H-bridge chips are not intended for driving high current stepper motors. They are really intended for driving DC motors.
You need to get a proper stepper motor driver board that takes step and direction signals from the Arduino and has the ability to limit the current to protect the motor while driving it with a high voltage - 20, 30 50 volts. if you read the Pololu website about their A4988 driver board you will get the idea. HOWEVER the A4988 cannot provide 3 amps for your motor so you are faced with using more commercial drivers such as a Gecko. Try Ebay - search for 3amp or 5amp stepper driver boards.
If your project uses a few motors you can buy boards that drive 3 or 4 motors and that may work out cheaper.
...R