MnS Poster

<BODY BGCOLOR="#FFFFFF"> <CENTER><FONT SIZE="+4"><B> Bonding in Transition <BR> Metal Sulphides -<BR> MnS</B></FONT><P></CENTER> <BR> <CENTER><IMG SRC="image/crest100.gif"></CENTER> <BR> <BR> <BR> <H3> <CENTER>Rob Hines<P> School of Chemistry, University of Bristol,<br> Cantocks Close, Bristol BS8 1TS<P></CENTER> <P> <HR> <BR> <IMG SRC="image/go.gif"><P> <IMG SRC="image/gol.gif"> <HR> <P> <BR> <CENTER><H2><FONT COLOR="#0000EE"> Why?<P> </FONT></H2></CENTER> <P> <IMG SRC="image/bulblue.gif"> MnS is the limiting component of the dilute magnetic semiconductors Cd<SUB>1-x</SUB>Mn<SUB>x</SUB>S and Zn<SUB>1-x</SUB>Mn<SUB>x</SUB>S. These compounds exhibit outstanding magneto-optical properties.<P> <P> <IMG SRC="image/bulblue.gif"> MnS is an important component in steel manufacture.<P> <P> <IMG SRC="image/bulblue.gif"> MnS (and sulphides in general) have considerable geological relevance.<P> <P> <IMG SRC="image/bulblue.gif"> The electronic structure of transition metal sulphides/oxides is notoriously <i><FONT COLOR="#0000EE">difficult</FONT></i> to calculate due to the unpaired electrons.<P> <P> <IMG SRC="image/bulblue.gif"> Conventional solid state physics methods (e.g. density functional theory) are <i><FONT COLOR="#0000EE">unsuccessful</FONT></i> in this area, often predicting a metallic rather than an insulating state!!!<P> <P> <IMG SRC="image/bulblue.gif"> Hartree-Fock theory, which is a traditional <i>ab initio</i> technique for describing chemical bonding, has only recently been extended to solids in the program CRYSTAL.<P> <P> <IMG SRC="image/bulblue.gif"> CRYSTAL has been used to predict successfully the correct electronic and magnetic structure of a number of transition metal oxides. <P> <P> <IMG SRC="image/bulblue.gif"> Numerical accuracy can be made high enough to study energy differences of 10<SUP>-6</SUP> hartrees per cell!!<P> <P> <IMG SRC="image/bulblue.gif"> Our objective is to answer the question:<P> <P> <P> <CENTER><FONT COLOR="#0000EE"> <b>Can the Hartree-Fock method predict<br> the complex electronic and magnetic<br> structures of MnS ?</b><P> </FONT></CENTER> <P> <HR> <P> <CENTER><H2><FONT COLOR="#0000EE"> Crystal Structures<P> </FONT></H2></CENTER> <P> <P> MnS adopts the cubic NaCl (rocksalt) structure under normal conditions (alpha-MnS). However, MnS crystals adopting the zinc blende structure (beta-MnS) can also be grown under appropriate conditions.<P> <P> <P> <P> <P> <P> <CENTER><TABLE> <TR ALIGN="middle"><TD><IMG SRC="image/fccc.gif"><TD><IMG SRC="image/blendec.gif"> <TR ALIGN="middle"><TD><H3>The Rocksalt (NaCl)<BR>Structure<TD><H3>The Zinc Blende (ZnS)<BR>Stucture </TABLE></CENTER> <P> <P> <BR> <CENTER><H2><FONT COLOR="#0000EE"> Magnetic Structures<P> </FONT></H2></CENTER> <P> <P> Mn<SUP>2+</SUP> has 5 d-electrons and is observed in a high spin configuration (i.e. t<SUB>2g</SUB><SUP>3</SUP>, e<SUB>g</SUB><SUP>2</SUP>) in both alpha- and beta-MnS. This leads to a number of possible `spin structures' and these are shown opposite. <P> Both alpha-(rocksalt) and beta-(zinc blende) MnS have a face centred cubic array of cations so the magnetic structures shown apply to both allotropes.<P> <BR> <IMG SRC="image/bulblue.gif"> Alpha-MnS adopts the antiferromagnetic AF2 structure.<P> <P> <IMG SRC="image/bulblue.gif"> Beta-MnS is observed in the AF3 configuration.<P> <BR> <HR> <CENTER><TABLE> <TR ALIGN="middle"><TD><IMG SRC="image/fccf.gif"><TD><IMG SRC="image/fccaf1c.gif"> <TR ALIGN="middle"><TD><H3>Ferromagnetic<TD><H3>Antiferromagnetic AF1 <TR ALIGN="middle"><TD><IMG SRC="image/fccaf2c.gif"><TD ROWSPAN=2><IMG SRC="image/key.gif"> <TR ALIGN="middle"><TD><H3>Antiferromagnetic AF2 <TR ALIGN="middle"><TD COLSPAN=2><IMG SRC="image/fccaf3c.gif"> <TR ALIGN="middle"><TD COLSPAN=2><H3>Antiferromagnetic AF3 </TABLE></CENTER> <HR> <BR> <CENTER><H2><FONT COLOR="#0000EE"> Results<P> </FONT></H2></CENTER> <P> <H2>alpha-MnS</H2><P> <TABLE> <TR><TD><H3>a<SUB>expt</SUB> = 