Magnetic gradiometers are tools for geophysical exploration. The magnetic gradient is normally calculated by subtracting the outputs of two total field magnetometers which are separated by a baseline. Here we present a unique device that directly measures magnetic gradients using only a single string as its sensing element. The main advantage of a direct string magnetic gradiometer is that only gradients can induce second harmonic string vibrations. A high common mode rejection ratio is thus naturally achieved without any balancing technique. Performance depends on the ability to dissipate heat while minimizing air damping. By combining high current, an elevated temperature and low pressure, we can easily achieve sensitivity of 0.18 nT/m/. Further increases in sensitivity can be attained by optimizing the sensing element. In this paper we present an in-depth study of the most critical parameters of the magnetic gradiometer. We describe the design for the next generation of sensor, which will reach the required sensitivity of 0.01 nT/m/ using only 1 W of power. By combining a few single-axis magnetic gradiometer modules, it will be possible to deploy a full tensor magnetic gradiometer with more than sufficient sensitivity for airborne geophysical applications.