Heusler alloys are a class of intermetallic compounds that have a stoichiometric composition of X2YZ (also known as Full-Heusler structure), where atoms X and Y are transition metals or lanthanides, and atom Z belongs to main group elements. Periodic table in Figure 1 presents the most common Heusler alloy elements. Heusler alloys are named after German chemist Friedrich Heusler, who discovered the group of alloys in 1903. Heusler alloys are still actively studied due to their wide range of chemical and physical properties, many of which have been discovered in 1980s after the discovery of Heusler alloys' half-metallic nature.
Figure 1. Periodic table of typical elements present in X2YZ heusler alloys. (Figure: Joona Pekkanen, inspired by reference)
Classification and structure
Heusler alloys can be classified into several different categories according their chemical structure. Even though these subclasses are based on Full-Heusler alloys, they exhibit different compositions and crystal structures, which also provide unique properties for these materials. Overall, Heusler alloys can be divided into three main classes: full-Heuslers, inverse-Heuslers, and half-Heuslers. In addition to these ternary Heusler structures, Heusler alloys also cover binary and quaternary Heusler structures.
Full-Heusler compounds are the base of Heusler alloys with complete Heusler structure X2YZ (2:1:1). Full-Heusler alloys exhibit face-centered cubic (FCC) crystal structure with space group Fm-3m (225), and they have four interpenetrating FCC lattices. Two of these lattices are occupied by the X atoms at position (¼, ¼, ¼). Y atoms occupy position (½, ½, ½) and Z atoms position (0, 0 ,0).  Face-centered cubic lattice of full-Heusler alloy Cu2MnAl is presented in Figure 2.
Figure 2. Face-centered cubic lattice of full-Heusler Cu2MnAl. (Figure: Joona Pekkanen, data ICSD #57695)
Inverse-Heuslers are derived from full-Heuslers and hence have the same chemical composition X2YZ (2:1:1) as full-Heuslers, but their structure is inversed as the name proposes. In the crystal structure of inverse-Heuslers, the transition metal atoms occupy the tetrahedral sites, as the main group elements locate in the octahedral sites. Inverse-Heusler compounds also crystallize in face-centered cubic lattice, however their space group F-43m (216) differs from full-Heusler compounds. Inverse-Heusler structure of Ti2MnAl is presented in Figure 3.
Figure 3. Face-centered cubic lattice of inverse-Heusler Ti2MnAl. (Figure: Joona Pekkanen, data ICSD #29682)
Half-Heuslers are Heusler alloys with chemical composition of XYZ (1:1:1). The half-Heusler compounds exhibit covalent and ionic parts, as the structure is missing on of the X atoms. Therefore, half-Heusler structure is also non-centrosymmetric. Like the inverse-Heuslers, half-Heuslers also exhibit face-centered cubic crystal structure with space group F-43m (216). Half-Heusler structure of NiMnSb is presented in figure 4. More information about half-Heuslers can be found from page Half-Heusler phases.
Figure 4. Face-centered cubic lattice of half-Heusler NiMnSb. (Figure: Joona Pekkanen, data ICSD #643108)
Binary and Quaternary Heuslers
The three before mentioned main Heusler classes, full-, inverse-, and half-Heuslers are all ternary classes. In addition to these, Heusler alloys are sometimes extended to binary and quaternary structures. These structures are caused by structural variations and chemical substitutions. Even though the structure starts to move further from the classical full-Heusler structure, they are important part of Heusler alloy research due to their interesting properties and possibilities in future semiconductor industry. Binary Heuslers have chemical composition of X3Z for example Fe2In, and they exhibit face-centered cubic structure and space group Fm-3m (225). Quaternary Heuslers then again have two different X atoms from transition group in the structure, forming chemical composition of XX'YZ, for example CoFeMnSi. Quaternary Heuslers exhibit face-centered cubic structure with space group F-43m (216). As can be noticed, binary Heuslers exhibit same structural composition as full-Heuslers, while quaternary Heuslers follow the structure of half- and inverse-Heuslers.
Heusler alloys have huge potential in future technology applications due to their extensive properties. This chapter briefly discusses some of the most interesting properties found amongst Heusler alloys.
One of the most significant steps in Heusler alloy research was the discovery of their half-metallic character. Half-metallicity is a feature of a material, which makes it possible for the substance to act as a conductor for one electron spin orientation, while acting as a semiconductor or insulator for the opposite spin orientation. This half-metallic gap is caused by the band structure of the material, as there's an overlapping in the minority spin valence band and majority spin conduction band, which is not existing in reverse side. Band structure of Full-Heusler Cr2MnSb is presented in figure 5. In the figure, overlapping band structure with spin-up orientation (a) is clear, while the energy gap remains in place on the spin-down orientation (b).  Therefore, half-metallic materials are often classified as hybrid materials, falling between semiconductors and metals. Many Heusler alloys exhibit half-metallic character, and therefore, they are actively researched for example for future spintronic applications.
Figure 5. The band structure of full-Heusler Cr2MnSb, (a) spin-up orientation, (b) spin-down orientation.  (License: CC BY 4.0)
Ferromagnetism was one of the first researched properties of Heusler alloys. Ferromagnetism isn't the most common property of a material, and it's typically associated with only few elements, including iron, cobalt, nickel and some of their alloys. Therefore, discovery of ferromagnetism in Heusler alloys, such as Cu2MnAl, where none of these before mentioned elements is present, has driven the research of Heusler alloys for a long time. Some Heusler alloys also exhibit ferromagnetic shape-memory effect, which has led to further research of Heusler alloys' magnetic properties. Later also antiferromagnetism was found in Heusler alloys. In ferromagnetic material, the adjacent ions align themselves to oppose each other, resulting in zero magnetic effect. Heusler alloys' extensive magnetic properties depend strongly on, local geometry or their chemical composition.
Heusler alloys have also interesting thermal properties as some Heusler alloys exhibit caloric effect. Caloric effect is defined as an adiabatic temperature change or an isothermal entropy change, which is caused by external stimulus applied to the substance. Some Heusler alloys are known to exhibit magnetocaloric effect, mechanocaloric effect and some even multicaloric effect. As suggested by the name, in magnetocaloric effect the Heusler alloy's temperature changes due to external magnetic force. Magnetocaloric properties of Heusler alloys is studied for energy-efficient solid-state refrigerants. Especially Ni-Mn-In -based Heusler alloys are showing promising marks on the field. Mechanocaloric effect then again occurs when the substance is subjected to external mechanical stress. Combination of these two effects, is highly interesting topic in amongst scientists due to the amplifying factor the two effects have on each other. For example on research conducted on Ni-Mn-In-Co alloy, its hysteresis reduced significantly, when substance under pressure was brought into varying magnetic field, resulting in enhanced solid-state cooling power. Overall, the research of multicaloric effect on Heusler alloys dates back to the start of 2000s, so there is still loads to discover.
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