# Structural and magnetic properties of half-heusler alloys NiCrZ (Z = Si, P, Ge, As, Te): First principle study.

###### Abstract

We present a first principle study of new class of high- half-heusler ferromagnets NiCrZ (Z = Si, P, Ge, As, Te). The structure and magnetic properties are investigated through the calculation of the electronic structure, equilibrium lattice constant, magnetic exchange interaction and Curie temperature . The role of -elements and the influence of lattice expansion/compression are also studied. In alloys having 20 valence electrons, a pseudo-gap of the majority band can be formed at Fermi level. Otherwise, the half-metallicity and ferromagnetism at temperatures much higher than room temperature are found to be stable in a wide range of lattice expansion. Based on these results, NiCrZ can be expected to be promising materials for spintronics.

To exploit the great potential of spintronics, seeking for new magnetic materials and half metallic ferromagnets is one of the most important issues in materials physics. Half metallic ferromagnets, whose the electronic structure behaves like metals w.r.t the electrons of one spin direction and like semiconductors w.r.t. the spins in the opposite direction, have the extreme spin polarization at Fermi level and can achieve the ferromagnetism at temperatures higher than room temperature.

Since the pioneer work on the half-metallicity in half-heusler alloy NiMnSb by de Groot and collaborators groot () in 1983, heusler and half-heusler alloys have been attracted great attention in both theoretical and experimental study. Especially, the family of half-heusler alloy XYZ (X and Y are transition metals, and Z is an valence element), has been one of the most interested compounds webster (); galanakis (); han (); soulen (); bowen (); nanda (); an () due to the possibility of half-metallic ferromagnetism being achieved. Besides the extreme spin polarization has been verified han (); soulen (); bowen (), the ferromagnetism in the half-Heusler NiMnZ at temperatures ranging between 500K and 730K has been reported for Z= Pd, Pt and Sb webster () by experiments. Theoretically, the first principle study has predicted the half-metallic character in their electronic structure of many half-heusler alloys such as FeMnSb, CoMnSb and FeCrSb, etc. galanakis (); nanda (). Recently, the half-metallic ferromagnetism with very high Curie temperature () in a new class of half-heusler alloys NiMnZ (particularly, K for NiMnSi) has been predicted an (). Also, the half-metallic ferromagnetism with higher than room temperature can be expected even if Cr replace Mn in NiMnZ.

In this Letter, based on the first principle study of the structural and magnetic properties of NiCrZ (Z = Si, P, Ge, As and Te) we propose a new class of high- half-metallic ferromagnets. For this aim, we have carried out the calculation as follows. First, we perform the total energy calculation to evaluate the equilibrium lattice constant (ELC) by means of the generalized gradient approximation (GGA) within the framework of ultrasoft pseudo-potential (UPP) (thanks to STATE-Senri) and both of the muffin-tin (MTA) and atomic sphere approximations (ASA) within KKR-LSDA (thanks to AKaiKKR). Using ELC, we next calculate the density of states (DOS), magnetic exchange interaction between magnetic sites. Finally, using as the input data we calculate by employing three statistical approaches: mean field approximation (MFA), random phase approximation (RPA) and Monte Carlo simulation (MC).

Half-heusler alloys NiCrZ have structure. The study of structural property nanda (); an () shows the most stable configuration of NiYZ should be in phase (except Z being a lighter -element such as C and N) with Ni being located in the octahedral coordinated pocket (), Y at (), an -element Z at the body center () and a vacant site at . Ni atom possesses 10 valence electrons and Cr has 6 electrons. Therefore, the numbers of valence electrons per formula unit are 20, 21 and 22 corresponding to -elements of group IV, V and VI, respectively. Regarding to ”rule of 18” of the half-heusler alloys , the total magnetic moment of NiCrZ should be 2, and corresponding to Z of the groups IV, V and VI, respectively.

Alloy | |||
---|---|---|---|

NiCrSi\̇hfil10.2714 | 10.3243 | 10.4450 | |

NiCrP | 1̇0.2622 | 10.3823 | 10.5390 |

NiCrGe\̇hfil10.4521 | 10.5523 | 10.6652 | |

NiCrAs\̇hfil10.5631 | 10.6310 | 10.7966 | |

NiCrTe\̇hfil– | 11.5116 | 11.7980 |

Table 1 shows ELC calculated by means of three approximations: GGA within framework of UPP, MTA and ASA within LSDA. As can be seen from Tab. 1, MFA gives the lattice constant larger than ASA and UPP, whereas UPP gives the smallest one. However, the deviation between , and is considerably small (% for NiCrSi). In general, the lattice constant is larger if the atom radius is larger. However, UPP gives of NiCrP smaller than NiCrSi. Referring to the case of NiMnZ an (), we can also expect that the real lattice constant of NiCrZ might be arranged in the range from to .

The left panel of Fig. 1 illustrates DOS of the typical alloys standing in the compounds which possess the different numbers of valence electrons. The DOS of three alloys possessing 20 valence electrons (NiCrSi), 21 valence electrons (NiCrAs) and 22 valence electrons (NiCrTe) are plotted. The change of the electronic structure w.r.t the lattice constant is shown in the right panel for NiCrAs as a representative case. In addition, it should be noted that NiCrZ alloys with Z = Sn, Sb, Se and S are metals at ELC. Furthermore, NiCrZ with Z being an element of group IV exhibits a pseudo-gap of the majority band at in UPP calculation, and its electronic structure shows the low spin behavior at ELC but the high spin picture at sufficiently larger (about 0.5% larger than ELC).

As seen from the left panel of Fig. 1, while almost states of states of Ni concentrate at lower energies (in valence band) and are occupied, the states of Cr are distributed at both of the lower and higher energies and strongly polarized. The majority spin states of Cr distribute at the lower energies and are almost occupied. These states hybridize with states of Ni (and of Z elements) to form a band at . The minority spin states of Cr shift to the higher energies and are unoccupied, leading to the gap (that falls into) being formed in the minority band and the half-metallic character. For alloys possessing 21 valence electrons, Mn- states in the majority gap split into two bands and , and lies at the vary narrow valley which is formed between these bands. Moreover, while the half-metallic character is obvious in DOS calculated by LSDA, GGA combined in UPP gives a very narrow pseudo-gap at in the majority band of NiCrGe and NiCrAs, and the half-metallic behavior might be disappeared. The calculated total magnetic moment of NiCrSi is exactly in consistence with ”rule of 18”. Similarly, we have also obtained the half-metallic behavior of the remaining alloys NiCrZ (Z = P, Ge, As, Te) and the total magnetic moment of for Z of group IV and for Z of group V at , and (except NiCrGe and NiCrAs at . See also Tab. 2), and for Te at and .

To study the influence of the lattice expansion (or compression), we draw the DOS of NiCrAs at three different ELC in the right panel of Fig. 1. LSDA (black line) and GGA (blue line) calculations are given. Since the minority states of Cr- electrons in GGA result is shifted toward the higher energies while the majority band is mostly kept unchanged, the minority gap in GGA is wider than LSDA. For NiCrAs, the half-metallicity is destroyed at . As the lattice constant decreases, shifts toward the conduction band, the half-metallicity becomes more stabilized; however, the half-metallicity can be destroyed if is smaller than the threshold value at which falls into the conduction band. Except NiCrAs and NiCrGe whose the half-metallicity might be destroyed at , our calculation shows that the proposed alloys preserve the half-metallicity in a wider range of the expansion (compression) of the lattice cells.

To investigate the ferromagnetism in NiCrZ alloys, we calculate the magnetic exchange interaction at three values of ELC. The exchange interaction between two impurities at and sites, which are embedded in the ferromagnetic medium, is efficiently calculated by utilizing the magnetic force theorem. The frozen potential approximation oswald () is employed and Liechtenstein formula liech () is used for evaluation of . of NiCrZ at is illustrated in Fig.2. For alloys with , the magnetic exchange interaction is ferromagnetic at the , and nearest neighbors, but anti-ferromagnetic for the and nearest neighbor pairs. For , is ferromagnetic for the , and nearest neighbor pairs. Similar to NiMnZ an (), becomes ferromagnetic at distances up to the nearest neighbors for . Thus, with and becomes larger with increasing . For NiCrTe, due to the larger distance between atoms, becomes remarkably smaller than that of the other half-heusler alloys.

