If you hear a constant grinding noise from the front brakes, even when not pressing the brake pedal, it is possible the wheel hub has shifted in the steering knuckle causing the brake rotor to grind against the caliper bracket. The hub will need to be inspected (replaced if necessary) and Mazda has a repair procedure for this concern.
Car Problem Reports
Mazda Mazda3 Noise due to brake rotor grinding against caliper bracket
Mazda Mazda3 Problem
Average Mileage: 102,600 mi (84,000 mi - 120,800 mi)
Visitor, 2009 Mazda Mazda3, 103,000 mi
replaced my rotors, now the rotor is grinding against the caliper bracket.
there is a groove in my brand new rotor from driving less than a quarter mile.
Noise due to brake rotor grinding against caliper bracket only when steering right
Visitor, 2005 Mazda Mazda3, 120,800 mi
Rotor has ring ground into it due to caliper rubbing against it.
Brake pads are good, only grinds when making left turns.
Makes a metal to metal grinding sound with some shavings present on brake caliper mount.