Temporal variability in Earth's length of day and its connection with the geomagnetic field energy over the last 3,000 years

Historical records of lunisolar eclipses and star occultations provide us useful information on the variation of the length of day (LOD) over the last 3,000 years. Besides a steadily increasing trend caused by tidal friction effects, there is evidence for a 1300-year oscillation in the LOD. An adequate explanation for this phenomenon requires considering an interaction between the Earth's mantle and core. Several mechanisms in which the geomagnetic field is directly or indirectly involved have been suggested, including electromagnetic coupling or angular momentum exchange. This study explores the potential connection between fluctuations in the length of day and the energy of the Earth's magnetic field. Through a frequency domain analysis and correlation tests, we examined non-tidal observations in LOD and geomagnetic field energy, using the latest archaeoreconstructions of the global magnetic field spanning the last 3,000 years. As a result, we have found a shared 1,300-year period in the LOD and energy of the non-axial terms of the Earth's magnetic field. These findings are interesting and open a possibility for further research in this field to validate and enhance our understanding of the nature and underlying causes of this potential connection between the Earth's magnetic field and the temporal variability in the LOD