Quasi-quartet crystal electric field ground state
in a tetragonal CeAg2Ge2 single crystal
A. Thamizhavel ∗, R. Kulkarni, S. K. Dhar
Department of condensed matter physics and materials science,
Tata institute of fundamental research, Colaba, Mumbai 400 005, India
Abstract
We have successfully grown the single crystals of CeAg2Ge2, for the first time, by flux method and studied the anisotropic physical
properties by measuring the electrical resistivity, magnetic susceptibility and specific heat. We found that CeAg2Ge2 undergoes
an antiferromagnetic transition at TN = 4.6 K. The electrical resistivity and susceptibility data reveal strong anisotropic magnetic
properties. The magnetization measured at T = 2 K exhibited two metamagnetic transitions at Hm1 = 31 kOe andHm2 = 44.7 kOe,
for H ‖ [100] with a saturation magnetization of 1.6 µB/Ce. The crystalline electric field (CEF) analysis of the inverse susceptibility
data reveals that the ground state and the first excited states of CeAg2Ge2 are closely spaced indicating a quasi-quartet ground
state. The specific heat data lend further support to the presence of closely spaced energy levels.
Key words: CeAg2Ge2; CEF; quartet ground state; antiferromagnetism
PACS: 81.10.-h, 71.27.+a, 71.70.Ch, 75.10.Dg, 75.50.Ee
Compounds crystallizing in the ThCr2Si2 type struc-
ture are the most extensively studied among the strongly
correlated electron systems. A wide range of compounds
crystallize in this type of tetragonal crystal structure
and exhibit novel physical properties. Some of the promi-
nent examples include the first heavy fermion supercon-
ductor CeCu2Si2, pressure induced superconductors like
CePd2Si2, CeRh2Si2, CeCu2Ge2, unconventional metam-
agnetic transition in CeRu2Si2 etc. CeAg2Ge2 also crys-
tallizes in the tetragonal ThCr2Si2 type crystal structure.
Previous reports of CeAg2Ge2 were on polycrystalline
samples and there were conflicting reports on the antifer-
romagnetic ordering temperature [1,2,3]. Furthermore, the
ground state properties of CeAg2Ge2 are also quite intrigu-
ing. Neutron scattering experiments on a polycrystalline
sample could detect only one excited state at 11 meV indi-
cating that the ground state and the first excited states are
closely spaced. In order to study the anisotropic physical
properties and to study the crystalline electric field ground
state, we have grown the single crystals of CeAg2Ge2.
Single crystals of CeAg2Ge2 were grown by self flux
method, using Ag:Ge (75.5: 24.5) binary alloy, which forms
an eutectic at 650 ◦C, as flux. The details about the crystal
∗ Corresponding author. Tel: (81)22-2280-4556
Email address: thamizh@tifr.res.in (A. Thamizhavel).
growth process are given elsewhere [4]. Figure 1(a) shows
the temperature dependence of electrical resistivity of
CeAg2Ge2 for the current direction parallel to both [100]
and [001] directions. There is a large anisotropy in the
electrical resistivity. The electrical resistivity shows a shal-
low minimum at 20 K, marginally increases with decrease
in temperature down to 4.6 K. With further decrease in
the temperature the electrical resistivity drops due to the
reduction in the spin-disorder scattering caused by the an-
tiferromagnetic ordering of the magnetic moments, as seen
in the inset of Fig. 1(a). The antiferromagnetic transition
can be clearly seen at 4.6 K as indicated by the arrow in
the figure.
Figure 1(b) shows the temperature dependence of the
magnetic susceptibility along the two principle directions.
As can be seen from the figure there is a large anisotropy in
the susceptibility due to tetragonal crystal structure. The
high temperature susceptibility does not obey the simple
Curie-Weiss law; on the other hand it can be very well fit-
ted to a modified Curie-Weiss law which is given by χ =
, where χ0 is the temperature independent part
of the magnetic susceptibility and C is the Curie constant.
The value of χ0 was estimated to be 1.33 × 10
−3 and
1.41× 10−3 emu/mol forH ‖ [001] and [100], respectively
such that an effective moment of 2.54 µB/Ce is obtained for
Preprint submitted to Elsevier 25 October 2018
http://arxiv.org/abs/0704.0119v1
) J || [001]
[100]
CeAg2Ge2
3002001000
Temperature (K)
u)H || [100]
[001]
H || [001]
[100]
CeAg2Ge2
[100]
[001]
6040200
Magnetic Field (kOe)
CeAg2Ge2
[001]
H || [100]
T = 2 K
Fig. 1. (a) The temperature dependence of electrical resistivity of
CeAg2Ge2, inset shows the low temperature part, (b) Temperature
dependence of the magnetic susceptibility together with inverse mag-
netic susceptibility plot, solid lines indicate the CEF fitting and (c)
Magnetization of CeAg2Ge2 measured at T = 2 K.
temperatures above 100 K. In order to perform the CEF
analysis of the susceptibility data, we plotted the inverse
susceptibility as 1/(χ− χ0) versus T . The solid line in fig-
ure 1(b) are the fitting to the inverse susceptibility with the
CEF Hamiltonian given byHCEF = B
where Bm
and Om
are CEF parameters and the Stevens
operators respectively. The level splitting energies are esti-
mated to be ∆1 = 5 K and ∆2 = 130 K. It may be noted
that the first excited state is very close to the ground state
indicating that the ground state is a quasi-quartet state.
Figure 1(c) shows the field dependence of magnetization at
2 K. For H ‖ [100], the magnetization increases linearly
with the field and exhibit two metamagnetic transition at
Hm1 = 31 kOe and Hm2 = 44.7 kOe before it saturates at
1.6 µB/Ce at 70 kOe, indicating the easy axis of magneti-
zation. On the other hand the magnetization along [001] is
very small and varies linearly with field reaching a value of
0.32 µB/Ce at 50 kOe.
Figure 2(a) shows the temperature dependence of the
specific heat of CeAg2Ge2 together with the specific heat
of a reference sample LaAg2Ge2. The antiferromagnetic or-
dering is manifested by the clear jump in the specific heat
at TN = 4.6 K as indicated by the arrow. The inset of
Fig. 2(a) shows the Cmag/T versus T together with the
20151050
Temperature(K)
H // [100]
 0   kOe
 20 kOe
 40 kOe
 50 kOe
 60 kOe
 80 kOe
 100 kOe
 120 kOe
40200
Temperature (K)
R ln 2
R ln 4
Fig. 2. (a) Temperature dependence of the specific heat of CeAg2Ge2
and LaAg2Ge2. The inset shows the magnetic entropy. (b) The field
dependence of the specific heat of CeAg2Ge2 for the field applied
along the easy axis of magnetization, namely [100].
magnetic entropy. The entropy reaches R ln 4 not too far
away from the magnetic ordering temperature leading to
the conclusion that the ground state and the first excited
states are closely spaced or nearly degenerate, thus corrob-
orating our CEF analysis of the inverse susceptibility data.
Figure 2(b) shows the field dependence of the specific heat
for the field applied parallel to the easy axis of magnetiza-
tion namely [100]. With the increase in the magnetic field
the Néel temperature decreases and the antiferromagnetic
ordering apparently vanishes at a critical field of 50 kOe
indicating a possibility of a field induced quantum critical
point in this compound. However, further low temperature
measurements are necessary to confirm this.
In summary, we have successfully grown the single crys-
tals of CeAg2Ge2 by the flux method. CeAg2Ge2 orders an-
tiferromagnetically at TN = 4.6 K. The CEF analysis of the
inverse susceptibility data indicate the ground state and
the first excited states are closely spaced. The heat capacity
data support this quasi-quartet ground state. Furthermore,
the heat capacity in applied magnetic fields revealed that
the Néel temperature vanishes at a critical field of 50 kOe
indicating a possible field induced quantum critical point
in this compound.
References
[1] R. Rauchschwalbe et al., J. Less Common. Metals 111, (1985)
[2] G. Knopp et al., J. Magn. Magn. Mater. 63 & 64, (1987) 88.
[3] E. Cordruwish et al., J. Phase Equilibria 20, (1999) 407.
[4] A. Thamizhavel et al., Phys. Rev. B (2007) to be published
	References

  We have successfully grown the single crystals of CeAg$_2$Ge$_2$, for the
first time, by flux method and studied the anisotropic physical properties by
measuring the electrical resistivity, magnetic susceptibility and specific
heat. We found that CeAg$_2$Ge$_2$ undergoes an antiferromagnetic transition at
$T_{\rm N}$ = 4.6 K. The electrical resistivity and susceptibility data reveal
strong anisotropic magnetic properties. The magnetization measured at $T$ = 2 K
exhibited two metamagnetic transitions at $H_{\rm m1}$ = 31 kOe and $H_{\rm
m2}$ = 44.7 kOe, for $H \parallel$ [100] with a saturation magnetization of 1.6
$\mu_{\rm B}$/Ce. The crystalline electric field (CEF) analysis of the inverse
susceptibility data reveals that the ground state and the first excited states
of CeAg$_2$Ge$_2$ are closely spaced indicating a quasi-quartet ground state.
The specific heat data lend further support to the presence of closely spaced
energy levels.

Quasi-quartet crystal electric field ground state
in a tetragonal CeAg2Ge2 single crystal
A. Thamizhavel ∗, R. Kulkarni, S. K. Dhar
Department of condensed matter physics and materials science,
Tata institute of fundamental research, Colaba, Mumbai 400 005, India
Abstract
We have successfully grown the single crystals of CeAg2Ge2, for the first time, by flux method and studied the anisotropic physical
properties by measuring the electrical resistivity, magnetic susceptibility and specific heat. We found that CeAg2Ge2 undergoes
an antiferromagnetic transition at TN = 4.6 K. The electrical resistivity and susceptibility data reveal strong anisotropic magnetic
properties. The magnetization measured at T = 2 K exhibited two metamagnetic transitions at Hm1 = 31 kOe andHm2 = 44.7 kOe,
for H ‖ [100] with a saturation magnetization of 1.6 µB/Ce. The crystalline electric field (CEF) analysis of the inverse susceptibility
data reveals that the ground state and the first excited states of CeAg2Ge2 are closely spaced indicating a quasi-quartet ground
state. The specific heat data lend further support to the presence of closely spaced energy levels.
Key words: CeAg2Ge2; CEF; quartet ground state; antiferromagnetism
PACS: 81.10.-h, 71.27.+a, 71.70.Ch, 75.10.Dg, 75.50.Ee
Compounds crystallizing in the ThCr2Si2 type struc-
ture are the most extensively studied among the strongly
correlated electron systems. A wide range of compounds
crystallize in this type of tetragonal crystal structure
and exhibit novel physical properties. Some of the promi-
nent examples include the first heavy fermion supercon-
ductor CeCu2Si2, pressure induced superconductors like
CePd2Si2, CeRh2Si2, CeCu2Ge2, unconventional metam-
agnetic transition in CeRu2Si2 etc. CeAg2Ge2 also crys-
tallizes in the tetragonal ThCr2Si2 type crystal structure.
Previous reports of CeAg2Ge2 were on polycrystalline
samples and there were conflicting reports on the antifer-
romagnetic ordering temperature [1,2,3]. Furthermore, the
ground state properties of CeAg2Ge2 are also quite intrigu-
ing. Neutron scattering experiments on a polycrystalline
sample could detect only one excited state at 11 meV indi-
cating that the ground state and the first excited states are
closely spaced. In order to study the anisotropic physical
properties and to study the crystalline electric field ground
state, we have grown the single crystals of CeAg2Ge2.
Single crystals of CeAg2Ge2 were grown by self flux
method, using Ag:Ge (75.5: 24.5) binary alloy, which forms
an eutectic at 650 ◦C, as flux. The details about the crystal
∗ Corresponding author. Tel: (81)22-2280-4556
Email address: thamizh@tifr.res.in (A. Thamizhavel).
growth process are given elsewhere [4]. Figure 1(a) shows
the temperature dependence of electrical resistivity of
CeAg2Ge2 for the current direction parallel to both [100]
and [001] directions. There is a large anisotropy in the
electrical resistivity. The electrical resistivity shows a shal-
low minimum at 20 K, marginally increases with decrease
in temperature down to 4.6 K. With further decrease in
the temperature the electrical resistivity drops due to the
reduction in the spin-disorder scattering caused by the an-
tiferromagnetic ordering of the magnetic moments, as seen
in the inset of Fig. 1(a). The antiferromagnetic transition
can be clearly seen at 4.6 K as indicated by the arrow in
the figure.
Figure 1(b) shows the temperature dependence of the
magnetic susceptibility along the two principle directions.
As can be seen from the figure there is a large anisotropy in
the susceptibility due to tetragonal crystal structure. The
high temperature susceptibility does not obey the simple
Curie-Weiss law; on the other hand it can be very well fit-
ted to a modified Curie-Weiss law which is given by χ =
, where χ0 is the temperature independent part
of the magnetic susceptibility and C is the Curie constant.
The value of χ0 was estimated to be 1.33 × 10
−3 and
1.41× 10−3 emu/mol forH ‖ [001] and [100], respectively
such that an effective moment of 2.54 µB/Ce is obtained for
Preprint submitted to Elsevier 25 October 2018
http://arxiv.org/abs/0704.0119v1
) J || [001]
[100]
CeAg2Ge2
3002001000
Temperature (K)
u)H || [100]
[001]
H || [001]
[100]
CeAg2Ge2
[100]
[001]
6040200
Magnetic Field (kOe)
CeAg2Ge2
[001]
H || [100]
T = 2 K
Fig. 1. (a) The temperature dependence of electrical resistivity of
CeAg2Ge2, inset shows the low temperature part, (b) Temperature
dependence of the magnetic susceptibility together with inverse mag-
netic susceptibility plot, solid lines indicate the CEF fitting and (c)
Magnetization of CeAg2Ge2 measured at T = 2 K.
temperatures above 100 K. In order to perform the CEF
analysis of the susceptibility data, we plotted the inverse
susceptibility as 1/(χ− χ0) versus T . The solid line in fig-
ure 1(b) are the fitting to the inverse susceptibility with the
CEF Hamiltonian given byHCEF = B
where Bm
and Om
are CEF parameters and the Stevens
operators respectively. The level splitting energies are esti-
mated to be ∆1 = 5 K and ∆2 = 130 K. It may be noted
that the first excited state is very close to the ground state
indicating that the ground state is a quasi-quartet state.
Figure 1(c) shows the field dependence of magnetization at
2 K. For H ‖ [100], the magnetization increases linearly
with the field and exhibit two metamagnetic transition at
Hm1 = 31 kOe and Hm2 = 44.7 kOe before it saturates at
1.6 µB/Ce at 70 kOe, indicating the easy axis of magneti-
zation. On the other hand the magnetization along [001] is
very small and varies linearly with field reaching a value of
0.32 µB/Ce at 50 kOe.
Figure 2(a) shows the temperature dependence of the
specific heat of CeAg2Ge2 together with the specific heat
of a reference sample LaAg2Ge2. The antiferromagnetic or-
dering is manifested by the clear jump in the specific heat
at TN = 4.6 K as indicated by the arrow. The inset of
Fig. 2(a) shows the Cmag/T versus T together with the
20151050
Temperature(K)
H // [100]
 0   kOe
 20 kOe
 40 kOe
 50 kOe
 60 kOe
 80 kOe
 100 kOe
 120 kOe
40200
Temperature (K)
R ln 2
R ln 4
Fig. 2. (a) Temperature dependence of the specific heat of CeAg2Ge2
and LaAg2Ge2. The inset shows the magnetic entropy. (b) The field
dependence of the specific heat of CeAg2Ge2 for the field applied
along the easy axis of magnetization, namely [100].
magnetic entropy. The entropy reaches R ln 4 not too far
away from the magnetic ordering temperature leading to
the conclusion that the ground state and the first excited
states are closely spaced or nearly degenerate, thus corrob-
orating our CEF analysis of the inverse susceptibility data.
Figure 2(b) shows the field dependence of the specific heat
for the field applied parallel to the easy axis of magnetiza-
tion namely [100]. With the increase in the magnetic field
the Néel temperature decreases and the antiferromagnetic
ordering apparently vanishes at a critical field of 50 kOe
indicating a possibility of a field induced quantum critical
point in this compound. However, further low temperature
measurements are necessary to confirm this.
In summary, we have successfully grown the single crys-
tals of CeAg2Ge2 by the flux method. CeAg2Ge2 orders an-
tiferromagnetically at TN = 4.6 K. The CEF analysis of the
inverse susceptibility data indicate the ground state and
the first excited states are closely spaced. The heat capacity
data support this quasi-quartet ground state. Furthermore,
the heat capacity in applied magnetic fields revealed that
the Néel temperature vanishes at a critical field of 50 kOe
indicating a possible field induced quantum critical point
in this compound.
References
[1] R. Rauchschwalbe et al., J. Less Common. Metals 111, (1985)
[2] G. Knopp et al., J. Magn. Magn. Mater. 63 & 64, (1987) 88.
[3] E. Cordruwish et al., J. Phase Equilibria 20, (1999) 407.
[4] A. Thamizhavel et al., Phys. Rev. B (2007) to be published
	References
