CHARACTERISTIC OF HEUSLER COMPOUND

Heusler alloys exhibit diverse characteristics depending on then compositions. The most common features of Heusler alloys are (1) half-metal, (2) semiconductor, and (3) semi-metal. Figure 9.6 demonstrates the density of states (DOS) of half-metal, a normal metal, semiconductor, and semimetal. An atomistic behavior of Heusler alloys can be analyzed by Slater Pauling rale. It is one of the necessary conditions of a Heusler alloy to examine the characteristics like metallic, semiconductor, or half-metal. It simply implies that the presence of electrons near Fermi level requires the numbers of charge earners per unit cell (Z| and Zj), where Z| signifies the number of spin-up electrons and Z refers to number spin-down electrons. Both Z and Z are integer numbers and their difference is also an integer, resulting in an integer moment (Fecher et al., 2005).

The linear behavior of the total magnetic moment with the total valence electrons is an extension of the Slater-Pauling rale (Slater, 1936; Pauling, 1938; Galanakis et al., 2006). It states that the total number of electrons is

Z_t = ZJ + ZJ in fenomagnets, where the Z, is the number of spin-up (ZJ) and spin-down (ZJ.) electrons per atom. The difference of ZJ and ZJ gives the total magnetic moment M_x = Z] - ZJ. Replacing Z| = M_x + ZJ in (M_t = Z - ZJ) results in M_t = (Z_t- 2ZJ) t/_B/atom. Magnetic behavior of Heusler compounds (half or full) can be determined (Galanakis et al., 2006). M_t = (Z, - 24) u_B/atom for the full-Heusler and M_x = (Z_t - 18) //_B/atom for the half-Heusler alloys (Galanakis et ah, 2006). Let us consider ferromagnetic full-Heusler compounds, Co₂MnAl and Fe₂VAl, whose electronic configurations are {Co:[Ar]4s²3d⁷}₂ {Mn:[Ar]4s³d⁵} {Al:[Ne]3s²3p¹} and {Fe:[Ar]4s²3d⁶}₂ {V:[Ar]4s³3d³} {Al:[Ne]3s²3p¹}, respectively.

Co₂MiiA1 will have total electrons count Z,= 9x2 + 7 + 3 = 28 around the Fermi energy (£V). Thus following the Slater Pauling’s rule of full-Heusler compound, w'e get M_x = (Z_t - 24) = 4.00 »_B/atom.

FIGURE 9.6 Schematic representation of the density of states for a half-metal compared to a normal metal, semiconductor, and semi-metal.

The finite integer value of magnetic moment is an evidence for these types of materials to exhibit half-metal ferromagnetic behavior. While in Fe₂VAl, Z_t= 8 x 2 + 5 + 3 = 24, M_t = (Z_t - 24) = 0.0 »_B/atom. The presence of magnetic moment equivalent to 0.0 ;/_B/atom gives NM behavior. Similar explanation also follows for half-Heusler compound with Slater-Pauling rule, M_x = (Z, - 18) n_B/atom. Following this mle, we have sorted out a few magnetic and noil-magnetic Heusler compounds as tabulated in Table 9.1. A selective number of Heusler compounds following the Slater-Pauling mle are also presented in Figure 9.7.

FIGURE 9.7 The expected total spin moments for the selected half-Heusler and fiill- Heusler alloys from Slater-Pauling rule. The dashed line represents the Slater-Pauling behavior (Adapted fr om Webster et al., 2006).

Half-Metal (HM)

Half-metallic behavior is reported in several materials like oxide perovskites (Ramirez, 2017) and double perovskites (Senate et al., 2007), Fe₃0₄ (Penicaud et al., 1992), and СЮ₂ (Schwarz, 1986). However, from experimental point of view the concrete proof of nearly complete spin polarization has only found in La_{2 3}SiT 3M11O3 at low temperatures (Park et al., 1998; Bowen et al., 2003). Unfortunately, all these materials show low Curie temperature below the room temperature that limits their application in technological devices. An attention has been shifted toward materials with high T_c. Heusler compound was discovered in 1903, but this material was not highlighted as an energy material almost for four decades. An important breakthrough came in 1983 when de Groot and co-workers discovered an interesting property called half-metallicity with high T_c (deGroot et al., 1984). Research on half-metallic ferromagnetic (HMF) is in progress among the family of Heusler compounds. Kubler and co-workers reported that the majority of Heusler alloys exhibit a semiconducting bandgap at the Fermi energy (£_F) in the minority spin DOS, while the majority spins are metallic. Half-metallic compounds exhibit 100% spin polarization at the Fermi level. The present day technological devices are based on the charge of an electron. For example, in memory devices like dynamic random access memory (DRAM), data are manipulated and stored as charge on capacitors. The disadvantage of charge-based electronic devices is that the information is often lost whenever the power is switched off. This inconvenience can be solved by making size compatible, faster, and reliable devices. An innovation to enslave electron spin is an additional functionality in giant magnetoresistance (GMR) (Baibich et al., 1988; Fert, 2005) in late 1980s, which utilizes the electron spin for information manipulation, storage, and transmission. Spin polarization is a method to define the quantitative degree of half-metallicity; however, a major issue is the definition of the spin polarization P. The electron spin polarization (P) at Fermi energy (£_F) of a material is defined by Soulen et al. (Soulen et al., 1998; Julliere, 1975) as:

