Home
Search
Collections
Journals
About
Contact us
My IOPscience
Disorder-driven non-Fermi liquid behavior in single-crystalline Ce2Co0.8Si3.2
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 016004 (http://iopscience.iop.org/0953-8984/26/1/016004) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 142.66.3.42 This content was downloaded on 07/09/2015 at 15:53
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 016004 (7pp)
doi:10.1088/0953-8984/26/1/016004
Disorder-driven non-Fermi liquid behavior in single-crystalline Ce2Co0.8Si3.2 M Szlawska and D Kaczorowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P Nr 1410, 50-950 Wrocław, Poland E-mail: [email protected] Received 23 September 2013, in final form 22 October 2013 Published 29 November 2013
Abstract A single crystal of the Ce-based ternary silicide Ce2 Co0.8 Si3.2 , which crystallizes with a hexagonal AlB2 -type related structure, was studied by means of magnetization, resistivity and heat capacity measurements. The compound was characterized as a Kondo paramagnet down to 0.4 K. Its low-temperature behavior is dominated by distinct non-Fermi liquid features, most likely arising due to structural disorder in the nonmagnetic-atom sublattice.
(Some figures may appear in colour only in the online journal)
1. Introduction
presence of structural disorder may lead to the coexistence of paramagnetic and Griffiths-type granular magnetic phases. The majority of the Ce-based ternary silicides with composition Ce2 TSi3 crystallize with the AlB2 -type structure or its ordered derivatives. At low temperatures, compounds with T = Ni, Cu, Rh, Pd, Ir and Au order antiferromagnetically [7–17], while ferromagnetic ordering is observed for the alloy with T = Pt [18]. Some of these phases, namely those with T = Cu, Pd and Au, simultaneously show some spin-glass-like features, which can be attributed to atomic disorder in their unit cells [19–23]. In the first literature report [24], the Co-bearing phase, Ce2 CoSi3 , was characterized as a mixed-valent system. However, subsequent investigations revealed that the compound is a paramagnetic Kondo lattice with a fairly stable 4f-shell of Ce3+ ions [25–29]. Recent examination of the electronic structure of Ce2 CoSi3 by means of photoemission spectroscopy indicated the significance of strong correlations between electrons from the Ce 4f-shell and Co 3d band [30]. An important finding was derived from the study of the low-temperature specific heat of the solid solution Ce2−x Lax CoSi3 [25], namely for all the alloys but pure Ce2 CoSi3 , an NFL-like upturn of the ratio C/T was found at low temperatures. The absence of similar features in the terminal compound was however ambiguous because its low-temperature specific heat was dominated by a magnetic phase transition of cerium oxide, present in the investigated sample as an impurity.
Diverse ground states in f-electron-based heavy-fermion systems are mostly governed by a subtle balance of competing Kondo and Rudermann–Kittel–Kasuya–Yoshida (RKKY) interactions [1]. Both phenomena depend on the product JN(EF ), where J represents an exchange coupling between f-electron spins and those of conduction electrons, while N(EF ) is the density of states at the Fermi level. The two key parameters can be easily modified by pressure or partial chemical substitution with a dopant differing from the given constituent by its atomic size or electronic configuration. For several years, special attention has been devoted to f-electron materials located at the verge of magnetic instability. It is generally believed that their non-trivial low-temperature physical properties, such as non-Fermi liquid (NFL) behavior or unconventional superconductivity, can be associated with the proximity to a quantum critical point (QCP), i.e. a second-order phase transition tuned to zero temperature by a non-thermal external factor [2, 3]. Often, the QCP scenario is applied also to non-stoichiometric or atomically disordered compounds. However, it has been recognized that crystallographic disorder can significantly modify the physical behavior, which may induce NFL features [4–6]. Basically, it occurs because of the wide distribution of Kondo and RKKY energy scales, typical for disordered phases. Moreover, in systems close to magnetic instability, the 0953-8984/14/016004+07$33.00
1
c 2014 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Table 1. Crystallographic and structure refinement data for Ce2 Co0.8 Si3.2 .
Motivated by the apparent divergence in the literature data for polycrystalline samples of Ce2 CoSi3 , we aimed at clarifying the electronic ground state in this silicide by studying its bulk properties on well-defined single crystals down to very low temperatures and in applied magnetic fields. However, our attempt to grow this material by the Czochralski pulling technique resulted in a crystal with a non-stoichiometric composition Ce2 Co0.8 Si3.2 . This outcome seems in line with an early report on the Ce–Co–Si system [31] that indicated a fairly extended homogeneity range for the phases CeCox Si2−x characterized by x = 0.3–0.5. Here, we present the results of our structural, magnetic, electrical transport and heat capacity measurements performed on the obtained crystal along the principal crystallographic directions. The properties of Ce2 Co0.8 Si3.2 are discussed in relation to those reported before for supposedly stoichiometric Ce2 CoSi3 .
