I'm ready to style arrows using arrows.meta library, though I haven't found any documentation with predefined arrow styles syntax. The only one I know is Stealth:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\begin{document}
\begin{tikzpicture}
\draw[black,step=1cm,thin] (0,0) grid (6,6);
\draw[-{>[scale=1.3,red,length=5mm,width=2mm]]},semithick] (0,1) -- (6,1);
\draw[-{Stealth[scale=1.3]},semithick] (0,1) -- (6,1);
\end{tikzpicture}
I'm seeking for angle 45 or angle 60 arrow tips used in arrows.meta.
