Origin of noncollinear magnetization coupling across <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Ru</mml:mi><mml:mi>X</mml:mi></mml:math> layers

We present a simple atomistic model for the description of noncollinear coupling in magnetic multilayers with hybrid spacer layers made Ru alloyed to ferromagnetic atoms such as Fe. In contrast previous analytical and micromagnetic models that explain by means lateral fluctuations constant, presented accounts atom-atom all three spatial dimensions within layer. The is able accurately predict dependence macroscopic bilinear biquadratic constants on spacer-layer composition thickness, showing much better quantitative agreement than lateral-fluctuation models. Moreover, it predicts virtually independent exchange stiffness layers, which goes beyond predictions This prediction validated experimental measurements.