Compound Space group Unit cell dimensions Volume Formula weight Calculated density Absorption coefficient θ range for data collection Ranges in hkl Reflections collected/unique Completeness to θ = 31.90◦ Refinement method Data/restraints/parameters Goodness of fit on F2 Final R indices (I ≥ 2σ (I)) R indices (all data) Extinction coefficient Largest diff. peak and hole
2. Experimental details A single crystal of ‘Ce2 CoSi3 ’ was grown by the Czochralski pulling method in a tetra-arc furnace under an ultra-pure argon atmosphere. The starting components were high-purity elements (Ce-3N, Co-4N, and Si-6N). The obtained crystal was a well-developed rod of about 3 mm in diameter and 40 mm in length. Single-crystal x-ray diffraction data were collected on an Oxford Diffraction four-circle diffractometer equipped with a CCD camera using Mo Kα radiation. Crystal structure refinement was done using the program S HELXL -97 [32]. Details of the single-crystal data collection and the structure refinement are given in table 1. The composition of the phase was checked by energy dispersive x-ray analysis using a Philips 515 scanning electron microscope equipped with an EDAX PV 9800 spectrometer. Magnetic measurements were performed in the temperature range 0.46–400 K and in magnetic fields up to 7 T using superconducting quantum interference device magnetometers (Quantum Design MPMS-5 and MPMS-7), the latter equipped with a 3 He refrigerator. Heat capacity was studied in the temperature interval 0.4–10 K in magnetic fields up to 9 T using a Quantum Design PPMS-9 platform. The temperature variations of the electrical resistivity were studied from 0.4 to 300 K in magnetic fields up to 9 T applied perpendicular to the flowing current, employing a Quantum Design PPMS-9 platform.
Ce2 Co0.8 Si3.2 P6/mmm a = 8.1037(7) Å c = 4.2204(3) Å 3 240.02(3) Å 418.91 g mol−1 5.778 g cm−3 22.11 mm−1 2.90◦ –31.90◦ −11 6 h 6 11 −11 6 k 6 11 −3 6 l 6 6 4102/202 [R(int) = 0.032] 99.5% Full-matrix least squares on F2 202/1/15 1.26 R1 = 0.018, wR2 = 0.032 R1 = 0.025, wR2 = 0.034 0.017(1) −3 0.52 and −1.22e Å
Both crystal structures are ordered variants of the AlB2 -type. The former one, first established from the single-crystal x-ray diffraction data [24], and then confirmed by x-ray measurements performed on powder samples [25, 27, 29], has a unit cell doubled within the basal hexagonal plane with respect to the AlB2 subcell (space group P6/mmm). In turn, the Er2 RhSi3 -type model, derived from the powder x-ray diffraction data [28], is characterized by doubling both a and c lattice parameters (space group P62c or P63 /mmc). The x-ray data collected in this work for the obtained single crystal of ‘Ce2 CoSi3 ’ corroborated the crystal structure model suggested in [24, 25, 27, 29], in which the unit cell is doubled exclusively within the basal hexagonal plane. However, the Rietveld refinements with free occupancy parameters indicated considerable mixing of cobalt and silicon atoms at the crystallographic 2d sites, with 20% of Co atoms being replaced by Si atoms, while the 6m sites were found fully occupied solely by silicon atoms. This finding yielded the actual composition of the investigated crystal to be Ce2 Co0.8 Si3.2 . Remarkably, also the EDX analysis of the crystal composition led to an excess of Si atoms in respect to the ideal 2:1:3 stoichiometry. The refined atomic coordinates and the displacement parameters of all the atoms in the unit cell of Ce2 Co0.8 Si3.2 are given in tables 2 and 3, respectively. As can be inferred from figure 1, Ce atoms build two-dimensional triangular networks separated by planes of Co and Si atoms. They occupy two inequivalent positions: Ce1 atoms are coordinated by twelve Si1 atoms with a Ce1–Si distance of 3.1775(13) Å, while Ce2 atoms have eight Si and four Co/Si nearest neighbors, with distances of 3.1312(7) Å and 3.1464(4) Å, respectively. In turn, Co/Si sites have trigonal planar Si coordination at the Co–Si distances of 2.2969(17) Å, while Si atoms form discrete Si6 rings with the Si–Si distance equal to 2.3802(17) Å. The main interatomic distances are given in table 4.
3. Results and discussion 3.1. Crystal structure As mentioned in section 1, most of the silicides Ce2 TSi3 adopt the AlB2 -type unit cell or its ordered derivatives. In the parent-type structure, Ce atoms occupy the aluminum 1a position, while T and Si atoms jointly share the boron 2d site. The compound Ce2 CoSi3 was reported in the literature to crystallize either with a structure closely related to U2 RuSi3 [33], or with the Er2 RhSi3 -type structure [10, 34]. 2
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Figure 2. Temperature dependences of the inverse molar magnetic susceptibility of Ce2 Co0.8 Si3.2 measured with a magnetic field of 0.1 T applied along and perpendicular to the c axis of the hexagonal unit cell. Solid line represents a fit of the modified Curie–Weiss law to the experimental data above 150 K. Inset displays low-temperature dependences of the magnetic susceptibility. Solid lines represent the power-law fit.
Figure 1. Crystal structure of Ce2 Co0.8 Si3.2 . Table 2. Atomic coordinates and equivalent isotropic thermal 2 displacement parameters (in Å × 103 ) for Ce2 Co0.8 Si3.2 . Ueq is defined as one third of the trace of the orthogonalized Uij tensor.
Atom
Site
x
y
z
U(eq)
Ce1 Ce2 Co/Si Si
1a 3f 2d 6m
0 1/2 2/3 0.1696(1)
0 0 1/3 0.3392(1)
0 0 1/2 1/2
5(1) 6(1) 10(1) 7(1)
Table 4. Interatomic distances in the Ce2 Co0.8 Si3.2 unit cell (in Å).
