FAIR VALUE DISCLOSURES (Schedule of the Carrying Amount, Fair Value, and Placement in the Fair Value Hierarchy of Financial Instruments) (Details) - USD ($) $ in Thousands	Mar. 31, 2016	Sep. 30, 2015
Financial instruments - assets
Investment securities held to maturity	$ 58,886	$ 52,614
Fair value of investment securities - held to maturity	59,573	53,248
Reported Value
Financial instruments - assets
Investment securities held to maturity	58,886	52,614
Loans	421,080	420,596
Financial instruments - liabilities
Certificates of deposit including retirement certificates	133,666	143,108
Borrowings	29,334	31,594
Fair Value
Financial instruments - assets
Fair value of investment securities - held to maturity	59,573	53,248
Loans	426,310	425,890
Financial instruments - liabilities
Certificates of deposit including retirement certificates	134,974	144,150
Borrowings	$ 29,957	$ 32,231
Fair Value, Inputs, Level 1 [Member]
Financial instruments - assets
Fair value of investment securities - held to maturity
Loans
Financial instruments - liabilities
Certificates of deposit including retirement certificates
Borrowings
Fair Value, Inputs, Level 2 [Member]
Financial instruments - assets
Fair value of investment securities - held to maturity	$ 59,573	$ 53,248
Loans
Financial instruments - liabilities
Certificates of deposit including retirement certificates	$ 134,974	$ 144,150
Borrowings	$ 29,957	$ 32,231
Fair Value, Inputs, Level 3 [Member]
Financial instruments - assets
Fair value of investment securities - held to maturity
Loans	$ 426,310	$ 425,890
Financial instruments - liabilities
Certificates of deposit including retirement certificates
Borrowings

Amount of interest-bearing domestic certificate of deposit liabilities.

No definition available.

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

- Definition

Fair value portion of debt instrument payable, including, but not limited to, notes payable and loans payable.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 10
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=49121117&loc=d3e13433-108611

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 825
-SubTopic 10
-Section 50
-Paragraph 12
-URI http://asc.fasb.org/extlink&oid=49121117&loc=d3e13476-108611

+ Details

Name:	us-gaap_DebtInstrumentFairValue
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Amount before other than temporary impairment (OTTI) accretion, of investments in debt securities classified as held-to-maturity.

+ References

No definition available.

+ Details

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

- Definition

Fair value of investments in debt securities classified as held-to-maturity.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 5
-Subparagraph (aa)
-URI http://asc.fasb.org/extlink&oid=27724398&loc=d3e27232-111563

Reference 2: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 5
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=27724398&loc=d3e27232-111563

Reference 3: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 50
-Paragraph 5
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=27724398&loc=d3e27232-111563

+ Details

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

- Definition

Fair value portion of loan receivable, including, but not limited to, mortgage loans held for investment, finance receivables held for investment, policy loans on insurance contracts.

+ References

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Glossary Loan
-URI http://asc.fasb.org/extlink&oid=6517073

+ Details

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

- Details

Name:	us-gaap_FairValueByMeasurementBasisAxis=us-gaap_CarryingReportedAmountFairValueDisclosureMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByMeasurementBasisAxis=us-gaap_EstimateOfFairValueFairValueDisclosureMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel1Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel2Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FairValueByFairValueHierarchyLevelAxis=us-gaap_FairValueInputsLevel3Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: