HELENE N. WHITE, Circuit Judge.
This diversity action alleging legal malpractice and several other claims was before us on a prior appeal from a subject-matter-jurisdiction dismissal for failure to meet the jurisdictional amount-in-controversy requirement. We reversed that dismissal and remanded for further proceedings. Plaintiff-Appellant Michael Brautigam, an attorney proceeding pro se, now challenges the district court’s order on remand affirming the report and recommendation of a magistrate judge. The issues are whether the district court properly concluded that the law of the case mandated dismissal of Brautigam’s malpractice claims against Defendant Geoffrey P. Damon on statute-of-limitations grounds; whether the district court should have granted Brautigam’s motion to file an amended complaint; whether [846]*846the district court erred in dismissing the claims against Defendant Daryl Crosth-waite; and whether the magistrate judge was biased. We affirm.1
I.
This court’s prior opinion explained:
In September [sic August] 2011, Brauti-gam sued [attorneys Geoffrey Damon, Daryl Crosthwaite, and Eric C. Deters, as well as Eric C. Deters & Assoc., alleging] breach of a fiduciary duty, legal malpractice, unjust enrichment, and negligence against all defendants; promissory estoppel against Damon only; and conversion against Damon and Crosth-waite ...
Brautigam alleged that he retained attorney Damon, a partner with Butko-vich & Crosthwaite Co., LPA (“B&C”), to represent him in two actions: (1) a legal malpractice action against Paul Hackett and others (“Hackett litigation”), and (2) a civil rights action against a judge for “falsely arresting Brautigam] and sentencing Brautigam] to six months in jail.” Damon accepted both cases on a contingency fee basis. Brautigam, however, paid Damon $16,500 of which Damon returned $10,000. Damon did not file the civil rights complaint, and Brautigam contends that he has lost his right to recover as a result.
On August 3, 2010, Damon moved to withdraw as Brautigam’s counsel in the Hackett litigation. The next day B&C mailed a letter to Brautigam, stating that Damon was no longer associated with B&C and asking him to elect whether he would like B&C to continue representing him in his “case(s).” According to Brautigam, he elected to proceed with B&C. In mid-August, he was advised that B&C would not be proceeding with the litigation and would help Brautigam transition to a new attorney; but. instead, B&C abandoned him as a client. In November 2010, Damon’s motion to withdraw was granted. That same month, Brautigam contends, he learned that Damon had left B&C and was working for Eric C. Deters & Associates.
The defendants in the Hackett litigation successfully moved for summary judgment. Brautigam’s complaint states that had “Damon met the applicable standard of care[,] properly conducted discovery[, and] properly responded to [defendants’] motion[s] for summary judgment,” defendants’ motions would not have been granted. Brautigam unsuccessfully appealed that judgment to the Ohio Court of Appeals....
In October 2013, Damon filed a motion to dismiss, arguing that the amount-in-controversy requirement was not satisfied. See Fed. R. Civ. P. 12(b)(1). A magistrate judge recommended granting that motion because Brautigám’s alleged damages bore no rational relationship to his legal claims and thus were not presented in good faith, and because Brau-tigam’s malpractice claims were valueless, Over Brautigam’s objections, the district court adopted the report and recommendation and dismissed the ac[847]*847tion for lack of subject-matter .jurisdiction ....
.... Brautigam sought three categories of damages: unreturned legal fees; recovery for his lost civil action; and damages for malpractice arising from Damon’s handling of the Hackett litigation. The district court concluded that the value of Brautigam’s claims was approximately $6,125, which was the unrefund-ed amount Brautigam paid to Damon ... [, and] determined that Brautigam’s claim for the loss of the civil suit was valueless because absolute judicial immunity provided a complete defense. Because a defense may not be considered in determining whether the plaintiff has satisfied the jurisdictional amount, the district court erred in excluding Brauti-gam’s valuation of these damages from consideration. See Kovacs [v. Chesley ], 406 F.3d [393,] 396 [(6th Cir. 2005)]. The district court also erred in excluding Brautigam’s malpractice damages from consideration. Those damages derived from Damon’s handling of the Hackett litigation. Brautigam maintained that Hackett settled a lawsuit without Brauti-gam’s permission. Damon filed a state-court malpractice action against Hackett seeking damages in excess of $75,000. Damon allegedly mishandled that suit and withdrew from the litigation, forcing Brautigam to proceed pro se and resulting in a judgment in Hackett’s favor. Brautigam appealed, and the state court of appeals concluded that because Brau-tigam never returned his settlement payment, Brautigam could not maintain an action attacking that settlement. The district court determined that because Damon’s action against Hackett could not succeed, Brautigam’s action against Damon was valueless. In his complaint, Brautigam alleged that had Damon handled the Hackett litigation appropriately, including advising him to return the settlement money, it would have been successful.
