LOANS RECEIVABLE, NET (Schedule of Activity in the Allowance for Loan Losses by Loan Category) (Details) - USD ($) $ in Thousands	12 Months Ended
Sep. 30, 2018	Sep. 30, 2017
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	$ 3,475	$ 3,056
Charge-offs	(386)	(990)
Recoveries	114	66
Provision	997	1,343
Balance at the end of period	4,200	3,475
One-to four-family residential [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	587	542
Charge-offs	(213)	(295)
Recoveries	87	36
Provision	226	304
Balance at the end of period	687	587
Commercial real estate [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	1,277	1,075
Charge-offs		(23)
Recoveries	23
Provision	240	225
Balance at the end of period	1,540	1,277
Construction [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	490	361
Charge-offs
Recoveries	3	12
Provision		117
Balance at the end of period	493	490
Home equity lines of credit [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	57	71
Charge-offs
Recoveries		14
Provision	52	(28)
Balance at the end of period	109	57
Commercial business [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	956	976
Charge-offs	(170)	(672)
Recoveries	1	4
Provision	364	648
Balance at the end of period	1,151	956
Other [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	6	9
Charge-offs	(3)
Recoveries
Provision	22	(3)
Balance at the end of period	25	6
Unallocated [Member]
Activity in the allowance for loan losses by loan category:
Balance at beginning of period	102	22
Charge-offs
Recoveries
Provision	93	80
Balance at the end of period	$ 195	$ 102

A valuation allowance for financing receivables that are expected to be uncollectible.

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

- Definition

Amount of recovery of financing receivables doubtful of collection that were previously charged off.

+ References

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

+ References

No definition available.

+ Details

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

- Definition

Amount of direct write-downs of financing receivables charged against the allowance.

+ References

+ Details

Name:	us-gaap_FinancingReceivableAllowanceForCreditLossesWriteOffs
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of expense related loan transactions, lease transactions, credit loss from transactions other than loan and lease transactions, and other loss based on assessment of uncollectability from the counterparty to reduce the account to their net realizable value.

+ 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 (c)(2)
-URI http://asc.fasb.org/extlink&oid=84173941&loc=SL6953423-111524

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04.11)
-URI http://asc.fasb.org/extlink&oid=114873765&loc=SL114874048-224260

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109223946&loc=d3e3602-108585

+ Details

Name:	us-gaap_ProvisionForLoanLeaseAndOtherLosses
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- 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: