manual creation of subdomain with separate nameservers

we have domain.com on server 1.1.1.1 , with nameservers on it too (that is ns1.domain.com and ns2.domain.com).
we want to create a subdomain and grant all managing rights to server 2.2.2.2 (that is let that server run own DNS server and manage that subdomain.domain.com, like first server does with domain.com). what records i should add on 1.1.1.1 server ?

i experimented and found out that this configuration works:

subdomain IN A 2.2.2.2
ns1.subdomain IN A 2.2.2.2
subdomain IN NS ns1.subdomain.domain.com.
ns2.subdomain IN A 2.2.2.2
subdomain IN NS ns2.subdomain.domain.com.

is this correct? maybe there are unnecessary records?

thank you

 

 

 

 

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