The ground state of metamagnetic materials can be controlled by magnetic field, promising new functionalities for spintronics applications. Yet, a microscopic understanding of the interplay of the electronic structure with the susceptibility to emergent orders is often missing, but would greatly facilitate optimization of the properties of metamagnetic materials. Here, we use low-temperature scanning tunneling microscopy (STM) and spectroscopy to study the metamagnetism in the trilayer ruthenate ${\mathrm{Sr}}_4{\mathrm{Ru}}_3{\mathrm{O}}_{10}$, combining STM-based magnetostriction measurements with quasiparticle-interference imaging (QPI) to elucidate the role of the microscopic electronic structure in the macroscopic metamagnetic properties. Our results highlight the importance of the orthorhombicity of the material for its metamagnetic properties, confirmed by magnetization measurements. Our QPI results show clear signatures of the minority spin bands crossing the Fermi energy and provide a link among the ferromagnetic properties, spin-orbit coupling, and the orthorhombicity of the crystal structure.

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• Local density of states
• Magnetic susceptibility
• Metamagnetism
• Spin-orbit coupling
• Density functional theory
• Green's function methods
• Scanning tunneling microscopy
• Scanning tunneling spectroscopy
• Tight-binding model