We report the performance of an LMA Yb-doped fiber, designed for increasing the transverse mode instability threshold and minimizing nonlinear effects in multi-kilowatt class fiber lasers, by reducing the thermo-optic coefficient of the fiber core, compared with that of standard aluminophosphosilicate Yb-doped fibers. A TMI-free 5.2 kW single-mode output power from a Yb 20/400 fiber with a 17.5 µm mode-field diameter was achieved in a broad bandwidth, co-pumped amplifier with 78% optical-to-optical efficiency, while a 4 kW signal output was attained in a 26 GHz linewidth amplifier. Negligible photodarkening loss was observed during 150 hour laser operation at 2 kW.