Writing μ (mu) in the text mode using Latin Modern Roman font

Question

Is there a way to write the literal μ character using the Latin Modern Roman font or another font with the same font aesthetics/characteristics?

The following gets me this error

{C:/Users/Diaa/AppData/Local/MiKTeX/fonts/map/pdftex/pdftex.map} Missing character: There is no μ (U+03BC) in font LatinModernRoman:mode=node;sc ript=latn;language=dflt;+tlig;family=rm;-liga;-dlig;!

\documentclass{article}

\tracinglostchars=3

\usepackage[english, bidi = basic, layout = lists]{babel}

\usepackage{fontspec}


% Set the main font
\setmainfont[
Ligatures = {NoCommon, NoRare},
Scale = 1.0,
Language = Default
]{Latin Modern Roman}


\babelfont{rm}
[Ligatures = {NoCommon, NoRare}, Scale = 1.0, Language = Default]
{Latin Modern Roman}

\babelfont{sf}
[Ligatures = {NoCommon, NoRare}, Scale = 1.0, Language = Default]
{Latin Modern Sans}

\begin{document}
    
    This is a text with μ
    
\end{document}

Answer 1

Latin Modern does not have Greek, but it does have micro (U+00B5) which is the most common use of an isolated mu in latin script.

\documentclass{article}

\tracinglostchars=3

\usepackage[english, bidi = basic, layout = lists]{babel}

\usepackage{fontspec}


% Set the main font
\setmainfont[
Ligatures = {NoCommon, NoRare},
Scale = 1.0,
Language = Default
]{Latin Modern Roman}


\babelfont{rm}
[Ligatures = {NoCommon, NoRare}, Scale = 1.0, Language = Default]
{Latin Modern Roman}

\babelfont{sf}
[Ligatures = {NoCommon, NoRare}, Scale = 1.0, Language = Default]
{Latin Modern Sans}

\begin{document}
    
    This is a text with µ
    
\end{document}

Answer 2

You can use a substitute font just for \mu

\documentclass{article}
\usepackage[english, bidi = basic, layout = lists]{babel}
\usepackage{fontspec}
\usepackage{newunicodechar}

\babelfont{rm}[
  Ligatures = {NoCommon, NoRare},
  Scale = 1.0,
  Language = Default
]{Latin Modern Roman}

\babelfont{sf}[
  Ligatures = {NoCommon, NoRare},
  Scale = 1.0,
  Language = Default
]{Latin Modern Sans}

\newfontfamily{\substituterm}{CMU Serif}
\newfontfamily{\substitutesf}{CMU Sans Serif}

\AddToHook{cmd/rmfamily/before}{\let\substitutemu\substituterm}
\AddToHook{cmd/sffamily/before}{\let\substitutemu\substitutesf}
\AtBeginDocument{\let\substitutemu\substituterm}
\newunicodechar{μ}{{\substitutemu μ}}


\begin{document}

This is a text with μ

\textit{This is a text with μ}

\textbf{This is a text with μ}

\textsf{This is a text with μ}

\textsf{\textit{This is a text with μ}}

\textsf{\textbf{This is a text with μ}}

\end{document}

Using U+00B5 MICRO doesn't seem appealing as it's difficult to imagine a worse rendering of mu as the one for micro in Latin Modern.

Answer 3

Egreg shows how to do a font-family substitution due to one character in LaTeX. Just for comparison, how to solve the analogical task in opTeX:

\fontfam[New CM]        % this family is accessible by \NewCM family selector
\fontfam[Latin Modern]  % current family is last loaded family: Latin Modern   

\adef μ{{\NewCM\fontsel \string μ}}  % substitution of μ by \NewCM μ

This is a text with μ

{\it This is a text with μ}

{\bf This is a text with μ}

{\sans\rm This is a text with μ}

{\sans\it This is a text with μ}

{\sans\bf This is a text with μ}

{\sans\bi This is a text with μ}

\bye

It seems easier to map μ (U+03BC) to (μ U+00B5) by \adef μ{µ} (inspired by David's answer) or most easy is to select a font family where the character is provided. For example \fontfam[NewCM] and no Latin Modern.