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SERVICING POLICY (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2025 | Sep. 30, 2024
Servicing Policy [Abstract] |  |
Loans sold with servicing retained | $ 19,000 | $ 6,400
Loans sold, servicing released | 0 | 0
Value of loans sold still being serviced | 1,100 | 1,400
Loans sold amount | $ 39,800 | $ 38,400

X
- Definition Value of loans sold during the period where servicing rights were released. + References No definition available. + Details
Name: | mgyr_LoansSoldServicingReleased
Namespace Prefix: | mgyr_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition The sum of the proceeds from the sale of loans. + References No definition available. + Details
Name: | mgyr_ProceedsFromSalesOfLoans
Namespace Prefix: | mgyr_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition The value of loans that have been sold by the company, but which are still being serviced. + References No definition available. + Details
Name: | mgyr_ValueOfLoansSoldStillBeingServiced
Namespace Prefix: | mgyr_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

X
- Definition Amount of decrease in allowance for credit loss on financing receivable from sale of loan. Excludes net investment in lease. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 326 -SubTopic 20 -Name Accounting Standards Codification -Section 50 -Paragraph 13 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479319/326-20-50-13 + Details
Name: | us-gaap_FinancingReceivableAllowanceForCreditLossLoanSold
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- References No definition available. + Details
Name: | us-gaap_TransfersAndServicingAbstract
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration