Abstract We have studied the effect of pressure on the electrical resistivity of the antiferromagnet CeMg 2 Cu 9 which crystallizes in the hexagonal structure. The structure is built up of alternating MgCu 2 Laves-type and CeCu 5 -type layers along the [0001] direction. The Néel temperature T N = 2.7 K at ambient pressure decreases with increasing pressure p and disappears at a critical pressure p c 2.5 GPa. Correspondingly, the residual resistivity ρ 0 and the coefficient A in a Fermi-liquid relation ρ = ρ 0 + AT 2 are found to have maximum values around p c . In cerium compounds, the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect compete with each other  Most cerium compounds order magnetically, when the RKKY interaction overcomes the Kondo effect at low temperatures. The magnetic order is formed by localized 4f moments. On the other hand, some cerium compounds such as CeCu 6 and CeRu 2 Si 2 show no long-range magnetic ordering, because the Kondo effect overcomes the RKKY interaction. Characteristic properties of these compounds are called heavy-fermion properties, with a large electronic 

A Thamizhavel

E Yamamoto

H Nakawaki

M Yamada

R Asai

R Settai

S Ikeda

T C Kobayashi

T Okubo

Y Inada

Yōnuki

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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 14 (2002) L305–L311 PII: S0953-8984(02)33720-2
LETTER TO THE EDITOR
Pressure study of an antiferromagnet, CeMg2Cu9
H Nakawaki1, Y Inada1,4, R Asai1, M Yamada1, T Okubo1, S Ikeda1,
A Thamizhavel1, T C Kobayashi2, R Settai1, E Yamamoto3 and
Y Ōnuki1,3
1 Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
2 Research Centre for Materials Science at Extreme Conditions, Osaka University, Toyonaka,
Osaka 560-8531, Japan
3 Advanced Science Research Centre, Japan Atomic Energy Research Institute, Tokai,
Ibaraki 319-1195, Japan
E-mail: inada@phys.sci.osaka-u.ac.jp
Received 13 February 2002
Published 28 March 2002
Online at stacks.iop.org/JPhysCM/14/L305
Abstract
We have studied the effect of pressure on the electrical resistivity of the
antiferromagnet CeMg2Cu9 which crystallizes in the hexagonal structure. The
structure is built up of alternating MgCu2 Laves-type and CeCu5-type layers
along the [0001] direction. The Néel temperature TN = 2.7 K at ambient
pressure decreases with increasing pressure p and disappears at a critical
pressure pc  2.5 GPa. Correspondingly, the residual resistivity ρ0 and
the coefficient A in a Fermi-liquid relation ρ = ρ0 + AT 2 are found to have
maximum values around pc.
In cerium compounds, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction and the
Kondo effect compete with each other [1, 2]. The former enhances long-range magnetic
ordering, in which the 4f electrons with magnetic moments are treated as localized electrons
and the indirect f–f interaction plays a predominant role via the conduction electrons. On the
other hand, the latter quenches the magnetic moments of the localized 4f electrons via spin
polarization of conduction electrons, consequently producing the singlet state with a binding
energy kBTK, where TK is called the Kondo temperature. Competition between the RKKY
interaction and the Kondo effect was discussed by Doniach [3], as a function of |Jcf |D(εF),
where |Jcf | is the magnitude of the magnetic exchange interaction and D(εF) is the electronic
density of states at the Fermi energy εF.
Most cerium compounds order magnetically, when the RKKY interaction overcomes the
Kondo effect at low temperatures. The magnetic order is formed by localized 4f moments. On
the other hand, some cerium compounds such as CeCu6 and CeRu2Si2 show no long-range
magnetic ordering, because the Kondo effect overcomes the RKKY interaction. Characteristic
properties of these compounds are called heavy-fermion properties, with a large electronic
4 Author to whom any correspondence should be addressed.
0953-8984/02/140305+07$30.00 © 2002 IOP Publishing Ltd Printed in the UK L305
L306 Letter to the Editor
specific heat coefficient γ : γ  104/TK (mJ K−2 mol−1) [1, 2]. In fact, the γ -value and the
Kondo temperature are 1600 mJ K−2 mol−1 and 5 K in CeCu6, and 350 mJ K−2 mol−1 and
20 K in CeRu2Si2. The heavy-fermion state in these compounds can be understood on the
basis of Fermi-liquid behaviour. The electrical resistivity ρ follows a well-known relation:
ρ = ρ0 + AT 2. The
√
A value is extremely large; this is correlated with an enhanced Pauli
susceptibility χ  χ0 (T → 0) and a large γ -value (=C/T : T → 0).
Recently a new aspect of cerium and uranium compounds with magnetic ordering has been
discovered. When pressure p is applied to these compounds with antiferromagnetic ordering
such as CeIn3 and CePd2Si2 [4], the Néel temperature TN decreases, and a quantum critical
point corresponding to the extrapolation TN → 0 is reached at p = pc. Here, |Jcf |D(εF) in the
Doniach model can be replaced by pressure. Surprisingly, superconductivity appears around
pc. A non-Fermi-liquid nature of these compounds is observed. Similar pressure-induced
superconductivity was reported for other compounds such as CeCu2Ge2 [5], CeRhIn5 [6] and
UGe2 [7]. The crossover from the magnetically ordered state to the non-magnetic state under
pressure, crossing the quantum critical point, is the most interesting issue for the strongly
correlated f-electron systems.
The purpose of present work is to study a similar pressure effect on another compound,
CeMg2Cu9. This compound is similar to CeMg2Ni9, with a hexagonal structure which is built
up of alternating MgNi2 Laves-type and CeNi5-type layers along the [0001] direction [8, 9].
The lattice parameter c (=23.846 Å) is extremely large compared to the a-value of 4.8706 Å
in CeMg2Ni9. CeMg2Cu9 is also hexagonal and it was recently clarified that it is of CeNi3
type [10]. CeMg2Cu9 orders antiferromagnetically below TN = 2.7 K, whereas CeMg2Ni9
is a non-magnetic compound. The large lattice parameter c in CeMg2Ni9 or CeMg2Cu9
corresponds to a flat Brillouin zone, which is expected to bring about a two-dimensional
electronic state as in CeRhIn5 [6]. We have studied the effect of pressure by measuring
the electrical resistivity under hydrostatic pressure p up to about 3 GPa in the temperature
range from room temperature to 90 mK. The Néel temperature TN is found to disappear at
pc  2.5 GPa.
Single crystals of CeMg2Cu9 were grown by the slow-cooling method. Highly pure ma-
terials of 3N (99.9% pure) Ce, 5N Mg, and 5N Cu with a starting composition of CeMg2.05Cu9
were sealed in a Mo crucible, which was heated up to 1400 ◦C and cooled down slowly under
an Ar atmosphere in an electric furnace; it took ten days in total to complete the growth. The
direction of the crystal with the hexagonal structure was determined by the x-ray Laue method.
The electrical resistivity was measured by the four-probe DC method in an indenter
pressure cell, with Daphne oil (7373) as a pressure-transmitting medium, which was cooled
down to 90 mK in a dilution refrigerator. The pressure value was determined from the
superconducting transition temperature of lead.
Figure 1 shows the temperature dependence of the electrical resistivity ρ, magnetic sus-
ceptibility χ , and specific heat C in the form of C/T . The current I was applied along the
(0001) plane or the c-plane. The resistivity shows a broad maximum around 50 K and decreases
sharply below TN = 2.7 K. Correspondingly, the magnetic susceptibility decreases slightly
below TN, and the specific heat shows a λ-like peak at TN. The Néel temperature TN = 2.7 K
and the electronic specific heat coefficient γ = 160 mJ K−2 mol−1, which is estimated by
extrapolation to T = 0 K in the ordered state, are the same as recent results [10]. The effective
magnetic moment µeff = 2.43 µB/Ce for H ‖ [101̄0] in the Curie–Weiss law is close to
2.54 µB of Ce3+, and the paramagnetic Curie temperature θp = −14 K is negative. The values
of µeff and θp are 2.24 µB/Ce and −8.3 K for H ‖ [112̄0], and 2.31 µB/Ce and −11 K for
H ‖ [0001]. The magnetization for three field directions indicates a metamagnetic transition
around 40 kOe. The inset in figure 1(b) shows the magnetization curve for H ‖ [101̄0].
Letter to the Editor L307
Figure 1. The temperature dependence of (a) the electrical resistivity, (b) the magnetic
susceptibility, and (c) the specific heat C in the form of C/T in CeMg2Cu9. The inset in (b)
shows the magnetization curve for H ‖ [101̄0].
The value of the magnetization for this direction at 70 kOe is slightly larger than those for
other directions; therefore this direction is most probably the easy axis of antiferromagnetism.
The resistivity maximum around 50 K is due to a combination of the Kondo effect and the
crystalline-electric-field effect. This compound is similar to the usual Kondo antiferromagnets,
such as CeCu2, with TN = 3.5 K and γ = 82 mJ K−2 mol [11]. We focus our interest on
the pressure effect around the critical pressure pc where the Néel temperature becomes zero,
although the magnetic structure and the two-dimensional electronic state, based on the unique
crystal structure, are also of interest.
Figure 2 shows the temperature dependence of the electrical resistivity under different
applied pressures. The resistivity maximum around 50 K at ambient pressure, mentioned above,
shifts to a lower temperature with increasing pressure up to 2.38 GPa, while the maximum
shifts to a higher temperature with further increasing pressure. This is closely related to a
steep decrease of the Néel temperature due to pressure, as shown in figures 3 and 4. The Néel
L308 Letter to the Editor
Figure 2. The temperature dependence of the electrical resistivity under pressure in CeMg2Cu9.
Figure 3. A logarithmic plot of the temperature dependence of the electrical resistivity under
pressure in CeMg2Cu9.
temperature TN = 2.7 K at ambient pressure decreases with increasing pressure: TN = 1.5 K
at p = 2.38 GPa and becomes zero at 2.56 GPa. The critical pressure pc is about 2.5 GPa.
With further increasing pressure, the resistivity maximum increases from 10 K at 2.56 GPa to
20 K at 2.85 GPa. This is because the Kondo temperature increases with increasing pressure.
The temperature dependence of the electrical resistivity under 2.85 GPa is similar to that for a
typical heavy-fermion compound CeCu6 [12].
The low-temperature resistivity follows the Fermi-liquid relation of ρ = ρ0 + AT 2, as
shown in figure 5. The resistivity for each pressure in figure 5 is shifted on the vertical
scale. Figure 6 shows the pressure dependence of the coefficient A and the residual
Letter to the Editor L309
Figure 4. The pressure dependence of the Néel temperature in CeMg2Cu9.
Figure 5. The T 2-dependence of the electrical resistivity under pressure in CeMg2Cu9. Broken
lines are guides to the eyes.
L310 Letter to the Editor
Figure 6. Pressure dependences of (a) A and (b) ρ0 for CeMg2Cu9.
resistivity ρ0. The Néel temperature becomes zero at pc  2.5 GPa, as mentioned above.
Correspondingly, the A- and ρ0-values become maximal around pc  2.5 GPa. The A-value
of 2.5 µ cm K−2 at pc  2.5 GPa is large, as compared to A = 50 µ cm K−2 for CeCu6
with γ = 1600 mJ K−2 mol−1 and A = 1 µ cm K−2 for UPt3 with γ = 420 mJ K−2 mol−1,
following the Kadowaki–Woods plot [13].
Around the critical pressure, non-Fermi-liquid behaviour and/or superconductivity were
observed in CeCu2Ge2 [5] and CeRhIn5 [6, 14], as described above. Superconductivity
often correlates with non-Fermi-liquid nature, as for CeCu2Ge2 and CeRhIn5. The T -linear
dependence of the electrical resistivity in ρ = ρ0 + A′T is characteristic of these compounds.
The residual resistivity ρ0 also correlates with the superconducting transition temperature Tc,
as discussed theoretically [15, 16].
On the other hand, the present electrical resistivity in CeMg2Cu9 exhibits a Fermi-liquid
nature. It is not clear whether this is closely related to the non-appearance of superconductivity.
We note that superconductivity is found in the Fermi-liquid state for CeRh2Si2 [17, 18] and
UGe2 [19]. It is also noted that the present large residual resistivity of ρ0 = 14 µ cm
at ambient pressure might enhance pair breaking in the superconductivity. In fact, we
confirmed that the sample of CeRh2Si2 with residual resistivity ratio (RRR) less than 30
showed no superconductivity, whereas superconductivity was clearly observed in the sample
with RRR = 110 [18].
Letter to the Editor L311
There is, however, another example where superconductivity is found in CeCu2Ge2 with
a large residual resistivity at ambient pressure [5]—almost the same value as for CeMg2Cu9.
The appearance of superconductivity is thus a very complicated phenomenon in the strongly
correlated f-electron systems. Future study of superconductivity in CeMg2Cu9 using a much
higher-quality sample would be beneficial.
We now summarize our experimental results. The antiferromagnet CeMg2Cu9 was
investigated by means of electrical resistivity measurements under hydrostatic pressure. The
Néel temperature decreases with increasing pressure, and the critical pressure is determined
as pc  2.5 GPa. Both the A- and ρ0-values of ρ = ρ0 + AT 2 become maximal around pc.
It is remarkable that the antiferromagnet CeMg2Cu9 is changed into a typical heavy-fermion
compound around pc.
We are grateful to Professor K Miyake for helpful discussion. This work was supported
by a Grant-in-Aid for Scientific Research COE(10CE2004) from the Ministry of Education,
Science, Sports and Culture.
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Condens. Matter 14 L29


Pressure study of an antiferromagnet, CeMg 2 Cu 9

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Pressure study of an antiferromagnet, CeMg 2 Cu 9

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