11 FIG. 11: (Color online) Distribution of Bragg peaks in the ( h, 0 , l ) reciprocal lattice plane. J$_{1}$ = − 1. J$_{2}$ = − 0 . 5, and J$_{3}$ is changed as a parameter. (a) Point A ( J$_{3}$ = − 0 . 5), (b) Point B ( J$_{3}$ = − 1 . 5), (c) Point C ( J$_{3}$ = − 2 . 0), (d) Point D ( J$_{3}$ = − 3 . 0), and (e) Point E ( J$_{3}$ = − 4 . 0). FIG. 9: (Color online) (a) h vs J$_{3}$ and (b) l vs J$_{3}$ along the scan C ( − 3 . 0 ≤ J$_{3}$ ≤ 0 and J$_{2}$ = − 0 . 4). J$_{1}$ = − 1. k = 0. A. The points A, B, C, D, and E with J$_{1}$ = − 1 . 0 and J$_{2}$ = − 0 . 5 Typical contour plot of ( h, 0 , l ) at the points A, B, C, D, and E in the ( J$_{2}$ , J$_{3}$ ) phase diagram are shown in Fig. 11. The point A ( J$_{3}$ = − 0 . 5) is in the phase with ( h = 0, k = 0, l = 1). The point B ( J$_{3}$ = -1.5) is in the helical phase with the a axis. The point C ( J$_{3}$ = − 2) is the phase boundary between the phase with ( h = 0 , k = 0 , l = 1) and the helical phase with the a axis. The points D ( J$_{3}$ = − 3 . 0) and E ( J$_{3}$ = − 4 . 0) are in the phase with ( h = 1 / 2 , k = 0 , l = 1 / 2). Typical contour plot of ( h, 0 , l ) at the points F and G in the ( J$_{2}$ , J$_{3}$ ) phase diagram are shown in Fig. 12. The point F ( J$_{3}$ = − 0 . 5) is in the phase with ( h = 0 , k = 0 , l = 1). The point G ( J$_{3}$ = − 1 . 5) is in the helical phase with the a axis. FIG. 10: (Color online) Phase diagram of J$_{3}$ vs J$_{2}$ : J$_{1}$ = − 1. H - a : helical order along the a axis. H - c : helical order along the c axis. The ordered phase with ( h = 1 / 2 , k = 0 , l = 1 / 2). The ordered phase with ( h = 0 , k = 0 , l = 1). The multicritical point is at ( J$_{2}$ = − 1, J$_{3}$ = − 1). The calculations of the contour plots are made at the points (A, B, C, · · · , P). The line J$_{2}$J$_{3}$ = J 2 1 is the first-order phase boundary. The line ( J$_{2}$ = − 1, J$_{3}$ > − 1) and the line ( J$_{3}$ = − 1, J$_{2}$ > − 1) are the second-order phase boundary. B. The points F and G with J$_{1}$ = − 1 . 0 and J$_{2}$ = 1 . 5 .