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LOANS RECEIVABLE, NET (Schedule of Troubled Debt Restructuring) (Details) $ in Thousands	12 Months Ended
	Sep. 30, 2022 USD ($) Integer	Sep. 30, 2021 USD ($) Integer
Financing Receivable, Troubled Debt Restructuring [Line Items]
Number of Loans | Integer		2
Investment Before TDR Modification		$ 330
Investment After TDR Modification		$ 340

X

- Definition

Amount of investment in financing receivables (after modification) modified by troubled debt restructurings.

+ References

No definition available.

+ Details

Name:	mgyr_InvestmentAfterTdrModification
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of investment in financing receivables (before modification) modified by troubled debt restructurings.

+ References

No definition available.

+ Details

Name:	mgyr_InvestmentBeforeTdrModification
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Number of financing receivables that have been modified by troubled debt restructurings.

+ References

No definition available.

+ Details

Name:	mgyr_NumberOfLoans
Namespace Prefix:	mgyr_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

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