Generally we talk about stress in case of thin films but same is applied to nanoparticles too.
I think if you are talking about nanopowders than its better to use disorder and heterogeneity terms rather than stress and strain. The ionic radii of the dopant and defect chemistry can introduced disorder in these type of nanopowders. Just an opinion (though not expert one) that Mn3+ is a Jahn Teller ion and you can take temperature dependent Raman data for different phonons and Jahn Teller modes to address the disorder issues.
It is necessary to clarify the nature of material ( nanopowders or nanoparticles in thin films). Usually, in ZnO Mn atoms substitute Zn sites. Thus we have Mn(2+) ions. The main state of these ions is orbital singlet. It means that a static Jahn-Teller effect don't occur and local deformation due to this effect absent. However, stress may be presense in the film since the ionic radius of Mn2+ (0.83 A) is larger than the ionic radius of Zn 2+ (0.74 A). Raman scattering measurements may allow to study the presence such stress in the films (broadening of Raman lines).
Yuriy Gnatenko clearly illustrates the ionic radius situation. Since ZnO nanopowders must have oxygen vacancies which might can alter the oxidation state of Mn. Can we proceed the discussion in this scenario.l
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