**2. Half-metallic ferrimagnetic materials**

The cubic crystal structure of full-Heusler Zr2YZ variants exhibits two magnetic sublattices, coupled to each other. Thus, the two Zr atoms are located in tetrahedral lattice sites and interact to each other. In addition, Zr and Y atoms form a second and more delocalized magnetic sublattice. Therefore, ferrimagnetic interaction between the Zr and Y atoms is frequently reported phenomena.

The total spin-polarized density of states of a typical half metallic ferrimagnetic material exhibits in the spin-up channel a semiconducting band gap while in the spin-down channel a metallic behavior. A relevant example is illustrated in **Figure 1** for Zr2CrAl (unpublished results). The main contribution to the total density of states from spin-down channel comes from transition metal constituent elements, and these results are consistent with other published information [21].

Desirable candidates for magnetoelectronic devices, half-metallic ferrimagnetic compounds provide an unequivocal advantage over their ferromagnetic counterparts by reduction of the magnetic moment due to the ferrimagnetic interaction resulted from compensation of partial magnetic moments of the two different magnetic sublattices. This phenomenon is illustrated in **Figure 2** (unpublished results) for the Zr2CrAl compound, where one can notice the magnetic moment of Cr atoms, partially compensated by magnetic moments of Zr located in the two different sublattices and having different neighborhoods. Similar DFT outcome were reported for Zr2YZ (Y = Cr, V, Z = Al, Ga, In, Pb, Sn, Tl) [21–24].

**Figure 3** (unpublished results) exhibits the position of the Fermi level and the width of the energy gap in spin-up channel as function of the lattice parameter. According to theoretical investigations, the Zr2CrAl compound is a potential ideal candidate for spintronics, due to the presence of a steady energy gap in only one spin channel, for a large lattice parameter range.

**Table 1** summarizes the published results regarding Zr2CrZ (Z = Al, Ga, In) [21, 22]. As can be seen, the energy band gap (Eg) from spin-up channel increases as the atomic radii of Z elements increase. The ferrimagnetic interaction occurs between the zirconium atoms from both sublattice and the chromium ones, phenomena which are reflected by the opposite sign of the partial magnetic moments of Zr and Cr atoms. The total magnetic moment per f.u. for all compounds strictly follow the Slater Pauling rule described earlier.

In the ideal case of a fully compensated magnetic moment, a half-metallic ferromagnetic material would be obtained, useful to be applied in a junction device as a stable spin-polarized electrode based on spin-transfer effect.

**93**

**Figure 2.**

**Figure 1.**

*Zr2CrAl at optimized lattice parameter.*

*Zr-Based Heusler Compounds for Biomedical Spintronic Applications*

The theoretical results from in literature for Zr2VZ (Z = Al, Ga, In, Si, Ge, Sn, Pb) [23, 24] report that the most energetically favorable crystalline structure comparing with the Hg2CuTi structure has the prototype Cu2MnAl and in this configuration the materials do not present half-metallic properties. However, the Hg2CuTi type structure can be synthesized experimentally due to the negative entropy of formation. In the inverse Heusler crystalline structure, the Zr2VZ exhibits half metallic ferrimagnetic characteristics, the partial magnetic moment of Vanadium

*Partial and total density of states (PDOS and TDOS) of half-metallic ferrimagnetic Heusler compound,* 

being opposite to the one of zirconium atoms.

*Partial and total magnetic moments in Zr2CrAl Heusler compound.*

*DOI: http://dx.doi.org/10.5772/intechopen.93372*

*Zr-Based Heusler Compounds for Biomedical Spintronic Applications DOI: http://dx.doi.org/10.5772/intechopen.93372*

**Figure 1.**

*Magnetic Materials and Magnetic Levitation*

**2. Half-metallic ferrimagnetic materials**

between the Zr and Y atoms is frequently reported phenomena.

results are consistent with other published information [21].

spin channel, for a large lattice parameter range.

follow the Slater Pauling rule described earlier.

a stable spin-polarized electrode based on spin-transfer effect.

minimization.

Heusler compounds.

Pb, Sn, Tl) [21–24].

The information about the experimental preparation and electronic structure of Zr-based Heusler compounds with true half-metallic properties are still scarce. Therefore, to understand the properties of potential zirconium-based Heusler compounds, in the beginning, theoretical investigations can be performed via density functional theory (DFT). Self-consistent calculations using a "muffin-tin" model and various approximations to describe the exchange and correlation interactions can lead to valuable information about the energetically favorable crystalline structure, electronic configuration, or magnetic properties by means of the total energy

This chapter gives a comprehensive overview of the key electronic structures and magnetic properties usually found in half-metallic zirconium-based full-

The cubic crystal structure of full-Heusler Zr2YZ variants exhibits two magnetic sublattices, coupled to each other. Thus, the two Zr atoms are located in tetrahedral lattice sites and interact to each other. In addition, Zr and Y atoms form a second and more delocalized magnetic sublattice. Therefore, ferrimagnetic interaction

The total spin-polarized density of states of a typical half metallic ferrimagnetic material exhibits in the spin-up channel a semiconducting band gap while in the spin-down channel a metallic behavior. A relevant example is illustrated in **Figure 1** for Zr2CrAl (unpublished results). The main contribution to the total density of states from spin-down channel comes from transition metal constituent elements, and these

Desirable candidates for magnetoelectronic devices, half-metallic ferrimagnetic compounds provide an unequivocal advantage over their ferromagnetic counterparts by reduction of the magnetic moment due to the ferrimagnetic interaction resulted from compensation of partial magnetic moments of the two different magnetic sublattices. This phenomenon is illustrated in **Figure 2** (unpublished results) for the Zr2CrAl compound, where one can notice the magnetic moment of Cr atoms, partially compensated by magnetic moments of Zr located in the two different sublattices and having different neighborhoods. Similar DFT outcome were reported for Zr2YZ (Y = Cr, V, Z = Al, Ga, In,

**Figure 3** (unpublished results) exhibits the position of the Fermi level and the width of the energy gap in spin-up channel as function of the lattice parameter. According to theoretical investigations, the Zr2CrAl compound is a potential ideal candidate for spintronics, due to the presence of a steady energy gap in only one

**Table 1** summarizes the published results regarding Zr2CrZ (Z = Al, Ga, In) [21, 22]. As can be seen, the energy band gap (Eg) from spin-up channel increases as the atomic radii of Z elements increase. The ferrimagnetic interaction occurs between the zirconium atoms from both sublattice and the chromium ones, phenomena which are reflected by the opposite sign of the partial magnetic moments of Zr and Cr atoms. The total magnetic moment per f.u. for all compounds strictly

In the ideal case of a fully compensated magnetic moment, a half-metallic ferromagnetic material would be obtained, useful to be applied in a junction device as

**92**

*Partial and total density of states (PDOS and TDOS) of half-metallic ferrimagnetic Heusler compound, Zr2CrAl at optimized lattice parameter.*

**Figure 2.** *Partial and total magnetic moments in Zr2CrAl Heusler compound.*

The theoretical results from in literature for Zr2VZ (Z = Al, Ga, In, Si, Ge, Sn, Pb) [23, 24] report that the most energetically favorable crystalline structure comparing with the Hg2CuTi structure has the prototype Cu2MnAl and in this configuration the materials do not present half-metallic properties. However, the Hg2CuTi type structure can be synthesized experimentally due to the negative entropy of formation. In the inverse Heusler crystalline structure, the Zr2VZ exhibits half metallic ferrimagnetic characteristics, the partial magnetic moment of Vanadium being opposite to the one of zirconium atoms.

#### **Figure 3.**

*The positions of the highest occupied states from the valence band (solid rhombs) and of the lowest unoccupied states from the conduction band (solid stars) of total DOSs (spin-up channel) for Zr2CrAl as function of the lattice parameter.*


#### **Table 1.**

*Calculated lattice parameters, partial, total magnetic moments, and energy band gap in Zr2CrZ (Z = Al, Ga, In).*
