We report the effect of hydrostatic pressure on the magnetic and structural properties of the shape-memory Heusler alloy Ni 50 Mn 35 In 15 . Magnetization and x-ray diffraction experiments were performed at hydrostatic pressures up to 5 GPa using diamond anvil cells. Pressure stabilizes the martensitic phase, shifting the martensitic transition to higher temperatures and suppresses the ferromagnetic austenitic phase. Above ∼ 3 GPa, where the martensitic-transition temperature approaches the Curie temperature in the austenite, the magnetization shows no indication of ferromagnetic ordering anymore. We further find an extremely large temperature region with a mixture of martensite and austenite phases, which directly relates to the magnetic properties.Heusler alloys which exhibit a martensitic structural transformation in proximity to a ferromagnetic (FM) phase have attracted much attention due to the multiple functional properties connected to the coupling of the structural transition to magnetic degrees of freedom, such as shape memory [1][2][3], magnetocaloric [4,5], and barocaloric effects [6]. In the austenitic phase in NiMn-based alloys the Mn moments order ferromagnetically, which arises mainly due to the RKKYexchange interaction [7][8][9]. In the martensitic state, which can form in a simple tetragonal, a complex monoclinic, or an orthorhombic layered structure, a strong competition between FM and antiferromagnetic interactions exists, leading to a high sensitivity of the physical properties on the interatomic distances. The application of pressure is, therefore, an important tool to study the relationship of magnetism and crystal structure, without altering the intrinsic properties unintentionally, or introducing additional disorder in the structure, like in the case of element substitution. In Ni-Mn-Z (Z = In, Sb, Sn), application of a small pressure p < ∼ 1 GPa stabilizes the martensitic phase and, therefore, the martensitic transition temperature increases strongly upon increasing pressure, while the effect on the Curie temperature in the austenitic phase, T A C , is rather small [10][11][12][13]. In closely related compounds, it has been reported that low pressures can improve the magnetocaloric effect [13] or lead to a large barocaloric effect [6].At ambient pressure, the shape-memory Heusler alloy Ni 50 Mn 35 In 15 undergoes on cooling a paramagnetic to FM transition at T A C ≈ 313 K, followed by a first-order martensitic structural transformation from a cubic high-temperature to a low-temperature modulated structure [14] at T M ≈ 248 K [5,15]. On heating the reverse martensitic transition takes place at T A ≈ 261 K. The magnetostructural transition drives the material from the FM state to a state with a small remaining magnetization. Upon further cooling ferrimagnetic order develops in the martensitic phase below T M C ≈ 200 K [5,15]. In this Letter, we study the effect of hydrostatic pressure on the magnetic and structural properties of the Heusler alloy Ni 50 Mn 35 In 15 . While the FM transitio...