South East Double Arrow in Latex

Requires LuaLaTeX (or XeLaTeX):

\documentclass{article}
\usepackage{unicode-math}
\begin{document}
$\Searrow$
\end{document}

---

You could also load the symbol from another font, e.g. txfonts.

\documentclass{article}
\DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n}
\DeclareMathSymbol{\Searrow}{\mathrel}{symbolsC}{117}
\begin{document}
$\Searrow$
\end{document}

The newtxmath and newpxmath math font packages provide macros called \Nearrow, \Nwarrow, \Swarrow and \Searrow. These arrows (a) take up the same width as \Rightarrow and \Leftarrow, respectively, and (b) are 1.4 times as long as \Rightarrow and \Leftarrow.

If you either don't wish to use the newtxmath and newpxmath math font packages -- say, because you don't like or aren't allowed to use Times Roman and Palatino fonts -- or find that the arrows produced by \Nearrow, \Nwarrow, \Swarrow and \Searrow look too long, it's straightforward (by using the \rotatebox macro of the graphicx package) to create angled double-struck arrows that (a) take up the same width as \Rightarrow and (b) are as long \Rightarrow as.

\documentclass{article}
\usepackage{newtxmath} % or: \usepackage{newpxmath}

\usepackage{graphicx} % for '\rotatebox' macro
\newcommand\myrot[1]{\mathrel{\rotatebox[origin=c]{#1}{$\Rightarrow$}}}
% create four new angled double-struck arrows
\newcommand\NEarrow{\myrot{45}}
\newcommand\NWarrow{\myrot{135}}
\newcommand\SWarrow{\myrot{-135}}
\newcommand\SEarrow{\myrot{-45}}

\begin{document}
\[
\begin{array}{c}
a \Rightarrow b\\ \hline
a \Nearrow b\\
a \Nwarrow b\\
a \Swarrow b\\
a \Searrow b\\ \hline
a \NEarrow b\\
a \NWarrow b\\
a \SWarrow b\\
a \SEarrow b
\end{array}
\]
\end{document}