Abstract:
Density functional theory calculations using the pseudopotential-plane-wave approach are employed to investigate the structural and magnetic properties of epitaxial CrAs thin films on GaAs001. Motivated by recent reports of ferromagnetism in this system, we compare zinc-blende CrAs films continuing the lattice structure of the GaAs substrate and CrAs films with a bulklike orthorhombic structure epitaxially matched to three units of the GaAs001 lattice. We find that even for very thin films with three Cr layers the bulklike crystal structure is energetically more favorable than zinc-blende CrAs on GaAs001. CrAs films with orthorhombic structure, even if under epitaxial strain, preserve the antiferromagnetic order of CrAs bulk. In the light of our calculations, it appears likely that the magnetic hysteresis loop measured in ultrathin CrAs/GaAs001 films originates from uncompensated antiferromagnetic moments near the CrAs/GaAs interface. In conclusion, our results do not support earlier proposals that thick CrAs films could be employed as perfectly matched spin-injection electrode on GaAs.
As bulk material, CrAs forms orthorhombic crystals with the MnP structure that can be envisaged as a simpler NiAstype crystal structure in which Cr atoms are alternately displaced in opposite directions. In this phase, CrAs shows antiferromagnetic AF behavior, and its spin structure has been described as a double helix.13 Hence, bulk CrAs is not very attractive for spintronics. The use of CrAs for spin injection relies crucially on the modification of its magnetic and/or structural properties in epitaxial films. However, from the theoretical point of view, first-principles studies indicate that ZB binary half metals are rarely stabilized by coherent epitaxy. Xie et al.14 compared density functional total energies of the bulk 3d transition-metal chalcogenides in ZB and NiAs-type structures and found a rather high energy for the metastable ZB CrAs. Zhao et al.15 performed a more accurate comparison, taking into account the tetragonal distortion in the films induced by the substrate. They compared the total energies of the tetragonally distorted bulk ZB and the NiAs structure of six binary alloys including CrAs and looked for the critical lattice parameter after which the tetragonally distorted ZB structure becomes more stable. They concluded that there is no such transition in CrAs, and CrSe is the only alloy for which the transition to a ferromagnetic ZB structure is thermodynamically favorable for an epitaxially strained film. These findings cast some doubt on the claimed ZB structure of CrAs films. Moreover, the magnetic moment in half-metallic ZB CrAs is calculated to be 3 B Ref. 16 while the values derived from the experimental saturation magnetization are markedly lower.
BULK CrAs
The stable ground state structure of bulk CrAs is an MnP-type orthorhombic lattice space group Pnma with a double-spiral antiferromagnetic spin structure along the c axis.13 In this structure, both Mn and As atoms are sitting on the 4c Wyckoff positions: x, 1 4 ,z, −x, 3 4 ,−z, 1 2 −x, 3 4 , 1 2 +z, 1 2 +x, 1 4 , 1 2 −z. It is evident from Fig. 1 that the MnP-type structure is a slightly distorted NiAs-type structure. Since the distortions in thin films and in bulk could be different, both structures were included in our search for the stable state of the CrAs alloy. In the MnP-type lattice MP, compared to NiAs-type NA, the Cr2 and Cr3 atoms move toward each other, leading to substantial change in the magnetic state of the system will be shown below. In the MP ground state, CrAs has a noncollinear spin structure in which all Cr magnetic moments are in the xy plane and the angles between them are: Cr1,Cr2 = Cr3,Cr4 =−120° and Cr1,Cr4 = Cr2,Cr3 = 183°.13 Thus, CrAs shows antiferromagnetic behavior. In this work, we restrict ourselves to collinear magnetic structures, as the energy differences due to noncollinear structures are expected to be small. Approximating all angles by 180° leads to the collinear structure closest to the real ground state of CrAs. In Fig. 2 this structure, called AFh, is shown along with other possible collinear antiferromagnetic states for both the MP and NA crystal structure. In addition to these antiferromagnetic states we have also studied the FM state of MP and NA structures, as well as the AF and FM states of the ZB lattice. In the following, two sets of calculations are performed for all these states: calculations with full structural optimization, and calculations where epitaxial constraints are applied.
In the fully optimized calculations all lattice parameters and internal atomic positions were relaxed to find out the theoretical ground state of the system. By fitting the BirchMurnaghan equation of state to the obtained total energies as a function of volume, structural properties of the systems were determined. The results are listed in Table I. The corresponding energy-volume curves are also shown in Fig. 3. It is observed from Table I that MP-AFh is the most stable among the states considered. This is in agreement with the experimental ground state. Theoretical lattice constants in this state are also close to the experimental values, indicating small influence of the noncollinear magnetic state of CrAs on its structural parameters. The MP-AFx state does not appear in Table I because this system, during structural relaxation, changes to the NA-AFx state.
BULK CrAs
The stable ground state structure of bulk CrAs is an MnP-type orthorhombic lattice space group Pnma with a double-spiral antiferromagnetic spin structure along the c axis.13 In this structure, both Mn and As atoms are sitting on the 4c Wyckoff positions: x, 1 4 ,z, −x, 3 4 ,−z, 1 2 −x, 3 4 , 1 2 +z, 1 2 +x, 1 4 , 1 2 −z. It is evident from Fig. 1 that the MnP-type structure is a slightly distorted NiAs-type structure. Since the distortions in thin films and in bulk could be different, both structures were included in our search for the stable state of the CrAs alloy. In the MnP-type lattice MP, compared to NiAs-type NA, the Cr2 and Cr3 atoms move toward each other, leading to substantial change in the magnetic state of the system will be shown below. In the MP ground state, CrAs has a noncollinear spin structure in which all Cr magnetic moments are in the xy plane and the angles between them are: Cr1,Cr2 = Cr3,Cr4 =−120° and Cr1,Cr4 = Cr2,Cr3 = 183°.13 Thus, CrAs shows antiferromagnetic behavior. In this work, we restrict ourselves to collinear magnetic structures, as the energy differences due to noncollinear structures are expected to be small. Approximating all angles by 180° leads to the collinear structure closest to the real ground state of CrAs. In Fig. 2 this structure, called AFh, is shown along with other possible collinear antiferromagnetic states for both the MP and NA crystal structure. In addition to these antiferromagnetic states we have also studied the FM state of MP and NA structures, as well as the AF and FM states of the ZB lattice. In the following, two sets of calculations are performed for all these states: calculations with full structural optimization, and calculations where epitaxial constraints are applied.
In the fully optimized calculations all lattice parameters and internal atomic positions were relaxed to find out the theoretical ground state of the system. By fitting the BirchMurnaghan equation of state to the obtained total energies as a function of volume, structural properties of the systems were determined. The results are listed in Table I. The corresponding energy-volume curves are also shown in Fig. 3. It is observed from Table I that MP-AFh is the most stable among the states considered. This is in agreement with the experimental ground state. Theoretical lattice constants in this state are also close to the experimental values, indicating small influence of the noncollinear magnetic state of CrAs on its structural parameters. The MP-AFx state does not appear in Table I because this system, during structural relaxation, changes to the NA-AFx state.
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