FHLB stock per value.

No definition available.

Name:	mgyr_FHLBStockPerValue
Namespace Prefix:	mgyr_
Data Type:	dtr:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

The percentage of pension plan.

+ References

No definition available.

+ Details

Name:	mgyr_PensionPlanRate
Namespace Prefix:	mgyr_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Revenue from contracts with customers included in service charges.

+ References

No definition available.

+ Details

Name:	mgyr_RevenueFromContractsWithCustomersIncludedInServiceCharges
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Aggregate dividends declared during the period for each share of common stock outstanding.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1

+ Details

Name:	us-gaap_CommonStockDividendsPerShareDeclared
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount, before allowance for credit loss, of accrued interest on investment in debt security measured at amortized cost (held-to-maturity).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 3B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-3B

+ Details

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

- Definition

The per share amount of a dividend declared, but not paid, as of the financial reporting date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482913/230-10-50-3

+ Details

Name:	us-gaap_DividendsPayableAmountPerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Percentage of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482685/740-10-50-12

Reference 2: http://www.xbrl.org/2003/role/exampleRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 231
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482663/740-10-55-231

+ Details

Name:	us-gaap_EffectiveIncomeTaxRateContinuingOperations
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Carrying amount as of the balance sheet date of interest earned but not received. Also called accrued interest or accrued interest receivable.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477802/946-310-45-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-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

+ Details

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

- Definition

The total amount of other operating income, the components of which are not separately disclosed on the income statement, from items that are associated with the entity's normal revenue producing operation.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 220
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2

+ Details

Name:	us-gaap_OtherOperatingIncome
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- 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 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(23)(c))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

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

- Details

Name:	us-gaap_DebtInstrumentAxis=mgyr_ACLMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES (Details) - USD ($) $ / shares in Units, $ in Thousands		12 Months Ended
	Nov. 22, 2024	Sep. 30, 2024	Sep. 30, 2023	Oct. 31, 2024
Summary of Significant Accounting Policies [Line Items]
Available-for-sale securities		$ 225
FHLB stock per value (in Dollars per share)		$ 100
Accrued interest receivable		$ 4,600
Revenue from contracts with customers included in service charges		1,100	$ 1,600
Other operating income		$ 81	$ 89
Income tax rate		25.00%
Pension plan		28.00%
Cash dividend per share (in Dollars per share)				$ 0.05
Dividend of per share (in Dollars per share)	$ 0.04
ACL [Member]
Summary of Significant Accounting Policies [Line Items]
Available-for-sale securities		$ 162