We report a comprehensive investigation of the anisotropic magnetism and magnetic field-induced transitions in single crystals of the orthorhombic system TbAlGe, a member of the topological $R\mathrm{AlGe}$ (where $R$ denotes rare earth) family with the highest ordering temeprature in the $R\mathrm{Al}X$ ($X=\mathrm{Si},\mathrm{Ge}$) series. With a single rare-earth site with triangular coordination in its $Cmcm$ orthorhombic unit cell, TbAlGe harbors complex magnetic interactions that yield two antiferromagnetic transitions at 40 and 8 K in zero field, and a rich cascade of metamagnetic transitions that only appear for fields directed along the crystallographic $a$-axis. Combining electrical resistivity, magnetization, and heat capacity measurements with magnetotransport experiments performed up to 41.5 T, we construct a magnetic phase diagram mapping the multiple magnetic phases of TbAlGe, and we discuss the complex interplay between localized $4f$ magnetism and itinerant electronic topology, establishing TbAlGe as a compelling platform for exploring tunable magnetic semimetal physics.

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• Magnetic interactions
• Magnetism
• Magnetotransport
• Intermetallic compounds
• Rare-earth magnetic materials
• Single crystal materials
• Crystal growth
• Resistivity measurements