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FINANCIAL INSTRUMENTS WITH OFF-BALANCE SHEET RISK - Schedule of Information Regarding Derivatives (Details) - USD ($) $ in Thousands	3 Months Ended	12 Months Ended
	Dec. 31, 2024	Sep. 30, 2024
Customer Interest Rate Swaps [Member]
Classified in Other Assets:
Notional Amount	$ 34,599	$ 34,890
Average Maturity (Years)	2 years 10 months 24 days	3 years 2 months 12 days
Weighted Average Fixed Rate	4.96%	4.96%
Weighted Average Variable Rate	1 Mo. BSBY + 2.44	1 Mo. BSBY + 2.44
Fair Value	$ 1,510	$ 1,405
Classified in Other Assets [Member]
Classified in Other Assets:
Notional Amount	$ 34,599	$ 34,890
Average Maturity (Years)	2 years 10 months 24 days	3 years 2 months 12 days
Weighted Average Fixed Rate	4.96%	4.96%
Fair Value	$ 1,510	$ 1,405
3rd Party Interest Rate swaps [Member]
Classified in Other Assets:
Notional Amount	$ 34,599	$ 34,890
Average Maturity (Years)	2 years 10 months 24 days	3 years 2 months 12 days
Weighted Average Fixed Rate	4.96%	4.96%
Weighted Average Variable Rate	1 Mo. BSBY + 2.44	1 Mo. BSBY + 2.44
Fair Value	$ 1,510	$ 1,405
Classified in Other Liabilities [Member]
Classified in Other Assets:
Notional Amount	$ 34,599	$ 34,890
Average Maturity (Years)	2 years 10 months 24 days	3 years 2 months 12 days
Weighted Average Fixed Rate	4.96%	4.96%
Fair Value	$ 1,510	$ 1,405

X

- Definition

Weighted Average Variable Rate.

+ References

No definition available.

+ Details

Name:	mgyr_DerivativesWeightedAverageVariableRate
Namespace Prefix:	mgyr_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

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

X

- Definition

Average fixed interest rate related to the group of interest rate derivatives.

+ References

No definition available.

+ Details

Name:	us-gaap_DerivativeAverageFixedInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

X

- Definition

Average remaining period until maturity of the derivative contract, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	us-gaap_DerivativeAverageRemainingMaturity1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Fair value of the assets less the liabilities of a derivative or group of derivatives.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482907/825-10-50-10

+ Details

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

X

- Definition

Nominal or face amount used to calculate payment on derivative.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-1B

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1A
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-1A

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	na
Period Type:	instant

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mgyr_ClassifiedInOtherAssetsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mgyr_ThirdPartyInterestRateSwapsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

X

- Details

Name:	us-gaap_DerivativeInstrumentRiskAxis=mgyr_ClassifiedInOtherLiabilitiesMember
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