In Ohio, a legal malpractice claim has four elements: (1) there was an attorney-client relationship giving rise to a duty; (2) the attorney breached that duty; (3) the plaintiff suffered damages; and (4) the damages were proximately caused by the attorney’s breach. E.B.P., Inc. v. Cozza & Steuer [119 Ohio App.3d 177], 694 N.E.2d 1376, 1378 (Ohio Ct. App. 1997), “[A] settlement of the underlying action [does not] always operate[ ] as a waiver of a client’s malpractice claim against his attorney.” Id. at 1379. Thus, Brautigam has stated a claim under Ohio law. Crosthwaite argues that Brautigam cannot establish causation. But Brautigam is not required to prove causation to satisfy the amount-in-controversy requirement. See Kovacs, 406 F.3d at 397; Vahila v. Hall [77 Ohio St.3d 421], 674 N.E.2d 1164, 1168-69 (Ohio 1997). Whether the claim will succeed is a merits assessment. Thus, on the face of Brautigam’s complaint, it does not appear to a legal certainty that Brautigam has not satisfied the jurisdictional amount,... the district court should not have dismissed this action for lack of subject-matter jurisdiction.
The district court dismissed Brautigam’s claims against the Deters defendants for breach of fiduciary duty, legal malpractice, unjust enrichment, and negligence. On appeal, Brautigam argues that his claims should not have been dismissed because he continued to receive legal bills from Damon while Damon was employed at Eric C. Deters & Associates, and Damon corresponded with him using Eric C. Deters & Associates’ stationery. The attorney-client relationship is terminated when there is an affirmative act by either party signaling the end of the relationship. Flynt v. Brownfield, [848]*848Bowen & Bally, 882 F.2d 1048, 1051 (6th Cir. 1989); Duvall v. Manning, No. 2010-L-069, 2011 WL 2119912, at*4 (Ohio Ct. App. May 27, 2011). In August 2010 [by letter dated August 4, 2010], B&C notified Brautigam that Damon had left B&C, and Brautigam stated that he wanted to continue being represented by B&C. That same month [on August 3, 2010] Damon filed a motion to withdraw as Brautigam’s counsel and mailed a copy of that motion to Brauti-gam. Damon and Brautigam both took affirmative acts that terminated the attorney-client relationship. Damon did not start working for Eric C. Deters & Associates until September 2010—after Damon and Brautigam had severed their relationship. Brautigam does not point to any evidence that he entered into an attorney-client relationship with the Deters defendants, and there is no basis for finding that the Deters defendants owed a duty to Brautigam. The district court properly dismissed Brautigam’s claims against the Deters defendants.
Accordingly, the district court’s judgment is affirmed in part and reversed in part, and this action is remanded for further proceedings.
Brautigam v. Damon et al., No. 14-3400, R. 30-1/Order entered 2/25/15 (emphasis added).
In addition to a claim of legal malpractice, Brautigam’s first amended complaint, filed in September 2011, alleged claims of breach of fiduciary duty, unjust enrichment, negligence, and conversion as to Defendants Damon and Crosthwaite, and promissory estoppel as to Damon alone. The first amended complaint dropped B&C and Joseph Butkovich as defendants. Thus, only Brautigam’s claims against Damon and Crosthwaite were at issue on remand.
Damon admitted stealing from B&C in March 2013 and was disbarred in May 2013. In September 2013, Brautigam sought to file a second amended complaint, which added factual allegations of fraud but did not seek to add a fraud count. The motion was denied as moot due to the dismissal for lack of subject-matter jurisdiction.
