Metamaterials with magnetic properties have been widely investigated with rather complex two- and three-dimensional resonant structures. Here we propose conceptually and demonstrate experimentally a mechanism for broadband optical magnetism in simpler one-dimensional systems. We experimentally demonstrate that alternating high-index dielectric/metal multilayer hyperbolic metamaterials can exhibit a strong magnetic response including variously µ>1 to µ<0. By engineering the electric permittivity as well, we reveal an epsilon and mu near zero regime. We show that modifications of internal metamaterial structure can lead to either type I or type II magnetic hyperbolic dispersion, thereby generalizing the notion of a hyperbolic metamaterial to encompass both TE and TM polarizations in simple multilayer geometries. Finally, we show that a negative magnetic response can give rise to TE interface-bound states, analogous to their TM counterparts, surface plasmon polaritons
