# Magnetic Field Effect on the Handedness of Electrodeposited Heusler Alloy
## 1 Introduction
### Magnetic Effect in Electrochemistry  
The experimental results that were obtained in the field of magneto-electrochemistry can be rationalized based on classical electromagnetism laws. The electrostatic force acting on the ions of charge \(q\), in solution, is given by Equation (1) and (2). The latter allow to rationalize the effect of the magnetic field on the electrolyte conductivity, featuring ion migration under a given applied electric field \(E\). With the simultaneous presence of a magnetic field \(B\), which yields a Lorentz type force, on the moving ion of charge \(q\)[15; 16]:  
\[F=qE \tag{1}\]  
\[F=q(E+v\times B) \tag{2}\]  
where \(v\) is the speed of the ion in the electrolyte solution. Equation (2) represents the deviation of the motion of ions from a simple linear trajectory [17]. The Lorentz force is maximized when the current and magnetic field are perpendicular and minimized when they are parallel. On the whole, the observed experimental behaviour is addressed as the magneto-hydrodynamics (MHD) effect [18]. Further on, Equation (3) gives due reason to the force acting on a moving ion in a non-uniform magnetic field [1]:  
\[\overset{\rightarrow}{F}_{mag}=\frac{\chi_{m}B^{2}\overset{\rightarrow}{ \
abla}c}{2\mu_{0}}+\frac{\chi_{m}c_{0}B\overset{\rightarrow}{\
abla}B}{\mu_ {0}} \tag{3}\]  
In Equation (3) \(\chi_{m}\) is the molar magnetic susceptibility, \(\mu_{0}\) is the free space permeability, and \(c_{0}\) is the bulk concentration of the magnetic species. This expression of \(\overset{\rightarrow}{F}_{mag}\) consists of two terms: the first term of the right-hand side of Equation (3) is the paramagnetic gradient force (which depends on the gradient of the concentration); the second term in Equation (3) is the field gradient force (which can be significant even in the case of a uniform magnetic field: it can be found close to the rough surface of a ferromagnetic electrode). Note that Equations (1)-(3) do not account for any spin related effect, as well as any symmetry related effect, or spin-chirality interaction. Application of a magnetic field on the bulk electrolyte mass transport can be rationalized within such a classical based approach [19]. Indeed, the application of a magnetic field in the electro-deposition yields chiral patterns of either clockwise or anticlockwise handedness, depending on the magnetic field orientation with respect to the electrode surface [20]. The inhomogeneity due to the confinement of the electrode and the size of the magnet could generate vortexes all around the electrode, and even smaller vortices on the electrodeposited asperities [21]. For this reason, even when the current and magnetic field are nominally parallel, numerous works have found that the inherent inhomogeneity (e.g., edge effects) of electrodes and magnets can lead to local variations in both current and magnetic field, resulting in significant and complex convective flows [16]. Furthermore, X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses proved the occurrence of modifications in the deposited chemical composition, and in the surface roughness as well, of an electrodeposition process that was carried out in the presence of a magnetic field [22]. Similar results are observed in the electropolymerization of organic compounds too, where asymmetric induction is observed in the polyaniline electropolymerization under high magnetic fields [23]. The importance of these studies rests in the possible use of these materials as catalysts and sensors in the field of enantirecognition [24; 25; 26; 27; 28; 29; 30; 31; 32].