On remand, Defendants argued, and the magistrate judge agreed, that the opinion of the court of appeals established the law of the case and compelled the district court to dismiss Brautigam’s malpractice claims against Damon as barred by Ohio’s one-year statute of limitations. Ohio Rev. Code § 2305.11. The magistrate judge concluded that Brautigam’s remaining claims were subsumed under his legal-malpractice claim and recommended those be dismissed as well. The district court overruled Brautigam’s objections to the magistrate judge’s recommendation that summary judgment be granted on the legal-malpractice claim on statute-of-limitations grounds and rejected Brautigam’s argument that Damon’s pre-billing worksheets established that he continued to represent Brautigam until within a year of Brautigam’s filing this action. Also on remand, Brautigam sought leave to file a third amended complaint that would add a fraud count and a gross-negligence count. The magistrate judge recommended that leave to amend be denied. The district court adopted the magistrate judge’s Report and Recommendation in its entirety.
II.
We review the district court’s grant of summary judgment on statute-of-limitations grounds de novo. Smith v. Ameritech, 129 F.3d 857, 863 (6th Cir. 1997). This court’s prior determination that Brauti-gam’s legal-malpractice claim against Damon was barred by Ohio’s one-year statute [849]*849of limitations is the law of the case; the mandate rule “requires lower courts to adhere to the commands of a superior court.... Accordingly, [u]pon remand of the case for further proceedings after a decision by the appellate court, the trial court must ‘proceed in accordance with the mandate and the law of the case as established on appeal.’ ” Allard Enters., Inc. v. Advanced Programming Res., Inc., 249 F.3d 564, 569-70 (6th Cir. 2001) (citations omitted). It is true that this court on Brau-tigam’s first appeal determined that his complaint stated a claim of legal malpractice against Damon and Crosthwaite, but that was solely in the context of reviewing whether Brautigam met the amount-in-controversy requirement of diversity jurisdiction. See PID 3002; Brautigam v. Damon et al., No. 14-3400, R. 30-1/Order entered 2/25/15. We ruled definitively that the attorney-client relationship between Brautigam and Damon was severed when Damon moved to withdraw as Brautigam’s counsel in the Hackett litigation and Brau-tigam responded to B&C’s August 4, 2010 letter by electing to be represented by B&C, rather than Damon. Brautigam does not contest that these events preceded the filing of his complaint by more than one year. The district court was not free to ignore our ruling on this matter and thus properly determined that Brautigam’s legal-malpractice claim against Damon was barred.
Brautigam presents no argument regarding the dismissal of his remaining claims against Damon: breach of fiduciary duty, unjust enrichment, negligence, conversion, and promissory estoppel, and thus has abandoned those claims. See Enertech Elec., Inc. v. Mahoming Cty. Comm’rs, 85 F.3d 257, 259 (6th Cir. 1996).
III.
The district court did not abuse its discretion in adopting the magistrate judge’s recommendation to deny Brauti-gam’s motion for leave to amend. See Coe v. Bell, 161 F.3d 320, 341 (6th Cir. 1998) (holding that review of denial of motion for leave to amend is for abuse of discretion).
Brautigam attached to his motion for leave to amend a proposed third amended complaint, which added a fraud count alleging:
128. Defendant Damon committed fraud against Plaintiff and others by accepting cases he did not intent [sic] to properly prosecute in exchange for whatever money he could fleece from clients. Damon “played” his clients along, taking as much money as possible for as long as possible, and then seeking to withdraw on a pretext, and then hiding behind “a fee dispute” with the client. Defendant Crosthwaite committed fraud by allowing this to happen either through willful ignorance or acting in concert with Damon to obtain fees that Damon was generating, including fees from Plaintiff. Defendant Crosthwaite further committed fraud by actively concealing the true facts regarding Damon’s serial predation from clients in the 4 August 2010 letter sent to Plaintiff and substantially similar letters sent to B&C’s other clients. Crosthwaite intended to and did mislead Plaintiff and other B&C clients as to the true facts of Damon’s theft, in a fraudulent attempt to induce B&C clients including Plaintiff, to select serial predator Damon as their counsel.
129. Defendant Crosthwaite is also liable for fraud in that, in possession of highly credible information indicating that Defendant Damon was a serial predator, Defendant Crosthwaite, acting in concert with Defendant Damon, both affirmatively represented and deliberately omitted this information so that clients of B&C such as Plaintiff were not able [850]*850to make an informed decision as to who should represent them, and how to proceed. Defendant Crosthwaite. also directed that B&C office manager Pattianne Menden to lie and/or affirmatively mislead B&C clients as to the true facts concerning Damon’s serial predation in an underhanded attempt to fraudulent [sic] induce B&C’s clients to select known serial predator Damon as their counsel, thus shielding B&C and Defendant Crosthwaite from liability from their active participation in this ongoing fraud. This scheme was in furtherance of their mutual goals of avoiding being named in malpractice suits and making payments to clients for the money stolen from them. Defendant Crosthwaite was also instrumental in seeing that all restitution payments went to B&C; no restitution payments were made to clients of B&C.
PID 2490-91. Brautigam attached as exhibits documents including: Damon’s indictment for theft of $61,553.98 from B&C spanning from on or about January 1, 2009 through July 31, 2010; Damon’s guilty plea to fourth-degree felony theft, entered March 11, 2013 in the Hamilton County Court of Common Pleas; Damon’s suspension from the practice of law in the Southern District of Ohio on August 1, 2013; and Damon’s disbarment by the Supreme Court of Ohio. The one-page memorandum Brautigam submitted in support of his motion stated in its entirety:
Plaintiff filed his complaint on 15 August 2011, his First Amended Complaint on 12 September 2011, and Motion for Leave to File Second Amended Complaint on 17 September 2013. Since that time, the case has been overtaken by events, as there have been significant developments related to the case, including but not limited to Defendant Damon’s felony conviction for his disbarment. Additionally, some minimal discovery has taken place, which Plaintiff has incorporated into the TAC [Third Amended Complaint]. The Motion for Leave to File the Second Amended Complaint, was not acted on, and Magistrate Judge Litkovitz directed that a new document be filed, if warranted.
Neither Defendant Damon nor Defendant Crosthwaite will be prejudiced by the Court granting leave to file the SAC [presumably, second amended complaint]. The SAC removes confusion as to Defendants who are no longer in the case.
PID 2429.
Both Damon and Crosthwaite opposed Brautigam’s motion for leave to amend. Noting that the case had been pending for over four years, but acknowledging that Brautigam was not responsible for “this inordinate delay,” the magistrate judge determined that amendment would be futile and unduly prejudice Defendants. The district court agreed.
As the magistrate judge acknowledged, through no fault of his own, Brautigam’s motion for leave to amend to file a second amended complaint, filed on September 17, 2013, was denied as moot when the district court dismissed the complaint for lack of subject-matter jurisdiction. The first appeal to this court then took a year. The order reversing and remanding issued on April 7, 2015, and Brautigam filed the instant motion for leave to amend soon after, on June 12, 2015. Under these circumstances, in the interest of fairness, we analyze Brautigam’s motion as if he had filed it on September 17,2013.
Brautigam alleged in his initial complaint that he became aware, in or about November 2010, that Damon maintained a separate IOLTA account, in violation of ethics rules, while employed at B&C. PID [851]*8518/Complaint filed 8/5/2011. The initial complaint also alleged that in or about July 2010 B&C fired Damon “for stealing client funds, and other malfeasance.” PID 11; that on or about April 15, 2011, the Cincinnati Bar Association filed a complaint against Damon for stealing client funds; and that Damon breached his fiduciary duty to Brautigam by failing to file actions as he had promised, by failing to vigorously pursue Brautigam’s claims, and by taking Brautigam’s money for services that were either not completed or did not meet the applicable standard of care.
The allegations against Damon in Brau-tigam’s initial and first amended complaints largely overlap with those in the proposed third amended complaint; the only real difference is that the third amended complaint explicitly pleaded a claim of fraud, which is subject to a four-year limitations period. See Ohio Rev. Code Ann. § 2305.09. But Brautigam’s cursory memorandum in support of his motion for leave to amend failed to explain why the fraud count against Damon was not subsumed under the prior allegations or why the district court’s discretion should be exercised in his favor to permit amendment at that point in the litigation.2
Brautigam’s first amended complaint, filed in September 2011, alleged that Crosthwaite, through B&C, negligently hired Damon “with actual and constructive knowledge that the thief Geoffrey P. Damon was, in fact, a thief who was preying on clients.” PID 112. The first amended complaint further alleged that Crosthwaite had actual and constructive knowledge that Damon was maintaining a separate IOLTA account, that Crosthwaite knew or should have known that Damon was stealing from clients and failing to meet the standard of care in his representation, and that Crosthwaite was responsible for the acts and omissions of Damon. Brautigam’s third amended complaint sought to add allegations regarding B&C’s August 4, 2010 letter to clients regarding their representation preference. As with the allegations against Damon, the motion to amend did not adequately explain why the fraud claim was not subsumed under a prior allegation. Additionally, the fraud allegations against Crosthwaite are largely based on an alleged scheme to mislead clients into choosing to proceed .with Damon, rather than with B&C. However, it is undisputed that Brautigam opted to proceed with B&C as counsel. Thus, these allegations would have been futile if permitted. We find no abuse of discretion in the denial of leave to file the third amended complaint.3
IV.
