First principles generation of magnetic Hamiltonians and phase diagrams of frustrated magnets

Research in frustrated and complex magnetism has made enormous progress in recent years. Improved sample growing and experimental techniques have changed the focus from perfecting material realizations of single or few parameter kagome or triangular lattice model Hamiltonians to a wealth of materials with low symmetry, lattice distortions and complex threedimensional networks. Determining the magnetic Hamiltonian of such materials is often not feasible with simple fits to experimental data. However, an accurate density functional theory based energy mapping technique with statistical safeguards promises to be a step forward, allowing unbiased determination of completely non-intuitive hierarchies of exchange interactions. This will be illustrated with a number of recent examples. In the quest for quantum spin liquids, there are new fascinating possibilities to realize them in three dimensions: From five exchange couplings of equal rank in K₂Ni₂(SO₄)₃, energy mapping shows that two trillium lattices are in competition with a strong bipartite lattice coupling and puts the material on the verge of a 3D quantum spin liquid (QSL) of nickel S=1 spins [1]. The DFT based method also identifies a highly frustrated hyperkagome network in PbCuTe₂O₆ that explains the experimental QSL signatures [2]. In BaCoSiO₄, energy mapping identifies the cause for a complex magnetic order where the magnetic cobalt sites are partitioned into three entwined networks; together with tiny frustration and anisotropic interactions, this leads to a magnetic field control of toroidal moments [3]. In atacamite Cu₂Cl(OH)₃, the relevant Hamiltonian is impossible to guess due to the crystal distortion; it turns out that intricate 3D couplings of sawtooth chains can explain the magnetization dynamics [4]. For the distorted lattice of Y-kapellasite Y₃Cu₉(OH)₁₉Cl₈, energy mapping identifies a three parameter kagome lattice Hamiltonian with a very interesting phase diagram [5].