Correction to: Nature Communications https://doi.org/10.1038/s41467-023-41775-9, published online 06 October 2023

  1. 1.

    Error location: Missing symbols - within a single Eq. (3).

Error: missing symbol in the second component of Eq. (3) of the Article (identically, Eq. (10) from Supplementary Information).

Correction text: The original version of this Article contained an error in Eq. (3) (Eq. (10) from Supplementary Information). The second component of the reactance tensor must include the average reactance Xsw, and incorrectly read:

$${{{{\bf{X}}}}}_{\rho \rho }= {X}_{sw}(1+{a}_{X}^{\max }{{{{\bf{M}}}}}_{\rho \rho }\,\sin ({{\mbox{arg}}}({{{{\bf{E}}}}}_{\rho }/{{{{\bf{J}}}}}_{\rho })))\\ {{{{\bf{X}}}}}_{\rho \phi }= {a}_{X}^{\max }{{{{\bf{M}}}}}_{\rho \phi }\,\sin ({{\mbox{arg}}}({{{{\bf{E}}}}}_{\phi }/{{{{\bf{J}}}}}_{\rho }))\\ {{{{\bf{X}}}}}_{\phi \rho }= {{{{\bf{X}}}}}_{\rho \phi }\\ {{{{\bf{X}}}}}_{\phi \phi }= {X}_{sw}(1-{a}_{X}^{\max }{{{{\bf{M}}}}}_{\rho \rho }\,\sin ({{\mbox{arg}}}({{{{\bf{E}}}}}_{\rho }/{{{{\bf{J}}}}}_{\rho }))).$$

The correct form of Eq. (3) is:

$${{{{\bf{X}}}}}_{\rho \rho }= {X}_{sw}(1+{a}_{X}^{\max }{{{{\bf{M}}}}}_{\rho \rho }\,\sin ({{\mbox{arg}}}({{{{\bf{E}}}}}_{\rho }/{{{{\bf{J}}}}}_{\rho })))\\ {{{{\bf{X}}}}}_{\rho \phi }= |{X}_{sw}{a}_{X}^{\max }{{{{\bf{M}}}}}_{\rho \phi }\,\sin ({{\mbox{arg}}}({{{{\bf{E}}}}}_{\phi }/{{{{\bf{J}}}}}_{\rho }))\\ {{{{\bf{X}}}}}_{\phi \rho }= {{{{\bf{X}}}}}_{\rho \phi }\\ {{{{\bf{X}}}}}_{\phi \phi }= {X}_{sw}(1-{a}_{X}^{\max }{{{{\bf{M}}}}}_{\rho \rho }\,\sin ({{\mbox{arg}}}({{{{\bf{E}}}}}_{\rho }/{{{{\bf{J}}}}}_{\rho }))).$$

This typo has no impact on the results presented, which are derived from numerical models based on the correct expression of reactance tensors.