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\begin{document}
\title{Non-uniform coupling model of the Cr$_8$Ni ring}
\author{\underline{M. Antkowiak}}
\affiliation{Faculty of Physics, Adam Mickiewicz University, Poznań, Poland}
\author{Ł. Kucharski}
\affiliation{Faculty of Physics, Adam Mickiewicz University, Poznań, Poland}
\author{G. Kamieniarz}
\affiliation{Faculty of Physics, Adam Mickiewicz University, Poznań, Poland}
\begin{abstract}
We analysed the~magnetic properties of a~ring of~eight chromium ions doped with one nickel ion, denoted in~short Cr$_8$Ni. By making calculations for smaller rings we~have demonstrated that the~chromium and~nickel anisotropies can be neglected for modeling the~susceptibility in~the~considered temperature range due to~their relatively low values. Omission of~anisotropy allowed us to~make simulations for three models with different degrees of~diversification of~the~exchange integrals between chromium ions, using a~genetic algorithm. The models revealed better agreement with experiment than those previously known from literature. We~also calculated the~magnetization in~a~magnetic field and~compared the~results with experimental data, which so far have not been taken into account for modelling. We~calculated the~energy structure as a~function of~the~ratio of~the~exchange integral between chromium and~nickel ions to~the remaining integrals, and~have determined the~energy differences for the~selected transitions, which may be expected to~be observed in~the~INS experiment.


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\textit{This work was supported in part by the MNISW grant No. 579138. Numerical calculations were carried out on the platforms of the PSNC in Poznań and the TASK in~Gdańsk, Poland.}
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\end{abstract}
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