Semimetals and Half-metals
Abstract Semimetals and half-metals are two concepts whose translations in Chinese are similar or the same. However, these two concepts are distinct, which is explained in this text.
1. Semimetals
The definition of the "semimetal" is an element having some properties characteristic of metals and others of non-metals. Many metalloids give rise to an amphoteric oxide (e.g. arsenic or antimony) and many are semiconductors. This definition is found in an online encyclopedia, whose URL and name I have forgotten.
We can find more information about semimetals on our text book. The energy bands of semimetals shown in Figure 1 on page 174 are different from other substances in that two bands of them are narrower than those of others. Reading the text and the description under the figure, I think that the reason of drawing two narrow bands is to show that parts of these two bands share the same energy value, as shown below. Thus, even at absolute zero, one band can be almost filled and the other band can be nearly empty, as the description under Figure 1 on page 174 says.
Consequently, at absolute zero, electrons in a semimetal have the freeness to move among those bands sharing energy values. Therefore, semimetals still have some conduction at absolute zero, while semiconductors have little and become insulators, because electrons in semiconductors, whose bands shares no energy values, have to fill the lowest energy levels(bands) and hence have little freeness at absolute zero.
Consequently, at absolute zero, electrons in a semimetal have the freeness to move among those bands sharing energy values. Therefore, semimetals still have some conduction at absolute zero, while semiconductors have little and become insulators, because electrons in semiconductors, whose bands shares no energy values, have to fill the lowest energy levels(bands) and hence have little freeness at absolute zero.
2. Half-metals
A half-metal is a solid with an unusual electronic structure. For electrons of one spin it is a metal with a Fermi surface, but for the opposite spin there is a gap in the spin-polarized density of states, like a semiconductor or insulator. This definition presupposes a magnetically ordered state to define the spin quantization axis. The responses of a half-metal to electric and magnetic field at zero temperature are quite different. There is electric conductivity, but no high-field magnetic susceptibility.[2]
There are three categories of half-metals: those with (1) covalent band gaps, (2) charge-transfer band gaps, and (3) d-d band gaps[3]. The origin of the covalent band gap is strongly related with semiconductors of group III-V type, for instance, GaAs. The band structure, interactions, and bonding for the semiconducting spin direction of this category are very much equivalent to that in the group III-V semiconductors. One example of this category is NiMnSb. Half metals of Category (2) are found in strongly magnetic compounds, where the d bands of the transition metal are empty for the minority spin direction and the itinerant s, p electrons of the transition metal have been localized on the anions. Thus compounds in this category are naturally strong magnets. The occurrence of the band gap for one spin direction is not very dependent on the crystal structure. An instance of Category (2) is CrO2. Half-metals in Category (3) show rather narrow bands, so that gaps occur between crystal-field split bands. The exchange splitting can be such that the Fermi level is positioned in a gap for one spin direction only. Materials of this category are weak magnets. Examples are Fe3O4, Mn2VAl.
Although the degree of spin polarization in half-metals should be 100% at absolute zero, neglecting spin-orbit interactions, the half-metallicity with a clear band gap around the Fermi energy level for the minority spin can be partly suppressed by defects, spin excitations at increased temperature, or non-quasiparticle states[4]. Even at low temperature and in the defect-free case, the spin-orbit interaction is still a question. For example, an experiment shows the value of P=85% or P=90% in (Ga, Mn)As, where P is defined by
.
Here the subscription "↑" denotes the majority density of states, while "↓" the minority. And the theoretical calculation considering spin-orbit interaction gives the value P=91.9%, which agrees the experiment and confirms the existence of spin-orbit interaction in this half-metal.
.Here the subscription "↑" denotes the majority density of states, while "↓" the minority. And the theoretical calculation considering spin-orbit interaction gives the value P=91.9%, which agrees the experiment and confirms the existence of spin-orbit interaction in this half-metal.
To sum up, semimetals and half-metals are two distinct concepts, although their Chinese translations may be the same or similar. Semimetals are the materials that have two or more energy bands that have energy-value-sharing parts, which causes their conduction at absolute zero. Half-metals are the materials shows conduction by charge carriers (usually electrons) of one spin direction exclusively.
References
[1] Introduction to Solid State Physics
[2] J. M. D. Coey and M. Venkatesan, Journal of Applied Physics, Vol. 91, No. 10, 8345-8350 (2002)
[3] Fang, de Wijs, and de Groot, J. Appl. Phys., Vol. 91, No. 10, 8340-8344 (2002)
[4] Ph. Mavropoulos, K. Sato, R. Zeller, and P. H. Dederichs, Physical Review B, 69, 054424 (2004)
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