A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion CeCoIn5 when a magnetic field was applied parallel to the ab-plane. Here, we conduct 115^In NMR studies of this material in a PERPENDICULAR field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the H-T phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to H//ab, the FFLO region for H perpendicular to the ab-plane shows a sizable decrease, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing H perpendicular to the ab-plane results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.
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