LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of ALL by Loan Category) (Details) - USD ($) $ in Thousands	Jun. 30, 2018	Sep. 30, 2017
Allowance for Loan Losses:
Balance - Allowance for loans losses	$ 3,985	$ 3,475
Individually evaluated for impairment
Collectively evaluated for impairment	3,985	3,475
Balance - Loans receivable	502,658	473,991
Loan balance individually evaluated for impairment	5,350	7,455
Loan balance collectively evaluated for impairment	497,308	466,536
One-to four-family residential [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	534	587
Individually evaluated for impairment
Collectively evaluated for impairment	534	587
Balance - Loans receivable	181,024	178,336
Loan balance individually evaluated for impairment	1,253	3,124
Loan balance collectively evaluated for impairment	179,771	175,212
Commercial real estate [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,488	1,277
Individually evaluated for impairment
Collectively evaluated for impairment	1,488	1,277
Balance - Loans receivable	216,058	207,118
Loan balance individually evaluated for impairment	3,680	4,088
Loan balance collectively evaluated for impairment	212,378	203,030
Construction [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	512	490
Individually evaluated for impairment
Collectively evaluated for impairment	512	490
Balance - Loans receivable	29,663	22,622
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	29,663	22,622
Home equity lines of credit [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	116	57
Individually evaluated for impairment
Collectively evaluated for impairment	116	57
Balance - Loans receivable	19,232	18,536
Loan balance individually evaluated for impairment	58
Loan balance collectively evaluated for impairment	19,174	18,536
Commercial business [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,177	956
Individually evaluated for impairment
Collectively evaluated for impairment	1,177	956
Balance - Loans receivable	51,188	41,113
Loan balance individually evaluated for impairment	359	243
Loan balance collectively evaluated for impairment	50,829	40,870
Other [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	4	6
Individually evaluated for impairment
Collectively evaluated for impairment	4	6
Balance - Loans receivable	5,493	6,266
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	5,493	6,266
Unallocated [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	154	102
Individually evaluated for impairment
Collectively evaluated for impairment	154	102
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

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=84173941&loc=SL6953423-111524

+ 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

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 (h)
-URI http://asc.fasb.org/extlink&oid=84173941&loc=SL6953423-111524

+ 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

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 (h)
-URI http://asc.fasb.org/extlink&oid=84173941&loc=SL6953423-111524

+ 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 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03.7(d))
-URI http://asc.fasb.org/extlink&oid=6876686&loc=d3e534808-122878

Reference 2: 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=84173941&loc=SL6953423-111524

Reference 3: 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=82894903&loc=d3e15032-111544

Reference 4: 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=84173941&loc=SL6953423-111524

Reference 5: 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=82891408&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: