The work is reported in Nature journal.
Earth`s active core contrasts sharply with that of our neighbour Mars, whose strong early magnetic field died around four billion years ago.
Our planet`s magnetic field is generated deep in the planet by the turbulent motion of the electrically conducting molten iron of the outer core.
It aligns compass needles north-south, but also protects Earth from the solar storms that the Sun throws out relentlessly.
At the poles, these storms produce Aurora - northern or southern lights. But they can also work destructively to strip away ozone in the upper atmosphere, an important shield against the Sun`s harmful ultraviolet radiation.
It has been suggested that life on Earth has thrived because the magnetic field has allowed this protective atmosphere to persist over hundreds of millions of years.
The turbulent motion of iron in the liquid outer core is partly generated by excess heat in the centre of the Earth being transferred upwards and outwards by convection, and partly by the slow solidification of the solid inner core at the very heart of the planet.
As the iron at the centre of the Earth freezes, forming the inner core, it expels light and buoyant impurities into the liquid outer core. They rise and boost convection in the outer core, amplifying the magnetic field.
The Earth`s magnetic field is good for at least another billion years (Image snapshot of field strength. Red is strong; blue is weak)
An increase in magnetic field is a signature that scientists have been searching for in the rocks of the deep geological past: a recording of the onset of core solidification.
The lead author of the paper, Dr Andy Biggin of the University of Liverpool, UK, commented: "The timing of the first appearance of solid iron or `nucleation` of the inner core is highly controversial, but is crucial for determining the properties and history of the Earth`s interior."
The question of when molten iron in the heart of the planet started to freeze and form the inner core has, recently, been the topic of vigorous scientific discussion.
Estimates and models of inner core formation rely on understanding the properties of iron under the extreme conditions at the centre of the Earth - pressures of more than three million atmospheres, and temperatures of around 6,000C.
Dr Biggin added: "The theoretical model which best fits our data indicates that the core is losing heat more slowly than at any point in the last 4.5 billion years and that this flow of energy should keep the Earth`s magnetic field going for another billion years or more."
Dr Richard Harrison of the University of Cambridge, who was not involved in the study, told the BBC: "Studying the magnetism of ancient rocks is a huge scientific challenge, because old rocks can lose their magnetic memory, or the magnetic signals they carry can become overwritten and corrupted (just like the files on your hard drive).
"However, it is one of the best ways to look for concrete evidence of when the core started to solidify.
"Although data are scarce, this study applied strict quality controls to decide which data were the most reliable and then used statistics to demonstrate that a boost to Earth`s the magnetic field occurred 1,300 million years ago. If this turns out to be the elusive signature of inner core growth, then we may have to revise our ideas about the core yet again!".
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