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The gravitomagnetic tidal Love number of a slowly rotating body wascalculated previously under the assumption that the velocity perturbationcreated by the tidal field consists of an induction piece proportional to thevector potential, and a rotational piece that scales with $\Omega$, the body'sangular velocity. The second part of this assumption is wrong: the rotationalpiece of the velocity perturbation scales in fact like $\Omega^0 = 1$. Theprevious calculations are therefore incorrect, and the purpose of this paper isto repair the mistake. To keep the technical difficulties to a minimum, thetreatment here is restricted to a post-Newtonian expansion carried out toleading order -- previous calculations of the gravitomagnetic Love number wereperformed in full general relativity. On the other hand, the computationpresented here is not restricted to a stationary tidal field. I show that thecorrect scaling of the velocity perturbation with $\Omega$ leads to thepromotion of the Love number to a Love tensor $k_{jk}^{\ \ pq}$, a four-indexobject that relates the body's current quadrupole moment $S_{jk}$ to thegravitomagnetic tidal moment ${\cal B}_{pq}$. The tensorial nature of thisquantity has to do with the fact that each $e^{im\phi}$ piece of the tidalforce gives rise to an $m$-specific velocity perturbation, and therefore to aLove number that depends on $m$. The collection of these $m$-specific Lovenumbers makes up the Love tensor $k_{jk}^{\ \ pq}$.

Gravitomagnetic Love tensor of a slowly rotating body: post-Newtonian theory