where P ^ (^ef ) and P ^ (^ef ) are the dependent density of states at the £_F The j and J, denote the spin-up and spin-down states, respectively.

TABLE 9.1 List of Selected Heusler Alloys (Half-Metals and Semiconductors) Based on Slater-Pauling Rule.

TABLE 9.1 (Continued)

Co2MnAl: A full-Heusler compound exhibiting half-metallic (HM) behavior

After observing several works on X₂YZ series from both theoretical and experimental fronts, it is highly motivating to continue further research to explore for future techno logical applications. In this section, we have discussed the electronic and magnetic properties of Co₂MnAl, a full- Heusler alloy. Fermi level is used to analyze the electronic properties of the systems with an asymmetry of the band structure. The majority spin band is a metal (i.e., dispersed DOS at Ef), whereas the minority band has semiconducting bandgap (i.e., a bandgap at Ei). The result of metal semiconductor hybrid governs the 100% spin polarization. Therefore, the alloy will have fully spin polarized current and is vital for spin injection in spintronic devices. The presence of small DOS in the conduction band (CB) is due to five majority electrons in the Mn-d orbital. On the other hand, the majority of unfilled states are available in the conduction region mainly for minority electrons. The mechanism that leads to formation of the minority bandgap is a result of d-d hybridization among the d-block elements discussed somewhere else (Galanakis et al., 2006; Webster et al., 2006; Galanakiset al., 2005). It is known that the bandgap in the minority DOS of Co2-based Heusler compounds arises from the hybridization of d electrons of the d-orbitals of Col and Co2 atoms and as well as Y atoms sitting adjacent as shown in Figure 9.8. hi the first step, the d orbitals of each Co-Co atoms couple as a result of their symmetry that forms bonding (e_g, t_2g) and antibonding (e_u, h_u) states. In the second step, the hybridized Co-Co states interact with the d states of Mil atoms. The doubly degenerate Co d-e_g orbitals hybridize with the de_g (d_z², d_x²._y²) orbitals of the Mn-d states, giving rise to bonding and antibonding states, situated below’ and above the Fermi level, respectively. The d-t_2g Co orbitals couple with the d-t_2g (d_xy, dyx, dzx) states of the Mil atom, giving rise to a low-lying triplet t_2g state with a bonding character and a triplet antibonding t_2g above the Fermi level. The remaining antibonding states of Co orbitals (e_u and t_Ul) do not take part in the hybridization, since there are no Mn atoms with the same symmetry group thus remain non-bonded. Therefore, a real minority gap exists in the Co₂MnAl Heusler compound. The size of the gap is related to the splitting d-d hybridization of Co-Co interaction, hi the above discussion, the A1 atom has negligible contribution. Al atom helps in positioning the Fermi level within the minority band gap. However, the s and p orbitals have significant role in the distribution of electrons in various distinguishable symmetry states (t_2g and e_g) at Co and Mn sites (Kandpal et al., 2006). This will give an importance not only in stabilizing the L2i structure, but also to predict the magnetic moments at the Co and Mn sites.

FIGURE 9.8 Schematic illustration of the origin of the minority bandgap in XiYZ Heusler compounds.

The presence of low-lying s and p states does not contribute directly in the foimation of the minority bandgap. These states contribute in counting the total number of elections of occupied and empty states. The energy bands were plotted for Co₂MnAl for both the spin channels as shown in Figure 9.9. For spin up, the Co₂MnAl alloy is a metal in which the majority bands (spin up) crosses the Fermi level (£_F) in rather all higher symmetries. On the other hand, the minority bands (spin down) show a bandgap, the transition is along the highest energies of occupied band at Г and the lowest unoccupied band lies at the X. This gives an indirect energy bandgap of -0.70 eV along Д direction. The partial DOS of each atom are also presented in Figure 9.10. From Figure 9.10 (a-d), it is clear that the effect of Mn-atom is more prominent than Co atom in creating the bandgap in spin down channel.

FIGURE 9.9 Half-metallic full-Heusler compound (C02M11AI) with spin up band structure (left), total DOS (middle), and spin down band structure (right).

FIGURE 9.10 DOS plots of C'OiMnSn. (a) Co (d, d„) and Mil (d, d._g) states in spin up; (b) Co (d, d_e„) and Mn (d, d„) states in spin down; (c) Co (d, d_ti_g) and Mn (d, d,2_g) states ш spin up and (d) Co (d, d^) and Mn (d, d,2_g) states in spin down.

TABLE 9.2 Total and Partial Magnetic Moments.

Application ofHM Heusler Alloy in Spintronic Devices

The spin-based electronics that manipulate the election spin degree of freedom is termed as spintronic, where the spin of an electron is tuned by an applied magnetic field that orients the spin for polarization. These polarized electrons are used to control the electric current. The ultimate goal is to develop a device that utilizes the spin of an electron. Once the spin functionality is added, it will provide significant versatility to future electronic products. Magnetic spin properties of electrons are used in many applications such as giant magnetoresistance (GMR), tunneling magnetoresistance (TMR) (Mathon et al., 2001; Ikeda et al., 2008), magnetic memory (MRAM) (Sbiaa et al., 2011; Bhatti et al., 2017) etc. Materials that undergo phase transition from semiconductor to ferromagnetic above room temperature are potential for a new generation of spintronic devices with enhanced electrical and optical properties. The field of spintronic revolutionized the digital world at post discovery of GMR effect (Baibich et al., 1988; Fert, 2005), and this discovery was the Nobel Prize winning work. The GMR effect occurs due to alignment of the spin of electrons with the applied magnetic field that includes the variation in the resistance of a material. A schematic component of spintronic is presented in Figure 9.11.

FIGURE 9.11 Spintronic and its components.

GMR is a quantum mechanical effect of magnetoresistance observed in multilayer composites of alternating ferromagnetic and non-magnetic layers as shown in Figure 9.12(a). The impact is to see a noteworthy change in the electrical resistance that relies on the magnetization of the nearby ferromagnetic layers whether they are in a parallel or an antiparallel arrangement. The overall resistance is moderately low for parallel arrangement and generally high for antiparallel arrangement. The direction of magnetic polarization can be controlled by applied magnetic field. The impact relies upon the scattering of electrons on the spin-polarization. TMR is upgradation of spin-valve GMR, in which electrons are incident perpendicular with their spins orientation on layers separated by a thin insulating tunnel barrier (replacing the magnetic layer) as shown in Figure 9.12 (b). This permits to accomplish bigger impedance, a bigger magnetoresistances at negligible temperature. TMR has now outclassed GMR in MRAMs and disk drives, specifically for high surface densities and recording.

The mam application of GMR sensor is to read data in hard disk drives, biosensors, micro-electro-mechanical systems (MEMS) (Bhatti et al., 2017) and magneto-resistive random-access memory (MRAM) that stores one bit of information is shown in Figure 9.12 (c). The magnetic memory is based on the storage of spin orientations. The p-type layer depleted in the p-n junction when negative voltage is applied, defonning the spin orientation. This state can be taken as '‘0” bit or erase memoiy cell. When the voltage is removed.

the concentration of the holes increases. A quantum coupling effect between the holes and the magnetic atom creates the spin alignment. This state can be considered as “1” bit or writes memory cell. The memory devices are equipped with a magnetic sensor etched with layers in the semiconductor. The supersensitive sensor detects the state of magnetization, which exists or not is determined by the device’s potentiality as a read memory.

FIGURE 9.12 (a) Schematic diagram of GMR with multilayer structure consisting of ferromagnetic Heusler alloys and semiconducting spacers, (b) Structure of TMR with insulating middle layer between two ferromagnetic Heusler alloys align parallel and antiparallel, (c) Orientation of electron spin in magnetic memory with representation of “0” and “1” bit with respect to electron spin. (Reprinted adapted a) Liu, et al, 2015. b) Inomata, nd. c) Urbaniak. nd.)