LOANS RECEIVABLE, NET - Schedule of Loans Receivable (Details) - USD ($) $ in Thousands	Sep. 30, 2025	Sep. 30, 2024
Schedule of Loans Receivable [Line Items]
Total loans receivable	$ 858,899	$ 781,216
Net deferred loan costs	(1,546)	(1,054)
Total loans receivable, net	857,353	780,162
One-to-four family residential [Member]
Schedule of Loans Receivable [Line Items]
One-to-four family residential	242,454	246,201
Commercial real estate [Member]
Schedule of Loans Receivable [Line Items]
Commercial real estate	533,213	461,319
Construction and land [Member]
Schedule of Loans Receivable [Line Items]
Construction and land	29,287	22,722
Home equity loans and lines of credit [Member]
Schedule of Loans Receivable [Line Items]
Home equity loans and lines of credit	31,778	24,728
Commercial business [Member]
Schedule of Loans Receivable [Line Items]
Commercial business	20,048	24,011
Other [Member]
Schedule of Loans Receivable [Line Items]
Other	$ 2,119	$ 2,235

Amount of commercial business.

No definition available.

Name:	mgyr_CommercialBusiness
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of home equity lines of credit.

+ References

No definition available.

+ Details

Name:	mgyr_HomeEquityLinesOfCredit
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of deferred costs incurred to originate loans and leases from face amounts of acquired loans.

+ References

No definition available.

+ Details

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

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

No definition available.

+ Details

Name:	mgyr_LoansReceivableGrossCarryingAmount
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of family residential.

+ References

No definition available.

+ Details

Name:	mgyr_OnetoFourfamilyResidential
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- 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

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 310
-SubTopic 20
-Name Accounting Standards Codification
-Section 40
-Paragraph 7
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481628/310-20-40-7

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-2

+ Details

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

- Definition

Unsecured short-term debt instrument issued by corporations which are highly liquid investments that are both readily convertible to known amounts of cash and so near their maturity that they present insignificant risk of changes in value because of changes in interest rates. Generally, only investments with original maturities of three months or less qualify under that definition. Original maturity means original maturity to the entity holding the investment. For example, both a three-month US Treasury bill and a three-year Treasury note purchased three months from maturity qualify as cash equivalents. However, a Treasury note purchased three-years ago does not become a cash equivalent when its remaining maturity is three months.

+ References

No definition available.

+ Details

Name:	us-gaap_CommercialPaperAtCarryingValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of structure or a modification to a structure under construction. Includes recently completed structures or modifications to structures that have not been placed into service.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 360
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482099/360-10-50-1

+ Details

Name:	us-gaap_ConstructionInProgressGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount, after allowance for credit loss, of accounts and financing receivables, classified as noncurrent. Includes, but is not limited to, notes and loan receivable.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-2

+ Details

Name:	us-gaap_LongTermAccountsNotesAndLoansReceivableNetNoncurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount due from parties in nontrade transactions, classified as other.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 944
-SubTopic 605
-Name Accounting Standards Codification
-Section 55
-Paragraph 14
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477548/944-605-55-14

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 944
-SubTopic 605
-Name Accounting Standards Codification
-Section 55
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477548/944-605-55-11

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 280
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 49
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482785/280-10-55-49

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(5)(a)(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(3)(a)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

Name:	us-gaap_OtherReceivables
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_Residential1To4FamilyRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ConstructionLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_HomeEquityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_FinancingReceivableOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: