Change mantissa sep on axis exponent

I have the following latex code generating a plot.
I want to change the scientific notation mantissa sep to a times not cdot, this is for the y axis (x10-4). I don’t want all the other numbers to be in scientific notation too.

I have tried pgfkeys{/pgf/number format/sci generic/mantissa sep=times}
but that has not worked. What do I need to change

documentclass{standalone}
usepackage{pgfplots}
pgfplotsset{compat=1.5}
begin{document}
definecolor{mycolor1}{rgb}{0.00000,0.44700,0.74100}%
definecolor{mycolor2}{rgb}{0.85000,0.32500,0.09800}%
begin{tikzpicture}
pgfkeys{/pgf/number format/sci generic/mantissa sep=times}

begin{axis}[%
width=(hsize/2),
height=(hsize/2),
scale only axis,
xmin=0,
xmax=0.5,
xlabel near ticks,
xlabel={Density $lambda$},
ymin=0,
ymax=0.00035,
ylabel near ticks,
ylabel={Rate, ($s^{-1}$)},
axis x line*=bottom,
axis y line*=left,
xmajorgrids,
ymajorgrids,
legend style={legend cell align=left, align=left}
]
addplot [color=mycolor1, mark=o, mark options={solid, mycolor1}]
  table[row sep=crcr]{%
1e-05   0.000349984346613178
0.0250095   0.000294763280950208
0.100008    0.000223262905327838
0.1750065   0.000189761632377871
0.250005    0.000168814588345592
0.3250035   0.000153988764794569
0.400002    0.000142726344312675
0.4750005   0.000133766561301556
0.5 0.000131160050335831
};label{rate_plot}
addlegendentry{Rate}

end{axis}

end{tikzpicture}%

end{document}

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