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LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of Troubled Debt Restructuring) (Details) $ in Thousands	6 Months Ended
	Mar. 31, 2022 USD ($) Loans
Financing Receivable, Troubled Debt Restructuring [Line Items]
Number of Loans | Loans	1
Investment Before TDR Modification	$ 218
Investment After TDR Modification	$ 249
One-to four-family residential [Member]
Financing Receivable, Troubled Debt Restructuring [Line Items]
Number of Loans | Loans	1
Investment Before TDR Modification	$ 218
Investment After TDR Modification	$ 249

X

- Definition

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

+ References

No definition available.

+ Details

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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

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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

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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

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

X

- Details

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Namespace Prefix:
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Balance Type:
Period Type: