**Abstract**

Full-Heusler compounds exhibit a variety of magnetic properties such as non-magnetism, ferromagnetism, ferrimagnetism and anti-ferromagnetism. In recent years, they have attracted significant attention as potential thermoelectric (TE) materials that convert thermal energy directly into electricity. This chapter reviews the theoretical and experimental studies on the TE properties of magnetic full-Heusler compounds. In Section 1, a brief outline of TE power generation is described. Section 2 introduces the crystal structures and magnetic properties of full-Heusler compounds. The TE properties of full-Heusler compounds are presented in Sections 3 and 4. The relationship between magnetism, TE properties and order degree of full-Heusler compounds is elaborated.

**Keywords:** full-Heusler compounds, half-metal, spin-gapless semiconductor, thermoelectric properties, order degree

### **1. Introduction**

Thermoelectric (TE) power generation using TE devices is one of the key technologies to solve global energy problem, owing to its availability of direct conversion of thermal energy into electricity [1–3]. A schematic figure of a TE device is shown in **Figure 1**. It consists of n- and p-type TE materials connected in series electrically with metal electrodes and arranged thermally in parallel. The TE materials are wedged between ceramic plates. When one side of the device is heated and the other side is cooled, electrons and holes in the n- and p-type TE materials, respectively, diffuse from the hot side to the cold side, thus generating a flow of electric current.

To commercialise TE devices, there is a need to improve their TE efficiency. The maximum TE efficiency, *η*max, is an increasing function of the dimensionless figure-of-merit, *zT*, expressed as:

$$\eta\_{\text{max}} = \frac{T\_{\text{H}} - T\_{\text{C}}}{T\_{\text{H}}} \frac{\sqrt{\mathbf{1} + zT} - \mathbf{1}}{\sqrt{\mathbf{1} + zT} + T\_{\text{C}}/T\_{\text{H}}},\tag{1}$$

where *T*<sup>H</sup> and *T*<sup>C</sup> are the heating and cooling temperature, respectively. The dimensionless figure-of-merit, *zT*, is determined by TE properties (*S*: Seebeck

**Figure 1.** *Schematic figure of a thermoelectric (TE) power generation device.*

coefficient, *σ*: electrical conductivity, *κ*: thermal conductivity) of the individual TE materials in the device.

$$
\omega T = \frac{\mathbb{S}^2 \sigma}{\kappa} T,\tag{2}
$$

disordered phase, all the atoms are randomly distributed in the 8*c*, 4*b* and 4*a* sites, thus resulting in the A2 structure. In such a structure, all the sites are equivalent, which are expressed as a bcc lattice (prototype: W, space group: *Im*3*m*). There are other disordered phases, including the DO3 and B32a structures. The former is caused by the random distribution of the *X*, *X'* and *Y* atoms at the 8*c* and 4*b* sites (prototype: BiF3, space group: *Fm*3*m*). In the B32a structure, the 8*a* (0 0 0) and 8*b* (1/2 1/2 1/2) sites are occupied by the *X*/*Y* and *X'*/*Z* atoms, respectively. The

*Crystal structures of full-Heusler compounds. The Strukturbericht symbol and a prototype structure are written*

When the *X'* and *Y* atoms are of the same element, the chemical composition becomes *XX'*2*Z*, which crystallises in the X (XA or Xa) structure. This structure is called the inverse Heusler phase. The prototype is CuHg2Ti (or AgLi2Sb), and the space group is *F*43 *m*. In the structure, the *X* and *Z* atoms occupy the 4*d* (3/4 3/4 3/4) and 4*a* (0 0 0) sites, respectively, and the *X'* atoms occupy the 4*b* (1/2 1/2 1/2)

In addition to the above ternary full-Heusler compounds, there are quaternary full-Heusler compounds, *XX'YZ*, which crystallise in the *Y* structure (prototype: LiMgPdSn or LiMgPdSb, space group: *F*43 *m*). The *X*, *X'*, *Y* and *Z* atoms are situated at the 4*d*, 4*b*, 4*c* and 4*a* sites, respectively, occupying one of the fcc sublattices. It should be noted that the inverse Heusler and the quaternary full-Heusler phases are ordered phases, and any disorder among the constituent atoms causes a structural

Earlier theoretical studies demonstrated a half-metallic nature in full-Heusler compounds [7, 8]. Since then, many studies have been dedicated to investigate the electronic and magnetic properties of ternary and quaternary full-Heusler compounds. It has been revealed that full-Heusler compounds exhibit a variety of electronic properties; they exhibit the properties of semiconductors [9–18], spingapless semiconductors (SGSs) [19–26], semimetals [27–29], metals [30–34] and half-metals (HMs) [32, 35–78]. Considering the magnetic properties, they have been reported to exhibit nonmagnetism [9–11, 14–18], ferromagnetism [12, 19– 24, 30–33, 36–46, 48–58, 61–66, 68–78], ferrimagnetism [13, 30, 35, 47, 59, 60, 67] and antiferromagnetism [25, 26, 34]. The full-Heusler, inverse Heusler and quaternary Heusler compounds obey the Slater-Pauling rule [79–81]: the total spin

change; the structure changes to the B2, A2, DO3 or B32a structure.

prototype is NaTl (space group: *Fd*3*m*).

*above and below each crystal structure, respectively.*

*Magnetic Full-Heusler Compounds for Thermoelectric Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.92867*

and 4*c* (1/4 1/4 1/4) sites.

**67**

**Figure 2.**

where *T* is the absolute temperature. The product *S*<sup>2</sup> *σ* is called the power factor (PF), which is a measure of electric power generated using the TE material. To achieve high TE efficiency (standard levels for practical use are *zT* > 1 and PF <sup>&</sup>gt; <sup>2</sup> � <sup>10</sup>�<sup>3</sup> W/K<sup>2</sup> m), high *S*, high *σ* and low *κ* are required. To meet these requirements, a variety of TE materials have been explored, such as chalcogenides, skutterudites, clathrates, silicides, Zintl compounds, half-Heusler compounds and oxides [1–3]. Most of these materials are semiconductors because in general they have high *S* than metals. However, recent theoretical and experimental studies have revealed that metals, in particular, half-metallic full-Heusler compounds have relatively high *S* as well as high *σ*. In addition, their junction with a metal electrode is robust compared to that of semiconductors, which is also an advantage.

In Section 2, the crystal structures and magnetic properties of full-Heusler compounds are introduced. Sections 3 and 4 demonstrate that magnetic full-Heusler compounds are promising for the TE power generation device.
