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\begin{document}
\title{Structure and properties of
EuAl$_{2}$Si$_{2}$, EuAl$_{2}$Ge$_{2}$, YbAl$_{2}$Si$_{2}$ 
and YbAl$_{2}$Ge$_{2}$}

\author{ Amensisa Abdi\\
	 \\         Department of Physics
            \\          University of Cincinnati 
              \\         Cincinnati, Ohio 45221\\[1em]}
\date{March 04, 2002 }
\maketitle
\begin{abstract}Ln$Al_{2}X_{2}$ (Ln=Eu, Yb; X=Si,Ge) compounds are synthesized by
 heating the elements at 1070$-$1270 K. They are observed to crystallize in the 
Ca$Al_{2}Si_{2}$-type structure (space group P\={3}m1) with lattice constants (\AA):
 Yb$Al_{2}Ge_{2}$: a=4.179, c=7.069. Eu$Al_{2}Ge_{2}$: a=4.214, c=7.320.
Eu$Al_{2}Si_{2}$:a=4.181, c=7.259. Magnetic susceptibility measurements of 
Eu$Al_{2}Si_{2}$ and Eu$Al_{2}Ge_{2}$ has shown paramagnetic behavior above 50 K with 
experimental magnetic moments of 7.82 $\mu_{\beta}$/Eu and 7.90
 $\mu_{\beta}$/Eu respectively indicating divalent Eu. Antifromagnetic behavior is also detected at
 $T_{N}$=35.5 for 
Eu$Al_{2}Si_{2}$ and at $T_{N}$= 27.5 for Eu$Al_{2}Ge_{2}$. A typical behavior of an 
intermediate-valent compound 
is observed for Yb$Al_{2}Si_{2}$.  A linear dependence of the inverse of susceptibility on
 temperature 
has been seen between 100 and 300 K with a reduced moment of 2.57 $\mu_{\beta}$/Yb.
 A strong negative 
Curie temperature of $–382$ K is obtained. LMTO band structure calculations and experimental 
results confirm that all compounds are metallic between 8 and 320 K.   \\[1em]
\end{abstract}

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\section*{1. Introduction}


A$M_{2}X_{2}$ compounds (A= rare- or alkaline earth metal; M=metal; X=main group 3-6 element) 
favorably crystallize in the Th$Cr_{2}Si_{2}$ structure~\cite{refA}. In contrast to this, the metallic 
aluminum silicides and germanides Ln$Al_{2}X_{2}$ (Ln=rare-earth metal, X=Si, Ge) crystallize in 
the trigonal Ca$Al_{2}Si_{2}$-type structure~\cite{refA}. The band gap of Ln$Al_{2}X_{2}$ is vanishingly 
small when the electronegativity difference of the atoms $Al_{2}X_{2}$ is small~\cite{refB}. Therefore, the
surplus electron does not destabilize the structure as it would do if the energy gap is
present. So the metallic behavior of Ln$Al_{2}X_{2}$ is, not a result of the surplus electron, 
just the electronic structure itself is that of a metal. In other words, every compound 
A$Al_{2}X_{2}$ with X=Si or Ge and Ca$Al_{2}Si_{2}$ structure is expected to be metallic,
regardless the valence of the base metal A. 

In contrast to the pure trivalent rare earth metals, europium and ytterbium have an enhanced 
stability of the divalent states ($4f^{7}$ and $4f^{14}$-shells) and occur as 
$Eu^{2+}$/$Eu^{3+}$ and $Yb^{2+}$/$Yb^{3+}$, respectively. In addition to the above mentioned 
arguments, the question arises whether the rare-earth atoms in Eu$Al_{2}X_{2}$ and 
Yb$Al_{2}X_{2}$ are di- or trivalent. A good probe for this is the magnetism of the 4f-shell:
$Eu^{2+}$ has a magnetic moment of 7.94 $\mu_{\beta}$, $Eu^{3+}$ is nonmagnetic as $Yb^{2+}$ is, and 
$Yb^{3+}$ has a moment of 4.45 $\mu_{\beta}$.
Magnetic measurements and a neutron diffraction experiment with $EuAl_{2}Si_{2}$ resulted 
considerably rescued magnetic moments for Eu about 7 $\mu_{\beta}$ in these compounds, which 
indicates intermediate valance. In this paper, the single-crystal 
structures of $EuAl_{2}X_{2}$ and $YbAl_{2}X_{2}$.The crystal structure of $YbAl_{2}Si_{2}$ was recently 
reported by us~\cite{refB}, $YbAl_{2}Ge_{2}$ was characterized only by powder data so far~\cite{refC}. In this 
paper b, we report the single-crystal structures of $EuAl_{2}X_{2}$ and $YbAl_{2}X_{2}$,
 electrical conductivity and magnatic measurements are reported.



\section*{2. Experimental}

All compounds were synthesized by direct reaction of the elements in corundum 
Crucibles at a temperature between is 
1020 and1170 K. in quartz glass tubes under dry argon atmosphere. The first inhomogeneous 
products were homogenized in an argon-filled glove box and
 annealed twice at temprature between 1170 and 1270 K for 50 h. The resulting gray powders 
deteriorate slowly when 
exposed to; single crystals show metallic luster.
Single-crystal data of Eu$Al_{2}Si_{2}.  EuAl_{2}SGe_{2}, EuAl_{2}Si_{2}$ 
and Yb$Al_{2}Ge_{2}$ were collected with an automated 
four-circle diffractometer STOE AED-2 (Mo-Ka1, graphite monochromator, $\omega/\theta$-scan,
 $3^{o} <2q<80^{o}$). 
Absorption effects were collected by acquiring $\Psi-scan$ data, structure refinements were 
performed with the SHELXL-97~\cite{refD} package.
Electrical conductivities of all compounds were measured polycrystalline pellets using a 
four-probe dc current reversal technique between
 8 and 300 K.
The magnetic susceptibility of polycrystalline piece of  Ln$Al_{2}X_{2}$  compounds was measured
 with a SQUID 
Magnetometer between 2 and 300 K with magnetic flux densities up to 
5.5 T.
Self-consistent band structure calculations were performed using the LMTO method in its scalar 
relativistic version (program LMTO-ASA47)~\cite{refA}. The basis sets consisted of 6s, 5d, 4f orbital for
 Eu/Yb, 
3s, 3p for Si/Al and 4s, 4p for Ge. The 6p orbitals for Eu/Yb, 3d for Si/Al and 4d for Ge were 
treated by the downfolding technique ~\cite{refB}. To achieve space filling within the atomic sphere 
approximation, interstitial spheres are introduced to avoid too large overlap of the 
atom-centered spheres. The empty sphere positions and radii were calculated using an 
automatic procedure developed by Krier et al.~\cite{refC}. Owing to the magnetic properties of the 4f-shell, 
spin-polarized calculations were performed using the exchange-correlation potential by Bart and 
Hedin [2].

\section*{3. Results and discussion}
\subsection*{3.1 Structure refinements}

Refinements of the single-crystal data Eu$Al_{2}Si_{2}$,  Eu$Al_{2}Ge_{2}$, 
and Yb$Al_{2}Ge_{2}$ converged rapidly with the atomic positions of Ca$Al_{2}Si_{2}$ 
(space group P\={3}m1) as starting parameters~\cite{refA}. The results are summarized in the table below(Figere1). In 
 Ca$Al_{2}Si_{2}$-type, the Si(Ge) atoms form a slightly distorted hexagonal close packing  
with Al occupying half the tetrahedral and the Ln (Ln=Yb,Eu) atoms half the octahedral voids. 
With regard to the Al-Si(Ge) bond distances, a main feature of the structure is a double layer
 of puckered AlSi(G) hexagons as shown in Figure 2. Herein the Al atoms are coordinated 
tetrahedrally by Si(Ge), which is itself  surrounded umbrella-like by four Al atoms. 
The rare-earth atoms are located on hexagonal prisms build of six Si(Ge). Due to the 
puckering of the AlSi(Ge) hexagons, the Ln-Al distances are longer compared with the Ln-Si(Ge). 
The latter ones correspond to the sums of the atomic radii of Ln and the covalent radii for 
Si(Ge) for all compounds except $YbAl_{2}Si_{2}$  with slightly smaller Yb-Si bond lengths 
(-3.4\%). This may be a hint for an intermediate valence state of Yb because the radius for 
Yb$^{3+}$ is smaller than for Yb$^{2+}$.


The ratio between the length of the Al-Si(Ge) bonds within and between the AlSi(Ge) hexagons 
indicates that Eu$Al_{2}Ge_{2}, compounds are CaAl_{2}Si_{2}$-type structure. The structure
 refinements measurement give the value of 0.959, 0.967, 0.964 and 0.962 for Yb$Al_{2}Ge_{2}$, 
Eu$Al_{2}Ge_{2}, EuAl_{2}Si_{2} and YbAl_{2}Si_{2}$  respectively~\cite{refA}. From this all compounds
 described here are expected to contain divalent rare-earth atoms.
\begin{figure}[htb]
\centerline{\psfig{figure=CrystalographicData.ps,height=3.5in}}
\caption{Crystallographic data~\cite{refA}}
\end{figure}

\begin{figure}[htb]
\centerline{\psfig{figure=CrystalStructure.ps,height=2.5in}}
\caption{Crystal structure of Ln$Al_{2}Si{2}$~\cite{refA}}
\end{figure}