In order to study the volume expansion effect on the magnetic exchange interaction as well as , we demonstrate the change of versus the lattice expansion in Fig. 3. of the typical half-heusler alloys corresponding to and is calculated for the nearest neighbor pairs at lattice constants (circles), (squares) and (triangles). Generally, of all alloys decreases with increasing . of alloys possessing 21 valence electrons increases with , whereas of alloys with and decreases. Since the dominant contributions to come mostly from the nearest neighbors at short distances (say, at the and neighbor pairs), of alloys with and 22 actually decreases with . For NiCrP, can slightly increases in the range from to because the considerably increases, but since ’s change according to an increase of at the range of larger is very small whereas becomes more anti-ferromagnetic, decreases for .

Alloy | ||||
---|---|---|---|---|

NiCrSi | 778 | 606 | 634 | |

() | 758 | 591 | 615 | |

605 | 477 | 493 | ||

NiCrGe | 669 | 562 | 550 | |

() | 587 | 465 | 470 | |

NiCrP | 974 | 777 | 805 | |

() | 992 | 784 | 810 | |

953 | 739 | 782 | ||

NiCrAs | 1044 | 808 | 858 | |

() | 1025 | 785 | 829 | |

NiCrTe | 665 | 588 | 605 | |

() | 601 | 544 | 562 |

After calculating , the calculation of is carried out by three statistical approaches: the Monte Carlo simulation , the mean field approximation (, where is Boltzmann constant), and the random phase approximation hilbert (); bouz () (, where is the Fourier transform of the exchange parameter ). Using , we evaluate . To perform MC simulation, the Metropolis algorithm binder () is applied to calculate the thermal average of the magnetization and its powers. Then, the cumulant crossing method proposed by Binder binder () is employed and the fourth order cumulant is calculated as a function of temperature for different cell sizes (, and conventional fcc cells) to find the universal fixed-point at . Obtained results are shown in Tab. 2.

It should be emphasized that with a similar method our theoretical (745K) of NiMnSb an () is in very good agreement with the experimental result (K) webster (). Similar to the case of NiMnZ an (), MFA overestimates even at 100% magnetic atoms, whereas RPA underestimates. As usual, the MC simulation gives the between values obtained by RPA and MFA at the same lattice constant. As expected, of all alloys is higher than room temperature and arranges from 858K to 550K (at ). The lowest corresponds to NiCrGe with K at . The highest (K at ) corresponds to NiCrAs and the next are NiCrP (805K), NiCrSi (634K) and NiCrTe (605K). It is noted that, obtained here is calculated based on the electronic structure within KKR-LSDA. GGA combined in UPP shows a pseudo-gap in the majority band of NiCrZ which possesses 20 valence electrons; hence, UPP calculation will shows a lower for NiCrGe and NiCrSi. Except NiCrAs and NiCrGe whose the half-metallicity is considerably sensitive with an increase of the lattice constant because of closed to the valence band edge, the half-metallicity in the remaining alloys can be preserved when varies in the range of .

In summary, we have investigated the structure and magnetic properties of the half-heusler alloys NiCrZ (Z = Si, P, Ge, As, Te). The phase stability is considered. The ELCs are predicted by three approximations within the pseudo-potential method and KKR-LSDA as well. Using the obtained equilibrium lattice constants, the magnetic exchange interaction is calculated and then the evaluation of is performed by employing MFA, RPA and Monte Carlo simulation. The volume dependence of the electronic structure and magnetic exchange interaction as well as are also discussed. Following the obtained results, we propose a new half-metallic high- half-heusler alloys NiCrZ (Z = Si, P, Ge, Te) whose half-metallicity can be preserved in a wide range of lattice expansion.

Acknowledgements

This research was partially supported by a Grant-in-Aid for Scientific Research in Priority Areas ”Quantum Simulators and Quantum Design” (No. 17064014) and ”Semiconductor Nanospintronics,” a Grand-in-Aid for Scientific Research for young researchers, JST- CREST, NEDO-nanotech, the 21st Century COE, and the JSPS core-to-core program ”Computational Nano-materials Design.” We are grateful to Prof. H. Akai and Prof Y. Morikawa (Osaka Univ.) for providing us with the first principle calculation packages.

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