\documentclass[aps,prb,10pt,twocolumn]{revtex4}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[usenames]{color} % colors
\usepackage{bm} % bold math
\usepackage{dcolumn} % decimal alignment in tables

% --------SYMBOL DEFINITIONS ---------
\def\CrO{Cr$_2$O$_3$}
\def\HoMO{HoMnO$_3$}
\def\ErMO{ErMnO$_3$}
\def\YbMO{YbMnO$_3$}
\def\LuMO{LuMnO$_3$}
\def\LuFO{LuFeO$_3$}
\def\RMO{$R$MnO$_3$}
\def\RFO{$R$FeO$_3$}
\def\Zm{Z^{\rm m}}
\def\Ze{Z^{\rm e}}
\def\Op{O$_{\rm P}$}
\def\Ot{O$_{\rm T}$}
% ----------------------------------------------------------

%-------- COLORS --------------
\def\Red#1{\textcolor{red}{#1}}
\def\Blue#1{\textcolor{blue}{[#1]}}
\def\Magenta#1{\textcolor{magenta}{#1}}
%----------------------------------


\begin{document}

\title{Supplementary material for ``Magnetic charge and the
magnetoelectricity in hexagonal manganites \RMO\ and ferrites \RFO''}

\author{Meng Ye}
\affiliation{Department of Physics \& Astronomy, Rutgers University,
Piscataway, New Jersey 08854, USA}

\author{David Vanderbilt}
\affiliation{Department of Physics \& Astronomy, Rutgers University,
Piscataway, New Jersey 08854, USA}

% \date{\today}

\begin{abstract}
In Tables I-II of the main text, we provided detailed information
on the Born charge tensors and force constant eigenvalues only
for the two representative materials \LuMO\ and \LuFO.  Here,
we provide the same information for the other materials covered
by this study.  Note that the values given in the last two columns of
each table are redundant with those given in Tables I-II of the
main text.
\end{abstract}

\maketitle

\begin{table}[h!]
\begin{center}
\begin{ruledtabular}
    \caption{Atomic Born charge tensors $\Ze$
    (in units of $|e|$) for \RMO\
    and \LuFO\ in the A$_2$ phase. TM\,=\,Mn, Fe.}
    \begin{tabular}{cddddd}
        &\multicolumn{1}{c}{\HoMO}
        &\multicolumn{1}{c}{\ErMO}
        &\multicolumn{1}{c}{\YbMO}
        &\multicolumn{1}{c}{\LuMO}
        &\multicolumn{1}{c}{\LuFO}\\ \hline
    $\Ze_{xx}$(R$_1$)   & 3.69& 3.67& 3.62& 3.61& 3.79\\
    $\Ze_{zz}$(R$_1$)   & 4.16& 4.15& 4.11& 4.12& 3.94\\
    $\Ze_{xx}$(R$_2$)   & 3.76& 3.73& 3.67& 3.66& 3.84\\
    $\Ze_{yx}$(R$_2$)   & 0.13& 0.13& 0.13& 0.13& 0.15\\
    $\Ze_{zz}$(R$_2$)   & 4.07& 4.05& 4.00& 3.96& 3.88\\
    $\Ze_{xx}$(TM)      & 3.16& 3.17& 3.17& 3.17& 2.96\\
    $\Ze_{zx}$(TM)      & 0.41& 0.42& 0.43& 0.44& 0.21\\
    $\Ze_{yy}$(TM)      & 3.25& 3.25& 3.26& 3.26& 3.01\\
    $\Ze_{xz}$(TM)      & 0.07& 0.07& 0.07& 0.07&-0.02\\
    $\Ze_{zz}$(TM)      & 4.02& 4.01& 3.97& 3.95& 4.16\\
    $\Ze_{xx}$(\Ot$_1$) &-1.95&-1.94&-1.92&-1.92&-2.19\\
    $\Ze_{zx}$(\Ot$_1$) & 0.24& 0.24& 0.24& 0.25& 0.25\\
    $\Ze_{yy}$(\Ot$_1$) &-2.05&-2.03&-2.00&-2.00&-2.28\\
    $\Ze_{xz}$(\Ot$_1$) & 0.19& 0.19& 0.19& 0.19& 0.11\\
    $\Ze_{zz}$(\Ot$_1$) &-3.24&-3.24&-3.20&-3.19&-3.21\\
    $\Ze_{xx}$(\Ot$_2$) &-1.95&-1.93&-1.91&-1.90&-2.15\\
    $\Ze_{zx}$(\Ot$_2$) &-0.20&-0.20&-0.20&-0.20&-0.19\\
    $\Ze_{yy}$(\Ot$_2$) &-1.88&-1.87&-1.85&-1.85&-2.13\\
    $\Ze_{xz}$(\Ot$_2$) &-0.18&-0.18&-0.18&-0.18&-0.11\\
    $\Ze_{zz}$(\Ot$_2$) &-3.38&-3.38&-3.34&-3.33&-3.30\\
    $\Ze_{xx}$(\Op$_1$) &-3.01&-3.01&-3.01&-3.00&-2.40\\
    $\Ze_{zz}$(\Op$_1$) &-1.58&-1.57&-1.54&-1.54&-1.61\\
    $\Ze_{xx}$(\Op$_2$) &-3.05&-3.05&-3.06&-3.05&-2.45\\
    $\Ze_{yx}$(\Op$_2$) &-0.03&-0.03&-0.03&-0.03&-0.02\\
    $\Ze_{zz}$(\Op$_2$) &-1.47&-1.46&-1.43&-1.43&-1.52\\
    \end{tabular} \end{ruledtabular}
\end{center}
\end{table}

