A magnetic tunnel junction device has a tunnel barrier made of a material consisting essentially of an oxide or nitride of one or more of gallium and indium. An oxide or nitride of aluminum may be included as part of this tunnel barrier material. In one embodiment the tunnel barrier is an oxide of a gallium-aluminum alloy (Ga.sub.75 Al.sub.25). The Ga oxide tunnel barrier may be formed by sputter deposition of Ga, followed by a plasma oxidation, or by depositing Ga from an effusion source in the presence of oxygen gas or in the presence of more reactive oxygen provided by an atomic oxygen source or other source. The tunnel barrier layer may also be formed as a bi-layer structure with an aluminum oxide layer formed directly on one of the ferromagnetic layers of the device, followed by a gallium oxide layer formed directly on the aluminum oxide layer. By appropriate selection of the amounts of gallium and or aluminum, or the thicknesses of the aluminum oxide and gallium oxide in the bi-layer structure, the tunnel barrier energy height can be tuned to a selected value. The magnetic tunnel junction devices made with the improved tunnel barrier material show a substantially reduced tunnel barrier energy height (and thus lower resistance-area values) compared to conventional devices using aluminum oxide tunnel barriers, without a reduction in magnetoresistance.