You are the victim of legacy command-and-control thinking. The roles you describe have responsibilities, but they are not "leaders" of the team in the traditional sense either alone or in combination.
Scrum Teams Have Roles, Not Leaders
According to the official Scrum Guide:
The Scrum Team consists of a Product Owner, the Development Team, and a Scrum Master. Scrum Teams are self-organizing and cross-functional. Self-organizing teams choose how best to accomplish their work, rather than being directed by others outside the team.
A self-organizing team isn't directed by traditional leaders from outside or inside the team. Instead, each role on the team plays a vital part in delivering value to the customer. You can read the entire section of the Scrum Guide for a description of each role, but in short:
- The Scrum Master is a process referee responsible for helping the team understand and make the most of the framework.
- The Product Owner is a value referee responsible for communicating and prioritizing features.
- "Development Teams are structured and empowered by the organization to organize and manage their own work."
If you like sports metaphors, it's like zone defense: each member of the team has a region of responsibility, and must collaborate, trust, and rely on the rest of the team to be effective. No one is "in charge" of the team, although effective teams will certainly have team members who display leadership qualities.
Structure your teams to be cross-functional, make sure they are empowered, and ensure that everyone understands their role within the team. Encourage collaboration and a sense of shared purpose, rather than fostering a culture of leaders and followers. That is the embodiment of the principles behind the Agile Manifesto.