Criticise an author’s publicity material (10)

I believe the answer is:

animadvert

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'criticise' is the definition.
(I've seen this before)

'an author's publicity material' is the wordplay.
'author's' becomes 'I'm' ('I am' referring to the author of the crossword).
'publicity material' becomes 'advert' (I can't justify this - if you can you should give a lot more credence to this answer).
'an'+'im'+'advert'='ANIMADVERT'

Can you help me to learn more?

(Other definitions for animadvert that I've seen before include "comment critically" , "Criticize" , "Censure" , "Criticise" .)

I've seen this clue in The Times.

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