A method of recording information bits in a magnetic storage medium, the method comprising positioning a first conductor adjacent to a magnetic recording medium, the conductor having a width and a length, wherein a distance between the first conductor and the magnetic recording medium is less than or equal to the width and the length, and passing a first current through the conductor of sufficient magnitude to produce a magnetic field in the magnetic medium greater than one Tesla and having a magnetic field gradient in a cross track direction and a down track direction greater than 100 Oe/nm over a bit dimension. The thickness of the first conductor can be less than or equal to the distance between the first conductor and the magnetic recording medium. The current density in the conductor can be greater than 109 ampere/cm2, and the length of the conductor can be less than 100 nm. The current can be applied as one or more pulses in a predetermined clock cycle time. The magnetic field can be augmented by using an additional conductor, an adjacent ferromagnetic film, and/or a magnetic yoke and coil. Magnetic recording heads and disc drives that record data in accordance with the method are also included.