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COMMITMENTS (Details) - Schedule of Balance Sheet Information Related to Leases - USD ($) $ in Thousands	Sep. 30, 2024	Sep. 30, 2023
Schedule of Balance Sheet Information Related to Leases [Abstract]
Operating lease right-of-use asset	$ 2,223	$ 2,687
Operating lease liabilities	$ 2,413	$ 2,944
Weighted average remaining lease term in years	6 years	6 years 4 months 24 days
Weighted average discount rate	2.40%	2.20%

X

- Definition

Indicates line item in statement of financial position that includes operating lease liability.

+ References

No definition available.

+ Details

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

X

- Definition

Indicates line item in statement of financial position that includes operating lease right-of-use asset.

+ References

No definition available.

+ Details

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

X

- References

No definition available.

+ Details

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

X

- Definition

Weighted average discount rate for operating lease calculated at point in time.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(4)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

+ Details

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

X

- Definition

Weighted average remaining lease term for operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 53
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479589/842-20-55-53

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (g)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-4

+ Details

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