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OTHER REAL ESTATE OWNED (Details) - USD ($) $ in Thousands	12 Months Ended
	Sep. 30, 2025	Sep. 30, 2024
Other Real Estate Owned [Abstract]
Real estate owned properties	$ 2,200	$ 3,700
Real estate sold properties total	1,800
Real estate write down	$ 57

X

- Definition

Real estate sold properties total.

+ References

No definition available.

+ Details

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

X

- Definition

Real estate write down.

+ References

No definition available.

+ Details

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

X

- References

No definition available.

+ Details

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

X

- Definition

Amount of expense recognized in the income statement for a decrease in valuation of real estate owned (REO).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10)(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

+ Details

Name:	us-gaap_RealEstateOwnedValuationAllowanceProvision1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration