From my understanding, ARGMIN is just the value of the independent variable(s) that correspond to the global minimum in the dependent variable. Your one-dimensional example is thus wrong. No matter which location you place the "0", your formula always returns 0.

a = [1, 2, 3, 4, 0, 6, 7, 8]
argmin = SORT(MIN(a, DIMENSION = 1))
argmin = 0

The correct formula for ARGMIN would be as follows, which by the way will work for N dimensions:

argmin = array_indices(a,where(a EQ min(a)))

You can test this with a sample 2D array:

a = [[5, 1, 2, 3, 1, 5, 6, 7, 8],[15, 11, 12, 13,11, 15, 16, 17, 18],[[25, 21, 22, 23,21, 25, 26, 27,28]]]
argmin = array_indices(a,where(a EQ min(a)))
print, argmin
1 0
4 0

In my original array, the minimum value (1) occurs twice. Once in [Column 1, Row 0] and also at [Column 4, Row 0].

Hope this helps.