Without citing authority, Brauti-gam also asserts that the magistrate judge “is severely biased” against him and should have ruled on his affidavit of bias and prejudice. Appellant Br. 33-36. The district court adequately addressed this argument in overruling Brautigam’s objections to the magistrate judge’s Report and Recommendation:
Plaintiffs Affidavit of Bias and Prejudice (Doc. 134) alleges bias and preju[852]*852dice ... and requests that [the magistrate judge] recuse herself from further participation in this case. The Affidavit attaches, and relies wholly upon, a Complaint of Judicial Misconduct that Plaintiff filed in the United States Court of Appeals for the Sixth Circuit.
Recusal is only warranted where a “reasonable, objective person, knowing all of the circumstances, would have questioned the judge’s impartiality.” See Hughes v. United States, 899 F.2d 1495, 1501 (6th Cir. 1990). This is an objective standard and it is not based “on the subjective view of a party.” Browning v. Foltz, 837 F.2d 276, 279 (6th Cir. 1988).... Plaintiffs subjective speculation alone is insufficient to support his allegation of judicial bias....
Here, Plaintiffs allegations of bias relate to the Magistrate Judge’s conclusions in the case based on her view of the law, not based on any personal bias. Moreover, Plaintiffs allegations are wholly speculative. For example, Plaintiff speculates that the Magistrate Judge dismissed his case “to control her calendar and to protect then 94 year old Senior Judge Spiegel.” However, he offers no evidence in support of his conclusory allegations. Furthermore, the Court of Appeals dismissed Plaintiffs Complaint of [Judicial Misconduct], finding no support for his allegations. Specifically, the Court concluded that “[t]he gravamen of the complaint is the complainant’s dissatisfaction with the subject judge’s Report and Recommendation.” (Order with Supporting Memorandum, Case No. 06-15-90035). The Court further concluded “[t]hat part of the complaint that charges the subject judge with recommending dismissal of the complaint in order to control her calendar, which is based on the date that document was entered on ■ the docket, is frivolous and/or lacks sufficient evidence from which an inference that misconduct has occurred can be made.” (Id.). Thus, Plaintiffs argument is not well-taken.
PID 3118-20.4
V
Brautigam also claims that the district court did not “truly conduct a meaningful de novo review of the magistrate judge’s Report and Recommendation” and overlooked his theory of the case that includes fraud. He cites no facts or authority in support of either argument and neither warrants discussion; the district court’s decision states that it “reviewed the comprehensive findings of the Magistrate Judge and considers de novo all of the filings in this matter.” PID 3114.
VI.
Although Brautigam does not explicitly challenge the grant of summary judgment in Crosthwaite’s favor, ■ Crosth-waite addresses the merits of that ruling. We agree with the magistrate judge that summary judgment in Crosthwaite’s favor was proper on the basis that Brautigam introduced no evidence that he and Crosthwaite had an attorney-client relationship and Crosthwaite could not be held liable for legal malpractice committed by Damon on a respondeat superior theory:
Turning to the merits of plaintiffs legal malpractice claim against defendant Crosthwaite, “it is well-settled that the first, and indispensable, element of a direct claim for legal malpractice is the existence of an attorney-client relationship.” Nat’l Union Fire Ins. Co. v. Pittsburgh, PA v. Wuerth, 540 F.Supp.2d [853]*853900, 913 (S.D. Ohio 2007), aff'd 349 Fed.Appx. 983 (6th Cir. 2009) (citing Krahn v. Kinney [43 Ohio St.3d 103], 538 N.E.2d 1058 (Ohio 1989)) .... To demonstrate this essential element of his legal malpractice claim against Crosthwaite, plaintiff relies solely on the Court of Appeals’ finding that plaintiff “has stated a claim under Ohio law.” For the reasons discussed above, plaintiff cannot rely on the Court of Appeals’ finding that he has stated a claim for legal malpractice to satisfy the more demanding summary judgment standard.... Plaintiff has failed to introduce any evidence to demonstrate the existence of an attorney-client relationship with Crosth-waite. There is no dispute that plaintiff was represented by Damon at all relevant times. Further, plaintiff alleges that “[a]t all relevant times [he] was [Represented by B&C, [n]ever Damon [a]lone.” In support of his position, plaintiff relies on: (1) his deposition testimony that he hired B&C and was represented by the firm; (2) a contingency fee agreement which plaintiff concededly never signed pursuant to which Damon purportedly agreed to take plaintiffs case “on behalf of B&C”; and (3) the inclusion of the firm’s name on pleadings filed in the state court case.... This evidence is not material to the question of whether Crosthwaite as an individual member of the B&C law firm represented plaintiff and had an attorney-client relationship with him. Plaintiff has not introduced any other evidence to show that Crosthwaite represented him in the Hackett litigation or agreed to represent him in the case against Judge Ruehl-man. Thus, plaintiff has failed to carry his burden on summary judgment to produce sufficient evidence to permit a reasonable factfinder to conclude he had an attorney-client relationship with Crosthwaite. Plaintiff cannot prevail on his legal malpractice claim against defendant Crosthwaite under a direct theory of liability.
Nor can plaintiff hold defendant Crosth-waite liable for any legal malpractice committed by Damon under a theory of vicarious liability or respondeat superi- or. Under this theory of liability, an employer is vicariously or secondarily liable for the negligence of its employee, whose liability is primary, [citations omitted] “For the wrong of a servant acting within the scope of his authority, the plaintiff has a right of action against either the master or the servant, or against both ...” [Taylor v. Belmont Cmty. Hosp., No. 09 BE 30, 2010 WL 3328650, at *2 (Ohio App. 7th Dist. Aug. 16, 2010) ] (quoting Losito v. Kruse, 136 Ohio St. 183, 187, 24 N.E.2d 705 (1940))....
Under Ohio law, a legal professional association is liable upon contract and for the torts of an attorney performed within his or her actual or apparent authority. David v. Schwarzwald, Robiner, Wolf & Rock Co., L.P.A. [79 Ohio App.3d 786], 607 N.E.2d 1173, 1183 (Ohio App. 8th Dist. 1992) (citing Reinter [Reiner] v. Kelley, 8 Ohio App.3d 390, 457 N.E.2d 946, 951 (Ohio App. 10th Dist. 1983)). Further, individual shareholders of a legal professional association can be held liable for the debts of his association. KMS Energy, Inc. v. Titmas [81 Ohio App.3d 293,] 610 N.E.2d 1080, 1081 (Ohio App. 9th Dist. 1992) (citing Gov. Bar. R. III) (each member of a limited liability company “shall be jointly and severally liable for any liability of the firm based upon a claim arising from acts and omissions in the rendering of legal services while he or she was a member, partner, or equity holder....”).
[854]*854Plaintiffs legal malpractice claim against Crosthwaite which is premised on the theory of vicarious liability must fail because plaintiff does not seek to hold Damon’s employer, B&C, vicariously liable for Damon’s torts. Plaintiff has not named B&C as a defendant in this lawsuit and, therefore, the legal professional association cannot be held liable in this matter for Damon’s tortious acts and omissions. Plaintiff has presented the Court with no authority that Crosth-waite, as an individual member of a law firm, may be held vicariously liable under the circumstances of this case. Because plaintiff has not brought a claim against B&C, there is no basis for imposing vicarious liability on Crosthwaite as an individual member of the firm for any torts committed by Damon.
PID 3004-07 (citations omitted).
We AFFIRM the district court’s adoption of the magistrate judge’s report and recommendation; but regarding the grant of summary judgment in Crosthwaite’s favor, we AFFIRM for the reasons stated by the magistrate judge and not on statute-of-limitations grounds.5