LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR CREDIT LOSSES - Schedule of Loan Portfolio (Details) - USD ($) $ in Thousands	6 Months Ended	12 Months Ended
Mar. 31, 2025	Sep. 30, 2024
One-to-Four Family Residential [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	$ 10,321	$ 32,624
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	33,408	42,084
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	40,444	31,805
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	30,058	25,970
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	24,262	29,998
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	107,453	83,378
Revolving Loans Amortized Cost Basis	1,547	342
Revolving Loans Converted to Term
Total	247,493	246,201
One-to-Four Family Residential [Member] \| Revolving Credit Facility [Member]
One-to-four family residential
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Commercial Real Estate [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	43,117	88,597
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	87,468	84,674
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	89,687	66,412
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	66,537	64,573
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	57,246	29,568
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	146,977	122,845
Revolving Loans Amortized Cost Basis	4,204	3,718
Revolving Loans Converted to Term		932
Total	495,236	461,319
Commercial Real Estate [Member] \| Revolving Credit Facility [Member]
One-to-four family residential
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Construction and Land [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024		5,650
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	9,522	10,061
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	2,448
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020		1,156
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	5,527	4,069
Revolving Loans Amortized Cost Basis		1,786
Revolving Loans Converted to Term
Total	17,497	22,722
Construction and Land [Member] \| Revolving Credit Facility [Member]
One-to-four family residential
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Home Equity Loan [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	631	1,585
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	1,365	1,561
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	1,494	1,600
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	1,702	309
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	852	247
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	2,372	1,220
Revolving Loans Amortized Cost Basis	18,793	17,902
Revolving Loans Converted to Term		304
Total	27,209	24,728
Home Equity Loan [Member] \| Revolving Credit Facility [Member]
One-to-four family residential
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Commercial Business [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	249	2,062
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	1,300	507
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	487	2,517
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	2,116	2,298
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	1,115	802
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	2,669	2,565
Revolving Loans Amortized Cost Basis	13,109	13,072
Revolving Loans Converted to Term		188
Total	21,045	24,011
Commercial Business [Member] \| Revolving Credit Facility [Member]
One-to-four family residential
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Other [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	74	61
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	20
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022		47
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	36
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020		9
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	1,428	1,771
Revolving Loans Amortized Cost Basis	194	347
Revolving Loans Converted to Term
Total	1,752	2,235
Other [Member] \| Revolving Credit Facility [Member]
One-to-four family residential
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Current period gross charge-offs
Performing [Member] \| One-to-Four Family Residential [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	10,321	32,624
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	33,408	42,084
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	40,363	31,711
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	30,058	25,970
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	24,262	29,976
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	107,453	83,378
Revolving Loans Amortized Cost Basis	1,547	342
Revolving Loans Converted to Term
Total	247,412	246,085
Performing [Member] \| Home Equity Loan [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	631	1,585
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	1,365	1,561
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	1,494	1,600
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	1,702	309
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	852	247
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	2,372	1,220
Revolving Loans Amortized Cost Basis	18,793	17,902
Revolving Loans Converted to Term		304
Total	27,209	24,728
Performing [Member] \| Other [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	74	61
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	20
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022		47
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	36
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020		9
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	1,428	1,771
Revolving Loans Amortized Cost Basis	194	347
Revolving Loans Converted to Term
Total	1,752	2,235
Non-performing [Member] \| One-to-Four Family Residential [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	81	94
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020		22
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total	81	116
Non-performing [Member] \| Home Equity Loan [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Non-performing [Member] \| Other [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Pass [Member] \| Commercial Real Estate [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	43,117	88,597
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	87,468	84,674
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	89,687	66,412
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	66,537	64,573
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	57,246	29,568
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	146,977	122,605
Revolving Loans Amortized Cost Basis	4,204	3,718
Revolving Loans Converted to Term		932
Total	495,236	461,079
Pass [Member] \| Construction and Land [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024		5,650
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	9,522	10,061
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	2,448
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020		1,156
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	5,527	4,069
Revolving Loans Amortized Cost Basis		1,786
Revolving Loans Converted to Term
Total	17,497	22,722
Pass [Member] \| Commercial Business [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024	249	2,062
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023	1,300	507
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022	487	2,517
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021	2,116	2,298
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020	1,115	802
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior	2,669	2,565
Revolving Loans Amortized Cost Basis	13,109	13,072
Revolving Loans Converted to Term		188
Total	21,045	24,011
Special Mention [Member] \| Commercial Real Estate [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior		124
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total		124
Special Mention [Member] \| Construction and Land [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Special Mention [Member] \| Commercial Business [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Substandard [Member] \| Commercial Real Estate [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior		116
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total		116
Substandard [Member] \| Construction and Land [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Substandard [Member] \| Commercial Business [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Doubtful [Member] \| Commercial Real Estate [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Doubtful [Member] \| Construction and Land [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total
Doubtful [Member] \| Commercial Business [Member]
One-to-four family residential
Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024
Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023
Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022
Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021
Term Loans Amortized Cost Basis by Origination Fiscal Year 2021/ 2020
Term Loans Amortized Cost Basis by Origination Fiscal Year Prior
Revolving Loans Amortized Cost Basis
Revolving Loans Converted to Term
Total

