FIG. 14: (Color online) Distribution of Bragg peaks in the ( h, 0 , l ) reciprocal lattice plane. J$_{1}$ = − 1. J$_{2}$ = − 2, and J$_{3}$ is changed as a parameter. (a) M ( J$_{3}$ = − 0 . 2), (b) N ( J$_{3}$ = − 0 . 5), (c) O ( J$_{3}$ = − 0 . 7), and (d) P ( J$_{3}$ = − 0 . 8). FIG. 12: (Color online) Distribution of Bragg peaks in the ( h, 0 , l ) reciprocal lattice plane. J$_{1}$ = − 1. J$_{2}$ = 1 . 5, and J$_{3}$ is changed as a parameter. (a) F ( J$_{3}$ = − 0 . 5) and (b) G ( J$_{3}$ = − 1 . 5). FIG. 13: (Color online) Distribution of Bragg peaks in the ( h, 0 , l ) reciprocal lattice plane. J$_{1}$ = − 1. J$_{2}$ = − 1 . 5, and J$_{3}$ is changed as a parameter. (a) H ( J$_{3}$ = − 0 . 2), (b) I ( J$_{3}$ = − 0 . 5), (c) J ( J$_{3}$ = − 0 . 667), (d) K ( J$_{3}$ = − 1 . 2), and (e) L ( J$_{3}$ = − 1 . 5). phase with the c axis and is on the line ( J$_{2}$ + J$_{3}$ = 2 J$_{1}$ ). The point J ( J$_{3}$ = − 0 . 667) is on the phase boundary between the helical phase with the c axis and the phase with ( h = 1 . 2 , k = 0 , l = 1 / 2). The points K ( J$_{3}$ = − 1 . 2) and L ( J$_{3}$ = − 1 . 5) are in the phase with ( h = 1 / 2 , k = 0 , l = 1 / 2). Typical contour plot of ( h, 0 , l ) at the points M, N, O, and P in the ( J$_{2}$ , J$_{3}$ ) phase diagram are shown in Fig. 14 The point M ( J$_{3}$ = − 0 . 2) is in the helical phase along the c axis. The point N ( J$_{3}$ = − 0 . 5) is on the phase boundary ( J$_{2}$ + J$_{3}$ = 2 J$_{1}$ ) between the helical phase with the c axis and the phase with ( h = 1 . 2 , k = 0 , l = 1 / 2). The points O ( J$_{3}$ = − 0 . 7) and P ( J$_{3}$ = − 0 . 8) are in the phase with ( h = 1 / 2 , k = 0 , l = 1 / 2). What is the three dimensional (3D) spin structure which is characterized with the wavevector of the mag- netic Bragg peaks? The vector of spin at the site R$_{i}$ of the real lattice space is given by where S = 3 / 2, we assume that the phase factor φ is equal to zero, and Q is defined as Typical contour plot of ( h, 0 , l ) at the points H, I, J, K, and K in the ( J$_{2}$ , J$_{3}$ ) phase diagram are shown in Fig. 13. The point H ( J$_{3}$ = − 0 . 2) is in the helical phase along the c axis. The point I ( J$_{3}$ = − 0 . 5) is in the helical C. The points H, I, J, K, and L with J$_{1}$ = − 1 . 0 and J$_{2}$ = − 1 . 5 IX. 3D SPIN STRUCTURES D. The points M, N, O, and P with J$_{1}$ = − 1 . 0 and J$_{2}$ = − 2 12 S$_{i}$ = S [cos( Q · R$_{i}$ ) e$_{x}$ + sin( Q · R$_{i}$ φ ) e$_{y}$ ] Q = ( ha $^{∗}$, ka$^{∗}$, lc$^{∗}$) .