The spin polarization is defined as the ratio of the density of states of up-spin and down-spin electrons at a Fermi level, P=(D_up-D_down)/(D_up+D_down), as shown in Fig. 1. Since the density of states of up-spin and down-spin electrons are equal in paramagnetic materials, P=0 for paramagnetic materials. On the other hand, since the density of state of up-spin and down-spins are different in ferromagnetic materials, P is larger than 0, but smaller than 1 for ferromagnetic materials. The P values of Fe and Co are known to be around 0.5. If a material has a band gap in the minority band (semiconducting) at a Fermi level and exhibits metallic behavior in the majority band, the density of state of the minority band is zero at the Fermi level. In this case, since only up-spin electrons are present at the Fermi level, P=1. This type of material is called "half-metal" because it exhibits both metallic and semiconducting behaviors.

Fig. 1 Density of states of paramagnetic, ferromagnetic and ferromagnetic half-metal materials and the definition of the electron spin polarization, P.

The first half-metallic ferromagnets were C1_b-type half-Heusler alloys (Fig. 2), NiMnSb and PtMnSb, which were predicted by de Groot et al. (PRL 50, 2024 (1983)) from the electronic band structure calculations. Subsequently, various other half metallic ferromagnetic materials have been studied, such as oxides CrO₂₂, Fe₃O₄₃, double perovskites Sr₂FeReO₆₄, pyrites CoS₂₅, and zinc-blend type CrAs₆ and CrSb₇. Many studies on the magnetic tunnel junctions (MTJs) using the above materials have been carried out; however, large values of tunneling magnetoresistance (TMR) have not been reported at room temperature because of their low Curie temperature. For industrial applications, half-metallic materials must have high Curie temperature, hence, the L2₁ type full-Heusler alloys are now believed to be the most promising half metallic ferromagnetic materials. Recently, Galanakis et al. (PRB 67, 104417 (2003)) studied full-Heusler quaternary alloys such as X₂Y_1-xY'xZ, (X_1-xX'x)₂YZ and X₂YZ_1-xZ'_x and found the possibility of obtaining new half-metallic systems with predefined electronic and magnetic properties. Theoretical calculations on the electronic band structure of B2-type and L2₁-type Co₂Cr_1-xFe_xAl exhibit a half-metallic behavior for the lower concentration range of x. In addition, the Curie temperature (T_c) of the Co₂Cr_1-xFe_xAl alloy increases from 330 K for x=0.0 to 1170 K for x=1.0. Subsequently, Co₂Cr_1-xFe_xAl has been experimentally investigated and a large negative magnetoresistive effect of 30% at room temperature was observed by Block et al. (J. Sol. Stat. Chem. 176, 646 (2003))for the Co₂Cr_0.6Fe_0.4Al bulk alloy. Following this result, Inomata et al. (JMMM 282, 269 (2004)) prepared a spin valve type tunneling junction with a Co₂Cr_0.6Fe_0.4Al (CCFA) electrode on thermally oxidized silica and reported TMR values of 27% and 19% at 5K and room temperature (RT), respectively. However, these values are significantly lower than those expected from highly spin polarized materials according to Julliere's formula.

Fig. 2 Atomic structure of full and half Heusler alloys

In the search of MTJs with high TMR value, MTJs are being fabricated based on only theoretical predictions of P. However, many investigations have shown that the high P values as predicted by band gap calculations are not achieved in actual materials partly because of the difficulty of achieving stoichiometric fully ordered states in thin film processing. Sometimes, the phases assumed by band calculations cannot be present in the thermodynamical equilibrium condition. The lack of accuracy in band calculations is also hinders the development of MTJ's with high TMR values. Depending on models employed in band calculations, the value of P ranges from 0 to 1. Therefore, materials search using more direct measurement of spin polarization is strongly desired. For experimental measurement of spin polarization, point contact Andreev reflection method is know to be most reliable.