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Equity - Narrative (Details)
 3 Months Ended 9 Months Ended 12 Months Ended
May 20, 2024
USD ($)
$ / shares
Feb. 28, 2020
USD ($)
shares
Sep. 30, 2024
USD ($)
entity
$ / shares
shares
Jun. 30, 2024
shares
Mar. 31, 2024
shares
Sep. 30, 2023
USD ($)
shares
Jun. 30, 2023
shares
Mar. 31, 2023
shares
Sep. 30, 2024
USD ($)
entity
$ / shares
shares
Sep. 30, 2023
USD ($)
shares
Dec. 31, 2023
entity
$ / shares
shares
Dec. 31, 2022
USD ($)
$ / shares
shares
Sep. 06, 2024
USD ($)
Dec. 31, 2020
shares
Class of Stock [Line Items]                            
Common stock, shares outstanding (in shares)     44,978,969           44,978,969   27,460,161      
Common stock, par value per share (in dollars per share) | $ / shares     $ 0.01           $ 0.01   $ 0.01      
Common stock, shares authorized (in shares)     125,000,000           125,000,000   125,000,000      
Stock repurchased and retired during period | $                 $ 19,100,000          
Preferred stock, par value per share (in dollars per share) | $ / shares                       $ 25.00    
Exchange of preferred shares and warrants (in shares)           0       0        
Preferred stock, shares authorized (in shares)     25,000,000           25,000,000   25,000,000      
Common stock authorized | $   $ 25,000,000.0                        
Stock repurchased (in shares)     0     0     0 0        
Stock repurchased, value | $                 $ 5,100,000          
Treasury stock (in shares)     1,664,365           1,664,365   1,035,785      
Sale of common stock, net of offering costs | $                 $ 14,000,000 $ 17,181,000        
Number of non controlling interest subsidiaries | entity     2           2   3      
Open market purchases                            
Class of Stock [Line Items]                            
Stock repurchased (in shares)   525,039             525,039   525,039      
At-the-Market Program                            
Class of Stock [Line Items]                            
Common stock authorized | $     $ 100,000,000           $ 100,000,000       $ 400,000,000  
Sale of common stock (in shares)     0     2,182,152     0 2,621,742        
Sale of common stock, net of offering costs | $           $ 14,300,000       $ 17,200,000        
AS Ajax E II LLC                            
Class of Stock [Line Items]                            
Ownership percentage by parent (as percent)     0.00%           0.00%   53.10%      
2017-D                            
Class of Stock [Line Items]                            
Ownership percentage by parent (as percent)     50.00%           50.00%   50.00%      
Great Ajax II REIT                            
Class of Stock [Line Items]                            
Ownership percentage by parent (as percent)     99.90%           99.90%   99.90%      
Thetis Asset Management LLC                            
Class of Stock [Line Items]                            
Treasury stock (in shares)     777,414           777,414          
Treasury stock, received (in shares)     628,580               148,834      
Gregory                            
Class of Stock [Line Items]                            
Treasury stock, received (in shares)     361,912               361,912      
7.25% Series A preferred stock                            
Class of Stock [Line Items]                            
Preferred stock, shares issued (in shares)     0           0   424,949     2,307,400
Preferred stock, liquidation preference per share (in dollars per share) | $ / shares     $ 25.00           $ 25.00   $ 25.00      
Preferred stock, shares outstanding (in shares)     0           0   424,949      
5.00% Series B preferred stock                            
Class of Stock [Line Items]                            
Preferred stock, shares issued (in shares)     0           0   1,135,590     2,892,600
Preferred stock, liquidation preference per share (in dollars per share) | $ / shares     $ 25.00           $ 25.00   $ 25.00      
Preferred stock, discount (in percent)                       2.50%    
Preferred stock, shares outstanding (in shares)     0           0   1,135,590      
Rithm | Secured Debt | Line of Credit                            
Class of Stock [Line Items]                            
Stock price of common stock (in dollars per share) | $ / shares $ 4.87   $ 4.87           $ 4.87          
Sale of stock, consideration received on transaction | $ $ 14,000,000               $ 14,000,000.0          
Preferred stock                            
Class of Stock [Line Items]                            
Preferred stock discount | $     $ 0     $ 0     $ 0 $ 0   $ 8,200,000    
Preferred stock | 7.25% Series A preferred stock                            
Class of Stock [Line Items]                            
Exchange of shares (in shares)                 424,949          
Stock repurchased and retired during period, shares (in shares)                       1,882,451    
Exchange of preferred shares and warrants (in shares)         424,949                  
Preferred stock, shares outstanding (in shares)     0 0 0 424,949 424,949 424,949 0 424,949 424,949 424,949    
Preferred stock | 5.00% Series B preferred stock                            
Class of Stock [Line Items]                            
Exchange of shares (in shares)                 1,135,590          
Stock repurchased and retired during period, shares (in shares)                       1,757,010    
Stock repurchased and retired during period | $                       $ 88,700,000    
Stock repurchased and retired during period, average price per share (in dollars per share) | $ / shares                       $ 24.37    
Exchange of preferred shares and warrants (in shares)         1,135,590                  
Preferred stock, shares outstanding (in shares)     0 0 0 1,135,590 1,135,590 1,135,590 0 1,135,590 1,135,590 1,135,590    
Common stock                            
Class of Stock [Line Items]                            
Common stock, shares outstanding (in shares)     44,978,969 45,605,549 36,992,019 25,808,681 23,627,677 23,509,446 44,978,969 25,808,681 27,460,161 23,130,956    
Sale of shares (in shares)       2,874,744   2,182,152 94,012 345,578 2,874,744          
Stock-based management termination fee expense (in shares)       3,174,645         3,174,645          
Exchange of shares (in shares)       2,581,694 9,464,524       12,046,218          
Exchange of preferred shares and warrants (in shares)       2,581,694 9,464,524                  
Treasury stock, received (in shares)     628,580       4,176              
Issuance of shares under dividend reinvestment plan (in shares)     0     0     0 0