Magnetic Materials (LNMM), School of Physical Sciences, National Institute of Science Education and Research (NISER), HBNI, Jatni-752050, India'
author:
- Braj Bhusan Singh
- Koustuv Roy
- Pushpendra Gupta
- Takeshi Seki
- Koki Takanashi
- Subhankar Bedanta
title: 'High spin mixing conductance and spin interface transparency at $Co_2Fe_{0.4}Mn_{0.6}Si$ Heusler alloy and Pt interface'
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Introduction 
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Spin transport across interfaces in ferromagnetic (FM)/heavy metal (HM) systems are important to develop future spintronics devices \[1,2\]. Spin orbital torque \[3,4\], spin transfer torque \[1,2\], spin pumping/inverse spin Hall effect \[5$-$9\], spin Seeback effects \[[10]{}$-$[12]{}\], etc. are major phenomenon which are predominantly affected by interface spin transport in FM/HM systems. Spin pumping is an efficient method to produce pure spin current ($J_s$), which is the flow of spin angular momentum, and investigate the spin propagation across FM/HM interfaces. The efficiency of spin transport at FM/HM interfaces is understandable by the factor known as effective spin mixing conductance ($g_{r}^{\uparrow \downarrow}$), which is related to $J_s$ by the expression\[2\].

$$\label{equation1}
    J_s = \frac{\hbar}{4 \pi}g_{r}^{\uparrow \downarrow}\hat{m} \times \frac{d \hat{m}}{dt}$$

where $\hat{m}$ is the unit vector of magnetization. $J_s$ can be converted into transverse voltage ($V_{ISHE }$) by inverse spin Hall effect (ISHE) \[13\]:

$$\label{eqiation2}
    V_{ISHE 