Equity compensation shares.

No definition available.

Name:	mgyr_EquityCompensationShares
Namespace Prefix:	mgyr_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The percentage of repurchase additional.

+ References

No definition available.

+ Details

Name:	mgyr_PercentageOfRepurchaseAdditional
Namespace Prefix:	mgyr_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Principal and interest payable term.

+ References

No definition available.

+ Details

Name:	mgyr_PrincipalAndInterestPayableTerm
Namespace Prefix:	mgyr_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

The amount represents unvested stock options and stock awards.

+ References

No definition available.

+ Details

Name:	mgyr_UnvestedStockOptionsAndStockAwards
Namespace Prefix:	mgyr_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Value of property contributed in noncash investing and financing activities.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482913/230-10-50-4

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482913/230-10-50-3

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 5
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482913/230-10-50-5

+ Details

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

- Definition

The aggregate fair value amounts of derivative instruments that contain credit-risk-related contingent features that are in a net liability position at the end of the reporting period. For nonderivative instruments that are designated and qualify as hedging instruments, the fair value amounts are the carrying value of the nonderivative hedging instrument, including the adjustment for the foreign currency transaction gain (loss) on that instrument.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 815
-SubTopic 10
-Section 50
-Paragraph 4H
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480434/815-10-50-4H

+ Details

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

- Definition

Variable interest rate in effect as of the balance sheet date related to the interest rate derivative.

+ References

No definition available.

+ Details

Name:	us-gaap_DerivativeVariableInterestRate
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of expense for employee benefit and equity-based compensation.

+ References

No definition available.

+ Details

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

- Definition

Price of a single share of a number of saleable stocks of a company.

+ References

No definition available.

+ Details

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

- Definition

Number of allocated shares held by the Employee Stock Option Plan at balance sheet date. Allocated shares are shares that have been assigned to individual participant accounts based on a known formula.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 718
-SubTopic 40
-Section 50
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480489/718-40-50-1

+ Details

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

- Definition

Number of suspense shares held by the Employee Stock Option Plan at balance sheet date. Suspense shares are shares that have not been released, committed to be released or allocated to individual participant accounts.

+ References

+ Details

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

- Definition

Per share or per unit amount of equity securities issued.

+ References

No definition available.

+ Details

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

- Definition

The fair value of stock issued in noncash financing activities.

+ References

+ Details

Name:	us-gaap_StockIssued1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Number of shares of stock issued attributable to transactions classified as other.

+ References

No definition available.

+ Details

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

- Definition

Total number of shares issued during the period, including shares forfeited, as a result of Restricted Stock Awards.

+ References

+ Details

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

- Definition

Amount of noncash expense for option under share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482740/230-10-45-28

+ Details

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

- Definition

Number of shares that have been repurchased during the period and have not been retired and are not held in treasury. Some state laws may govern the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-SubTopic 10
-Topic 505
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481112/505-10-50-2

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 505
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481004/946-505-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(4)(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-3

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-03(i)(2))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479886/946-10-S99-3

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(28))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

Reference 6: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480008/505-10-S99-1

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(29))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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

- Definition

The maximum number of securities classified as temporary equity that are permitted to be issued by an entity's charter and bylaws. Temporary equity is a security with redemption features that are outside the control of the issuer, is not classified as an asset or liability in conformity with GAAP, and is not mandatorily redeemable. Includes any type of security that is redeemable at a fixed or determinable price or on a fixed or determinable date or dates, is redeemable at the option of the holder, or has conditions for redemption which are not solely within the control of the issuer. If convertible, the issuer does not control the actions or events necessary to issue the maximum number of shares that could be required to be delivered under the conversion option if the holder exercises the option to convert the stock to another class of equity. If the security is a warrant or a rights issue, the warrant or rights issue is considered to be temporary equity if the issuer cannot demonstrate that it would be able to deliver upon the exercise of the option by the holder in all cases. Includes stock with put option held by ESOP and stock redeemable by holder only in the event of a change in control of the issuer.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(27)(b))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480566/210-10-S99-1

+ Details

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

- Definition

Number of previously issued common shares repurchased by the issuing entity and held in treasury.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 505
-SubTopic 30
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481549/505-30-45-1

+ Details

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

- Details

Name:	us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

STOCK-BASED COMPENSATION AND STOCK REPURCHASE PROGRAM (Details) - USD ($)			3 Months Ended		12 Months Ended
	Dec. 08, 2022	Aug. 25, 2022	Dec. 31, 2023	Dec. 31, 2022	Dec. 31, 2022	Sep. 30, 2021	Sep. 30, 2023
STOCK-BASED COMPENSATION AND STOCK REPURCHASE PROGRAM (Details) [Line Items]
Equity compensation shares		547,400
Shares of restricted stock			293,200		293,200
Stock option compensation expense (in Dollars)			$ 63,000	$ 69,000
Stock award compensation expense (in Dollars)			98,000	111,000
Unvested stock options and stock awards (in Dollars)			$ 2,400,000
Percentage of repurchase additional	5.00%
Average price (in Dollars per share)	$ 11.51
Stock repurchase program shares	120,062		217,084
Authorized shares			337,146
Treasury stock shares			442,873				423,641
ESOP purchase of shares						312,800
Common stock (in Dollars)						$ 3,400,000
Average cost per share (in Dollars per share)						$ 10.77
Variable interest rate						3.25%
Principal and interest payable term						30 years
Shares allocated to participants							170,335
Shares unallocated to participants							290,313
Aggregate fair value (in Dollars)							$ 3,300,000
Contribution expense (in Dollars)			$ 50,000	$ 41,000
Common Stock [Member]
STOCK-BASED COMPENSATION AND STOCK REPURCHASE PROGRAM (Details) [Line Items]
Average price (in Dollars per share)	$ 337,146
Restricted Stock [Member]
STOCK-BASED COMPENSATION AND STOCK REPURCHASE PROGRAM (Details) [Line Items]
Shares of restricted stock			124,320		156,400