**1. Introduction**

From the discovery of exchange bias (EB) in CoO particle [1], more work has been done on this area both experimentally and theoretically due to its potential applications in various fields such as spintronic devices, permanent magnets, magnetic recording, read head and giant magnetoresistive sensors, etc. [2–5]. EB arises in the presence of applied magnetic field after cooling the materials and it is connected with the exchange anisotropy formed at the interface between an antiferromagnetic (AFM) and ferromagnetic (FM) materials. The whole phenomenon at low temperature shifts the hysteresis loops along the field axis. This similar kind of phenomenon is observed in multilayer films, small oxide particles, nanostructures and inhomogeneous materials [6–9]. In addition to this, the EB phenomenon is also observed in materials which contains spin glass phase [10]. Recently, Ni-Mn-X (X = Ga, Sb, In, Sn) Heusler-based alloy systems achieved great attention due to their immense applications in magnetic refrigeration, magnetic actuated devices and spintronic devices [11, 12]. The different composition of Ni-Mn-Sn alloy shows a wide physical properties such as magnetic field-induced transition, inverse magnetocaloric effect (IMCE), giant magnetoresistance, giant Hall effect, giant magnetothermal conductivity, magnetic superelasticity effects, exchange bias and shape memory effect [13–17].

The recent observation of EB in the Ni-Mn-based alloys shows an intense interest in the further study of magnetic properties. Due to the different occupations of Mn atoms in the Sn sites as well in the Ni sites, the Ni-Mn-Sn alloy will have excess content of Mn atom. Hence the EB property is very sensitive to the excess Mn. The Ni2MnSn Heusler alloy crystallizes in L21 structure, in which the Ni atoms occupy in the (1/2, 1/2, 1/2) and (0, 0, 0) sites, Mn atoms occupy in the (1/4, 1/4, 1/4) site and Sn atoms occupy in the (3/4, 3/4, 3/4) site [18]. In the Mn-rich alloys, the excess Mn occupying Ni and Sn sites couples antiferromagnetically to surrounding Mn atoms on the regular Mn sites [19]. Also the decrease of Mn-Mn distance may lead to AFM exchange between each other in the martensite phase at low temperature. The EB behaviour has been studied in Ni-Mn-X (X = Sb, Sn, In) alloys by several authors [20–23]; particularly in Ni-Mn-Sn alloy, the EB behaviour has been investigated either by varying the Ni/Sn or Mn/Sn concentration [24, 25]. The structural effects, magnetic property and magnetic entropy change have been studied by varying Ni-Mn concentration in the Ni50-xMn37+xSn13 (0 ≤ x ≤ 4) Heusler alloy system [26]. In the Ni50-xMn37+xSn13 alloy system, the cubic austenite phase was stabilized by the excess Mn content at room temperature. The martensitic transition temperature decreases from 305 to 100 K by increasing the Mn concentration. The exchange bias blocking temperature (TEB) was found to decrease drastically from 149 to 9 K with increasing Mn concentration. In this work, we have taken up a detailed study on the effect of varying Ni-Mn concentration on EB properties in the bulk Ni50-xMn37+xSn13 alloys. This chapter explains the EB behaviour by varying Ni-Mn concentration in Ni-Mn-Sn alloys.
