**4. Half-metallic ferromagnetic materials**

Ferromagnetic zirconium-based half-metallic Heusler compounds represent another category of materials of specific interest in biomedical spintronic applications where a good response to an external magnetic moment is required and that is mainly related to their large total magnetic moment. From theoretical point of view, the materials which exhibit a metallic character in the majority density of states and a band gap in the minority one, around the Fermi level and the metallic total density of states resulted from summation of partial density of states of all elements are classified as half-metallic ferromagnets.

A typical example of density of states for a half-metallic ferromagnet is exemplified in case of Zr2CoAl [30–34] (see **Figure 8**). In the majority channel, the significant contribution to density of states comes from the zirconium, located in the origin of unit cell and the cobalt atom. The band gap from minority channel (**Figure 9**) is formed between the 3d t2g electrons of Co and the 4d t2g unoccupied electrons of Zr located in origin and 4d t2g occupied Zr electrons locate in the 4c Wyckoff position of Hg2CuTi prototype structure. This type of hybridization between the Y element and the two X atoms of a X2YZ Heusler compounds is often reported for half-metallic ferromagnets.

In general, the half metallic ferromagnetic properties characterized by the presence of a semiconducting band gap in the minority spin channel of density of states continue to be maintained for a large enough range of lattice parameter in order to be stable from experimental point of view. This means that even if the unit cell volume increases or decreases the material would present a high spin polarization typical for half metallic materials. In case of Zr2CoAl, the transition from metal behavior to half metallic characteristic occurs at a 6.43 A lattice parameter, and it remains stable at experimentally achievable increases of unit cell volume (**Figure 10**) [30–34]. By definition, in the case of a ferromagnetic material, a net magnetization may be measurable because even if the majority and minority density of states is identical and equally occupied; these are shifted against each other. The total magnetic moment is obtained by adding the partial magnetic moments of constituent elements as presented in **Figure 11**.

**Table 3** overviews the state of the art ferromagnetic zirconium-based Heusler compounds. Most alloys incorporate cobalt, and the main elements carry an irrelevant partial magnetic moment. However, the influence of main elements over the energy band gap from spin-down channel is significant. The average width of band gap from spin-down channel is large enough to provide stable half-metallic characteristics for a large deformation of the unit cell. All results

#### **Figure 8.**

*Partial and total density of states (PDOS, TDOS) of half-metallic ferromagnetic Heusler compound, Zr2CoAl, at optimized lattice parameter.*

**99**

**Figure 9.**

**Figure 10.**

**Figure 11.**

*Zr2CoAl Heusler compound.*

*at equilibrium lattice parameter.*

*Zr-Based Heusler Compounds for Biomedical Spintronic Applications*

gathered in **Table 3** are obtained based on density functional theory calculations, and these are influenced by the pseudo-potential used for electron-ionic core interaction. This is the reason for various reported band gaps of such compounds, as for example, the band gap reported by Ref [32] which is lower

*The partial and total magnetic moments as a function of lattice constant for half-metallic ferromagnetic* 

*The band structure of Zr2CoAl for majority and minority spin channel, in the right and left panel, respectively,* 

*The positions of highest bonding states from the valence band (solid purple rhombs) and of lowest anti-bonding states from conduction band (solid magenta stars) of total DOSs for Zr2CoAl as function of lattice constants.*

*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 9.**

*Magnetic Materials and Magnetic Levitation*

reported for half-metallic ferromagnets.

constituent elements as presented in **Figure 11**.

electrons of Zr located in origin and 4d t2g occupied Zr electrons locate in the 4c Wyckoff position of Hg2CuTi prototype structure. This type of hybridization between the Y element and the two X atoms of a X2YZ Heusler compounds is often

In general, the half metallic ferromagnetic properties characterized by the presence of a semiconducting band gap in the minority spin channel of density of states continue to be maintained for a large enough range of lattice parameter in order to be stable from experimental point of view. This means that even if the unit cell volume increases or decreases the material would present a high spin polarization typical for half metallic materials. In case of Zr2CoAl, the transition from metal behavior to half metallic characteristic occurs at a 6.43 A lattice parameter, and it remains stable at experimentally achievable increases of unit cell volume (**Figure 10**) [30–34]. By definition, in the case of a ferromagnetic material, a net magnetization may be measurable because even if the majority and minority density of states is identical and equally occupied; these are shifted against each other. The total magnetic moment is obtained by adding the partial magnetic moments of

