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We present the results of a joint XMM-Newton and NuSTAR observation (200 ks)of the galaxy cluster Abell 523 at $z=0.104$. The peculiar morphology of thecluster radio halo and its outlier position in the radio power P(1.4 GHz) -X-ray luminosity plane make it an ideal candidate for the study of radio-X-raycorrelations and for the search of inverse Compton (IC) emission. Weconstructed thermodynamic maps derived from the XMM observations to describe indetail the physical and dynamical state of the ICM. We performed apoint-to-point comparison in terms of surface brightness between the X-ray andradio emissions, to quantify their morphological discrepancies. Making use ofNuSTAR's hard X-ray focusing capability, we looked for IC emission bothglobally and locally, after modeling the purely thermal component with amulti-temperature description. The thermodynamic maps suggest the presence of asecondary merging process that could be responsible for the peculiar radio halomorphology. This hypothesis is supported by the comparison between the X-rayand radio surface brightnesses, which shows a broad intrinsic scatter and aseries of outliers. The global NuSTAR spectrum can be explained by purelythermal gas emission, and there is no convincing evidence that an IC componentis needed. The $3\sigma$ upper limit on the IC flux in the 20-80 keV band is inthe range $\left[2.2 - 4.0\right] \times 10^{-13} \, \mathrm{erg} \,\mathrm{s}^{-1} \, \mathrm{cm}^{-2}$, implying a lower limit on the magneticfield strength in the range $B > [0.23 - 0.31] \, \mu G$. Locally, we lookedfor IC emission in the central region of the cluster radio halo finding a$3\sigma$ upper limit on the 20-80 keV non-thermal flux of $3.17 \times10^{-14} \, \mathrm{erg} \, \mathrm{s}^{-1} \, \mathrm{cm}^{-2}$, correspondingto a lower limit on the magnetic field strength of $B \gtrsim 0.81 \, \mu G$.

A joint XMM-NuSTAR observation of the galaxy cluster Abell 523: constraints on Inverse Compton emission