Fig. 2

Equilibrium configurations of antiferromagnets in a confined structure. Depending on the Dzyaloshinskii-Moriya (DM) interaction, l_z = cos(φ) takes a (a) symmetric (S) or (b) antisymmetric (AS) configuration. Here, φ is described as a Jacobi amplitude function φ = am(u|m) with elliptic modulus m that is the solution of the sine-Gordan (SG) equation. The exact solution is obtained with two conditions: 1) φ(l_w/2) = π or 0 and 2) dφ/dz = 2d_y/J at z = 1 or z = l_w where l_w is wire length in Néel space. The stationary state is calculated from the Landau Lifshitz Gilbert equation when the time goes to infinity and therefore is the solution of the SG model (solid line). As the DM energy increases, l_z becomes a pure spiral configuration of φ = kz with wavevector k = 2d_y/J (solid line and open circle for n = 5). However, as the DM energy decreases, there is a deviation between the pure spiral approximation and the SG model (solid line and open circle for n = 2). Here, d_c is the critical DM energy where d_y > d_c changes a domain wall state into a chiral state