\newpage

\begin{table}[h!]
\begin{center}
\begin{ruledtabular}
    \caption{Eigenvalues of the force-constants matrix  ($\rm{eV}/{\AA}^2$)
    for IR-active modes in \RMO\ and \LuFO\ in the A$_2$ phase, and for
    \HoMO\ in the A$_1$ phase}
    \begin{tabular}{ddddd}
        \multicolumn{1}{c}{\HoMO} &
        \multicolumn{1}{c}{\ErMO} &
        \multicolumn{1}{c}{\YbMO} &
        \multicolumn{1}{c}{\LuMO} &
        \multicolumn{1}{c}{\LuFO} \\ \hline
        \multicolumn{5}{l}{Longitudinal $A_1$ modes}\\
         4.23 &  4.23 & 4.25 &4.24  &3.48  \\ 
         7.11 &  7.18 & 7.35 &7.44  &6.70  \\ 
         8.14 &  8.27 & 8.60 &8.74  &8.41  \\ 
        10.77 & 10.90 &11.34 &11.51 &11.47 \\
        13.69 & 13.82 &13.98 &14.01 &12.03 \\
        14.85 & 15.03 &15.42 &15.60 &15.59 \\
        21.32 & 21.60 &22.36 &22.66 &20.53 \\
        25.44 & 25.57 &25.67 &25.87 &22.83 \\
        35.99 & 35.68 &35.54 &35.82 &28.46 \\
      \multicolumn{5}{l}{Transverse $E_1$ modes}\\
         3.23 & 3.37 & 3.27 & 3.32 & 3.56 \\
         4.22 & 4.25 & 4.49 & 4.68 & 4.62 \\
         5.96 & 6.28 & 6.63 & 6.73 & 6.97 \\
         7.59 & 6.93 & 7.01 & 7.35 & 8.09 \\         
         8.41 & 8.56 & 8.57 & 8.63 & 8.83 \\
         9.29 & 8.99 & 9.31 & 9.56 & 9.24 \\
         9.65 &10.12 &10.95 &11.36 &11.37 \\
        11.23 &11.25 &12.02 &12.46 &12.46 \\
        12.57 &12.85 &12.95 &13.02 &13.85 \\
        13.29 &13.54 &13.77 &14.09 &14.92 \\
        16.41 &16.76 &16.57 &16.49 &16.87 \\
        17.49 &17.52 &17.38 &17.37 &17.35 \\
        22.79 &23.02 &23.16 &23.36 &21.19 \\
        36.18 &37.99 &37.54 &37.75 &28.75 \\
    \end{tabular} \end{ruledtabular}
\end{center}
\end{table}



\end{document}
