I have performed linear buckling analysis using contact load to find Eigen value in Abaqus Cae. But I found that contact did not work properly for some sections.
Essentially, linear buckling analysis (Eign buckling analysis) cannot be combined with nonlinearities such as contact or nonlinear material properties.
To perform bucking analysis incorporating contact, nonlinear geometric analysis is required.
I do not know what kind of beam you mean, but the following references could be helpful:
Seif, Mina, and Benjamin W. Schafer. "Local buckling of structural steel shapes." Journal of Constructional Steel Research 66.10 (2010): 1232-1247.
Zeinoddini, V. M., and B. W. Schafer. "Simulation of geometric imperfections in cold-formed steel members using spectral representation approach." Thin-Walled Structures 60 (2012): 105-117.