content_image/415963.jpg content_image/415980.jpg content_image/415975.jpg content_image/415976.jpg content_image/415977.jpg content_image/415981.jpg
<img src='content_image/415963.jpg'>

in the reciprocal lattice plane of ( h, k = h, l ), where ϵ = 0 . 29771. 

<img src='content_image/415980.jpg'>

## A. The contour plot of J ( h, 0 , l ) in the ( h, 0 , l ) reciprocal lattice plane 

Using the numerical calculation of the contour plot us- ing the Mathematica, we find the location of the magnetic Bragg peaks in the ( h, 0 , l ) reciprocal lattice, where 

<img src='content_image/415975.jpg'>

takes a maximum, where J$_{1}$ = − 1, J$_{2}$ = p$_{2}$J$_{1}$ = − 1 . 68469. Figures 4(a)-(f) show the contour plot of J ( h, 0 , l ) in the reciprocal lattice plane of ( h, 0 , l ), where J$_{3}$ = p$_{3}$J$_{1}$ ( p$_{3}$ < 0 . 5935) and J$_{3}$ is changed as a param- eter ( J$_{3}$ = − 0 . 2 , − 0 . 3 , − 0 . 4). As is predicted above, we find that the magnetic Bragg peaks appear at 

<img src='content_image/415976.jpg'>

where ϵ = 0 . 29771 and is independent of p$_{3}$ ( p$_{3}$ < 0 . 5935). Note that the essential results are independent of the choice of p$_{3}$ at least for 0 . 2 ≤ p$_{3}$ ≤ 0 . 4. 

## B. The contour plot of J ( h, k = h, l ) in the ( h, k = h, l ) reciprocal lattice plane 

Using the contour plot of the J ( h, k = h, l ), we find the location of the magnetic Braggs in the ( h, h, l ) reciprocal lattice, where 

<img src='content_image/415977.jpg'>

The location of the magnetic Bragg peaks is given by 

## C. The contour plot in the ( h, k, l ) plane with l = 2 n 

Using the contour plot of the Mathematica, we find the location of the magnetic Braggs in the ( h, k, l = 2 n ) reciprocal lattice, where 

<img src='content_image/415981.jpg'>

## VI. NUMERICAL CALCULATION 

