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A new generation magnetic spectrometer in space will open the opportunity to investigate the frontiers in direct high-energy cosmic ray measurements and to precisely measure the amount of the rare antimatter component in cosmic rays beyond the reach of current missions. We propose the concept for an Antimatter Large Acceptance Detector In Orbit (ALADInO), designed to take over the legacy of direct measurements of cosmic rays in space performed by PAMELA and AMS-02. ALADInO features technological solutions conceived to overcome the current limitations of magnetic spectrometers in space with a layout that provides an acceptance larger than 10 m2 sr. A superconducting magnet coupled to precision tracking and time-of-flight systems can provide the required matter–antimatter separation capabilities and rigidity measurement resolution with a Maximum Detectable Rigidity better than 20 TV. The inner 3D-imaging deep calorimeter, designed to maximize the isotropic acceptance of particles, allows for the measurement of cosmic rays up to PeV energies with accurate energy resolution to precisely measure features in the cosmic ray spectra. The operations of ALADInO in the Sun–Earth L2 Lagrangian point for at least 5 years would enable unique revolutionary observations with groundbreaking discovery potentials in the field of astroparticle physics by precision measurements of electrons, positrons, and antiprotons up to 10 TeV and of nuclear cosmic rays up to PeV energies, and by the possible unambiguous detection and measurement of low-energy antideuteron and antihelium components in cosmic rays.