How to Define and Calculate the Degree of Spin Polarization in Ferromagnets
Abstract:
Different ways to define and calculate the degree of spin polarization in a ferromagnet are discussed, particularly with respect to spin-polarized tunneling and Andreev reflection at the boundary between superconductor and ferromagnet. As an example, the degree of spin polarization for different experiments in Fe and Ni is calculated in the framework of the local spin density approximation and used to illustrate the differences between various definitions of spin polarization.
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http://dx.doi.org.sci-hub.tw/10.1103/PhysRevLett.83.1427
Although solid state physicists use the notion of a degree of spin polarization (DSP) of a ferromagnet (FM) rather often, it is not well defined. While the total magnetization is uniquely defined as the difference between the number of spin up and spin down electrons, it tells us little about how much different spins do contribute to transport properties. In view of the growing number of experiments probing spin polarization [1], it becomes increasingly more important to be able to calculate the DSP in the framework of the conventional band theory (and eventually beyond it). Importantly, the DSP can be defined in several different ways. In order to compare the calculations with the experimental data it is crucial to make sure that a proper definition of the DSP is used. In particular, spin-polarized tunneling in various forms [1], including Andreev reflection [2], provides valuable information about the spin dependence of the electronic structure, but this information may be obscure and not very useful unless the measurements are backed by the calculation appropriate for the experiment in question. Let us consider an extreme example, the so-called halfmetallic magnets. Such systems do not have any electrons at the Fermi level in one of the two spin channels; they have 100% spin polarization according to any sensible definition. On the other hand, for a regular magnetic metal, which has Fermi surfaces in both spin channels, it is not obvious a priori how to define the degree of spin polarization.
Although solid state physicists use the notion of a degree of spin polarization (DSP) of a ferromagnet (FM) rather often, it is not well defined. While the total magnetization is uniquely defined as the difference between the number of spin up and spin down electrons, it tells us little about how much different spins do contribute to transport properties. In view of the growing number of experiments probing spin polarization [1], it becomes increasingly more important to be able to calculate the DSP in the framework of the conventional band theory (and eventually beyond it). Importantly, the DSP can be defined in several different ways. In order to compare the calculations with the experimental data it is crucial to make sure that a proper definition of the DSP is used. In particular, spin-polarized tunneling in various forms [1], including Andreev reflection [2], provides valuable information about the spin dependence of the electronic structure, but this information may be obscure and not very useful unless the measurements are backed by the calculation appropriate for the experiment in question. Let us consider an extreme example, the so-called halfmetallic magnets. Such systems do not have any electrons at the Fermi level in one of the two spin channels; they have 100% spin polarization according to any sensible definition. On the other hand, for a regular magnetic metal, which has Fermi surfaces in both spin channels, it is not obvious a priori how to define the degree of spin polarization.
Hello, my name is Dr Abderrahmane Reggad. I'm a 51 year old and I am a researcher in materials' sciences. 
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