Electronic orbital currents and polarization in Mott insulators

Strongly correlated electron insulators are one of the most important classes of materials in modern solid-state physics. We demonstrate that certain classes of Mott insulators, that usually are geometrically frustrated, exhibit unexpected charge effects: for certain spin textures, spontaneous circular electric currents or nonuniform charge distribution exist in the ground state of Mott insulators. In addition, low-energy “magnetic” states contribute comparably to the dielectric and magnetic response functions, ${ϵ}_{ik}\left(\omega \right)$ and ${\mu }_{ik}\left(\omega \right)$, leading to interesting phenomena such as dipole-active ESR transitions, rotation of the electric-field polarization, and resonances which may be common to both functions producing a negative refraction index in a window of frequencies.

Figure 1

(Color online) (a) Ground states with nonzero electric current of the $C_3$ invariant Heisenberg triangle. The circular arrows indicate circular currents, and $\left(+,-\right)$ indicate the sign of the scalar chirality. (b)–(d) Noncoplanar spin configuration in a pyrochlore lattice. (b) Four spins point inward along the principal diagonals; the net currents are zero. (c) Three spins point inward while the other one points outwards leading to a net current circulating in the opposite triangle. (d) Two spins point inward and the other two point outward. The orbital current circulates in a loop formed by four edges of the tetrahedron.

Figure 2

Example of a system with uniform scalar spin chirality but no net currents in the interior bonds due to cancellation between the contributions from the adjacent triangles (dashed arrows). A net current (full arrows) appears on the perimeter because such bonds belong to only one triangle.

Figure 3

(Color online) (a) Example of magnetic state with nonzero polarization indicated by the arrow. The two spins inside the oval form a singlet and the unpaired spin can be up or down. This is one of the degenerate ground states of the antiferromagnetic Heisenberg Hamiltonian on an equilateral triangle, which according to Eq. (8), has a nonzero electric-dipole moment. (b) Example of electric polarization induced by a magnetic field $\mathbf{B}$.

Figure 4

(Color online) Spin configurations on a kagome lattice that lead to a current or charge ordering in an applied magnetic field. a) The “umbrella” phase induced by a field perpendicular to the plane has a uniform current ordering. The $\pm$ signs denote directions of current. (b) The same as (a) for staggered current ordering. (c) Spin ordering induced by field for a Heisenberg model on a kagome lattice.[25, 26] The elongated ovals indicate a resonant valence bond state on the corresponding hexagons, while the little circles represent spins that are polarized along the field direction. This structure is accompanied by charge ordering: the charges on sites belonging to hexagons and those on isolated sites should be different.

Figure 5

(Color online) (a) Ferroelectricity induced by dimerization of a sawtooth chain. (b) Domain boundary between two degenerate ground states.

Figure 6

(Color online) Magnetic energy levels of a single triangle with Dzyaloshinsky-Moriya interaction. (a) As a function of applied dc magnetic field. Blue (red) arrows show transitions induced by ac electric (magnetic, EPR) field. (b) As a function of a dc electric field.