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Context. Radio halos are megaparsec-scale diffuse radio sources{ mostly}located at the centres of merging galaxy clusters. The common mechanism invokedto explain their origin is the re-acceleration of relativistic particles causedby large-scale turbulence. Aims. Current re-acceleration models predict that asignificant number of halos at high redshift should be characterised by verysteep spectra ($\alpha<-1.5$) because of increasing inverse Compton energylosses. In this paper, we investigate the spectral index properties of a sampleof nine clusters selected from the second Planck Sunyaev-Zel'dovich catalogueshowing diffuse radio emission with the Low Frequency Array (LOFAR) in the120-168 MHz band. This is the first time that radio halos discovered at lowfrequencies are followed up at higher frequencies. Methods. We analysedupgraded Giant Metrewave Radio Telescope (uGMRT) observations in Bands 3 and 4,that is, 250-500 and 550-900 MHz respectively. These observations were combinedwith existing LOFAR data to obtain information on the spectral properties ofthe diffuse radio emission. Results. We find diffuse radio emission in theuGMRT observations for five of the nine high-$z$ radio halos previouslydiscovered with LOFAR. For those, we measure spectral indices in the range of$-1$ to $-1.4$. For the uGMRT non-detections, we estimated that the halosshould have a spectral index steeper than $-1.5$. We also confirm the presenceof one candidate relic. Conclusions. Despite the small number of clusters, wefind evidence that about half of the massive and merging clusters at highredshift host radio halos with a very steep spectrum. This is in line withtheoretical predictions, although larger statistical samples are necessary totest models.

A LOFAR-uGMRT spectral index study of distant radio halos