In one aspect, a linear sensor includes at least one magnetoresistance element that includes a first spin valve and a second spin valve positioned on the first spin valve. The first spin valve includes a first set of reference layers having a magnetization direction in a first direction and a first set of free layers having a magnetization direction in a second direction orthogonal to the first direction. The second spin valve includes a second set of reference layers having a magnetization direction in the first direction and a second set of free layers having a magnetization direction in a third direction orthogonal to the first direction and antiparallel to the second direction. The first direction is neither parallel nor antiparallel to a direction of an expected magnetic field.