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FINANCIAL INSTRUMENTS WITH OFF-BALANCE-SHEET RISK - Schedule of Financial Instruments with Off-Balance-Sheet Risk (Details) - USD ($) $ in Thousands | Sep. 30, 2025 | Sep. 30, 2024
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Financial instruments whose contract amounts represent credit risk |  |
Financial instruments - contract amounts | $ 111,057 | $ 117,539
Letters of credit [Member] |  |
Financial instruments whose contract amounts represent credit risk |  |
Financial instruments - contract amounts | 820 | 620
Unused lines of credit [Member] |  |
Financial instruments whose contract amounts represent credit risk |  |
Financial instruments - contract amounts | 80,867 | 88,272
Fixed rate loan commitments [Member] |  |
Financial instruments whose contract amounts represent credit risk |  |
Financial instruments - contract amounts | 3,395 | 1,804
Variable rate loan commitments [Member] |  |
Financial instruments whose contract amounts represent credit risk |  |
Financial instruments - contract amounts | $ 25,975 | $ 26,843

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

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- 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: |

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

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