Ce1
Ce2
Table 3. Anisotropic thermal displacement parameters for the 2 atoms in Ce2 Co0.8 Si3.2 (in Å × 103 ). The anisotropic temperature factor exponent takes the form: −2π 2 [h2 a∗2 U11 + · · · + 2hka∗ b∗ U12 ].
Ce1 Ce2 Co/Si Si
U11
U22
U33
U23
U13
U12
4(1) 6(1) 5(1) 5(1)
4(1) 5(1) 5(1) 5(1)
6(1) 6(1) 20(1) 10(1)
0 0 0 0
0 0 0 0
2(1) 3(1) 2(1) 1(1)
Co/Si Si
3.2. Magnetic properties
k
µ2eff . 8(T − θP )
Si Ce2 Ce1 Si Co/Si Ce1 Ce2 Ce2 Si Ce2 Co/Si Si Ce2 Ce1
3.1813(14) 4.0519(7) 4.2204(3) 3.1353(7) 3.1505(2) 4.0519(7) 4.0519(7) 4.2204(3) 2.2979(18) 3.1505(2) 2.2979(18) 2.3808(18) 3.1353(7) 3.1813(14)
θP = −240 K for B k c. The so-obtained effective magnetic moments µeff are close to the value predicted for free Ce3+ ions within the Russell–Saunders coupling scenario (2.54 µB ). The large negative values of the paramagnetic Curie temperature θP probably signal Kondo interactions with a large characteristic energy scale. Moreover, the k considerable difference between θP⊥ and θP likely arises due to magnetocrystalline anisotropy being naturally inherent to a layered hexagonal structure with distinctly different lattice parameters a and c (cf section 3.1). At low temperatures, both components of the magnetic susceptibility deviate from the modified Curie–Weiss behavior, likely because of gradual depopulation of the crystalline electric field levels with decreasing temperature. For the point symmetry of both Ce sites in the unit cell of Ce2 Co0.8 Si3.2 it is expected that the ground multiplet 2 F5/2 of each ion splits into three doublets. As can be inferred from the inset to figure 2, down to 0.46 K, which was the terminal temperature of our measurements, no features that might hint at any magnetic ordering were
Figure 2 shows the temperature dependences of the reciprocal molar magnetic susceptibility of single-crystalline Ce2 Co0.8 Si3.2 taken with a magnetic field of 0.1 T, applied parallel and perpendicular to the c axis of the hexagonal unit cell. At high temperatures, above about 150 K, both dependences are somewhat curvilinear and can be described by a modified Curie–Weiss law in the form χ = χ0 +
12 6 2 8 4 2 4 2 3 6 1 2 4 2
(1)
Taking into account the expected magnetic contribution due to 3d electrons of Co atoms [30], one may anticipate that the temperature independent term χ0 in the above expression should be close to the Pauli-type magnetic susceptibility χ0 ' 4 × 10−4 emu mol−1 of La2 CoSi3 [25]. With this assumption, equation (1) can be well fitted to the experimental data (see figure 2), and the resulting parameters are µ⊥ eff = k ⊥ 2.5 µB , θP = −130 K for B ⊥ c and µeff = 2.4 µB , 3
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Figure 3. Magnetic field variation of magnetization of Ce2 Co0.8 Si3.2 recorded at 0.46 K with the field applied along two characteristic directions. Solid lines describe power-law dependences.
Figure 4. Temperature variations of the electrical resistivity of Ce2 Co0.8 Si3.2 measured with the current flowing along and perpendicular to the c axis. The solid line emphasizes logarithmic behavior.
found. The paramagnetic character of the ground state in the compound studied is further indicated by the shape of the field variations of the magnetization isotherms taken at the lowest achievable temperature (figure 3) that is typical for Ce-based paramagnets. The magnetization data corroborate the magnetocrystalline anisotropy in Ce2 Co0.8 Si3.2 , with the magnetization component measured along the crystallographic c axis being smaller than that taken within the hexagonal plane. As displayed in figure 3, the magnetization isotherms can be approximated by a power-law function σ ∝ Bλ with λ = 0.7 and λ = 0.8 for the magnetic field applied perpendicular and parallel to the c axis, respectively. Furthermore, the low-temperature magnetic susceptibility can be described below about 10 K by a power-law expression χ ∝ T λ−1 with λ = 0.6 for B ⊥ c and λ = 0.8 for B k c (see the inset to figure 2). Such σ (B) and χ (T) dependences are quite unusual for Fermi liquids but expected for Griffiths phases [5, 6]. Thus, the magnetic characteristics of Ce2 Co0.8 Si3.2 are fully in line with the presence of sizable atomic disorder in the nonmagnetic-atom sublattice, as established from the x-ray diffraction data.
entire temperature range, the change in the magnitude of both ρ ⊥ (T) and ρ k (T) is small, leading to the residual resistivity ratio (RRR = ρ(300 K)/ρ(0.4 K)) being close to 1 for both current directions. This feature most likely results from the crystallographic disorder in the single crystal studied. Figure 5 presents the low-temperature dependences of the electrical resistivity of Ce2 Co0.8 Si3.2 measured in zero field and several external magnetic fields. As marked, at low temperatures the resistivity changes as ρ(T) ∝ T n , with the exponent n equal to 1.3 and 1.0 for ρ ⊥ and ρ k , respectively. The observed NFL behavior is significantly different from the quadratic temperature dependence expected for a Kondo lattice. Instead, it is fully compatible with the Griffiths phase scenario [5, 6], indicated also by the magnetic data (see above) and the heat capacity data (see below) of Ce2 Co0.8 Si3.2 . Somewhat unexpectedly, application of the magnetic field does not result in the Fermi liquid behavior but brings about an appearance of upturns in both components of the resistivity. In zero field, these features were probably masked by a strong low-temperature NFL-decrease of the resistivity. Since the magnetic field reduces the drop, the weak contribution to the resistivity leading to the low-temperature upturn is better seen. With increasing magnetic field strength, the local minima in ρ ⊥ (T) and ρ k (T) shift toward higher temperatures. Interestingly, similar features were recently observed for the single crystal of Ce2 Co0.4 Rh0.4 Si3.2 [35]. The resistivity behavior of both phases closely resembles that reported for U2 CoSi3 [36]. For latter case, it was interpreted in terms of a weak localization effect and strong electron–electron interactions in a system with significant structural disorder. It seems likely that a similar approach is appropriate also for the two Ce-based silicides.
3.3. Electrical resistivity The temperature variations of the electrical resistivity of Ce2 Co0.8 Si3.2 , ρ ⊥ (T) and ρ k (T), measured with the electrical current flowing perpendicular and parallel to the hexagonal c axis, respectively, are shown in figure 4. At room temperature, both components of the resistivity have rather large magnitudes, being ρ ⊥ = 255 µ cm and ρ k = 235 µ cm. With decreasing temperature the ρ ⊥ component increases in a logarithmic manner, most likely due to the Kondo effect, undergoes through a broad maximum near 80 K, and then drops down to 246 µ cm measured at 0.4 K. In turn, ρ k is nearly temperature independent down to about 100 K, and at lower temperatures smoothly decreases, reaching a value of 206 µ cm at 0.4 K. Generally, over the
3.4. Heat capacity Figure 6 presents the low-temperature dependences of the specific heat over temperature ratio of single-crystalline Ce2 Co0.8 Si3.2 , measured in different magnetic fields applied 4
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Figure 5. Low-temperature dependences of the electrical resistivity of Ce2 Co0.8 Si3.2 measured with the current flowing perpendicular to (upper panel) and along (lower panel) the c axis in several magnetic fields applied in the c direction and within the basal plane, respectively. Solid lines are power-law fits described in the text.
Figure 6. Low-temperature variations of the specific heat of Ce2 Co0.8 Si3.2 measured with several magnetic fields applied along (upper panel) and perpendicular to (lower panel) the hexagonal c axis. The solid lines emphasize a power-law dependence.
feature of unclear origin may be observed at the lowest temperatures. At 0.4 K, the C/T value decreases from −2 measured in zero field down to about 200 mJ mol−1 Ce K −1 −2 150 mJ molCe K found in B = 9 T. Remarkably, in such a strong magnetic field, a Fermi liquid behavior with nearly constant C/T is seen at the lowest temperatures. In contrast, for B k c (see the lower panel of figure 6), the magnetic field effect is much smaller, namely even in a field of 9 T a clear upturn in C/T is still observed, and the C/T ratio −2 is reduced only to about 167 mJ mol−1 Ce K . The different response mimics the magnetocrystalline anisotropy seen in the magnetic data, where the crystallographic c axis was the direction of smaller field-dependent magnetization and smaller temperature-dependent magnetic susceptibility.
within the ab plane and along the c axis of the hexagonal unit cell. In zero magnetic field, no phase transition is seen on C/T(T), which proves that the studied compound remains intrinsically paramagnetic down to 0.4 K, and the measured sample was free of any magnetic impurities (here we recall that contamination by cerium oxide affected the previous heat capacity study on polycrystalline material of Ce2 CoSi3 [25]). The observed increase in the C/T ratio with decreasing temperature resembles the behavior reported for the solid solution Ce2−x Lax CoSi3 with x ≥ 0.25 [25]. Analytically, C/T(T) diverges as a power of the temperature C/T ∝ T λ−1 with the exponent λ = 0.6. The latter value is equal to that obtained for the low-temperature χ (T) variation measured with the magnetic field oriented perpendicular to the hexagonal c axis (see section 3.2). Furthermore, the behavior of the specific heat of Ce2 Co0.8 Si3.2 is consistent with the theoretical prediction for Griffiths phases [5, 6], and entirely in line with the magnetization and resistivity data. Upon applying a magnetic field perpendicular to the c axis (see the upper panel of figure 6), the NFL upturn in C/T(T) becomes systematically suppressed with increasing field. At the dependence measured in a field of 2 T, a tiny
4. Conclusions The cerium silicide Ce2 Co0.8 Si3.2 crystallizes with the AlB2 -related crystal structure, in which the lattice parameter a is doubled with respect to the parent subcell, while the parameter c is equal to that of the AlB2 -type subcell. The physical properties of the compound strongly reflect atomic disorder in its unit cell. Down to 0.4 K, no magnetic 5
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
phase transition is seen in the magnetic susceptibility, electrical resistivity, and heat capacity characteristics, hence proving that Ce2 Co0.8 Si3.2 remains paramagnetic down to the lowest temperatures. Furthermore, below about 10 K, distinct non-Fermi liquid features occur in all the bulk properties examined. With decreasing temperature the magnetic susceptibility and the specific heat over temperature ratio diverge in a power-law manner, whereas the electrical resistivity varies quasi-linearly. Moreover, the magnetization isotherms measured at 0.4 K are proportional to a power of the magnetic field strength. All these findings, and even the particular exponents in the power-law variations, are consistent with the theoretical predictions for Griffiths phases, which form because of crystallographic disorder in the system. For Ce2 Co0.8 Si3.2 , the presence of atomic disorder provides a straightforward explanation of the observed large values of the residual resistivity, small changes in the electrical resistivity with temperature, and the occurrence of some low-temperature minima in the resistivity measured in external magnetic fields. The effects of structural disorder may strongly influence the formation of the ground state, which is most likely governed by f-ligand hybridization, typical for Ce-based intermetallics. In Ce2 Co0.8 Si3.2 the latter interaction seems fairly strong, and brings about the enhanced electronic contribution to the specific heat, the large values of the paramagnetic Curie temperature, and the logarithmic temperature variation of the electrical resistivity. It is worth recalling here that the original aim of the present work was to examine the ground state properties of the stoichiometric phase Ce2 CoSi3 . The surplus amount of Si at the expense of Co in the single crystal grown appeared unintentionally. Curiously, a very similar result was obtained in our recent study of the solid solution between Ce2 CoSi3 and Ce2 RhSi3 , where the crystal Ce2 Co0.4 Rh0.4 Si3.2 was synthesized instead of the intended alloy Ce2 Co0.6 Rh0.4 Si3 [35]. The coincidence in the composition of these crystals may be accidental but it might also hint at somewhat higher thermodynamic stability of the ‘Ce2 CoSi3 ’ phases, in which Co cobalt atoms are replaced by Si atoms, at least at the applied experimental conditions of Czochralski growing process of both materials. It should be emphasized that the observed deviations from the ideal 2:1:3 stoichiometry are entirely consistent with several reports on the Ce–T–Si isothermal sections [31, 37–41], where the extended homogeneity ranges of the cerium silicides crystallizing with the AlB2 -type or related structures are indicated as Ce2 T1−x Si3+x . As regards the physical behavior of such materials, it may critically depend on their actual exact composition. The obvious effect of inherent crystallographic disorder is on the transport properties, but also the magnetic ground state can be fairly sensitive to structural defects, as proved for example for the so-called nonmagnetic-atom-disorder spin-glasses (NMAD SG). Prominent representatives of the latter group of systems are numerous U-based U2 TSi3 silicides with the AlB2 -type unit cells [42–48], and amidst them also the Co-bearing counterpart to the compound studied in the present work [36]. Naturally, small differences in the composition may account
for the diverse physical properties reported earlier for polycrystalline samples of ‘Ce2 CoSi3 ’. Obviously, very careful determination of the actual composition and crystal structure of the Ce2 TSi3 and U2 TSi3 phases is a prerequisite condition for reliable interpretation and understanding of their fairly complex low-temperature physical behaviors.
Acknowledgments The authors are grateful to L Gulay for his assistance in the crystal growth process and J St˛epie´n-Damm, A Gagor, ˛ and W Walerczyk for x-ray measurements. This work was supported by the Ministry of Science and Higher Education within research project No. IP 2011 054471. The authors thank Wrocław Center for Networking and Computing for access to the MATLAB license (grant no. 92).
References [1] Doniach S 1977 Valence Instabilities and Related Narrow Band Phenomena (New York: Plenum) [2] Stewart G R 2001 Rev. Mod. Phys. 73 797 [3] Löhneysen H v, Rosch A, Vojta M and Wölfle P 2007 Rev. Mod. Phys. 79 1015 [4] Miranda E and Dobrosavljevi´c V 2005 Rep. Prog. Phys. 68 2337 [5] Castro Neto A H, Castilla G and Jones B A 1998 Phys. Rev. Lett. 81 3531 [6] Castro Neto A H and Jones B A 2000 Phys. Rev. B 62 14975 [7] Rojas D P, Rodríguez Fernández J, Espeso J I, Gómez Sal J C, da Silva J C, Gandra F G, dos Santos A O and Medina A N 2010 J. Magn. Magn. Mater. 322 3192 [8] Szlawska M and Kaczorowski D 2012 Phys. Rev. B 85 134423 [9] Hwang J S, Lin K J and Tien C 1996 Solid State Commun. 100 169 [10] Chevalier B, Lejay P, Etourneau J and Hagenmuller P 1984 Solid State Commun. 49 753 [11] Das I and Sampathkumaran E V 1994 J. Magn. Magn. Mater. 137 L239 [12] Leciejewicz J, Stüsser N, Szytuła A and Zygmunt A 1995 J. Magn. Magn. Mater. 147 45 [13] Nakano T, Sengupta K, Rayaprol S, Hedo M, Uwatoko Y and Sampathkumaran E V 2007 J. Phys.: Condens. Matter 19 326205 [14] Kase N, Muranaka T and Akimitsu J 2009 J. Magn. Magn. Mater. 321 3380 ´ [15] Szlawska M, Kaczorowski D, Slebarski A, Gulay L and St˛epie´n-Damm J 2009 Phys. Rev. B 79 134435 [16] Saha S R, Sugawara H, Matsuda T D, Aoki Y, Sato H and Sampathkumaran E V 2000 Phys. Rev. B 62 425 [17] Szlawska M and Kaczorowski D 2011 Phys. Rev. B 84 094430 [18] Majumdar S, Sampathkumaran E V, Brando M, Hemberger J and Loidl A 2001 J. Magn. Magn. Mater. 236 99 [19] Majumdar S, Sampathkumaran E V, Berger St, Della Mea M, Michor H, Bauer E, Hemberger J and Loidl A 2002 Solid State Commun. 121 665 ´ [20] Szytuła A, Hofmann M, Penc B, Slaski M, Majumdar S, Sampathkumaran E V and Zygmunt A 1999 J. Magn. Magn. Mater. 202 365 [21] Sampathkumaran E V 2003 Acta Phys. Pol. B 34 999 [22] Li D X, Shiokawa Y, Nimori S, Haga Y, Yamamoto E, ¯ Matsuda T D and Onuki Y 2003 Physica B 329–333 506 [23] Yubuta K, Yamamura T, Li D X and Shiokawa Y 2009 Solid State Commun. 149 238 [24] Gordon R A, Warren C J, Alexander M G, DiSalvo F J and Pöttgen R 1997 J. Alloys Compounds 248 24 6
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
[38] Bodak O I, Kalychak Y M and Gladyshevskii E I 1974 Izv. Akad. Nauk SSSR Neorg. Mater. 10 450 [39] Gribanov A V, Seropegin Y, Tursina A I, Bodak O I, Rogl P and Noël H 2004 J. Alloys Compounds 383 286 [40] Lipatov A, Gribanov A, Grytsiv A, Rogl P, Murashova E, Seropegin Y, Giester G and Kalmykov K 2009 J. Solid State Chem. 182 2497 [41] Lipatov A, Gribanov A, Grytsiv A, Safronov S, Rogl P, Rousnyak J, Seropegin Y and Giester G 2010 J. Solid State Chem. 183 829 [42] Kaczorowski D and Noël H 1993 J. Phys.: Condens. Matter 5 9185 [43] Kaczorowski D and Pöttgen R 1993 J. Alloys Compounds 201 157 [44] Chevalier B, Pöttgen R, Darriet B, Gravereau P and Etourneau J 1996 J. Alloys Compounds 233 150 [45] Yubuta K, Yamamura K and Shiokawa Y 2006 J. Phys.: Condens. Matter 18 6109 [46] Li D X, Shiokawa Y, Homma Y, Uesawa A, Dönni A, ¯ Suzuki T, Haga Y, Yamamoto E, Homma T and Onuki Y 1998 Phys. Rev. B 57 7434 [47] Li D X, Dönni A, Kimura Y, Shiokawa Y, Homma Y, ¯ Haga Y, Yamamoto E, Honma T and Onuki Y 1999 J. Phys.: Condens. Matter 11 8263 [48] Szlawska M, Kaczorowski D and Reehuis M 2010 Phys. Rev. B 81 094423
[25] Majumdar S, Mahesh Kumar M, Mallik R and Sampathkumaran E V 1999 Solid State Commun. 110 509 [26] Majumdar S, Mahesh Kumar M, Mallik R and Sampathkumaran E V 2000 Physica B 281/282 367 [27] Majumdar S and Sampathkumaran E V 2000 Phys. Rev. B 62 8959 [28] Patil S, Iyer K K, Maiti K and Sampathkumaran E V 2008 Phys. Rev. B 77 094443 [29] Majumdar S and Sampathkumaran E V 2001 J. Magn. Magn. Mater. 223 247 [30] Patil S, Pandey S K, Medicherla V R R, Singh R S, Bindu R, Sampathkumaran E V and Maiti K 2010 J. Phys.: Condens. Matter 22 266602 [31] Bodak O I and Gladyshevskii E I 1970 Izv. Akad. Nauk SSSR Neorg. Mater. 6 1186 [32] Sheldrick G M 2008 Acta Crystallogr. A 64 112 [33] Pöttgen R, Gravereau P, Darriet B, Chevalier B, Hickey E and Etourneau J 1994 J. Mater. Chem. 4 463 [34] Gladyshevskii R E, Cenzual K and Parthé E 1992 J. Alloys Compounds 189 221 [35] Szlawska M and Kaczorowski D 2013 J. Phys.: Condens. Matter 25 255601 [36] Szlawska M, Gnida D and Kaczorowski D 2011 Phys. Rev. B 84 134410 [37] Bodak O I, Mis’kiv M G, Tyvanchuk A T, Kharchenko O I and Gladyshevskii E I 1973 Izv. Akad. Nauk SSSR Neorg. Mater. 9 864
7
Search
Collections
Journals
About
Contact us
My IOPscience
Disorder-driven non-Fermi liquid behavior in single-crystalline Ce2Co0.8Si3.2
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 016004 (http://iopscience.iop.org/0953-8984/26/1/016004) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 142.66.3.42 This content was downloaded on 07/09/2015 at 15:53
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 016004 (7pp)
doi:10.1088/0953-8984/26/1/016004
Disorder-driven non-Fermi liquid behavior in single-crystalline Ce2Co0.8Si3.2 M Szlawska and D Kaczorowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, P Nr 1410, 50-950 Wrocław, Poland E-mail: [email protected] Received 23 September 2013, in final form 22 October 2013 Published 29 November 2013
Abstract A single crystal of the Ce-based ternary silicide Ce2 Co0.8 Si3.2 , which crystallizes with a hexagonal AlB2 -type related structure, was studied by means of magnetization, resistivity and heat capacity measurements. The compound was characterized as a Kondo paramagnet down to 0.4 K. Its low-temperature behavior is dominated by distinct non-Fermi liquid features, most likely arising due to structural disorder in the nonmagnetic-atom sublattice.
(Some figures may appear in colour only in the online journal)
1. Introduction
presence of structural disorder may lead to the coexistence of paramagnetic and Griffiths-type granular magnetic phases. The majority of the Ce-based ternary silicides with composition Ce2 TSi3 crystallize with the AlB2 -type structure or its ordered derivatives. At low temperatures, compounds with T = Ni, Cu, Rh, Pd, Ir and Au order antiferromagnetically [7–17], while ferromagnetic ordering is observed for the alloy with T = Pt [18]. Some of these phases, namely those with T = Cu, Pd and Au, simultaneously show some spin-glass-like features, which can be attributed to atomic disorder in their unit cells [19–23]. In the first literature report [24], the Co-bearing phase, Ce2 CoSi3 , was characterized as a mixed-valent system. However, subsequent investigations revealed that the compound is a paramagnetic Kondo lattice with a fairly stable 4f-shell of Ce3+ ions [25–29]. Recent examination of the electronic structure of Ce2 CoSi3 by means of photoemission spectroscopy indicated the significance of strong correlations between electrons from the Ce 4f-shell and Co 3d band [30]. An important finding was derived from the study of the low-temperature specific heat of the solid solution Ce2−x Lax CoSi3 [25], namely for all the alloys but pure Ce2 CoSi3 , an NFL-like upturn of the ratio C/T was found at low temperatures. The absence of similar features in the terminal compound was however ambiguous because its low-temperature specific heat was dominated by a magnetic phase transition of cerium oxide, present in the investigated sample as an impurity.
Diverse ground states in f-electron-based heavy-fermion systems are mostly governed by a subtle balance of competing Kondo and Rudermann–Kittel–Kasuya–Yoshida (RKKY) interactions [1]. Both phenomena depend on the product JN(EF ), where J represents an exchange coupling between f-electron spins and those of conduction electrons, while N(EF ) is the density of states at the Fermi level. The two key parameters can be easily modified by pressure or partial chemical substitution with a dopant differing from the given constituent by its atomic size or electronic configuration. For several years, special attention has been devoted to f-electron materials located at the verge of magnetic instability. It is generally believed that their non-trivial low-temperature physical properties, such as non-Fermi liquid (NFL) behavior or unconventional superconductivity, can be associated with the proximity to a quantum critical point (QCP), i.e. a second-order phase transition tuned to zero temperature by a non-thermal external factor [2, 3]. Often, the QCP scenario is applied also to non-stoichiometric or atomically disordered compounds. However, it has been recognized that crystallographic disorder can significantly modify the physical behavior, which may induce NFL features [4–6]. Basically, it occurs because of the wide distribution of Kondo and RKKY energy scales, typical for disordered phases. Moreover, in systems close to magnetic instability, the 0953-8984/14/016004+07$33.00
1
c 2014 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Table 1. Crystallographic and structure refinement data for Ce2 Co0.8 Si3.2 .
Motivated by the apparent divergence in the literature data for polycrystalline samples of Ce2 CoSi3 , we aimed at clarifying the electronic ground state in this silicide by studying its bulk properties on well-defined single crystals down to very low temperatures and in applied magnetic fields. However, our attempt to grow this material by the Czochralski pulling technique resulted in a crystal with a non-stoichiometric composition Ce2 Co0.8 Si3.2 . This outcome seems in line with an early report on the Ce–Co–Si system [31] that indicated a fairly extended homogeneity range for the phases CeCox Si2−x characterized by x = 0.3–0.5. Here, we present the results of our structural, magnetic, electrical transport and heat capacity measurements performed on the obtained crystal along the principal crystallographic directions. The properties of Ce2 Co0.8 Si3.2 are discussed in relation to those reported before for supposedly stoichiometric Ce2 CoSi3 .
Compound Space group Unit cell dimensions Volume Formula weight Calculated density Absorption coefficient θ range for data collection Ranges in hkl Reflections collected/unique Completeness to θ = 31.90◦ Refinement method Data/restraints/parameters Goodness of fit on F2 Final R indices (I ≥ 2σ (I)) R indices (all data) Extinction coefficient Largest diff. peak and hole
2. Experimental details A single crystal of ‘Ce2 CoSi3 ’ was grown by the Czochralski pulling method in a tetra-arc furnace under an ultra-pure argon atmosphere. The starting components were high-purity elements (Ce-3N, Co-4N, and Si-6N). The obtained crystal was a well-developed rod of about 3 mm in diameter and 40 mm in length. Single-crystal x-ray diffraction data were collected on an Oxford Diffraction four-circle diffractometer equipped with a CCD camera using Mo Kα radiation. Crystal structure refinement was done using the program S HELXL -97 [32]. Details of the single-crystal data collection and the structure refinement are given in table 1. The composition of the phase was checked by energy dispersive x-ray analysis using a Philips 515 scanning electron microscope equipped with an EDAX PV 9800 spectrometer. Magnetic measurements were performed in the temperature range 0.46–400 K and in magnetic fields up to 7 T using superconducting quantum interference device magnetometers (Quantum Design MPMS-5 and MPMS-7), the latter equipped with a 3 He refrigerator. Heat capacity was studied in the temperature interval 0.4–10 K in magnetic fields up to 9 T using a Quantum Design PPMS-9 platform. The temperature variations of the electrical resistivity were studied from 0.4 to 300 K in magnetic fields up to 9 T applied perpendicular to the flowing current, employing a Quantum Design PPMS-9 platform.
