The first lifetime measurement used to study the magnetic response of halo nuclei is presented. The lifetime of the first excited state of the one-neutron halo nucleus 19 C has been measured by two complementary Doppler-shift techniques with the GRETINA array. The B(M1; 3/2 + →1/2 + g.s. ) strength of 3.21(25)×10 −3 µ 2 N determined for this decay represents a strongly hindered M1 transition among light nuclei. Shell model calculations predict a strong hindrance due to the near-degeneracy of the s 1/2 and d 5/2 orbitals among neutron-rich carbon isotopes, while tensor corrections and loosely bound effects are necessary to account for the remaining strength.PACS numbers: 21.10. Tg, 21.60.Cs, 23.20.Lv, 27.20.+n The electromagnetic response of atomic nuclei plays a central role in characterizing the static and dynamic nuclear properties in terms of spatial, spin and isospin degrees of freedom. The giant resonance is one famous example, exhibiting a significant strength from coherent collective motion between protons and neutrons [1]. Depending on the excitation energy region of nuclei, the electromagnetic transition strength can provide essential information to deduce internal configurations of nuclei, quantify collectivity and deformation, and constrain the nuclear equation of state.At the limit of nuclear stability, exotic structures can emerge due to the rearrangement of shell-model orbitals [2,3]. When the s-wave strength appears close to the threshold, quantum tunneling of valence neutrons leads to extended wave functions known as halos [4,5]. In this case, a new degree of freedom in collective modes is naïvely expected from a relative motion between the core and halo neutron, inducing so-called soft collective motions [6,7]. Non-resonant dipole excitations in light nuclei and pygmy dipole modes in medium and heavy nuclei have been extensively studied through Coulomb excitation with rare isotope beams, revealing a sizable electric dipole (E1) strength in the low-energy region [8]. However, the magnetic response of halo nuclei is not well understood, mainly due to difficulties in selectively inducing the magnetic excitation in intermediate-energy nuclear reactions [9]. Currently, only static magnetic properties have been studied for the one-neutron halo nucleus 11 Be through the β-NMR measurement of the magnetic moment [10] and hyperfine splitting measurement to deduce the magnetization radius [11]. Regarding the dynamic response, a hindered magnetic dipole (M1) strength has been observed for the 1/2, where a possible halo structure in the excited 1/2 + state is discussed.The present paper reports the first study on the dynamic magnetic response of the neutron halo nucleus 19 C. In a simplistic model of the halo, an s 1/2 neutron is coupled to a 0 + core, causing the low-energy M1 response to vanish due to the absence of a spinflip partner for the s 1/2 orbital. However, the realistic picture is more complex in 19 C, because non-negligible core-excitation components have recently been suggested by an inclusi...