STOCK-BASED COMPENSATION AND STOCK REPURCHASE PROGRAM (Schedule of stock option activity) (Details)	12 Months Ended
Sep. 30, 2022 USD ($) $ / shares shares
Share-Based Payment Arrangement, Noncash Expense [Abstract]
Number of stock options beginning balance \| shares
Number of stock options granted \| shares	293,200
Number of stock options exercised \| shares
Number of stock options forfeited \| shares
Number of stock options expired \| shares
Number of stock options ending balance \| shares	293,200
Weighted average exercise price granted \| $ / shares	$ 12.58
Weighted average exercise price exercised \| $ / shares
Weighted average exercise price forfeited \| $ / shares
Weighted average exercise price expired \| $ / shares
Weighted average exercise price ending balance \| $ / shares	$ 12.58
Weighted average remaining contractual life granted	9 years 11 months 23 days
Weighted average remaining contractual life ending balance	9 years 11 months 23 days
Aggregate intrinsic value granted \| $
Aggregate intrinsic value exercised \| $
Aggregate intrinsic value forfeited \| $
Aggregate intrinsic value expired \| $
Aggregate intrinsic value ending balance \| $
Aggregate intrinsic value exercisable \| $

No definition available.

Name:	mgyr_SharebasedCompensationArrangementBySharebasedPaymentExercisableAggregateIntrinsicValue
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

Name:	mgyr_SharebasedCompensationArrangementBySharebasedPaymentExercisedAggregateIntrinsicValue
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

Name:	mgyr_SharebasedCompensationArrangementBySharebasedPaymentExpiredAggregateIntrinsicValue
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

Name:	mgyr_SharebasedCompensationArrangementBySharebasedPaymentForfeitedAggregateIntrinsicValue
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

Name:	mgyr_SharebasedCompensationArrangementBySharebasedPaymentGrantedAggregateIntrinsicValue
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- References

No definition available.

+ Details

Name:	mgyr_WeightedAveragesRemainingContractualEndingBalance
Namespace Prefix:	mgyr_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

Name:	mgyr_WeightedAveragesRemainingContractualLifeGranted
Namespace Prefix:	mgyr_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- References

No definition available.

+ Details

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

- Definition

Number of options or other stock instruments for which the right to exercise has lapsed under the terms of the plan agreements.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExpirationsInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of shares under options that were cancelled during the reporting period as a result of occurrence of a terminating event specified in contractual agreements pertaining to the stock option plan.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Gross number of share options (or share units) granted during the period.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of options outstanding, including both vested and non-vested options.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Weighted average price at which grantees can acquire the shares reserved for issuance under the stock option plan.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Weighted average price at which option holders acquired shares when converting their stock options into shares.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price at which grantees could have acquired the underlying shares with respect to stock options of the plan that expired.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExpirationsInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average price at which grantees could have acquired the underlying shares with respect to stock options that were terminated.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Weighted average per share amount at which grantees can acquire shares of common stock by exercise of options.

+ References

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Intrinsic value of outstanding award under share-based payment arrangement. Excludes share and unit options.

+ References

No definition available.

+ Details

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

- Definition

Number of share options (or share units) exercised during the current period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(02)
-URI https://asc.fasb.org/extlink&oid=128089324&loc=d3e5070-113901

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI https://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-URI https://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 50
-Paragraph 2
-URI https://asc.fasb.org/extlink&oid=126973232&loc=d3e21463-112644

+ Details

Name:	us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

STOCK-BASED COMPENSATION AND STOCK REPURCHASE PROGRAM (Schedule of stock option activity) (Details)	12 Months Ended
	Sep. 30, 2022 USD ($) $ / shares shares
Share-Based Payment Arrangement, Noncash Expense [Abstract]
Number of stock options beginning balance \| shares
Number of stock options granted \| shares	293,200
Number of stock options exercised \| shares
Number of stock options forfeited \| shares
Number of stock options expired \| shares
Number of stock options ending balance \| shares	293,200
Weighted average exercise price granted \| $ / shares	$ 12.58
Weighted average exercise price exercised \| $ / shares
Weighted average exercise price forfeited \| $ / shares
Weighted average exercise price expired \| $ / shares
Weighted average exercise price ending balance \| $ / shares	$ 12.58
Weighted average remaining contractual life granted	9 years 11 months 23 days
Weighted average remaining contractual life ending balance	9 years 11 months 23 days
Aggregate intrinsic value granted \| $
Aggregate intrinsic value exercised \| $
Aggregate intrinsic value forfeited \| $
Aggregate intrinsic value expired \| $
Aggregate intrinsic value ending balance \| $
Aggregate intrinsic value exercisable \| $