**Table 3** overviews the state of the art ferromagnetic zirconium-based Heusler

*Partial and total density of states (PDOS, TDOS) of half-metallic ferromagnetic Heusler compound, Zr2CoAl,* 

compounds. Most alloys incorporate cobalt, and the main elements carry an irrelevant partial magnetic moment. However, the influence of main elements over the energy band gap from spin-down channel is significant. The average width of band gap from spin-down channel is large enough to provide stable half-metallic characteristics for a large deformation of the unit cell. All results

**98**

**Figure 8.**

*at optimized lattice parameter.*

*The band structure of Zr2CoAl for majority and minority spin channel, in the right and left panel, respectively, at equilibrium lattice parameter.*

#### **Figure 10.**

*The positions of highest bonding states from the valence band (solid purple rhombs) and of lowest anti-bonding states from conduction band (solid magenta stars) of total DOSs for Zr2CoAl as function of lattice constants.*

#### **Figure 11.**

*The partial and total magnetic moments as a function of lattice constant for half-metallic ferromagnetic Zr2CoAl Heusler compound.*

gathered in **Table 3** are obtained based on density functional theory calculations, and these are influenced by the pseudo-potential used for electron-ionic core interaction. This is the reason for various reported band gaps of such compounds, as for example, the band gap reported by Ref [32] which is lower


*h Ref [37]. i Ref [21].*

#### **Table 3.**

*Calculated lattice parameters, partial, total magnetic moments, and energy band gap in Zr2YZ (Y=Co, Ni; Z = Al, Ga, In, Si, Ge, Sn, Pb).*

than the other published results. In all compounds, the ferromagnetic interaction between constituent atoms is represented by similar signs of the partial magnetic moments. The total magnetic moments, following Slater-Pauling curve, are higher than for ferromagnetic half-metallic compounds, and as consequence, the compounds may present a better response to an external magnetic field. Theoretical results regarding zirconium-based half-metallic compounds containing nickel provide information about electronic structures and magnetic properties in alloys with Al and Ga. These intermetallic compounds theoretically behave like half-metals from the electronic structure point of view; however their reported total magnetic moments do not follow the Slater Pauling curve.

**101**

*Zr-Based Heusler Compounds for Biomedical Spintronic Applications*

In addition, the band gap from spin-down channel is significant lower than for

The individualized medicine and high precise diagnosis can benefit from the development of smart biosensors based on magnetic functionalities. Foreseeable applications of zirconium-based biosensors with half metallic character include the capability to measure, sense, or respond to magnetic stimuli desirable for in vivo

This chapter overviewed the recent advances of zirconium-based full-Heusler compounds from the point of view of electronic structure and magnetic properties. The representative materials described in this chapter obviously were selected to offer significant information to emphasis the certain differences in magnetic features: half-metallic ferrimagnetism, spin-gapless semiconducting, and half-metallic ferromagnetism. Based on this, the Y elements of Zr2YZ were selected from the most commonly used transition metals (Cr, Mn, and Co), while the Z element was identical in all compounds (Al). The purpose was to underline the influence of d electrons of Y elements and hybridization interaction between the electrons of zirconium and Y atoms over the macroscopic

Furthermore, the theoretical and experimental advances in designing and fabrication technology engage the construction of innovative materials to be integrated in biosensors with significant high throughput able to reform the

We acknowledge the fruitful discussions with Dr. P. Palade. This work was supported by grants of the Romanian Ministry of Research and Innovation, CCCDI – UEFISCDI, project number PN-III-P1-1.2-PCCDI-2017-0062 contract no 58 and project number PN-III-P1-1.2-PCCDI-2017-0871 contract no 47 as well as by the

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

sensitive detection of markers for diseases.

compounds incorporating cobalt.

**5. Conclusion**

magnetic properties.

biomedical field.

**Acknowledgements**

core program at NIMP.

In addition, the band gap from spin-down channel is significant lower than for compounds incorporating cobalt.
