Fig. 3: Helical spiral transformation for in-plane magnetic field.

a Magnetic moment as a function of applied field at T = 155 K is compared with the corresponding dM/dH curve. A small hysteresis is observed at H_c2. b Real part of the ac susceptibility (\({\chi }^{{\prime} }\)) data shows a clear transition at H_c1 and a weak step-like feature at H_c2. The inset shows increasing magnetisation in the M(H) curve obtained at the pulsed field facility up to 30 T at T = 10 K. c Magnetic field dependence of the \({{{{\bf{Q}}}}}_{2}^{{{{\rm{a}}}}}\) intensity and the longitudinal resistance (ρ_xx) at T = 155 K. Inset shows the plate-type crystal used for electrical transport measurements. d Longitudinal magnetoresistance measured in Phase III of Fe₃Ga₄ between 80 K and 340 K at every 10 K as a function of internal field B. The dashed lines represent phase boundaries corresponding to H_c1 and H_c2. A constant offset of 0.01 is applied between successive curves for better visualisation. Magnetic field variation of the e h- and f l- components of the \({{{{\bf{Q}}}}}_{1}^{{{{\rm{a}}}}}\) and \({{{{\bf{Q}}}}}_{2}^{{{{\rm{a}}}}}\) ICM reflections. g, h show the q_z changes with respect to applied magnetic field for the \({{{{\bf{Q}}}}}_{2}^{{{{\rm{a}}}}}\) and \({{{{\bf{Q}}}}}_{1}^{{{{\rm{a}}}}}\) reflections, respectively. In the region between H_c1 and H_c2 the q_z changes were fitted for all three temperatures with straight lines, they were extended (dotted lines) down to μ₀H = 0 T. Data shown in e–g were measured at T = 255 K, whereas for h T = 230 K.