Theory of Diamagnetic Susceptibility of Metals

Abstract

In order to calculate the diamagnetic susceptibility of real metals, we have generalized the pseudopotential method to the case of a metal in a magnetic field. A general equation of motion is obtained, from which we first derive an expression for the core diamagnetism. We then derive an expression for the diamagnetic susceptibility of Bloch electrons in a magnetic field in terms of a pseudopotential. If our pseudopotential is replaced by the actual lattice potential, the result reduces exactly to expressions derived by other authors for the diamagnetic susceptibility of Bloch electrons. However, we believe that our method is the simplest manner in which this result can be derived. By the use of the pseudopotential and degenerate perturbation theory we obtain the result in a form from which computation can be made easily. We have computed the diamagnetic susceptibility of all the alkali metals and of aluminum. From our expression, the diamagnetic susceptibility of any polyvalent metal to which our approximations apply can be easily computed. We have also found a satisfactory explanation of why certain metals have very high diamagnetic susceptibility. We contradict Glasser's conclusion that the diamagnetic susceptibility and the paramagnetic susceptibility are nonadditive, and correct some algebraic errors in the work of Samoilovich and Rabinovich.

Electrical Transport and Electronic Structure Calculation of Al-Ga Binary Alloys

“…Although the experimental techniques of the measurement of Knight shift have been developed much earlier, its theoretical development had been in a state of infancy and has been developed much later. The previous theoretical work, [20,[25][26][27][28][29][30], on the magnetic properties of metal substantiate the view that like the electrical resistivity, the nearly-free-electron (NFE) approximation is also valid for the theoretical treatment of various magnetic properties viz., the Knight shift, magnetic susceptibility, the Hall coefficient etc. We shall now present its concise theory within the framework of pseudopotential technique.…”

Temperature dependence of Knight shift for the metals Zn and Al

“…The previous theoretical work [3][4] on the magnetic properties of metals substantiates the view that like electrical resistivity, the nearly free electron approximation is also valid for the theoretical treatment of various magnetic properties viz,, Knight shift, magnetic susceptibility, Hall coefficient etc. The study of the plethora of literature on pseudopotential theory and specially Harrison's first principle technique brings out the fact that this property has not been studied through this technique except by Singh [5] who has applied it to some multivalent liquid metals.…”

Dupré–Blundell model for the Landau diamagnetism applied to electrons gyrating in a crystalline solid

“…Deviations of this situation can be obtained for large energy separations E latt between the neighboring levels. In this case the formula (14) should be extended into the power expansion…”

“…The change of S and E latt is considered in a plane k z = constant, so only the dependence of S and E latt on a 0 should be taken into account in (14) and (17). Because one quantum state occupies an area of (2π/L) 2 in the (k x , k y ) plane, the degeneracy p of one Landau level calculated from (16) is proportional to 2 2π eff 0…”