No definition available.

Name:	mgyr_OneToFourFamilyResidentialAbstract
Namespace Prefix:	mgyr_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of writeoff of financing receivable, charged against allowance for credit loss.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 13
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-13

Reference 2: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11B
-Subparagraph (c)(3)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-11B

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 79
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-79

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-6

+ Details

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

- Definition

Amortized cost of financing receivable originated more than five years prior to current fiscal year. Excludes net investment in lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 79
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-79

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-6

+ Details

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

- Definition

Amortized cost of financing receivable originated four years prior to current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amortized cost of financing receivable originated in current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amortized cost of financing receivable originated in fiscal year prior to current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amount of writeoff of financing receivable originated more than five years before current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amortized cost of financing receivable originated three years prior to current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amortized cost of financing receivable originated two years prior to current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amortized cost of financing receivable that can be withdrawn, repaid, and redrawn.

+ References

+ Details

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

- Definition

Amortized cost of revolving financing receivable converted to term loan.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 79
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-79

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-6A

+ Details

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

- Definition

Amount of writeoff of revolving financing receivable converted to term loan.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 79
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-79

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-6A

+ Details

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

- Definition

Amount of writeoff of financing receivable that can be withdrawn, repaid, and redrawn.

+ References

+ Details

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

- Definition

Amount of writeoff of financing receivable originated four years before current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amount of writeoff of financing receivable originated three years before current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amount of writeoff of financing receivable originated in current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amount of writeoff of financing receivable originated two years before current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amount of writeoff of financing receivable originated in fiscal year before current fiscal year. Excludes net investment in lease.

+ References

+ Details

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

- Definition

Amortized cost, before allowance for credit loss, of financing receivable. Excludes financing receivable covered under loss sharing agreement and net investment in lease.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479344/326-20-45-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 825
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482736/825-10-45-1A

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 948
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477011/948-310-45-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-13

Reference 5: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 7A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-7A

Reference 6: http://fasb.org/us-gaap/role/ref/otherTransitionRef
-Topic 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 29
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481962/310-10-50-29

Reference 7: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1405
-Paragraph a
-Subparagraph (1)
-Publisher SEC

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Name Regulation S-K (SK)
-Number 229
-Section 1405
-Paragraph a
-Subparagraph (2)
-Publisher SEC

Reference 9: http://www.xbrl.org/2009/role/commonPracticeRef
-Name Regulation S-K (SK)
-Number 229
-Section 1404
-Paragraph a
-Publisher SEC

Reference 10: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 80
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-80

Reference 11: http://www.xbrl.org/2003/role/exampleRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 79
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479294/326-20-55-79

Reference 12: http://www.xbrl.org/2003/role/disclosureRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(3)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 14
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-14

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Topic 326
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479319/326-20-50-5

+ Details

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

- Details

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

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_RevolvingCreditFacilityMember
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=mgyr_ConstructionAndLandMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

Name:	us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis=mgyr_CommercialBusinessMember
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_FinancialInstrumentPerformanceStatusAxis=us-gaap_PerformingFinancingReceivableMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_FinancialInstrumentPerformanceStatusAxis=us-gaap_NonperformingFinancingReceivableMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InternalCreditAssessmentAxis=us-gaap_PassMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InternalCreditAssessmentAxis=us-gaap_SpecialMentionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InternalCreditAssessmentAxis=us-gaap_SubstandardMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_InternalCreditAssessmentAxis=us-gaap_DoubtfulMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: