Time-dependent exchange creates the time-frustrated state of matter.

Magnetic systems governed by exchange interactions between magnetic moments harbor frustration that leads to ground state degeneracy and results in the new topological state often referred to as a frustrated state of matter (FSM). The frustration in the commonly discussed magnetic systems has a spatial origin. Here we demonstrate that an array of nanomagnets coupled by the real retarded exchange interactions develops a new state of matter, time frustrated matter (TFM). In a spin system with the time-dependent retarded exchange interaction, a single spin-flip influences other spins not instantly but after some delay. This implies that the sign of the exchange interaction changes, leading to either ferro- or antiferromagnetic interaction, depends on time. As a result, the system's temporal evolution is essentially non-Markovian. The emerging competition between different magnetic orders leads to a new kind of time-core frustration. To establish this paradigmatic shift, we focus on the exemplary system, a granular multiferroic, where the exchange transferring medium has a pronounced frequency dispersion and hence develops the TFM.

Continuous transformation between ferro and antiferro circular structures in [Formula: see text] frustrated Heisenberg model.

Frustrated magnetic compounds, in particular low-dimensional, are topical research due to the persistent uncovering of novel nontrivial quantum states and potential applications. The problem of this field is that many important results are scattered over the localized parameter ranges, while areas in between still contain hidden interesting effects. We consider the [Formula: see text] Heisenberg model on the square lattice and use the spherically symmetric self-consistent approach for spin-spin Green's functions in 'quasielastic' approximation. We have found a new local order in spin liquids: antiferromagnetic isotropical helices. On the structure factor we see circular concentric dispersionless structures, while on any radial direction the excitation spectrum has 'roton' minima. That implies nontrivial magnetic excitations and consequences in magnetic susceptibility and thermodynamics. On the [Formula: see text] exchange parameters globe we discover a crossover between antiferromagnetic-like local order and ferromagnetic-like; we find stripe-like order in the middle. In fact, our 'quasielastic' approach allows investigation of the whole [Formula: see text] globe.