Van Hove singularities (VHss) in the vicinity of the Fermi energy often play a dramatic role in the physics of strongly correlated electron materials. The divergence of the density of states generated by VHss can trigger the emergence of phases such as superconductivity, ferromagnetism, metamagnetism, and density wave orders. A detailed understanding of the electronic structure of these VHss is therefore essential for an accurate description of such instabilities. Here, we study the low-energy electronic structure of the trilayer strontium ruthenate Sr₄Ru₃O₁₀, identifying a rich hierarchy of VHss using angle-resolved photoemission spectroscopy and millikelvin scanning tunneling microscopy. Comparison of k-resolved electron spectroscopy and quasiparticle interference allows us to determine the structure of the VHss and demonstrate the crucial role of spin-orbit coupling in shaping them. We use this to develop a minimal model from which we identify a mechanism for driving a field-induced Lifshitz transition in ferromagnetic metals.

费米能附近的范霍夫奇点 (VHss) 通常在强相关电子材料的物理学中发挥着重要作用。 VHss产生的态密度的发散可以触发超导、铁磁性、亚磁性和密度波序等相的出现。因此，详细了解这些 VHss 的电子结构对于准确描述此类不稳定性至关重要。在这里，我们研究了三层钌酸锶Sr ₄ Ru ₃ O ₁₀的低能电子结构，使用角分辨光电子能谱和毫开尔文扫描隧道显微镜识别了丰富的VHss层次结构。k分辨电子能谱和准粒子干涉的比较使我们能够确定 VHss 的结构，并证明自旋轨道耦合在塑造它们中的关键作用。我们用它来开发一个最小模型，从中我们确定了驱动铁磁金属中场诱导的 Lifshitz 转变的机制。