Bose-Einstein Condensation in Quantum Magnets*

Quantum magnets are insulating paramagnets exhibiting low-lying energy levels of integer spins that are separated by a few meV and  tunable with the application of an external magnetic field. As demonstrated 60 years ago, integer spin states can be described in an elegant way as a gas of interacting bosons with hard-core repulsion. The boson concentration is controlled by the applied field, which acts as chemical potential. Uniaxial symmetry of the spin environment is a precondition for the gas of Bosons to condense in a phase coherent state (BEC), which is equivalent to field-induced XY-antiferromagnetism in spin language.

In my talk, I will discuss two examples of quantum magnets with field-induced magnetic order. The first one is NiCl₂-SC(NH₂)₂, also known as DTN, where Ni²⁺ single ion anisotropy D = 8.9K opens an energy gap between the S_z = 0 ground state and the S_z = ±1 first exited states. XY-antiferromagnetism is induced between H_c1 = 2T and H_c2 = 10.5T establishing DTN as a typical example for a single-Q BEC.

The second compound, AgVOAsO_4, is a quantum magnet based on V⁴⁺, S = 1/2 spins arranged in a complicated cross pattern of alternating spin chains with significant bond frustration. Measurements of the specific heat up to 28T reveal a double phase transition above 10T, where the spin gap closes. The double transition promotes AgVOAsO₄ as a promising candidate for multi-Q BEC, with Q being the wave vector of the single-particle ground state in boson language. Multi-Q BECs have the potential to host topological spin textures such as magnetic vortex crystals, equivalent to skyrmions in metallic systems, but were never observed so far.