Magnetism in tunable quantum rings

We have studied the spin structure of circular four-electron quantum rings using tunable confinement potentials. The calculations were done using the exact diagonalization method. Our results indicate that ringlike systems can have oscillatory flips between ferromagnetic and antiferromagnetic behavior as a function of the magnetic field. Furthermore, at constant external magnetic fields there were seen similar oscillatory changes between ferromagnetism and antiferromagnetism when the system parameters were changed. According to our results, the magnetism of quantum rings could be tuned by system parameters.

Figure 1

(Color online) Ground-state spin polarization as a function of the magnetic field $B$ for a four-electron parabolic quantum dot with Gaussian perturbations of different strengths $V_0$. The spin states are 0 (red/middle gray), 1 (green/light gray), and 2 (dark gray). The upper integers denote the number of central vortices found in each of the different states, and the integers surrounded by a ring denote the corresponding angular momenta. All states at zero magnetic field have angular momentum 0. If two subsequent states are separated by a solid line, the angular momentum increases by one when moving to the state at right, and if they are separated by a dashed line, the angular momentum increases by two.

Figure 2

Conditional wave functions consisting of the charge density, plotted with contour lines (logarithmic scale), and the phase of the wave function, illustrated by the grayscale shading. The fixed spin up electrons are marked with black triangles pointing up, and the spin down electrons with white triangles pointing down. The probe particle is marked with a larger triangle. The clusters consisting of central vortices (nodes), which can be considered as giant vortices, are denoted by circular arrows.

Figure 3

(Color online) Total angular momentum $L$ and spin $S$ of the ground states given as functions of the magnetic field $B$ for a four-electron parabolic ring with 40 meV confinement strength and radius $8a_B^{\ast }/\pi$, where $a_B^{\ast }$ is the effective Bohr radius. The Coulomb constant is (a) $C=0.1$, (b) $C=1$, and (c) $C=10$. The crosses denote states with magic angular momenta $L_k=L_{\text{MDD}}+kN$, where $k∊\left\{0,1,2,\dots \right\}$, $L_{\text{MDD}}=\left(N-1\right)N/2$ is the angular momentum of the maximum-density droplet (MDD), and $N$ is the number of electrons. The state with angular momentum $L_{\text{MDD}}$ is marked with a cross surrounded by a circle.