Double sided arrow notation for second-order tensors

You might use the old-arrows package that provides arrows with smaller tips. However, using the package would change all arrows in the document, which is possibly not desired, so we can fetch just the necessary bits:

documentclass{article}
usepackage{amsmath}

DeclareFontFamily{OMS}{oasy}{skewcharfont48 }
DeclareFontShape{OMS}{oasy}{m}{n}{%
         <-5.5> oasy5     <5.5-6.5> oasy6
      <6.5-7.5> oasy7     <7.5-8.5> oasy8
      <8.5-9.5> oasy9     <9.5->  oasy10
      }{}
DeclareFontShape{OMS}{oasy}{b}{n}{%
       <-6> oabsy5
      <6-8> oabsy7
      <8->  oabsy10
      }{}
DeclareSymbolFont{oasy}{OMS}{oasy}{m}{n}
SetSymbolFont{oasy}{bold}{OMS}{oasy}{b}{n}

DeclareMathSymbol{smallleftarrow}     {mathrel}{oasy}{"20}
DeclareMathSymbol{smallrightarrow}    {mathrel}{oasy}{"21}
DeclareMathSymbol{smallleftrightarrow}{mathrel}{oasy}{"24}

newcommand{tensor}[1]{overset{scriptscriptstylesmallleftrightarrow}{#1}}

begin{document}
$tensor{x}$                                                
end{document}

The definitions for smallrightarrow and smallleftarrow are not required, but they make no harm.