LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR LOAN LOSSES (Schedule of ALL by Loan Category) (Details) - USD ($) $ in Thousands	Mar. 31, 2022	Sep. 30, 2021
Allowance for Loan Losses:
Balance - Allowance for loans losses	$ 8,300	$ 8,075
Individually evaluated for impairment	224	224
Collectively evaluated for impairment	8,076	7,851
Balance - Loans receivable	618,452	594,617
Loan balance individually evaluated for impairment	8,799	11,068
Loan balance collectively evaluated for impairment	609,653	583,549
One-to four-family residential [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,113	1,136
Individually evaluated for impairment
Collectively evaluated for impairment	1,113	1,136
Balance - Loans receivable	206,083	203,019
Loan balance individually evaluated for impairment	1,537	2,711
Loan balance collectively evaluated for impairment	204,546	200,308
Commercial real estate [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	4,082	3,744
Individually evaluated for impairment
Collectively evaluated for impairment	4,082	3,744
Balance - Loans receivable	317,665	280,848
Loan balance individually evaluated for impairment	1,178	2,270
Loan balance collectively evaluated for impairment	316,487	278,578
Construction [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	803	594
Individually evaluated for impairment	234	224
Collectively evaluated for impairment	579	370
Balance - Loans receivable	26,847	20,350
Loan balance individually evaluated for impairment	4,580	4,580
Loan balance collectively evaluated for impairment	22,267	15,770
Home equity lines of credit [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	220	232
Individually evaluated for impairment
Collectively evaluated for impairment	220	232
Balance - Loans receivable	15,623	17,930
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	15,623	17,930
Commercial business [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	1,839	2,046
Individually evaluated for impairment
Collectively evaluated for impairment	1,839	2,046
Balance - Loans receivable	48,942	68,719
Loan balance individually evaluated for impairment	1,504	1,507
Loan balance collectively evaluated for impairment	47,438	67,212
Other [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	2	15
Individually evaluated for impairment
Collectively evaluated for impairment	2	15
Balance - Loans receivable	3,292	3,751
Loan balance individually evaluated for impairment
Loan balance collectively evaluated for impairment	3,292	3,751
Unallocated [Member]
Allowance for Loan Losses:
Balance - Allowance for loans losses	241	308
Individually evaluated for impairment
Collectively evaluated for impairment	241	308
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 https://asc.fasb.org/extlink&oid=123577603&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 https://asc.fasb.org/extlink&oid=123577603&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 https://asc.fasb.org/extlink&oid=123577603&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://www.xbrl.org/2009/role/commonPracticeRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 310
-SubTopic 10
-Section S99
-Paragraph 4
-Subparagraph (SAB Topic 6.L.1)
-URI https://asc.fasb.org/extlink&oid=122038336&loc=d3e74567-122707

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 https://asc.fasb.org/extlink&oid=123577603&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 https://asc.fasb.org/extlink&oid=121614798&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 https://asc.fasb.org/extlink&oid=123577603&loc=SL6953423-111524

+ 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 https://asc.fasb.org/extlink&oid=124259787&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: