First-principles theoretical studies of half-metallic ferromagnetism in CrTe

Using full-potential linear augmented plane-wave method (FP-LAPW) we have studied the stability and electronic properties of the chalcogenide CrTe in three competing structures: rocksalt (RS), zinc blende (ZB), and the NiAs-type (NA) hexagonal. Although the ground state is of NA structure, RS and ZB are interesting in that these fcc-based structures, which can perhaps be grown on various semiconductor substrates, exhibit half-metallic (HM) phases above some critical values of the lattice parameter. We find that the NA structure is not HM at its equilibrium volume while both ZB and RS structures are. The RS structure is more stable than the ZB with an energy that is lower by 0.25 eV/atom. While confirming previous results on the HM phase in ZB structure, we provide hitherto unreported results on the HM RS phase, with a gap in the minority channel and a magnetic moment of $4.0{\mu }_B/\text{f}\text{.u}\text{.}$ A comparison of total energies for the ferromagnetic (FM), nonmagnetic, and antiferromagnetic (AFM) configurations shows the lowest energy configuration to be FM for CrTe in all the three structures. The exchange interactions in the RS and ZB structures are studied for a wide range of the lattice parameter using the linear-response method and a mapping of the total energy to the classical Heisenberg model. These linear-response calculations are performed in the linear muffin-tin orbitals (LMTOs) basis, using the atomic sphere approximation (ASA). We have verified that the results of the electronic structure obtained via the LMTO-ASA method under local-density approximation (LDA) and $\text{LDA}+U$ schemes are in close agreement with those obtained via the more accurate FP-LAPW method. The results show that the exchange interactions in the RS structure are much more short ranged than in the ZB structure. Hence, for the RS structure the exchange interactions are also studied by using a nearest- and next-nearest-neighbor $\left(J_1\text{−}{J}_2\right)$ model and the energy differences between FM and two AFM states. These $J_1\text{−}{J}_2$ model results are obtained by using both the FP-LAPW and LMTO-ASA methods and compared with the linear-response results. The calculated Curie temperatures for the RS phase are consistently higher than those for the ZB phase.

Figure 1

(Color online) Energy as a function of volume per atom in the three-structural phases of CrTe, obtained via FP-LAPW GGA WIEN2K method.

Figure 2

(Color online) DOS for the RS structure, obtained via the FP-LAPW GGA method, at (a) the equilibrium lattice parameter $a=5.727\text{Å}$ for CrTe, (b) expanded lattice parameter $a=6.013\text{Å}$, the equilibrium value for RS-GeTe, a suitable substrate for growing RS CrTe.

Figure 3

(Color online) DOS for the NiAs structure at the (a) equilibrium volume $V_0$ $\left(c/a=1.5424,a=4.118\text{Å}\right)$ and (b) 10% expanded volume $V=1.1V_0$ $\left(c/a=1.5424\right)$, obtained via the FP-LAPW GGA method.

Figure 4

(Color online) Magnetic moment per f.u. for the NA, ZB, and RS structures obtained via FP-LAPW GGA calculations.

Figure 5

(Color online) Magnetic moment per f.u. versus lattice parameter for RS CrTe calculated by using LMTO-ASA method and LDA and $\text{LDA}+U$ $\left(U=1.02\text{eV},J=0\right)$ schemes (upper panel). Enhanced correlation effects incorporated via the $\text{LDA}+U$ method brings the results in close agreement with those obtained via FP-LAPW-GGA method (lower panel).

Figure 6

(Color online) Exchange interaction, computed by using the LMTO-Green’s-function method between the Cr atoms in the ZB and RS structures as a function of the lattice parameter. The two lattice parameters for the ZB structure chosen are above and below the equilibrium lattice parameter $5.727\text{Å}$ for the RS structure, obtained in the FP-LAPW GGA (WIEN2K) calculation.

Figure 7

(Color online) The RPA Curie temperature as a function of the lattice parameter for the ZB and RS structures of CrTe, calculated by considering the Cr-Cr interaction only and by using the FM reference state. The arrows indicate the equilibrium lattice-parameter values according to various calculations. The results for $T_c$ are somewhat affected by the “induced” moments on the Te atoms as well as the empty spheres used in the LMTO Green’s-function calculation. For ZB CrTe, this error, combined with strong AFM spin fluctuation for the lattice parameters in the range $\sim 5.7–6.0\text{Å}$, result in unphysical negative values of $T_c$ in this range (see text and also the discussion in Ref. 20 for details). Away from this range $T_c$ values are reliable, although somewhat underestimated.

Figure 8

(Color online) Comparison of the Curie temperatures in RS CrTe calculated using RPA and LMTO Green’s-function method for FM reference states with LDA and $\text{LDA}+U$, and DLM reference states with LDA.

Figure 9

(Color online) Comparison of the lattice Fourier transforms of the Cr-Cr exchange interactions in RS CrTe for the lattice parameter $5.727\text{Å}$ and the various cases discussed in the text.