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Loans Receivable, Net and Related Allowance for Credit Losses (Details)	3 Months Ended
	Dec. 31, 2023
Loans Receivable, Net [Abstract]
Commercial relationships, description	Generally, the external consultant reviews commercial relationships greater than $500,000 and/or criticized relationships greater than $250,000.

X

- Definition

Description of commercial relationships.

+ References

No definition available.

+ Details

Name:	mgyr_CommercialRelationshipsDescription
Namespace Prefix:	mgyr_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

Name:	us-gaap_ReceivablesAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration