- Email: [email protected]
Anisotropic magnetic, transport and thermodynamic properties of novel tetragonal Ce2RhGa12 compound
Journal of Alloys and Compounds 604 (2014) 379–383
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Anisotropic magnetic, transport and thermodynamic properties of novel tetragonal Ce2RhGa12 compound S. Nallamuthu a, T.P. Rashid a, V. Krishnakumar b, Celine Besnard c, Hans Hagemann d, Marian Reiffers e, R. Nagalakshmi a,⇑ a
Department of Physics, National Institute of Technology, Tiruchirappalli 620 0015, India Department of Physics, Periyar University, Salem 636 011, India Laboratory of Crystallography, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland d Department of Physical Chemistry, University of Geneva, Geneva, Switzerland e Faculty of Humanities and Natural Sciences, Presov University, Presov, Slovakia b c
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 26 December 2013 Received in revised form 7 March 2014 Accepted 12 March 2014 Available online 28 March 2014 Keywords: Intermetallic Anisotropy Heavy fermions Heat capacity Magnetization
We report on a comprehensive study of the magnetization, resistivity and heat capacity on the single crystals of Ce2RhGa12 synthesized using Ga flux. Single crystal X-ray diffraction data confirm the tetragonal Pb/nbm structure of Ce2RhGa12, which is isostructural to Ce2PdGa12. Ce2RhGa12 orders antiferromagnetically at TN = 3.5 K and exhibits anisotropic magnetic behavior, inferred from the magnetization and resistivity data, taken along the two principal crystallographic directions of the crystal, viz., along [1 0 0] and [0 0 1]. The anisotropic magnetic response of Ce2RhGa12 establishes [0 0 1] as the easy axis of magnetization, and a weak meta-magnetic transition is also observed in the magnetic isotherm at 2 K along the same axis. A sharp peak in specific heat signals the bulk antiferromagnetic transition at TN = 3.5 K, which shifts to lower temperatures in low applied fields. The electrical resistivity along the two directions shows metallic behavior from 300 K down to 1.8 K and establishes Ce2RhGa12 as a normal, trivalent cerium compound. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Cerium based ternary intermetallic compounds are extensively studied as they show a variety of ground states due to the competition between the RKKY (Ruderman-Kittel-Kausya-Yoshida) and the single ion Kondo exchange interactions. While the former favors a magnetic ground state, a strong Kondo interaction leads to a paramagnetic Fermi liquid with large effective electron masses [1–4]. Since the electronic heat capacity is proportional to effective mass, compounds with large values of the coefficient of electronic specific heat c (400 mJ/mol K2) are termed as heavy fermions compounds [5]. CePdGa6, for example, is a layered heavy fermion compound with specific heat coefficient c 300 mJ/Ce mol K2 [6,7], ordering antiferromagnetically at TN = 5.5 K. The structurally related compound Ce2PdGa12 is an antiferromagnet with Néel temperature TN = 11 K and c = 72 mJ/mol K2 [7]. Recently, we have reported the synthesis of single crystals of Ce2RhGa12 [8], which is isostructural to Ce2PdGa12, in which the ⇑ Corresponding author. Tel.: +91 04312503615. E-mail addresses: (R. Nagalakshmi).
[email protected],
http://dx.doi.org/10.1016/j.jallcom.2014.03.067 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
[email protected]
tetragonal structure is composed of Ce–Ga and RhGa8/2 layers similar to the arrangement in CePdGa6 [6]. A change in c has been observed when Pd is replaced by Cu or Ni in R2MGa12 (R = La, Ce) [9]. It was, therefore, of interest to explore the magnetic properties of Ce2RhGa12. We have measured the magnetization, heat capacity and electrical resistivity and we find that Ce2RhGa12 is an antiferromagnet with TN = 3.5 K. 2. Experimental details The details about the single crystal growth of Ce2RhGa12 have already been reported in [8] and will not be repeated here. A few crystals of appropriate size and orientation were chosen from that lot and used in the present study. The X-ray Laue analysis confirmed good quality of the single crystals by exhibiting distinct spots with four fold tetragonal symmetry. The crystals were oriented along the principal crystallographic directions, namely [1 0 0] and [0 0 1], by means of the Laue back reflection method using Mo X-ray source. The crystals were then cut along the a- and c-directions using spark erosion cutting machine for physical and magnetic property measurements. Single crystal X-ray diffraction data were collected at the Swiss Norwegian Beam Line at the European Synchrotron Facility, Grenoble France. For that a single crystal of Ce2RhGa12 was glued on a glass fiber and transferred to the cold stream of a nitrogen cryojet (T = 200 K). The crystal was split with two major domains tilted by about 3 degrees along the b axis. Only one domain was used for structure determination. The oriented and properly cut single crystals were used for physical
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S. Nallamuthu et al. / Journal of Alloys and Compounds 604 (2014) 379–383
moment. An anisotropy is observed in hp, which is ascribed to crystal electric field effect. The powder average hp of 24 K indicates an antiferromagnetic interaction between the cerium moments. The lack of agreement of measured v(T) with the theoretical Curie– Weiss fit at low temperatures is attributed to crystalline electric field (CEF) effect. The magnetic susceptibility for H//[0 0 1] shows a peak at TN = 3.5 K typical of an antiferromagnetic transition and arises due to the antiferromagnetic ordering of Ce moments as anticipated from a negative hp. v(T) for H//[0 0 1] is larger than H// [1 0 0] indicating that the tetragonal c-axis is relatively the easy axis of magnetization. The peak maximum of dv/dT is seen at TN = 3.5 K along H//[0 0 1] shown in Fig. 1(inset b). Also a mild anomaly at the same temperature is seen in the H//[1 0 0] direction as well. Fig. 2(a) shows the isothermal magnetization M(H) of Ce2RhGa12 measured along the principal crystallographic directions [1 0 0] and [0 0 1] up to 50 kOe at 2 K. The magnetization data were also taken at 3, 4 and 5 K and they are shown in Fig. 2(b). The data clearly establish [0 0 1] as the easy axis of magnetization, inferred from a relatively more rapid buildup of the magnetization at low fields, followed by a metamagnetic like transition at higher fields and a much larger saturation magnetization along [0 0 1]. The spin reorientation at the metamagnetic transition is also inferred from the derivative dM/dH (shown in inset Fig. 2(a)). Along the hard axis [1 0 0] the magnetization attains relatively smaller values. The metamagnetic transition is appreciably weakened at 3 K and vanishes at higher temperatures. The experimental saturation moment of Ce2RhGa12 along H//[0 0 1] easy axis reaches a value of about 1.79 lB/Ce at 50 kOe, which is less than the theoretical free ion value of Ce3+ gJJ = 2.14 lB/Ce. We attribute it to CEF effects.
property measurements. DC magnetization was measured as a function of temperature M(T) and magnetic field M(H) using a Quantum Design Magnetic Property Measurement System (MPMS), Superconducting Quantum Interference Device (SQUID) from 1.8 to 300 K. The electrical resistivity and heat capacity measurements were carried out using Quantum Design Physical Property Measurement System (PPMS) down to 1.8 K on the single crystals by the standard DC four-probe and heat-pulse relaxation technique respectively. The voltage and current leads (gold wire) for resistivity measurements were taken from the bar-shaped specimen using silver epoxy glue.
3. Results and discussion 3.1. Magnetic susceptibility and magnetization studies The main panel of Fig. 1 shows the susceptibility below 15 K, measured in an applied field of 100 Oe. The inverse susceptibility between 1.8 and 300 K and the derivative of susceptibility (dv/dT) are plotted in the insets Fig. 1(a and b) respectively. The data were taken with the field aligned along the two principal crystallographic directions [0 0 1] and [1 0 0], respectively. The high temperature magnetic susceptibility along both the principal directions was fitted to a modified Curie–Weiss law
v ¼ v0 þ
C ðT hp Þ
ð1Þ
where v0 is the temperature-independent term, hp is the paramagnetic Curie temperature and C is the Curie constant which can be expressed in terms of the effective moment as
C¼
l2eff x
ð2Þ
8
where x is the number of Ce atoms per formula unit. The solid lines in inset Fig. 1(a) are fits to Eq. (1) in the temperature interval of 60–300 K. The fitting parameters estimated are, v0 = 2.139 104 emu/mol, hp = 39 ± 2 K and leff = 2.74 ± 0.03 lB/Ce for H//[1 0 0] direction and v0 = 0, hp = 5 ± 2 K and leff = 2.76 ± 0.04 lB/Ce, for H//[0 0 1] direction. The inferred effective moment is slightly higher than the Hund’s rule J = 5/2 ground state value of free ion moment 2.54 lB/Ce, and shows trivalent Ce ions carrying a well localized 4f
3.2. Electrical resistivity The temperature dependent electrical resistivity q(T) of Ce2RhGa12 with J//[0 0 1] and J//[1 0 0] is shown in Fig. 3. The electrical resistivity shows a typical metallic behavior and it is
1.2
Ce2RhGa12
a
H=100 Oe χ-1 (mol/emu)
H//[001]
1.0
H//[001] H//[100]
150
H//[100]
100
50
0 0
50
100
150
200
250
300
Temperature (K) 0.20
0.6
b
0.15 0.10
dχ/dT[001] dχ/dT[100]
0.05
dχ /dT
χ (emu/mol)
0.8
0.4
3.5K
0.00 -0.05 -0.10 -0.15 -0.20 0
5
10
15
20
Temperature (K)
0.2
0.0 0
2
4
6
8
10
12
14
Temperature (K) Fig. 1. Magnetic susceptibility (v) of Ce2RhGa12 below 15 K in H = 100 Oe with H//[0 0 1] and H//[1 0 0] of the crystal. Inset (a) inverse susceptibility (v1) between 1.8 and 300 K; the solid lines are the Curie–Weiss fit and (b) the derivative of susceptibility (dv/dT).
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2.0 H//[100]
H//[001] dM/dH
Β
1.5
dM/dH
Ce2 RhGa12
0.8
Magnetization (μB/Ce)
2.0
Magnetization(μ /Ce)
H//[001] 1.2
(a)
T=2K
1.6
1.0 0.5 0.0 0
10000 20000 30000 40000 50000
Field (Oe)
0.4 0.0 1.8
2K 3K 4K 5K
1.2
(b)
H//[001] 2K 3K 3.5K 4K 5K
H//[100]
0.6
0.0 0
10
20
30
40
50
H (kOe) Fig. 2. Isothermal magnetization of Ce2RhGa12 measured with H//[1 0 0] and H//[0 0 1] as a function of magnetic field (a) at 2 K and (b) at selected temperatures.
J//[100]
Ce2RhGa12
100
J//[001]
ρ (μΩ μΩ Cm)
80
60 70
a
b
J//[100] H//[001] Ce2RhGa12
ρ (μΩ μΩ Cm)
ρ (μΩ μΩ Cm)
40
20
J//[001]
H//[100]
35
60
0 Oe 10 kOe 30 kOe 60 kOe 90 kOe
50
10 kOe 30 kOe 60 koe 90 kOe
30
25 0
5
10
15
20
25
30
0
2
4
0
50
100
150
6
8
10
12
14
Temperature (K)
Temperature(K)
0
200
250
300
Temperature (K) Fig. 3. Temperature dependent electrical resistivity q(T) of Ce2RhGa12 measured in zero magnetic field with current density parallel to a and c axis, respectively. Insets (a and b) shows q(T) versus T below 30 K in various fields along the -a- and -c- directions.
characterized by a prominent anisotropy arising possibly due to the large c/a ratio (2.6) and an anisotropic Fermi surface. A sharp slope change in the resistivity followed by a rapid decrease below TN = 3.5 K indicates the decrease in spin disorder scattering arising from the antiferromagnetic transition. At high temperatures, the resistivity decreases nearly linearly with the temperature. It may be noted that the resistivity does not exhibit Kondo like behavior which classifies Ce2RhGa12 as a normal trivalent cerium compound. The insets 3a and 3b show the temperature dependence of electrical resistivity q(T) below 30 K measured at various magnetic
fields up to 90 kOe. The magnetoresistivity MR, defined as MR = [R(H)–R(0)]/R(0), is negative in the entire range. Typically antiferromagnets show a positive MR below TN. Above 35 K the resistivity is almost independent of magnetic field strength. A few ripple like features in the resistivity near 150 K for H//[1 0 0] are attributed to noise in the data. 3.3. Heat capacity Bulk magnetic ordering is confirmed by heat capacity measurements. The temperature dependent heat capacity of Ce2RhGa12 and
S. Nallamuthu et al. / Journal of Alloys and Compounds 604 (2014) 379–383
6 6 6 C sch ðTÞ ¼ R6 6 4
3
Ei X Ei X 2 Ei X g i ekB T þ g i Ei ekB T g i Ei ekB T 7 7 7 i i i 7 !2 7 X 5 2 g i eEi =kB T T
ð3Þ
14 Δ1=33K
12
Δ2=109K
10
C4f
8
Schottky fit
6 4 2 0
0
5
10
15
20
25
30
Temperature (K) Fig. 5. Temperature dependence of the 4f-derived specific heat (C4f). Solid line represents the fit to the expression for the Schottky heat capacity.
2.0
12 Ce2 RhGa12
C4f
10
S4f
1.5
8 1.0
Rln2
6 4
0.5
i
2
where Ei’s are the CEF energy levels and gi the corresponding degeneracy. We can reproduce the broad peak in C4f by taking the two excited doublets lying at D1 = 33 K and D2 = 109 K above the ground state doublet. The 4f-derived entropy S4f was obtained by integrating the C4f/T against the temperature and is shown in Fig. 6. For calculating the entropy, heat capacity data below 1.8 K were smoothly extrapolated to T = 0. S4f reaches the theoretical value associated with a doublet (with effective spin ½) Rln 2 close to TN. Above TN, S4f increases rapidly because of the CEF level lying at 33 K. In order to examine the effect of the applied magnetic field on the bulk magnetic ordering, the heat capacity was measured with
0.0 0
5
10
15
20
0 30
25
Temperature (K) Fig. 6. The plots of C4f/T and S4f as a function of temperature.
H//[0 0 1] up to 90 kOe and it is plotted as C versus T in Fig. 7. It is seen that the peak in the heat capacity due to the magnetic ordering shifts to lower temperatures even in applied fields lower than 10 kOe. The zero-field sharp peak becomes broader in applied 25
200
4.0 3.5
C/T (J/mol K2)
160 140 120 100
Ce2RhGa12
La 2 RhGa 12 Ce 2 RhGa 12
3.0
20
2.5 2.0 1.5
C (J/mol K)
180
C (J/mol K)
S4f [J/Ce mol K]
2
16
C4f (J/mol K)
its isostructural nonmagnetic reference system La2RhGa12 is shown in Fig. 4. The zero field heat capacity data for Ce2RhGa12 manifest a clear peak at TN = 3.5 K attaining a value of 11.74 J/mol K typical of a second order phase transition. On the other hand, the heat capacity of La2RhGa12 increases monotonically with temperature typical of a paramagnetic compound. A fit of the expression C/ T = c + bT2 to the heat capacity of La2RhGa12 below 10 K, where c and b stand for the conduction electron and phonon contributions to the heat capacity, gives c = 8.54 mJ/mol K2 (0.66 mJ/g atom K2) which is comparable to that of Cu. The heat capacity of La2RhGa12 is used to estimate the magnetic contribution to the specific heat of Ce2RhGa12 by assuming that the phonon contribution to the heat capacity is identical in the two compounds. The magnetic 4f contribution C4f (plotted in Fig. 5) to the heat capacity is deduced by subtracting the heat capacity of La2RhGa12 from that of Ce2RhGa12. It is seen that the C4f in the paramagnetic state does not initially decrease with temperature but instead increases with a broad maximum around 15–25 K. Any short range order above TN would decrease with increasing temperature and therefore, the increase of C4f with temperature above TN is tentatively attributed to the existence of Schottky specific heat. The Schottky contribution arises from the thermal variation of the population of occupied CEF split levels of the Hund’s rule ground state multiplet. We have fitted the expression (Eq. (3)) for the Schottky heat capacity arising from three levels (in the tetragonal crystal potential, the sixfold degenerate level of Ce will split into three levels) to C4f.
C4f /T[J/Ce mol K2]
382
1.0 0.5 0.0
80
0
50
100
150
200
250
300
350
400
2
Temperature (K)
La2 RhGa12
60
3.5K
15
H=0kOe H=5kOe H=10kOe H=30kOe H=60kOe H=90kOe
10
Ce2 RhGa12
40
3.5K
5
20 0 0
10
20
30
40
50
Temperature (K)
0 0
2
4
6
8
10
12
14
16
18
20
Temperature (K) Fig. 4. Temperature dependent specific heat of Ce2RhGa12 and La2RhGa12. The inset shows the data of the two compounds below 20 K plotted as C/T versus T2. Solid lines are fitted to the expression C/T = c + bT2.
Fig. 7. Temperature dependent specific heat of Ce2RhGa12 in various applied magnetic fields.
S. Nallamuthu et al. / Journal of Alloys and Compounds 604 (2014) 379–383
fields and for fields exceeding 10 kOe the broad peak shifts to higher temperatures. We believe the temperature dependence of the heat capacity in the paramagnetic region in applied fields is influenced by the Schottky contribution to the heat capacity arising from the Zeeman splitting of the ground and the first excited state level at D1. In compounds that order magnetically at low temperatures like Ce2RhGa12, an estimate of the the Sommerfeld coefficient c is often derived by fitting the expression C/T = c + bT2 to the heat capacity data in the paramagnetic state. Using that procedure for the data between 8 and 20 K in Ce2RhGa12 furnishes a c of 423 mJ/mol K2. Such a large value of c would normally imply that Ce2RhGa12 is a heavy fermion material, which is characterized by an appreciable enhancement of the electronic mass arising due to the single ion Kondo effect. But there is a sizeable Schottky heat capacity in the temperature region 8–20 K and hence any extrapolation of the data to T = 0 K would give a false enhancement of the true electronic c which may be much lower [10]. Besides, it has to be kept in mind that the resistivity does not exhibit any signature of the Kondo effect and hence we attribute the apparently large c to CEF effect. 4. Conclusion We have studied the thermal, magnetic and electrical properties of the single crystals of tetragonal Ce2RhGa12 grown using Ga rich flux by means of the specific heat, magnetization, and electrical resistivity. All measurements show antiferromagnetic ordering at 3.5 K and the magnetization data show a large magnetocrystalline anisotropy, with [0 0 1] as the easy axis. The electrical resistivity does not show any signature associated with the single ion Kondo effect and thus shows that Ce2RhGa12 is a normal trivalent cerium compound. The existence of a low lying doublet at 33 K is inferred from the heat capacity data, which results in a significant Schottky heat capacity at low temperatures.
383
Acknowledgements The authors (R.N) thank Department of Atomic Energy (DAE), Board of Research in Nuclear Sciences (BRNS) Govt. of India for supporting this work under DAE Young Scientists Research Award (No: 2010/20/37P/BRNS/2513). Also this work has been partly supported (M.R.) by the Slovak grant agency VEGA 2/0070/12; by the Centre of Excellence CFNT MVEP of the Slovak Academy of Sciences; the CEX Nanofluid as the Centre of Excellence SAS; by the Structural funds EXTREM 26220120005 and NANOFLUID 26220120021. The authors (R.N, V.K, C.B, and H.H) are thankful to Indo-Swiss support for funding. We thank Yaroslav Filinchuk and Swiss-Norwegian Beam Lines at ESRF for the diffraction measurements, structure solution and the beam time allocation. References [1] E. Parthé, B. Chabot (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 48, Elsevier, New York, 1984. [2] A. Szytula, J. Leciejewicz (Eds.), Handbook of Crystal Structures and Magnetic Properties of Rare Earth Intermetallics, CRC Press, Boca Raton, FL, 1994. [3] P. Villars, L.D. Calvert (Eds.), Pearson’s Handbook of Crystallographic Data for Intermetallic Compounds, 2nd ed., American Society for Metals, Materials Park, OH, 1997. [4] Z. Fisk, D.W. Hess, C.J. Pethick, D. Pines, J.L. Smith, J.D. Thompson, J.O. Willis, Science 239 (1988) 33–42. [5] G.R. Stewart, Rev. Mod. Phys. 56 (1984) 754–787. [6] Robin T. Macaluso, S. Nakatsuji, H. Lee, Z. Fisk, M. Moldovan, D.P. Young, Julia Y. Chana, J. Solid State Chem. 174 (2003) 296–301. [7] J.N. Millican, S. Nakatsuji, H.-O. Lee, B. Carter, N.O. Moreno, Z. Fisk, J.Y. Chan, J. Solid State Chem. 178 (2005) 3547–3553. [8] R. Nagalakshmi, R. Kulkarni, S.K. Dhar, A. Thamizhavel, V. Krishnakumar, C. Besnard, H. Hagemann, M. Reiffers, Chem. Met. Alloys 4 (2011) 229–233. [9] Jung Young Cho, Jasmine N. Millican, Cigdem Capan, Dmitry A. Sokolov, Monica Moldovan, Amar B. Karki, David P. Young, Meigan C. Aronson, Julia Y. Chan, Chem. Mater. 20 (2008) 6116–6123. [10] K.A. Gschneidner Jr., J. Tang, S.K. Dhar, A. Goldman, Physica B 163 (1990) 507– 510.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Anisotropic magnetic, transport and thermodynamic properties of novel tetragonal Ce2RhGa12 compound S. Nallamuthu a, T.P. Rashid a, V. Krishnakumar b, Celine Besnard c, Hans Hagemann d, Marian Reiffers e, R. Nagalakshmi a,⇑ a
Department of Physics, National Institute of Technology, Tiruchirappalli 620 0015, India Department of Physics, Periyar University, Salem 636 011, India Laboratory of Crystallography, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland d Department of Physical Chemistry, University of Geneva, Geneva, Switzerland e Faculty of Humanities and Natural Sciences, Presov University, Presov, Slovakia b c
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 26 December 2013 Received in revised form 7 March 2014 Accepted 12 March 2014 Available online 28 March 2014 Keywords: Intermetallic Anisotropy Heavy fermions Heat capacity Magnetization
We report on a comprehensive study of the magnetization, resistivity and heat capacity on the single crystals of Ce2RhGa12 synthesized using Ga flux. Single crystal X-ray diffraction data confirm the tetragonal Pb/nbm structure of Ce2RhGa12, which is isostructural to Ce2PdGa12. Ce2RhGa12 orders antiferromagnetically at TN = 3.5 K and exhibits anisotropic magnetic behavior, inferred from the magnetization and resistivity data, taken along the two principal crystallographic directions of the crystal, viz., along [1 0 0] and [0 0 1]. The anisotropic magnetic response of Ce2RhGa12 establishes [0 0 1] as the easy axis of magnetization, and a weak meta-magnetic transition is also observed in the magnetic isotherm at 2 K along the same axis. A sharp peak in specific heat signals the bulk antiferromagnetic transition at TN = 3.5 K, which shifts to lower temperatures in low applied fields. The electrical resistivity along the two directions shows metallic behavior from 300 K down to 1.8 K and establishes Ce2RhGa12 as a normal, trivalent cerium compound. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Cerium based ternary intermetallic compounds are extensively studied as they show a variety of ground states due to the competition between the RKKY (Ruderman-Kittel-Kausya-Yoshida) and the single ion Kondo exchange interactions. While the former favors a magnetic ground state, a strong Kondo interaction leads to a paramagnetic Fermi liquid with large effective electron masses [1–4]. Since the electronic heat capacity is proportional to effective mass, compounds with large values of the coefficient of electronic specific heat c (400 mJ/mol K2) are termed as heavy fermions compounds [5]. CePdGa6, for example, is a layered heavy fermion compound with specific heat coefficient c 300 mJ/Ce mol K2 [6,7], ordering antiferromagnetically at TN = 5.5 K. The structurally related compound Ce2PdGa12 is an antiferromagnet with Néel temperature TN = 11 K and c = 72 mJ/mol K2 [7]. Recently, we have reported the synthesis of single crystals of Ce2RhGa12 [8], which is isostructural to Ce2PdGa12, in which the ⇑ Corresponding author. Tel.: +91 04312503615. E-mail addresses: (R. Nagalakshmi).
[email protected],
http://dx.doi.org/10.1016/j.jallcom.2014.03.067 0925-8388/Ó 2014 Elsevier B.V. All rights reserved.
[email protected]
tetragonal structure is composed of Ce–Ga and RhGa8/2 layers similar to the arrangement in CePdGa6 [6]. A change in c has been observed when Pd is replaced by Cu or Ni in R2MGa12 (R = La, Ce) [9]. It was, therefore, of interest to explore the magnetic properties of Ce2RhGa12. We have measured the magnetization, heat capacity and electrical resistivity and we find that Ce2RhGa12 is an antiferromagnet with TN = 3.5 K. 2. Experimental details The details about the single crystal growth of Ce2RhGa12 have already been reported in [8] and will not be repeated here. A few crystals of appropriate size and orientation were chosen from that lot and used in the present study. The X-ray Laue analysis confirmed good quality of the single crystals by exhibiting distinct spots with four fold tetragonal symmetry. The crystals were oriented along the principal crystallographic directions, namely [1 0 0] and [0 0 1], by means of the Laue back reflection method using Mo X-ray source. The crystals were then cut along the a- and c-directions using spark erosion cutting machine for physical and magnetic property measurements. Single crystal X-ray diffraction data were collected at the Swiss Norwegian Beam Line at the European Synchrotron Facility, Grenoble France. For that a single crystal of Ce2RhGa12 was glued on a glass fiber and transferred to the cold stream of a nitrogen cryojet (T = 200 K). The crystal was split with two major domains tilted by about 3 degrees along the b axis. Only one domain was used for structure determination. The oriented and properly cut single crystals were used for physical
380
S. Nallamuthu et al. / Journal of Alloys and Compounds 604 (2014) 379–383
moment. An anisotropy is observed in hp, which is ascribed to crystal electric field effect. The powder average hp of 24 K indicates an antiferromagnetic interaction between the cerium moments. The lack of agreement of measured v(T) with the theoretical Curie– Weiss fit at low temperatures is attributed to crystalline electric field (CEF) effect. The magnetic susceptibility for H//[0 0 1] shows a peak at TN = 3.5 K typical of an antiferromagnetic transition and arises due to the antiferromagnetic ordering of Ce moments as anticipated from a negative hp. v(T) for H//[0 0 1] is larger than H// [1 0 0] indicating that the tetragonal c-axis is relatively the easy axis of magnetization. The peak maximum of dv/dT is seen at TN = 3.5 K along H//[0 0 1] shown in Fig. 1(inset b). Also a mild anomaly at the same temperature is seen in the H//[1 0 0] direction as well. Fig. 2(a) shows the isothermal magnetization M(H) of Ce2RhGa12 measured along the principal crystallographic directions [1 0 0] and [0 0 1] up to 50 kOe at 2 K. The magnetization data were also taken at 3, 4 and 5 K and they are shown in Fig. 2(b). The data clearly establish [0 0 1] as the easy axis of magnetization, inferred from a relatively more rapid buildup of the magnetization at low fields, followed by a metamagnetic like transition at higher fields and a much larger saturation magnetization along [0 0 1]. The spin reorientation at the metamagnetic transition is also inferred from the derivative dM/dH (shown in inset Fig. 2(a)). Along the hard axis [1 0 0] the magnetization attains relatively smaller values. The metamagnetic transition is appreciably weakened at 3 K and vanishes at higher temperatures. The experimental saturation moment of Ce2RhGa12 along H//[0 0 1] easy axis reaches a value of about 1.79 lB/Ce at 50 kOe, which is less than the theoretical free ion value of Ce3+ gJJ = 2.14 lB/Ce. We attribute it to CEF effects.
property measurements. DC magnetization was measured as a function of temperature M(T) and magnetic field M(H) using a Quantum Design Magnetic Property Measurement System (MPMS), Superconducting Quantum Interference Device (SQUID) from 1.8 to 300 K. The electrical resistivity and heat capacity measurements were carried out using Quantum Design Physical Property Measurement System (PPMS) down to 1.8 K on the single crystals by the standard DC four-probe and heat-pulse relaxation technique respectively. The voltage and current leads (gold wire) for resistivity measurements were taken from the bar-shaped specimen using silver epoxy glue.
3. Results and discussion 3.1. Magnetic susceptibility and magnetization studies The main panel of Fig. 1 shows the susceptibility below 15 K, measured in an applied field of 100 Oe. The inverse susceptibility between 1.8 and 300 K and the derivative of susceptibility (dv/dT) are plotted in the insets Fig. 1(a and b) respectively. The data were taken with the field aligned along the two principal crystallographic directions [0 0 1] and [1 0 0], respectively. The high temperature magnetic susceptibility along both the principal directions was fitted to a modified Curie–Weiss law
v ¼ v0 þ
C ðT hp Þ
ð1Þ
where v0 is the temperature-independent term, hp is the paramagnetic Curie temperature and C is the Curie constant which can be expressed in terms of the effective moment as
C¼
l2eff x
ð2Þ
8
where x is the number of Ce atoms per formula unit. The solid lines in inset Fig. 1(a) are fits to Eq. (1) in the temperature interval of 60–300 K. The fitting parameters estimated are, v0 = 2.139 104 emu/mol, hp = 39 ± 2 K and leff = 2.74 ± 0.03 lB/Ce for H//[1 0 0] direction and v0 = 0, hp = 5 ± 2 K and leff = 2.76 ± 0.04 lB/Ce, for H//[0 0 1] direction. The inferred effective moment is slightly higher than the Hund’s rule J = 5/2 ground state value of free ion moment 2.54 lB/Ce, and shows trivalent Ce ions carrying a well localized 4f
3.2. Electrical resistivity The temperature dependent electrical resistivity q(T) of Ce2RhGa12 with J//[0 0 1] and J//[1 0 0] is shown in Fig. 3. The electrical resistivity shows a typical metallic behavior and it is
1.2
Ce2RhGa12
a
H=100 Oe χ-1 (mol/emu)
H//[001]
1.0
H//[001] H//[100]
150
H//[100]
100
50
0 0
50
100
150
200
250
300
Temperature (K) 0.20
0.6
b
0.15 0.10
dχ/dT[001] dχ/dT[100]
0.05
dχ /dT
χ (emu/mol)
0.8
0.4
3.5K
0.00 -0.05 -0.10 -0.15 -0.20 0
5
10
15
20
Temperature (K)
0.2
0.0 0
2
4
6
8
10
12
14
Temperature (K) Fig. 1. Magnetic susceptibility (v) of Ce2RhGa12 below 15 K in H = 100 Oe with H//[0 0 1] and H//[1 0 0] of the crystal. Inset (a) inverse susceptibility (v1) between 1.8 and 300 K; the solid lines are the Curie–Weiss fit and (b) the derivative of susceptibility (dv/dT).
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2.0 H//[100]
H//[001] dM/dH
Β
1.5
dM/dH
Ce2 RhGa12
0.8
Magnetization (μB/Ce)
2.0
Magnetization(μ /Ce)
H//[001] 1.2
(a)
T=2K
1.6
1.0 0.5 0.0 0
10000 20000 30000 40000 50000
Field (Oe)
0.4 0.0 1.8
2K 3K 4K 5K
1.2
(b)
H//[001] 2K 3K 3.5K 4K 5K
H//[100]
0.6
0.0 0
10
20
30
40
50
H (kOe) Fig. 2. Isothermal magnetization of Ce2RhGa12 measured with H//[1 0 0] and H//[0 0 1] as a function of magnetic field (a) at 2 K and (b) at selected temperatures.
J//[100]
Ce2RhGa12
100
J//[001]
ρ (μΩ μΩ Cm)
80
60 70
a
b
J//[100] H//[001] Ce2RhGa12
ρ (μΩ μΩ Cm)
ρ (μΩ μΩ Cm)
40
20
J//[001]
H//[100]
35
60
0 Oe 10 kOe 30 kOe 60 kOe 90 kOe
50
10 kOe 30 kOe 60 koe 90 kOe
30
25 0
5
10
15
20
25
30
0
2
4
0
50
100
150
6
8
10
12
14
Temperature (K)
Temperature(K)
0
200
250
300
Temperature (K) Fig. 3. Temperature dependent electrical resistivity q(T) of Ce2RhGa12 measured in zero magnetic field with current density parallel to a and c axis, respectively. Insets (a and b) shows q(T) versus T below 30 K in various fields along the -a- and -c- directions.
characterized by a prominent anisotropy arising possibly due to the large c/a ratio (2.6) and an anisotropic Fermi surface. A sharp slope change in the resistivity followed by a rapid decrease below TN = 3.5 K indicates the decrease in spin disorder scattering arising from the antiferromagnetic transition. At high temperatures, the resistivity decreases nearly linearly with the temperature. It may be noted that the resistivity does not exhibit Kondo like behavior which classifies Ce2RhGa12 as a normal trivalent cerium compound. The insets 3a and 3b show the temperature dependence of electrical resistivity q(T) below 30 K measured at various magnetic
fields up to 90 kOe. The magnetoresistivity MR, defined as MR = [R(H)–R(0)]/R(0), is negative in the entire range. Typically antiferromagnets show a positive MR below TN. Above 35 K the resistivity is almost independent of magnetic field strength. A few ripple like features in the resistivity near 150 K for H//[1 0 0] are attributed to noise in the data. 3.3. Heat capacity Bulk magnetic ordering is confirmed by heat capacity measurements. The temperature dependent heat capacity of Ce2RhGa12 and
S. Nallamuthu et al. / Journal of Alloys and Compounds 604 (2014) 379–383
6 6 6 C sch ðTÞ ¼ R6 6 4
3
Ei X Ei X 2 Ei X g i ekB T þ g i Ei ekB T g i Ei ekB T 7 7 7 i i i 7 !2 7 X 5 2 g i eEi =kB T T
ð3Þ
14 Δ1=33K
12
Δ2=109K
10
C4f
8
Schottky fit
6 4 2 0
0
5
10
15
20
25
30
Temperature (K) Fig. 5. Temperature dependence of the 4f-derived specific heat (C4f). Solid line represents the fit to the expression for the Schottky heat capacity.
2.0
12 Ce2 RhGa12
C4f
10
S4f
1.5
8 1.0
Rln2
6 4
0.5
i
2
where Ei’s are the CEF energy levels and gi the corresponding degeneracy. We can reproduce the broad peak in C4f by taking the two excited doublets lying at D1 = 33 K and D2 = 109 K above the ground state doublet. The 4f-derived entropy S4f was obtained by integrating the C4f/T against the temperature and is shown in Fig. 6. For calculating the entropy, heat capacity data below 1.8 K were smoothly extrapolated to T = 0. S4f reaches the theoretical value associated with a doublet (with effective spin ½) Rln 2 close to TN. Above TN, S4f increases rapidly because of the CEF level lying at 33 K. In order to examine the effect of the applied magnetic field on the bulk magnetic ordering, the heat capacity was measured with
0.0 0
5
10
15
20
0 30
25
Temperature (K) Fig. 6. The plots of C4f/T and S4f as a function of temperature.
H//[0 0 1] up to 90 kOe and it is plotted as C versus T in Fig. 7. It is seen that the peak in the heat capacity due to the magnetic ordering shifts to lower temperatures even in applied fields lower than 10 kOe. The zero-field sharp peak becomes broader in applied 25
200
4.0 3.5
C/T (J/mol K2)
160 140 120 100
Ce2RhGa12
La 2 RhGa 12 Ce 2 RhGa 12
3.0
20
2.5 2.0 1.5
C (J/mol K)
180
C (J/mol K)
S4f [J/Ce mol K]
2
16
C4f (J/mol K)
its isostructural nonmagnetic reference system La2RhGa12 is shown in Fig. 4. The zero field heat capacity data for Ce2RhGa12 manifest a clear peak at TN = 3.5 K attaining a value of 11.74 J/mol K typical of a second order phase transition. On the other hand, the heat capacity of La2RhGa12 increases monotonically with temperature typical of a paramagnetic compound. A fit of the expression C/ T = c + bT2 to the heat capacity of La2RhGa12 below 10 K, where c and b stand for the conduction electron and phonon contributions to the heat capacity, gives c = 8.54 mJ/mol K2 (0.66 mJ/g atom K2) which is comparable to that of Cu. The heat capacity of La2RhGa12 is used to estimate the magnetic contribution to the specific heat of Ce2RhGa12 by assuming that the phonon contribution to the heat capacity is identical in the two compounds. The magnetic 4f contribution C4f (plotted in Fig. 5) to the heat capacity is deduced by subtracting the heat capacity of La2RhGa12 from that of Ce2RhGa12. It is seen that the C4f in the paramagnetic state does not initially decrease with temperature but instead increases with a broad maximum around 15–25 K. Any short range order above TN would decrease with increasing temperature and therefore, the increase of C4f with temperature above TN is tentatively attributed to the existence of Schottky specific heat. The Schottky contribution arises from the thermal variation of the population of occupied CEF split levels of the Hund’s rule ground state multiplet. We have fitted the expression (Eq. (3)) for the Schottky heat capacity arising from three levels (in the tetragonal crystal potential, the sixfold degenerate level of Ce will split into three levels) to C4f.
C4f /T[J/Ce mol K2]
382
1.0 0.5 0.0
80
0
50
100
150
200
250
300
350
400
2
Temperature (K)
La2 RhGa12
60
3.5K
15
H=0kOe H=5kOe H=10kOe H=30kOe H=60kOe H=90kOe
10
Ce2 RhGa12
40
3.5K
5
20 0 0
10
20
30
40
50
Temperature (K)
0 0
2
4
6
8
10
12
14
16
18
20
Temperature (K) Fig. 4. Temperature dependent specific heat of Ce2RhGa12 and La2RhGa12. The inset shows the data of the two compounds below 20 K plotted as C/T versus T2. Solid lines are fitted to the expression C/T = c + bT2.
Fig. 7. Temperature dependent specific heat of Ce2RhGa12 in various applied magnetic fields.
S. Nallamuthu et al. / Journal of Alloys and Compounds 604 (2014) 379–383
fields and for fields exceeding 10 kOe the broad peak shifts to higher temperatures. We believe the temperature dependence of the heat capacity in the paramagnetic region in applied fields is influenced by the Schottky contribution to the heat capacity arising from the Zeeman splitting of the ground and the first excited state level at D1. In compounds that order magnetically at low temperatures like Ce2RhGa12, an estimate of the the Sommerfeld coefficient c is often derived by fitting the expression C/T = c + bT2 to the heat capacity data in the paramagnetic state. Using that procedure for the data between 8 and 20 K in Ce2RhGa12 furnishes a c of 423 mJ/mol K2. Such a large value of c would normally imply that Ce2RhGa12 is a heavy fermion material, which is characterized by an appreciable enhancement of the electronic mass arising due to the single ion Kondo effect. But there is a sizeable Schottky heat capacity in the temperature region 8–20 K and hence any extrapolation of the data to T = 0 K would give a false enhancement of the true electronic c which may be much lower [10]. Besides, it has to be kept in mind that the resistivity does not exhibit any signature of the Kondo effect and hence we attribute the apparently large c to CEF effect. 4. Conclusion We have studied the thermal, magnetic and electrical properties of the single crystals of tetragonal Ce2RhGa12 grown using Ga rich flux by means of the specific heat, magnetization, and electrical resistivity. All measurements show antiferromagnetic ordering at 3.5 K and the magnetization data show a large magnetocrystalline anisotropy, with [0 0 1] as the easy axis. The electrical resistivity does not show any signature associated with the single ion Kondo effect and thus shows that Ce2RhGa12 is a normal trivalent cerium compound. The existence of a low lying doublet at 33 K is inferred from the heat capacity data, which results in a significant Schottky heat capacity at low temperatures.
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Acknowledgements The authors (R.N) thank Department of Atomic Energy (DAE), Board of Research in Nuclear Sciences (BRNS) Govt. of India for supporting this work under DAE Young Scientists Research Award (No: 2010/20/37P/BRNS/2513). Also this work has been partly supported (M.R.) by the Slovak grant agency VEGA 2/0070/12; by the Centre of Excellence CFNT MVEP of the Slovak Academy of Sciences; the CEX Nanofluid as the Centre of Excellence SAS; by the Structural funds EXTREM 26220120005 and NANOFLUID 26220120021. The authors (R.N, V.K, C.B, and H.H) are thankful to Indo-Swiss support for funding. We thank Yaroslav Filinchuk and Swiss-Norwegian Beam Lines at ESRF for the diffraction measurements, structure solution and the beam time allocation. References [1] E. Parthé, B. Chabot (Eds.), Handbook on the Physics and Chemistry of Rare Earths, vol. 48, Elsevier, New York, 1984. [2] A. Szytula, J. Leciejewicz (Eds.), Handbook of Crystal Structures and Magnetic Properties of Rare Earth Intermetallics, CRC Press, Boca Raton, FL, 1994. [3] P. Villars, L.D. Calvert (Eds.), Pearson’s Handbook of Crystallographic Data for Intermetallic Compounds, 2nd ed., American Society for Metals, Materials Park, OH, 1997. [4] Z. Fisk, D.W. Hess, C.J. Pethick, D. Pines, J.L. Smith, J.D. Thompson, J.O. Willis, Science 239 (1988) 33–42. [5] G.R. Stewart, Rev. Mod. Phys. 56 (1984) 754–787. [6] Robin T. Macaluso, S. Nakatsuji, H. Lee, Z. Fisk, M. Moldovan, D.P. Young, Julia Y. Chana, J. Solid State Chem. 174 (2003) 296–301. [7] J.N. Millican, S. Nakatsuji, H.-O. Lee, B. Carter, N.O. Moreno, Z. Fisk, J.Y. Chan, J. Solid State Chem. 178 (2005) 3547–3553. [8] R. Nagalakshmi, R. Kulkarni, S.K. Dhar, A. Thamizhavel, V. Krishnakumar, C. Besnard, H. Hagemann, M. Reiffers, Chem. Met. Alloys 4 (2011) 229–233. [9] Jung Young Cho, Jasmine N. Millican, Cigdem Capan, Dmitry A. Sokolov, Monica Moldovan, Amar B. Karki, David P. Young, Meigan C. Aronson, Julia Y. Chan, Chem. Mater. 20 (2008) 6116–6123. [10] K.A. Gschneidner Jr., J. Tang, S.K. Dhar, A. Goldman, Physica B 163 (1990) 507– 510.