Figure 1

Magnetic insulating phase of spin-one bosons in optical lattice with an odd number of atoms per site $N$. Magnetization is fixed inside the lobes but varies continuously inside the Canted Nematic phase. The latter has an expectation value of the nematic order parameter $Q_{ab}$ in the plane perpendicular to the direction of magnetic field. For sufficiently large magnetic field the system becomes fully polarized with $S=N$ (not shown here). The insert shows the ground state magnetization (per site) as a function of magnetic field for $2z{N}^2{t}^2/U_0=5U_2$. Note that near $H=0$, magnetization grows linearly with magnetic field and quickly reaches the $S_{\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{,}\mathrm{z}}=1$ plateau.Reuse & Permissions

Figure 2

Magnetic insulating phase in optical lattice with an even number of atoms per site. The insert is for $2z{N}^2{t}^2/U_0=2U_2$.Reuse & Permissions

Figure 3

A system of spin-one bosons in an optical lattice confined by a parabolic potential. In the insulating regime the cloud breaks into insulating domains with different integer filling factors. When magnetic field gradient is applied parallel to the long axis of the trap, magnetization plateaus develop inside individual insulating domains.Reuse & Permissions

Figure 4

A system of spin-one bosons with a nonzero total magnetization in an optical lattice (no external magnetic field). Magnetization gets distributed among regions with odd filling factors and is pushed out of the regions with even fillings.Reuse & Permissions