We have measured the spin susceptibility of the underdoped high temperature superconductor, YBa2Cu4O8 by Gd 3+ electron spin resonance in single crystals and aligned powders at several magnetic fields between 3 and 15.4 T. At low temperatures and high fields, the spin susceptibility of the CuO2 planes is enhanced slightly in the B c orientation with respect to the B ⊥ c orientation. The enhancement in an applied field of 15.4 T (≈ 0.15 Hc2) at 16 K (0.2 Tc) is approximately 10 percent of the susceptibility measured at Tc. Such a small magnitude suggests that the second critical field of superconductivity, Hc2 ≈ 100 T, would not suppress the pseudogap. This work demonstrates the potential of high field ESR in single crystals for studying high Tc superconductors. 74.25.Nf, 74.72.Bk, 76.30.Kg The structure of vortex lines in high temperature superconductors (HTSCs) may shed light on the microscopic mechanism of superconductivity. The earliest dwave pairing theories implied that the zero temperature spin susceptibility should scale with magnetic field as (B/H c2 ) 1/2 [1,2] in contrast to the linear dependence in an s-wave superconductor. A rigorous solution of the Bogoliubov-de Gennes equations in the mixed state [3] reveals that quasiparticles in d-wave superconductors are not bound to vortices, and predict a space averaged density of states (DOS) N (0) ∝ (B/H c2 ) γ , where 0.4 ≤ γ ≤ 1 depending on the temperature and the model used [4,5]. A number of experiments were targeted at the field dependence of the DOS in YBa 2 Cu 3 O 7−δ . Scanning tunneling microscopy [6] resolves the DOS at and around vortices, but is unsuitable to measure the total DOS [7]. Bulk experiments on nearly optimally doped YBa 2 Cu 3 O 7−δ include heat capacity [8], infrared transmission [9], thermal conductivity [10], and high field muon spin rotation [11]. Most of these experiments, together with early NMR on planar copper and oxygen [12], indicated some increase in the DOS with magnetic field but were inconclusive about its magnitude.Underdoped HTSCs-which also possess a pseudogap in the normal state-are of special interest, as it is unclear how the pseudogap is related to the d-wave superconducting gap. An indication whether high magnetic fields suppress the pseudogap or not may contribute to understanding its nature. Also, most theoretical calculations of the quasiparticle spectra in HTSCs depend on the assumption that Landau's theory of the Fermi-liquid is applicable below T c , which is still to be justified by experiments. A recent 63 Cu NMR study on YBa 2 Cu 4 O 8 at high fields [13] reports a sizeable field induced DOS for B in the (a, b) plane, implying a large enhancement for B c. In contrast, we show that for B c the DOS enhancement is small and incompatible with a suppression of the pseudogap at B = H c2 .In this Letter, we report the spin susceptibility of YBa 2 Cu 4 O 8 obtained by high field electron spin resonance (ESR) spectroscopy of Gd 3+ in Gd:3+ is a non-perturbing probe of the CuO 2 spin polarization [14]. We se...