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Correlation between fixed effect and random intercept

Hi,
I am working with a random intercept model. I have the usual "X" vector of
covariates and one id variable which will make up the random intercept.
For example,
Response variable: Production of maize
Covariate: Size of plot
ID variable: Household_ID

I need to acknowledge that there is correlation between the FIXED EFFECT
coefficient of plot size and the estimated random intercept. It is my model
assumption.

Does lme4 assume this correlation or do I have to make changes in the
formula so that it gets considered?

Thank you!

Regards,
Yashree