Spin-lattice coupling in magnetocaloric Gd5(Ge,Si)4 alloys by $in$ $situ$ x-ray pair distribution analysis in magnetic field

Using in situ x-ray pair distribution analysis in magnetic field, we study the strong spin-lattice coupling in archetypal magnetocaloric Gd5(Ge,Si)4 alloys manifested by the presence of a first order paramagnetic (PM)-to-ferromagnetic (FM) phase transition that can be triggered by either decreasing temperature in zero magnetic field or increasing magnetic field at constant temperature. We find that the coupling arises from the tendency of Gd-(Si,Ge) slabs in the alloys to reversibly slide against each other to both pack closely and couple ferromagnetically. We also find that, locally, the packing of slabs in FM phases induced by decreasing temperature in zero field is different from that in FM phases of the same chemical composition induced by increasing magnetic field isothermally, indicating that temperature and magnetic field are coupled but not necessarily equivalent control variables for triggering phase transitions in strongly correlated systems.