Anomalous lattice compression and magnetic ordering in CuO at high pressures: A structural study and first-principles calculations

The structural and magnetic properties of multiferroic CuO have been studied by means of neutron and x-ray powder diffraction at pressures up to 11 and 38 GPa, respectively, and by first-principles theoretical calculations. Anomalous lattice compression is observed, with enlargement of the lattice parameter $a$, reaching a maximum at $P=13\mathrm{GPa}$, followed by its reduction at higher pressures. The lattice distortion of the monoclinic structure at high pressures is accompanied by a progressive change of the oxygen coordination around Cu atoms from the square fourfold towards the octahedral sixfold coordination. The pressure-induced evolution of the structural properties and electronic structure of CuO was successfully elucidated in the framework of full-electronic density functional theory calculations with range-separated HSE06, and meta–generalized gradient approximation hybrid M06 functionals. The antiferromagnetic (AFM) ground state with a propagation vector $q=(0.5,0,-0.5)$ remains stable in the studied pressure range. From the obtained structural parameters, the pressure dependencies of the principal superexchange magnetic interactions were analyzed, and the pressure behavior of the Néel temperature as well as the magnetic transition temperature from the intermediate incommensurate AFM multiferroic state to the commensurate AFM ground state were evaluated. The estimated upper limit of the Néel temperature at $P=38\mathrm{GPa}$ is about 260 K, not supporting the previously predicted existence of the multiferroic phase at room temperature and high pressure.

Figure 1

Computational model of the monoclinic structure of CuO, representing simplified antiferromagnetic spin alignment of Cu ions $(+/-)$, shown as blue spheres. The red spheres correspond to oxygen positions.

Figure 2

X-ray diffraction patterns of CuO measured at selected pressures and ambient temperature, and refined by the Rietveld method. Experimental points and calculated profiles are shown. Tick marks at the bottom represent the calculated positions of diffraction peaks.

Figure 3

The pressure variation of the unit cell volume in monoclinic CuO according to the synchrotron x-ray diffraction data and DFT/LCAO/TZVP calculations performed with different hybrid functionals. The $\mathrm{GGA}+\mathrm{U}$ results (VASP) from Rocquefelte et al. Ref. [10] are also given for comparison.

Figure 4

The lattice parameters and monoclinic angle of CuO as functions of pressure according to synchrotron x-ray measurements and theoretical calculations with the HSE06 and M06 functionals. The neutron powder diffraction data (NPD) from Ehrenberg et al. Ref. [11] are given for comparison. The lines are guides to the eye only.

Figure 5

The neutron diffraction patterns of CuO, measured at selected pressures up to 11 GPa and temperatures 10 and 290 K at scattering angles ${90}^{\circ }$ and ${45}^{\circ }$ (inset), and processed by the Rietveld method. The experimental points and calculated profiles are shown. The ticks below represent calculated positions of the nuclear peaks. The characteristic magnetic peak of the AFM ground state with $q=(1/2,0,-1/2)$ is marked as “AFM” in the inset.

Figure 6

(a) The monoclinic crystal structure of CuO. The fourfold coordinated Cu–O planes and tetrahedral coordination of Cu atoms around O atoms are shown. The two longest additional Cu–O distances are presented as dashed lines. (b) Schematic representation of the Cu–O–Cu zigzag chains oriented along the [10-1] and [101] crystallographic directions, with geometry of interatomic angles and relevant superexchange interactions.

Figure 7

The pressure dependencies of the oxygen coordinate $y$ (a), Cu–O bond distances (b), and intrachain (c) and interchain (d) Cu–O–Cu bond angles. The errors are within the symbol sizes. The squares show experimental results from the present neutron data, triangles show neutron data [Ref. 11], and circles indicate calculated results from present x-ray data. The results of the first-principles calculations under pressure (HSE06; M06) are given as dashed lines.

Figure 8

(Left) The pressure-induced changes in the Laplacian of electron density at the bond critical points defining the short $\left(x,y\right)$ and long $\left(z\right)$ Cu–O bonds as derived from the QTAIM analysis. (Right) The ELF surface $(s=0.76)$ for CuO at two extreme pressure conditions studied.

Figure 9

The pressure dependence of the density of electronic states (DOS) in antiferromagnetic CuO at $P=0$ and 37.5 GPa, according to the CRYSTAL14/HSE06/TZVP calculations for the $Z=8\mathrm{AFM}$ spin arrangement. The contributions from the $e_g$ and $t_{2g}$ states of Cu $\left(3d\right)$ are projected using the local coordinate system centered on Cu, where the $x$ and $y$ axes are directed approximately to four neighboring oxygen atoms. The top of the valence band is aligned to 0 eV.

Figure 10

(a) The experimental and calculated pressure dependencies of the Néel temperature of CuO. The triangles are experimental points derived from the neutron diffraction measurements. The solid curves represent calculations with the parameters $c=0.233$ and $\lambda =2.6$ (green line), and $c=0.274$ and $\lambda =1.5$ (brown line). The red dashed line indicates calculation by Rocquefelte et al. Ref. [10]. (b), (c) The experimental temperature dependencies of the monoclinic angle of CuO at $P=0$ (b) and 11 GPa (c).