Helicity-tunable spin Hall and spin Nernst effects in unconventional chiral fermion semimetals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi><mml:mo>=</mml:mo><mml:mi>Co</mml:mi><mml:mo>,</mml:mo><mml:mi>Rh</mml:mi></mml:math> ; <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Y</mml:mi><mml:mo>=</mml:mo><mml:mi>Si</mml:mi><…

Transition metal monosilicides CoSi, CoGe, RhSi, and RhGe in the chiral cubic B20 structure (the CoSi family) have recently been found to host unconventional fermions beyond spin-1/2 Weyl fermions, also exhibit exotic physical phenomena such as long Fermi arc surface states, gyrotropic magnetic effect, quantized circular photogalvanic effect. Thus, exploring novel spin-related transports these fermion semimetals may open a new door for spintronics spin caloritronics. In this paper, we study intrinsic Hall effect (SHE) Nernst (SNE) family based on ab initio relativistic band calculations. First, find that unlike nonchiral metals, two independent nonzero (Nernst) conductivity tensor elements, namely, ${\ensuremath{\sigma}}_{xy}^{z}$ ${\ensuremath{\sigma}}_{xz}^{y}$ (${\ensuremath{\alpha}}_{xy}^{z}$ ${\ensuremath{\alpha}}_{xz}^{y}$) instead of one element. Furthermore, SHC (${\ensuremath{\sigma}}_{xy}^{z}$ ${\ensuremath{\sigma}}_{xz}^{y}$) helicity are be correlated, thus enabling SHE detection structural chirality. Second, SNE some large. particular, calculated (SHC) is large $\ensuremath{-}140 (\ensuremath{\hbar}/\mathrm{e})$(S/cm). The (SNC) CoGe large, being $\ensuremath{-}1.3 (\ensuremath{\hbar}/\mathrm{e})$(A/m K) at room temperature. Due their semimetallic nature with low electrical conductivity, topological angles, comparable platinum metal. SNC compounds can increased by raising or lowering chemical potential to, e.g., nodes, via either doping gating. Our findings indicate transition not only would provide material platform semimetals, but could promising materials developing better spintronic caloritronic devices.