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FINANCIAL INSTRUMENTS WITH OFF-BALANCE SHEET RISK - Schedule of Financial Instruments with Off-Balance-Sheet Risk (Details) - USD ($) $ in Thousands	Mar. 31, 2026	Sep. 30, 2025
Financial instruments whose contract amounts represent credit risk
Financial instruments - contract amounts	$ 115,128	$ 111,057
Letters of Credit [Member]
Financial instruments whose contract amounts represent credit risk
Financial instruments - contract amounts	870	820
Unused Lines of Credit [Member]
Financial instruments whose contract amounts represent credit risk
Financial instruments - contract amounts	85,313	80,867
Fixed Rate Loan Commitments [Member]
Financial instruments whose contract amounts represent credit risk
Financial instruments - contract amounts	2,791	3,395
Variable Rate Loan Commitments [Member]
Financial instruments whose contract amounts represent credit risk
Financial instruments - contract amounts	$ 26,154	$ 25,975

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- Definition

The contractual amount of off-balance sheet lending-related financial instruments (e.g., commitments and guarantees), which represents the maximum possible credit risk should the counterparty draw upon the commitment or the entity be required to fulfill its obligation under the guarantee, and the counterparty subsequently fail to perform according to the terms of the contract.

+ References

No definition available.

+ Details

Name:	mgyr_FinancialInstrumentsContractAmounts
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

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- References

No definition available.

+ Details

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

X

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_StandbyLettersOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_FinancialInstrumentAxis=us-gaap_UnusedLinesOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_FinancialInstrumentAxis=mgyr_FixedRateLoanCommitmentsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_FinancialInstrumentAxis=mgyr_LoanOriginationCommitments1Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: