lattice site. Thus LBB diverges at pc with the mean size exponent gamma . The resistive susceptibility chi R(p) of Harris and Fisch (1977, 1978) is expanded graphically as a power series in p and it is found that term by term chi R(p)= Psi R(p)(S(p))2 where Psi R(p) is obtained from chi R(p) by ignoring contributions from nodal graphs. The above results are valid for bond and site dilution in any dimension. For bond dilution on the square lattice the authors have determined Psi R(p) to p17 and Pade analysis of the resulting series for chi R(p) shows that it diverges with exponent gamma R=3.654+or-0.017. Using a scaling relation the exponent t for the conductivity of the infinite cluster is estimated to be t=0.75+or-0.02.

Divergent Diamagnetism in Superconducting and Normal Metal Composites near the Percolation Threshold

The bare diamagnetic susceptibility chi of a composite superconductor below the percolation threshold p/sub c/ has been numerically calculated. A novel fitting procedure gives chiproportional(..delta..p)/sup -b/ near p/sub c/, with b = 1.29 in dimension d = 2, b = 0.35 in d = 3, the exponents agreeing between site and bond percolation to within 0.02 in both cases. Similar effects give a far-infrared absorption coefficient ..cap alpha.. in normal-metal--insulator composites varying as ..cap alpha..approx...omega../sup 2/(..delta..p)/sup() -s+b/2/ where s is the dielectric-constant exponent.

Wave vector-dependent spin susceptibility of iron above the Curie temperature

Microscopic calculations are given of the wavevector- and temperature-dependent spin susceptibility, chi (q), of itinerant-electron magnets by generalising the approach initiated by Hubbard and Hasegawa (1979-1983). The expressions for chi (q) in the limit of q=0 and q=Q (the antiferromagnetic wavevector) are shown to reduce to the results obtained previously by the present author. Detailed calculations of chi (q) of paramagnetic iron are made using the density of states generated by the recursion method. The amplitude of local moments evaluated by summing chi (q) over the BCC Brillouin zone using the classical fluctuation-dissipation theorem is nearly in agreement with effective moments deduced from the susceptibility chi (0). The equal-time and spatial spin-spin correlation functions are also calculated, and discussed with reference to recent neutron diffraction experiments.

Magnetic susceptibility measurements of (Ag0.5Cu0.5)100-xGexalloys in amorphous and liquid states

The magnetic susceptibility was measured in the temperature range 77-1200K for a number of (Ag0.5Cu0.5)100-xGex alloys in both amorphous and liquid states. The measured magnetic susceptibility chi exp is diamagnetic and is of the order of 10-5 EMU mol-1, being typical of non-magnetic simple metals. In its composition dependence just above the melting point, a minimum is observed in the range x=20-30. The temperature derivative delta chi exp/ delta T, in the liquid state also exhibits a sharp maximum. The amorphous phase is easily formed in this particular Ge composition range, where both chi exp and delta chi exp/ delta T show anomalies. The magnetic susceptibility of the amorphous state is further diamagnetic and its magnitude is close to the extrapolation of the chi exp value of the liquid state to low temperatures. Apart from the anomalies, the chi exp value in the liquid state can be well explained in terms of the free electron model. The anomalous behaviour at x=20-30 is ascribed either to the formation of pseudomolecules or to the coincidence of the Fermi wavenumber 2kF with the first peak of the structure factor.

Monte Carlo study of phase transitions in bond- and site-disordered Ising ferromagnets

By Monte Carlo simulations the phase transition is investigated for bond- and site-disordered Ising ferromagnets with special emphasis to the temperature dependence of the paramagnetic susceptibility chi 0(T) outside the real critical temperature range. For site-disordered systems a large temperature range of deviations from the Curie-Weiss law and a non-monotonic temperature dependence of the effective exponent gamma (T)=(T-Tc) chi 0(dchi 0-1/dT) was found, in close analogy with the experimentally observed behaviour of amorphous Heisenberg ferromagnets. Bond disorder affects the critical temperature Tc but has little influence on the temperature dependence of chi 0(T).

Magnetisation profiles for anisotropic spin glasses

The thermodynamic (field cooled) magnetisation is analysed throughout the spin glass domain (transverse T, longitudinal L or mixed LT phases) for a class of anisotropic m vector models, in the limit of a small collinear field. In zero field the field cooled susceptibility chi T( chi L) is independent of temperature throughout the T (L and LT) phases. In a finite collinear field the author observes the celebrated Parisi 'h43/' dependence of the field cooled magnetisation throughout the L and LT phases. For the T phase no simple characterisation is apparent.

Superconducting diamagnetism near the percolation threshold: numerical study

The authors investigate numerically the magnetic properties of a random superconducting network, which models random superconductor-insulator mixtures. Bonds between nearest-neighbour sites on a square lattice are chosen to be independently superconducting with probability p, and insulating with probability 1-p. A new numerical method is used to investigate loop statistics in these percolating networks. The diamagnetic susceptibility chi as a function of the superconducting fraction p is calculated. Close to the percolation threshold pc, chi shows a singular behaviour as a function of (pc-p). The numerical results exhibit a finite-size scaling which enables one to deduce the critical exponent of chi from calculations on relatively small samples. The numerical results are in good agreement with the predictions of recent scaling theory and differ from those made by previous workers.

Density of states and isomer shift on the rare-earth metal europium

The authors have calculated the energy band structure of BCC europium self-consistently by using the KKR method. The density of states curve has been computed by using Jepsen and Andersen's (1971) tetrahedron method. It has been confirmed that the Fermi energy EF lies near the dip of the density of states curve, from which the electronic specific heat coefficient gamma and the paramagnetic susceptibility chi are obtained, and their temperature variations are examined. Also they have made a quantitative calculation of the electronic density at the nucleus, and obtained the contribution of the conduction electrons to the isomer shift of the 151Eu nucleus: 2 Sigma mod Phi k(0) mod 2=0.44*1026 cm-3 atom-1.

Pressure dependence of the spin susceptibility in vanadium

Pressure dependence of the spin susceptibility chi spin in vanadium is calculated within the framework of the local spin density approximation. It is found that the change in chi spin due to pressure is mainly caused by the change in the density of states at the Fermi level; the contribution from the change in the exchange-correlation integral is very small. The calculated result is compared with experiment by using a simplified model for the volume dependence of the orbital susceptibility.

Theory of magnetic susceptibility of mixed-valent Ce0.76La0.14Th0.1

The authors derive an expression for the magnetic susceptibility ( chi ) of a mixed-valent system in which there is a continuous valence transition to a nearly integral valent phase, taking into account the crystal electric field (CEF) splitting of the localised levels. As an example, they calculate chi of Ce0.76La0.14Th0.1 in which CEF excitations have been observed for the first time in a mixed-valent system. There is a good agreement with experimental results.

Low-temperature specific heat and Kondo effect in the dilute uranium alloys (UxTh1-x)S and (UxTh1-x)Se

The specific heat of several metallic alloys, (UxTh1-x)S and (UxTh1-x)Se, have been measured between 1.5 and 10K. Large increases of the electronic specific heat coefficient gamma with x were observed at low uranium concentration (x<0.15):d gamma /dx=126 and approximately=450 mJ (U mol)-1K-2 for sulphides and selenides respectively. The normalised ratios between the 0K increments in the magnetic susceptibility chi and gamma , pi 2kB2 dchi /3 mu B2 d gamma , were found to be equal to 2.4 and 3.0 respectively. The results are consistent with a strong-coupled Kondo description (of characteristic temperature 150K for S and 50K for Se compounds) rather than with 5f virtual bound states at the Fermi level. Complementary magnetic susceptibility and electrical resistivity measurements have allowed the authors to determine the critical concentration for the ferromagnetism threshold in (UxTh1-x)Se:x approximately=0.27 (as compared with 0.43 for (UxTh1-x)S).

