Phenomena that are highly sensitive to magnetic fields can be exploited in sensors and non-volatile memories [1]. The scaling of such phenomena down to the single molecule level [2, 3] may enable novel spintronic devices [4]. Here we report magnetoresistance in a single molecule junction arising from negative differential resistance that shifts in a magnetic field at a rate two orders of magnitude larger than Zeeman shifts. This sensitivity to the magnetic field produces two voltage-tunable forms of magnetoresistance, which can be selected via the applied bias. The negative differential resistance is caused by transient charging [5][6][7] of an iron phthalocyanine (FePc) molecule on a single layer of copper nitride (Cu 2 N) on a Cu(001) surface, and occurs at voltages corresponding to the alignment of sharp resonances in the filled and empty molecular states with the Cu(001) Fermi energy. An asymmetric voltage-divider effect enhances the apparent voltage shift of the negative differential resistance with magnetic field, which inherently is on the scale of the Zeeman energy [8]. These results illustrate the impact that asymmetric coupling to metallic electrodes can have on transport through molecules, and highlight how this coupling can be used to develop molecular spintronic applications.Research into magnetoresistance [9, 10] has been driven by the widespread use of giant magnetoresistance (GMR) sensors in hard drives as well as other applications such as magnetoresistive random access memory (MRAM) [1]. To reach even higher storage densities, research has begun to concentrate on magnetoresistance at the atomic scale [2, 3, 11]. For a single molecule, however, the small area for enclosing flux and modest energy scales associated with electronic Zeeman shifts typically make it difficult to tune magnetoresistive phenomena with an external magnetic field.Another electron transport phenomenon with technological relevance is negative differential resistance (NDR) [5, 7,[12][13][14][15][16][17][18][19], in which an increase in voltage causes a decrease in current. Commercial devices, such as the resonant tunnelling diode, utilise these regions in specialised applications [20, 21]. Various mechanisms cause NDR at the atomic scale [5, 7,[12][13][14][15][16][17][18][19], though none are expected to have a magnetic field dependence that would shift the NDR on a scale larger than the Zeeman energy.Using low temperature scanning tunnelling microscopy (STM) (see Supplementary Methods), we observe an NDR effect for FePc molecules placed in a vacuum junction on top of 2 a Cu(001) surface capped with a single layer of Cu 2 N (Fig. 1). Cu 2 N is a thin insulator that can decouple the spins of magnetic atoms from the underlying surface [22]; FePc is a magnetic molecule that can be easily sublimed [23][24][25] and is observed to have interesting magnetic properties on thin insulating layers [26]. On Cu 2 N, FePc is centred above both Cu and N sites. The two binding sites can be differentiated using atomically resolved imaging a...