Magnetic diversity in stable and metastable structures of CrAs

We present results of electronic structure calculations of the bulk properties of CrAs. The crystalline structures of CrAs are investigated by the use of ab initio calculations with an unbiased swarm structural search under ambient and high pressure. Both the double helimagnetic and nonmagnetic phases in the neutron experiment are obtained and the pressure dependence of the magnetic phase transition is predicted. The $Pnma$ structure is the most stable structure below 33.1 GPa, meanwhile a magnetic phase transition of helimagnetic$\to$antiferromagnetic$\to$nonmagnetic is observed. The system tends to be antiferromagnetic after the double helimagnetic state near the optimal superconductivity regime without a crystal phase transition, which suggests that antiferromagnetic correlations between neighboring exchange interactions may be essential for the emergence of superconductivity in CrAs rather than a structural phase transition. Furthermore, the present results show that the $Pnma$ phase undergoes a pressure-induced phase transition to a cubic $P{2}_{1}3$ phase at 33.1 GPa. In addition, three low-enthalpy phases with a diverse magnetic order are identified as metastable states under ambient pressure. As the analytical results of the electronic structure, the three metastable structures, $P\overline{6}m2$ type A, $P\overline{6}m2$ type B, and $P4/nmm$, are antiferromagnetic, nonmagnetic, and ferromagnetic, respectively. An explanation for the interesting difference in the spin polarization is sought, in particular, for the covalent-ionic interactions between Cr and As atoms. The present results elucidate the structural and electronic properties of CrAs, and offer major implications as regards the diverse magnetic behaviors of CrAs.

Figure 1

Three-dimensional schematic representations of the stable and metastable phases for CrAs. (a) $Pnma$, (b) $P\overline{6}m2$ type A, (c) $P4/nmm$, and (d) $P\overline{6}m2$ type B. Blue atoms depict Cr, while green atoms represent As. Schematics of the structural polytypes: $o-{\mathrm{CrAs}}_6$ (the Cr atom is coordinated to six As atoms in an octahedral coordination), and $p-{\mathrm{CrAs}}_6$ (the Cr atom is coordinated to six As atoms in a triangular prismatic coordination).

Figure 2

Helimagnetic structure of MP-type CrAs. The magnetic moments of Cr atoms are represented by red arrows, and the evolution of the moments is shown for three unit cells along $c$. (a)–(c) are helical magnetic structures viewed from the $c, b$, and $a$ axis, respectively, and (d) is a solid view. Blue atoms depict Cr, while green atoms represent As.

Figure 3

Phonon spectra and phonon projected density of states (PDOS) of CrAs. (a) $Pnma$, (b) $P\overline{6}m2$ type A, (c) $P4/nmm$, and (d) $P\overline{6}m2$ type B. The absence of imaginary phonon frequencies in the entire Brillouin zone confirms the dynamical stability. The unit of phonon PDOS is $\mathrm{states}/{\mathrm{cm}}^{-1}$ per atom.

Figure 4

The electronic structures of CrAs. (a) $P\overline{6}m2$ type-A phase, where the partial density of states for two inequivalent Cr atoms and As atom are represented by red, green, and red solid lines. (b) $P4/nmm$ phase, where the electronic band structure for majority spin and minority spin is represented by black solid lines and red dotted lines, while the partial density of states for the majority-spin states of the Cr and As atoms are presented by red and blue solid lines, and the majority-spin states of the Cr and As atoms are presented by red and blue dotted lines. (c) $P\overline{6}m2$ type-B phase. The Fermi level is set to zero, and the unit of electronic projected density of states (PDOS) is states/eV/atom.

Figure 5

Electron localization function (ELF) maps of CrAs. (110) plane of (a) $P\overline{6}m2$ type A, (b) $P4/nmm$, and (c) $P\overline{6}m2$ type B. The maximum ELF value between Cr and As is about 0.8, indicating a weak covalentlike nature of the Cr-As bond. Blue and green balls indicate Cr and As atoms, respectively.

Figure 6

Three-dimensional charge density difference with the isosurface of CrAs. (a) $P\overline{6}m2$ type A, (b) $P4/nmm$, and (c) $P\overline{6}m2$ type B. Turquoise and yellow regions indicate depletion and accumulation of electrons, respectively. The isosurface plots (with a value of 0.01 $e/{\mathrm{bohr}}^3$) clearly illustrate the charge transfer from the Cr atom and distribution localized between Cr and As atoms, indicating a covalent interaction for all the phases. Blue and green balls indicate Cr and As atoms, respectively.

Figure 7

(a) Relative enthalpy per atom as a function of pressure for CrAs, referenced to the $Pnma$ structure. The phase-transition series orthorhombic $Pnma$ phase to cubic $P{2}_{1}3$ phase (33.1 GPa). Further calculations determined the stability of the $P{2}_{1}3$ phase up to 90 GPa. The inset shows the enthalpy of various types of magnetism for $Pnma$ as a function of pressure. The $Pnma$ phase changes magnetic ordering from double helimagnetic ordering to antiferromagnetic ordering (3.9 GPa) to nonmagnetic ordering (10.8 GPa). (b) Magnetic and structural phase-transitional diagram under pressure.

Figure 8

Phonon spectra for the high-pressure phases of (a) $Pnma$ at 30 GPa and (b) $P{2}_{1}3$ phase at 30, 60, and 90 GPa. The inset shows schematic representations of the $Pnma$ and $P{2}_{1}3$ phase, respectively. (c) Pressure dependence of the lattice parameter in the magnetically ordered state.