We report on simultaneous observations of the magnetar SGR J1745-2900 at frequencies $ u = 2.54$ to $225,rm{GHz}$ using the Nancay 94-m equivalent, Effelsberg 100-m, and IRAM 30-m radio telescopes. We detect SGR J1745-2900 up to 225 GHz, the highest radio frequency detection of pulsed emission from a neutron star to date. Strong single pulses are also observed from 4.85 up to 154 GHz. At the millimetre band we see significant flux density and spectral index variabilities on time scales of tens of minutes, plus variability between days at all frequencies. Additionally, SGR J1745-2900 was observed at a different epoch at frequencies 296 to 472 GHz using the APEX 12-m radio telescope, with no detections. Over the period MJD 56859.83-56862.93 the fitted spectrum yields a spectral index of $left<alpharight> = -0.4 pm 0.1$ for a reference flux density $left< S_{154} right> = 1.1 pm 0.2rm{,mJy}$ (with $S_{ u} propto { u}^{alpha})$, a flat spectrum alike those of the other radio-loud magnetars. These results show that strongly magnetized neutron stars can be effective radio emitters at frequencies notably higher to what was previously known and that pulsar searches in the Galactic Centre are possible in the millimetre band.
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