LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of ALL by Loan Category) (Details) - USD ($) $ in Thousands	Dec. 31, 2020	Sep. 30, 2020
Allowance for Loan Losses:
Balance - Allowance for loans losses	$ 7,130	$ 6,400
Individually evaluated for impairment	39	221
Collectively evaluated for impairment	7,091	6,179
Balance - Loans receivable	607,030	611,259
Loan balance individually evaluated for impairment	13,196	14,161
Loan balance collectively evaluated for impairment	593,834	597,098
One-to four-family residential [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,155	1,035
Individually evaluated for impairment
Collectively evaluated for impairment	1,155	1,035
Balance - Loans receivable	208,404	210,360
Loan balance individually evaluated for impairment	2,378	2,601
Loan balance collectively evaluated for impairment	206,026	207,759
Commercial real estate [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	3,408	3,232
Individually evaluated for impairment	10	46
Collectively evaluated for impairment	3,398	3,186
Balance - Loans receivable	260,296	248,134
Loan balance individually evaluated for impairment	4,335	4,405
Loan balance collectively evaluated for impairment	255,961	243,729
Construction [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	470	672
Individually evaluated for impairment	29	175
Collectively evaluated for impairment	441	497
Balance - Loans receivable	23,441	28,242
Loan balance individually evaluated for impairment	4,580	5,141
Loan balance collectively evaluated for impairment	18,861	23,101
Home equity lines of credit [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	267	179
Individually evaluated for impairment
Collectively evaluated for impairment	267	179
Balance - Loans receivable	19,837	19,373
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	19,837	19,373
Commercial business [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,716	1,034
Individually evaluated for impairment
Collectively evaluated for impairment	1,716	1,034
Balance - Loans receivable	91,215	100,993
Loan balance individually evaluated for impairment	1,903	2,014
Loan balance collectively evaluated for impairment	89,312	98,979
Other [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	2	1
Individually evaluated for impairment
Collectively evaluated for impairment	2	1
Balance - Loans receivable	3,837	4,157
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	3,837	4,157
Unallocated [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	112	247
Individually evaluated for impairment
Collectively evaluated for impairment	112	247
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: