First-principles study of an $S=1$ quasi one-dimensional quantum molecular magnetic material

We use density functional theory to study the structural, magnetic, and electronic structures of the organometallic quantum magnet ${\mathrm{NiCl}}_2\text{−}4\mathrm{SC}{\left({\mathrm{NH}}_2\right)}_2$ (DTN). Recent work has demonstrated the quasi one-dimensional nature of the molecular crystal and studied its quantum phase transitions at low temperatures. The system includes a magnetoelectric (ME) coupling and, when doped with Br, the presence of an exotic Bose-glass state. Using the generalized gradient approximation with inclusion of a van der Waals term to account for weak intermolecular forces and by introducing a Hubbard $U$ term to the total energy, we systematically show that our calculations reproduce the magnetic anisotropy, the intermolecular exchange coupling strength, and the magnetoelectric effect in DTN, which have been observed in previous experiments. Further analysis of the electronic structure gives insight into the underlying magnetic interactions, including what mechanisms may be causing the ME effect. Using this computationally efficient model, we predict what effect applying an electric field might have on the magnetic properties of this quantum magnet.

Figure 1

(Top) Two views of the the molecular unit making up the DTN molecular crystal. Four thiourea ligands surround the magnetic Ni ion. (Bottom) The DTN unit cell.

Figure 2

The $2\times 1\times 1$ ($ab$, green) and $1\times 1\times 2$ ($c$, purple) supercells used to calculate respective exchange-coupling $J$ values. The nodes correspond to Ni ions, and red arrows indicate the exchange interactions.

Figure 3

DOS of the DTN unit cell using the $\mathrm{GGA}\text{−}\mathrm{D}3+U$ approximation. Panel (a) is the total DOS. Panels (b)–(e) are orbital-resolved PDOS. Panel (b) shows $d_{3z^2-r^2}$ (red) and $d_{x^2-y^2}$ (blue) ($e_g$) orbitals of $\mathrm{Ni}(3d$); (c) S $3p$ orbitals forming S-Ni $\sigma$ bonds and $\pi$ bonds, respectively; and (d) and (e) $\mathrm{Cl}(3p$) orbitals of Cl1 and Cl2 identified in (f). Positive and negative values correspond to spin-majority and spin-minority channel, respectively. The Fermi level is set to zero. The shaded region is the inner energy window for constructing the Wannier-based tight-binding Hamiltonian. The cross section in a $1\times 1\times 2$ supercell in (f) shows the partial charge densities of Cl-Cl bonding and antibonding states labeled in (d) and (e).

Figure 4

(a) Isosurface of a Wannier function for the AFM $c$-axis supercell, indicating hybridization of Ni and Cl orbitals leading to a superexchange path along the Ni-Cl-Cl-Ni chain; (b) Wannier orbital in a cross section containing two Ni ions along a diagonal line of the lattice; and (c) on the $ab$ plane of the lattice.

Figure 5

Relative total energy as a function of the angle between the $c$ axis and the spin of the Ni ion for (top) the DTN molecule and (bottom) the DTN unit cell with the other inequivalent Ni ion spin fixed along the $c$ axis. The angles $\theta$ and $\varphi$ refer to the orientation angles in spherical coordinates.

Figure 6

Magnetoelectric coupling in DTN. The electric dipole moment (blue) and the $z$ component of the magnetization (red) are plotted as a function of the spin canting angle of the spin moment on the Ni cation.

Figure 7

Ionic and electronic contributions to the change in polarization of the DTN unit cell under applied strain.

Figure 8

The dependence of the magnetic anisotropy of bulk DTN on an electric field applied parallel to the $ab$ plane.