Magnetic materials can display many solutions to the electronic-structure problem, corresponding to different local or global minima of the energy functional. In Hartree-Fock or density-functional theory different single-determinant solutions lead to different magnetizations, ionic oxidation states, hybridizations, and inter-site magnetic couplings. The vast majority of these states can be fingerprinted through their projection on the atomic orbitals of the magnetic ions. We have devised an approach that provides an effective control over these occupation matrices, allowing us to systematically explore the landscape of the potential energy surface. We showcase the emergence of a complex zoology of self-consistent states; even more so when semi-local density-functional theory is augmented - and typically made more accurate - by Hubbard corrections. Such extensive explorations allow to robustly identify the ground state of magnetic systems, and to assess the accuracy (or not) of current functionals and approximations.

磁性材料可以显示电子结构问题的许多解决方案，对应于能量泛函的不同局部或全局最小值。在 Hartree-Fock 或密度泛函理论中，不同的单行列式解会导致不同的磁化强度、离子氧化态、杂化和位点间磁耦合。这些状态中的绝大多数可以通过它们在磁性离子原子轨道上的投影来识别。我们设计了一种方法，可以有效控制这些占据矩阵，使我们能够系统地探索势能表面的景观。我们展示了自洽状态的复杂生态学的出现；当半局域密度泛函理论通过哈伯德修正得到增强并通常变得更加准确时，情况更是如此。这种广泛的探索可以稳健地识别磁系统的基态，并评估当前泛函和近似值的准确性（或不准确性）。