Magnetic properties of U(FexCo1-x)2compounds

Reports the results of magnetic measurements performed on U(FexCo1-x)2 compounds in the temperature range 4.2-500K. For the Fe content x<0.62, the compounds show an exchange-enhanced paramagnetism. The magnetic susceptibility chi 0, is not temperature dependent. The chi 0 values increase with increasing Fe content. The compounds with x>0.62 are ferromagnetic. The saturation magnetisation decreases with increasing Co content. Above the Curie point, the data can be described by considering a Pauli paramagnetic term in addition to a Curie-Weiss behaviour. The composition dependence of the saturation magnetisation is analysed using the local environment model.

Magnetic properties of Gd(FeyAl1-y)3and (GdxY1-x)Fe3compounds

Reports the results of magnetic measurements performed on Gd(FeyAl1-y)3 and (GdxY1-x)Fe3 compounds over the temperature range 4.2-1300K. For x and y>or=0.2 the compounds are ferrimagnetically ordered. In this case, the reciprocal susceptibility chi -1 follows a Neel-type hyperbolic law. The YFe3 compound is ferromagnetic and chi -1 obeys a Curie-Weiss behaviour. Both mean iron moments determined from saturation measurements and Curie constants decrease, but only slowly, by increasing the aluminium or yttrium content. The composition dependence of the iron moments is ascribed to the reduced exchange splittings of Fe 3d states. The electron paramagnetic resonance studies on ferrimagnetic compounds show that the g values and the slope of the linewidth are temperature dependent. The data are analysed in a model which uses the molecular field approximation.

Measurement of the magnetic response function in UAs

Neutron inelastic scattering has been used to determine the imaginary part of the susceptibility chi "(Q,h(cross) omega ) in uranium arsenide. The measurements were performed on a time-of-flight spectrometer using a polycrystalline sample. In the paramagnetic state a broad (in energy) spectrum is found which can be characterised as a Lorentzian centred at zero energy with a half width 1/2 Gamma =17+or-3 meV. No evidence is found for any crystal-field levels below 40 meV. At the ordering temperature (TN=126K) the overall susceptibility decreases, as expected, but the dynamical part may still be characterised as a Lorentzian whose half width decreases gradually to 8+or-3 meV at 5K. Such a response in the ordered state, in which an apparently localised moment of 2.2 mu B resides on each U atom, is quite surprising, but is in agreement with experiments on single crystals in which no well defined excitations were found. At all temperatures the susceptibility peaks at the magnetic zone centre, showing the dominance of antiferromagnetic correlations. The results are discussed in terms of the systematics of the uranium rocksalt compounds and the need for realistic calculations of the ground state.

The paramagnetic state of itinerant electron systems with local magnetic moments. I. Static properties

A model previously used for treating thermodynamic properties is developed further to discuss the wave-vector-dependent susceptibility chi (q) and the associated static correlation functions. A consistent theory is given of the temperature dependence of the uniform susceptibility and of the wave-vector and temperature dependence of paramagnetic diffuse neutron scattering. The theory is applied quantitatively to CeFe2, Fe and MnSi above their magnetic ordering temperatures and to FeSi at high temperatures. In CeFe2 and MnSi the enhancement of the Curie constant and the forward scattering peak in the neutron data are both attributed to long-wavelength 'longitudinal' fluctuations of the magnetic moment superposed on strong transverse spin disorder. The situation is predicted to be similar in BCC Fe and this differs sharply from the strong short-range order picture of Prange and Korenman (1978), Capellmann (1979) and Sokoloff (1975).

Parisi solutions for the anisotropic spin glass problem

A Heisenberg spin glass with local uniaxial anisotropy is studied at mean field level in terms of a Parisi symmetry breaking scheme. It is shown that replica symmetry breaking leads to important modifications to the replica symmetric expressions for the susceptibilities chi T, chi L which signal the transitions in this system.

Shape dependence of the EPR linewidth, resonance field and spin-spin relaxation rate of EuS near Tc

The effect of sample shape on the measured EPR linewidth Delta H and resonance field Hr has been investigated at 9.2 GHz by experiments on EuS for temperatures from Tc ( approximately=16.55K) to about 60K. The data were taken on a thin, square disc of EuS for two orientations of the applied field H: (i) H|| the normal to the disc and (ii) H ⊥ to the normal. The observed values of Hr and Delta H for the two cases are different at most temperatures signifying the effect of the demagnetising fields. Using independent measurements of the magnetisations M and the uniform susceptibility chi, it is shown that the temperature dependence of Hr|| and Hr ⊥ is described well by the Huber-Seehra theory (1976) down to about 19K. The observed deviations from the theory below 19K are believed to be due to the non-linear behaviour of M versus H. Expressions are developed to relate the shape-independent internal spin relaxation time T12 to the measured linewidths (Delta H)|| and (Delta H)⊥. For the precritical region, 4 pi chi 1, 1/(T12) varies as chi-1, following the predicted conventional behaviour. These variations of 1/(T12) are understood to result from the dominant role of the dipole-dipole interaction in the spin relaxation in EuS.

A comparative study of the temperature-dependent magnetic susceptibilities of CuInX2(X=S, Se, Te)

The absolute magnetic susceptibilities chi of polycrystalline CuInSe2 (n-type) and CuInTe2 (p-type) are reported from liquid helium temperatures to 300K. The temperature dependence of chi in the two compounds can be fitted to the equation chi (10-6 cm3 mol-1)=- chi 0+C(1-exp(-E/2T))/(T+ theta ) in the whole temperature range. A physical basis for this equation is given which leads to the determination of carrier concentration (from C), the donor/acceptor activation energy E and the Curie-Weiss temperature theta . From the fit, the obtained parameters for CuInS2 CuInSe2 and CuInTe2 are respectively: chi 0=83.7, 97.9, 119.0;C=185.0, 128.6, 164.7; E(K)=200, 240, 140; and theta (K)=3.0, 2.9, 1.7. The presence of shallow donor/acceptor levels in CuInX2 is established and the values for the obtained activation energies (E) are comparable with the estimates reported from other studies. The positive constant theta suggests antiferromagnetic exchange interactions between localised charge carriers. However, no magnetic ordering is observed down to 4.2K in CuInS2 and CuInSe2 and down to 1.4K in CuInTe2.

Calculation of the static susceptibility χ(q) in orientationally disordered crystals with hard-core correlations: plastic CBr4and TBBA smectic B phase

In a previous paper (1981), a new method of calculating the static susceptibility chi (q) was developed with a view to studying the intermolecular correlations in orientationally disordered crystals. The purpose of the present paper is to apply this perturbative method to the typical case of orientationally disordered crystals with hard-core correlations as the plastic phase of CBr4 and the smectic B phase of TBBA. The calculation of the elastic diffuse neutron scattering leads to theoretical scattering patterns in good agreement with the experimental ones.

A data logging system for AC magnetic measurements (4.2-300K)

A semi-automated apparatus for the simultaneous measurement of various AC magnetic properties in low applied fields (<or approximately=1 kA m-1) over the temperature range 4.2-300K is described. The system is based on a variable temperature cryostat and a high resolution data logger capable of measuring ten signals to <or approximately=1 mu V resolution. The capability of the apparatus is demonstrated by the simultaneous measurement of AC susceptibility chi and its temperature modulation signal S for a single crystal of terbium. The design of a current amplifier used for generating the magnetic field and with the ability to sum AC and DC inputs is also described. A method of assessing the effects of an average demagnetising factor on chi and S measurements on irregularly shaped samples is presented.