LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of ALL by Loan Category) (Details) - USD ($) $ in Thousands	Jun. 30, 2020	Sep. 30, 2019
Allowance for Loan Losses:
Balance - Allowance for loans losses	$ 6,000	$ 4,888
Individually evaluated for impairment	221
Collectively evaluated for impairment	5,779	4,888
Balance - Loans receivable	612,469	523,001
Loan balance individually evaluated for impairment	11,959	10,354
Loan balance collectively evaluated for impairment	600,510	512,647
One-to four-family residential [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,069	731
Individually evaluated for impairment
Collectively evaluated for impairment	1,069	731
Balance - Loans receivable	213,415	190,415
Loan balance individually evaluated for impairment	2,170	1,405
Loan balance collectively evaluated for impairment	211,245	189,010
Commercial real estate [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	2,617	2,066
Individually evaluated for impairment	46
Collectively evaluated for impairment	2,571	2,066
Balance - Loans receivable	249,148	232,544
Loan balance individually evaluated for impairment	3,322	4,593
Loan balance collectively evaluated for impairment	245,826	227,951
Construction [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	687	511
Individually evaluated for impairment	175
Collectively evaluated for impairment	512	511
Balance - Loans receivable	23,350	28,451
Loan balance individually evaluated for impairment	5,141	2,900
Loan balance collectively evaluated for impairment	18,209	25,551
Home equity lines of credit [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	182	138
Individually evaluated for impairment
Collectively evaluated for impairment	182	138
Balance - Loans receivable	20,821	17,832
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	20,821	17,832
Commercial business [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,261	1,184
Individually evaluated for impairment
Collectively evaluated for impairment	1,261	1,184
Balance - Loans receivable	101,081	48,769
Loan balance individually evaluated for impairment	1,326	1,456
Loan balance collectively evaluated for impairment	99,755	47,313
Other [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1	8
Individually evaluated for impairment
Collectively evaluated for impairment	1	8
Balance - Loans receivable	4,654	4,990
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	4,654	4,990
Unallocated [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	183	250
Individually evaluated for impairment
Collectively evaluated for impairment	183	250
Balance - Loans receivable
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment

No definition available.

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

- Definition

The valuation allowance for financing receivables that are expected to be uncollectible that were collectively evaluated for impairment.

+ References

+ Details

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

- Definition

Amount of valuation allowance for financing receivables that are expected to be uncollectible that were individually evaluated for impairment.

+ References

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The balance of financing receivables that were collectively evaluated for impairment.

+ References

+ Details

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

- Definition

The balance of financing receivables that were individually evaluated for impairment.

+ References

+ Details

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

- Definition

Amount of allowance to cover probable credit losses on loans and leases. Includes carryover of or adjustments to the allowance for loan losses in connection with business combinations. Excludes allowance for loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (g)
-URI http://asc.fasb.org/extlink&oid=121611835&loc=SL6953423-111524

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 30
-Section 50
-Paragraph 2
-Subparagraph (b)(1)(ii)
-URI http://asc.fasb.org/extlink&oid=121614798&loc=d3e15032-111544

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 50
-Paragraph 11B
-Subparagraph (c)(1)
-URI http://asc.fasb.org/extlink&oid=121611835&loc=SL6953423-111524

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section S99
-Paragraph 4
-Subparagraph (SAB Topic 6.L.1)
-URI http://asc.fasb.org/extlink&oid=27010918&loc=d3e74567-122707

+ Details

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

- Definition

Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121593590&loc=d3e4428-111522

+ Details

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

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_Residential1To4FamilyRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialRealEstateMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_ConstructionLoansMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_HomeEquityMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_CommercialLoanMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_FinancingReceivableOtherMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=us-gaap_UnallocatedFinancingReceivablesMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: