  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.