5.2400 Å<TD><TD><TD><TD><H3>a<SUB>calc</SUB> = 5.4226 Å </TABLE> <CENTER><TABLE BORDER > <TR ALIGN="middle"><TH><H3>Spin Structure<TH><H3>Electronic Energy /a.u. per formula unit <TR ALIGN="middle"><TD><H3>Ferromagnetic<TD><H3>-1547.493021 <TR ALIGN="middle"><TD><H3>AF1<TD><H3>-1547.493025 <TR ALIGN="middle"><TD><H3><FONT COLOR="#EE0000">AF2<TD><H3><FONT COLOR="#EE0000">-1547.493208 <TR ALIGN="middle"><TD><H3>AF3<TD><H3>-1547.493100 </TABLE></CENTER> <P> <H2>beta-MnS</H2><P> <TABLE> <TR><TD><H3>a<SUB>expt</SUB> = 5.6060 Å<TD><TD><TD><TD><H3>a<SUB>calc</SUB> = 5.9030 Å </TABLE> <CENTER><TABLE BORDER > <TR ALIGN="middle"><TH><H3>Spin Structure<TH><H3>Electronic Energy /a.u. per formula unit <TR ALIGN="middle"><TD><H3>Ferromagnetic<TD><H3>-1547.493367 <TR ALIGN="middle"><TD><H3>AF1<TD><H3>-1547.493963 <TR ALIGN="middle"><TD><H3>AF2<TD><H3>-1547.493818 <TR ALIGN="middle"><TD><H3><FONT COLOR="#EE0000">AF3<TD><H3><FONT COLOR="#EE0000">-1547.493967 </TABLE></CENTER> <P> <BR> <IMG SRC="image/bulblue.gif"> The <i><FONT COLOR="#0000EE">correct</FONT></i> spin structures are predicted for both alpha-MnS and beta-MnS.<P> <P> <IMG SRC="image/bulblue.gif"> Our calculated lattice constants are accurate to ~2%.<P> <P> <IMG SRC="image/bulblue.gif"> The rocksalt structure is lowest in energy, in agreement with experiment, when correlation effects are taken into account.<P> <P> We can examine the electronic and magnetic structures in more detail by looking at:<P> <P> <IMG SRC="image/bulblue.gif"> The density of states - effectively the orbital ordering.<P> <P> <IMG SRC="image/bulblue.gif"> Charge density difference plots. These are obtained by subtracting the free ion electron densities from the total charge density and tell us how free ions are perturbed in the solid.<P> <P> <HR> <BR> <CENTER><IMG SRC="image/af2ados.gif"></CENTER> <BR> <BR> <BR> <CENTER><H2><FONT COLOR="#0000EE"> <i>Charge Density Difference Map for AF2 alpha-MnS</i><P> </FONT></H2></CENTER> <BR> <CENTER><IMG SRC="image/af2ac.gif"></CENTER> <P> <P> <CENTER><TABLE> <TR ALIGN="middle"><TD><TD><H3>Plotted in the basal (001) plane <TR ALIGN="middle"><TD><H3>positive difference - blue<TD><TD><H3>negative difference - red </TABLE></CENTER> <HR> <BR> <CENTER><IMG SRC="image/af3bdos.gif"></CENTER> <BR> <BR> <BR> <CENTER><H2><FONT COLOR="#0000EE"> <i>Charge Density Difference Map for AF3 beta-MnS</i><P> </FONT></H2></CENTER> <BR> <CENTER><IMG SRC="image/af3bc.gif"></CENTER> <P> <P> <CENTER><TABLE> <TR ALIGN="middle"><TD><TD><H3>Plotted in the (011) plane <TR ALIGN="middle"><TD><H3>positive difference - blue<TD><TD><H3>negative difference - red </TABLE></CENTER> <HR> <BR> <CENTER><H2><FONT COLOR="#0000EE"> Conclusions<P> </FONT></H2></CENTER> <P> <P> <P> <IMG SRC="image/bulblue.gif"> The Hartree-Fock method <i><FONT COLOR="#0000EE">is</FONT></i> successful at predicting the electronic and magnetic structures of MnS.<P> <P> <P> <IMG SRC="image/bulblue.gif"> This is a striking result - we are able to calculate very subtle differences between the magnetic states.<P> <P> <P> <IMG SRC="image/bulblue.gif"> A band gap is clearly evident in the density of states showing we have an insulating state (c.f. DF theory).<P> <P> <P> <IMG SRC="image/bulblue.gif"> Calculated charges indicate that both the rocksalt and zinc blende structures of MnS are largely ionic.<P> <P> <P> <IMG SRC="image/bulblue.gif"> The density of states show only the presence of spin-up electrons - i.e. we have a high spin state as observed experimentally.<P> <P> <P> <IMG SRC="image/bulblue.gif"> The splittings of the eg and t2g orbitals according to crystal field theory are <i><FONT COLOR="#0000EE">not</FONT></i> observed due to subtle effects including Coulombic and exchange interactions. Don't believe everything that you're taught !!<P> <P> <P> <P> Many thanks to my supervisor, Dr. Neil Allan, and our collaborator, Dr. Bill Mackrodt from St. Andrews.<P> </BODY>