Tunable large spin Hall and spin Nernst effects in the Dirac semimetals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Zr</mml:mi><mml:mi>X</mml:mi><mml:mi>Y</mml:mi><mml:mo> </mml:mo><mml:mo>(</mml:mo><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>Si</mml:mi><mml:mo>,</mml:mo><mml:mi>Ge</mml:mi><mml:mo>;</mml:mo><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="normal">S</mml:mi><mml:mo>,</mml:mo><mml:mi>Se</mml:mi><mml:mo>,</mml:mo><mml:mi>Te</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>

Abstract

ZrSiS-type compounds are Dirac semimetals and thus have been attracting considerable interest in recent years due to their topological electronic properties and possible technological applications. In particular, gapped Dirac nodes can possess large spin Berry curvatures and thus give rise to a large spin Hall effect (SHE) and a large spin Nernst effect (SNE), which may be used to generate pure spin current for spintronics and spin caloritronics without applied magnetic field or magnetic material. In this paper we study both SHE and SNE in $\mathrm{Zr}XY (X=\mathrm{Si},\mathrm{Ge};Y=\mathrm{S},\mathrm{Se},\mathrm{Te})$ based on ab initio relativistic band structure calculations. Our theoretical calculations reveal that some of these compounds exhibit large intrinsic spin Hall conductivity (SHC) and spin Nernst conductivity. For example, the calculated SHC of ZrSiTe is as large as $\ensuremath{-}755$ ($\ensuremath{\hbar}/e$) (S/cm). Since the electric conductivity of these Dirac semimetals is much smaller than that of platinum, which has the largest intrinsic SHC of $\ensuremath{\sim}2200$ ($\ensuremath{\hbar}/e$) (S/cm), this indicates that they will have a larger spin Hall angle (and hence a more efficient charge-spin-current conversion) than that of platinum. Remarkably, we find that both the magnitude and sign of the SHE and SNE in these compounds can be significantly tuned by changing either the electric field direction or spin current direction and may also be optimized by slightly varying the Fermi level via chemical doping. Analysis of the calculated band-decomposed and $k$-resolved spin Berry curvatures shows that the large SHE and SNE as well as their remarkable tunabilities originate from the presence of many slightly spin-orbit coupling-gapped Dirac nodal points and lines near the Fermi level in these Dirac semimetals. Our findings thus suggest that ZrSiS-type compounds are promising candidates for spintronic and spin caloritronic devices and will certainly stimulate further experiments on these Dirac semimetals.

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