Magnetoelectronics:

We are familiar with electronic devices which exploit the two charge carriers - electrons and holes in semiconductor to build devices. A new concept, which is rapidly merging into a reality, is the use of spin – up-spin and down-spin in a similar way to build spintronic devices. Magnetoelectronics is a sub-set of this new paradigm which concerns use of the spins in magnetic materials for such applications. In this chapter, the underlying principles behind this branch of magnetoelectronics would be introduced using the electronic structure of metals. The valance electrons in metals are delocalized and are called conduction electrons since they are involving the conduction process. These electrons can wander freely through the sample and are also known as itinerant electrons. In some cases the magnetic moments in metals are associated with the conduction electrons. In other cases, the magnetic moments remain localized. In both these cases paramagnetic and diamagnetic behaviours can occur. Ferromagnetism is possible under certain conditions. The itinerant theory of magnetism based on free electron theory is applicable to the magnetism of 3d series of elements such as iron, cobalt and nickel. The free electron model is a crude approximation to most real situations, but it is simple to consider and will allow the discussion to proceed a long way. The itinerant conduction band theory of paramagnetism developed by Pauli helps in understanding the influence of magnetic field on magnetization of a paramagnetic metal. This would then lead to a discussion on the band picture of a ferromagnetic metal. With the background the spin-up and spin-down bands in a ferromagnetic metal, it becomes easy to understand a new class of spintronic materials called half-metals. A discussion on spin polarized materials and spin-dependent transport would conclude our introduction to these novel materials.

This chapter will address the following points:

1. 1. How are the conduction electrons arranged in a normal metal in the absence of and presence of an applied magnetic field?
   
   
2. 2. How can these ideas be generalized to understand a ferromagnetic metal which has a net magnetization?
   
   
3. 3. What are half-metals? Why are they called spin polarized materials?
   
   
4. 4. How to understand spin-dependent transport in a quantitative manner?

Electronic structure of normal metals

The Drude model was the first attempt made to explain the electrical properties of metals using the idea of an electron gas that is free to move between positively charged ion cores [1, 2, 3]. This over simplistic model considered only collision between the electrons and the ion cores and ignored inter-electron collisions and interactions. This attempt to apply classical kinetic theory to electrons in metals failed to correctly predict the properties of metals with its main success being the reasonably correct prediction of the Weidemann-Franz ratio of metals at room temperature. Failure of the electron gas approach was diagnosed by Sommerfeld's model in which the electrons were treated as quantum mechanical particles. Sommerfeld replaced the classical Maxwell-Boltzmann distribution with Fermi-Dirac distribution and successfully predicted the experimentally observed temperature, dependence and magnitude of electronic specific heat, (thermal and electrical) conductivities and Weidemann-Franz ratio of metals. This model could also explain the temperature dependence of the magnetic susceptibility of metals. However, this model could not explain why certain materials are insulators or semiconductors and other experimentally observed features such as the correct value of the Hall coefficient, magnetoresistiance and Seebeck coefficient. Let us use the ideas of Sommerfeld's model to arrive at parameters relevant to understanding the electronic structure of metals.