\subsection*{3.2 Magnetic and electrical properties}

The temperature dependence of the inverse magnetic susceptibilities (1T measurements) of 
$EuAl_{2}Si_{2}$ and $EuAl_{2}Ge_{2}$ are shown in Figure 3. Above 80 K the susceptibilities 
Eu$Al_{2}Si_{2}$  obeys modified Curie-Weiss law $\chi = \chi_{o} + c/(T-\Theta$). The data is 
fitted above 80 K with modified Curie-Weiss resulting in a paramagnetic Curie temperature
 (Weiss constant) of 23 K, magnetic moment of 7.82 $\mu_{\beta}$/Eu and a temperature 
independent contribution of $\chi_{o}=14\times10^{-9}m^{3} mol^{-1}$. The temperature independent 
contribution is in the order of magnitude of Pauli paramagnet and most likely results from the 
conduction of this metallic compound ~\cite{refA}.

\begin{figure}[htb]
\centerline{\psfig{figure=InverseSusceptib.ps,height=3.5in}}
\caption{temperature dependence of the inverse magnetic susceptibility~\cite{refA}}
\end{figure}

\begin{figure}[htb]
\centerline{\psfig{figure=MagneticMoment.ps,height=2.5in}}
\caption{Field-Dependence of the magnetic moments~\cite{refA}}
\end{figure} 
The 1/$\chi$ versus T plot of Eu$Al_{2}Ge_{2}$  is almost linear. An evaluation of the data above 50 K
 according to the Curie-Weiss law resulted in an experimental magnetic moment of 7.90
 $\mu_{\beta}$/Eu and a Weiss constant of 23 K. 
At low external magnetic fields (0.002 T) antiferromagnetic ordering is detected at
 $T_{N}=35.5$ K for $EuAl_{2}Si_{2}$ and at $T_{N}= 27.5$ K for Eu$Al_{2}Ge_{2}$ in perfect 
agreement with the previous study~\cite{refB}. The magnetization behavior of Eu$Al_{2}Si_{2}$  
and $EuAl_{2}Ge_{2}$   is presented in Figure 4. At 50 K, well above the N\`{e}el temperature,
 the magnetization curves are almost linear as expected for a paramagnetic compound. 
At 4 K the magnetization of Eu$Al_{2}Si_{2}$   increases in a linear madder up to a critical 
field of B=1.3950 T and then shows a weaker increase. This may be ascribed to a metamagnetic 
(antiparallel to parallel spin alignment) or spin-flip transition. At the highest field strength 
about B=5.5 T the magnetization reached a value of 6.0 $\mu_{\beta}$/Eu at  4 K,
 comparable to the theoretical saturation magnetization of 7.0 $\mu_{\beta}$/Eu. 
The magnetization behavior of $EuAl_{2}Ge_{2}$ is quite similar with that of 
 $EuAl_{2}Si_{2}$. 

The temperature dependence of inverse magnetic susceptibility of $YbAl_{2}Si_{2}$ is shown in 
Figure 3. Between 100 and 300 K the 1/$\chi$ versus T plot is almost linear. In this temperature region, 
an experimental magnetic moment of $\mu_{exp}=2.57 \mu_{\beta}$/Yb can be determined 
according to the Curie-Weiss law $\chi$ = c/(T-$\Theta$). The corresponding paramagnetic Curie 
temperature of –382 K is strongly negative as the frequency observed for intermediate-valent
 compounds ~\cite{refD}. In view of single crystallographic ytterbium site, $YbAl_{2}Si_{2}$  may be 
classified as a homogeneously intermediate-valent compound.

The susceptibility versus temperature dependence of $YbAl_{2}Ge_{2}$   is presented in the 
lower part of Figure 3. Down to about 80 K the susceptibility is almost temperature independent 
with a room temperature value of 1.2$\times10^{-9}m^{3}mol^{-1}$, compatible with Pauli 
paramagnetism~\cite{refE}. 
The temperature dependencies of the electrical resistivities of $LnAl_{2}X_{2}$ compounds
  are shown in Figure 5. The value is normalized to the resistivity at 300 K. All samples 
showed very low resisitivities (about 0.2-1.2m$\Omega$) and metallic behavior between 8 and
 320 K. The peaks at 35 K for $EuAl_{2}Si_{2}$ and 27 K for $EuAl_{2}Ge_{2}$ coincide exactly
 with Neel temperatures determined by the SQUID experiments. Both ytterbium compounds show 
almost identical resistivities.

\begin{figure}[htb]
\centerline{\psfig{figure=ElectricalResistiv.ps,height=2.5in}}
\caption{Temperature dependence of resisitivity of compounds[1]}
\end{figure}


\section*{4. Conclusions }
Crystalographic data and magnetic susceptibility measurement shows that Ln$Al_{2}$X$_{2}$
compounds crystallize in the CaAl$_{2}$Si$_{2}$ type structure. All 
LnAl$_{2}$X$_{2}$ compounds are observed to be conductor between 8 and 320 K.
Since they have small band gap, conduction is due to the metalic element in the compound.
  



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\bibitem{refD} O.K. Andersen, Phys. Rev Lett. B12(1975)3060
\bibitem{refD} O. Jepsen, O.K. Andersen, Phys. Rev Lett. B97(1995)35
\end{thebibliography}
\end{document}