Ce2 Co0.8 Si3.2 P6/mmm a = 8.1037(7) Å c = 4.2204(3) Å 3 240.02(3) Å 418.91 g mol−1 5.778 g cm−3 22.11 mm−1 2.90◦ –31.90◦ −11 6 h 6 11 −11 6 k 6 11 −3 6 l 6 6 4102/202 [R(int) = 0.032] 99.5% Full-matrix least squares on F2 202/1/15 1.26 R1 = 0.018, wR2 = 0.032 R1 = 0.025, wR2 = 0.034 0.017(1) −3 0.52 and −1.22e Å
Both crystal structures are ordered variants of the AlB2 -type. The former one, first established from the single-crystal x-ray diffraction data [24], and then confirmed by x-ray measurements performed on powder samples [25, 27, 29], has a unit cell doubled within the basal hexagonal plane with respect to the AlB2 subcell (space group P6/mmm). In turn, the Er2 RhSi3 -type model, derived from the powder x-ray diffraction data [28], is characterized by doubling both a and c lattice parameters (space group P62c or P63 /mmc). The x-ray data collected in this work for the obtained single crystal of ‘Ce2 CoSi3 ’ corroborated the crystal structure model suggested in [24, 25, 27, 29], in which the unit cell is doubled exclusively within the basal hexagonal plane. However, the Rietveld refinements with free occupancy parameters indicated considerable mixing of cobalt and silicon atoms at the crystallographic 2d sites, with 20% of Co atoms being replaced by Si atoms, while the 6m sites were found fully occupied solely by silicon atoms. This finding yielded the actual composition of the investigated crystal to be Ce2 Co0.8 Si3.2 . Remarkably, also the EDX analysis of the crystal composition led to an excess of Si atoms in respect to the ideal 2:1:3 stoichiometry. The refined atomic coordinates and the displacement parameters of all the atoms in the unit cell of Ce2 Co0.8 Si3.2 are given in tables 2 and 3, respectively. As can be inferred from figure 1, Ce atoms build two-dimensional triangular networks separated by planes of Co and Si atoms. They occupy two inequivalent positions: Ce1 atoms are coordinated by twelve Si1 atoms with a Ce1–Si distance of 3.1775(13) Å, while Ce2 atoms have eight Si and four Co/Si nearest neighbors, with distances of 3.1312(7) Å and 3.1464(4) Å, respectively. In turn, Co/Si sites have trigonal planar Si coordination at the Co–Si distances of 2.2969(17) Å, while Si atoms form discrete Si6 rings with the Si–Si distance equal to 2.3802(17) Å. The main interatomic distances are given in table 4.
3. Results and discussion 3.1. Crystal structure As mentioned in section 1, most of the silicides Ce2 TSi3 adopt the AlB2 -type unit cell or its ordered derivatives. In the parent-type structure, Ce atoms occupy the aluminum 1a position, while T and Si atoms jointly share the boron 2d site. The compound Ce2 CoSi3 was reported in the literature to crystallize either with a structure closely related to U2 RuSi3 [33], or with the Er2 RhSi3 -type structure [10, 34]. 2
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Figure 2. Temperature dependences of the inverse molar magnetic susceptibility of Ce2 Co0.8 Si3.2 measured with a magnetic field of 0.1 T applied along and perpendicular to the c axis of the hexagonal unit cell. Solid line represents a fit of the modified Curie–Weiss law to the experimental data above 150 K. Inset displays low-temperature dependences of the magnetic susceptibility. Solid lines represent the power-law fit.
Figure 1. Crystal structure of Ce2 Co0.8 Si3.2 . Table 2. Atomic coordinates and equivalent isotropic thermal 2 displacement parameters (in Å × 103 ) for Ce2 Co0.8 Si3.2 . Ueq is defined as one third of the trace of the orthogonalized Uij tensor.
Atom
Site
x
y
z
U(eq)
Ce1 Ce2 Co/Si Si
1a 3f 2d 6m
0 1/2 2/3 0.1696(1)
0 0 1/3 0.3392(1)
0 0 1/2 1/2
5(1) 6(1) 10(1) 7(1)
Table 4. Interatomic distances in the Ce2 Co0.8 Si3.2 unit cell (in Å).
Ce1
Ce2
Table 3. Anisotropic thermal displacement parameters for the 2 atoms in Ce2 Co0.8 Si3.2 (in Å × 103 ). The anisotropic temperature factor exponent takes the form: −2π 2 [h2 a∗2 U11 + · · · + 2hka∗ b∗ U12 ].
Ce1 Ce2 Co/Si Si
U11
U22
U33
U23
U13
U12
4(1) 6(1) 5(1) 5(1)
4(1) 5(1) 5(1) 5(1)
6(1) 6(1) 20(1) 10(1)
0 0 0 0
0 0 0 0
2(1) 3(1) 2(1) 1(1)
Co/Si Si
3.2. Magnetic properties
k
µ2eff . 8(T − θP )
Si Ce2 Ce1 Si Co/Si Ce1 Ce2 Ce2 Si Ce2 Co/Si Si Ce2 Ce1
3.1813(14) 4.0519(7) 4.2204(3) 3.1353(7) 3.1505(2) 4.0519(7) 4.0519(7) 4.2204(3) 2.2979(18) 3.1505(2) 2.2979(18) 2.3808(18) 3.1353(7) 3.1813(14)
θP = −240 K for B k c. The so-obtained effective magnetic moments µeff are close to the value predicted for free Ce3+ ions within the Russell–Saunders coupling scenario (2.54 µB ). The large negative values of the paramagnetic Curie temperature θP probably signal Kondo interactions with a large characteristic energy scale. Moreover, the k considerable difference between θP⊥ and θP likely arises due to magnetocrystalline anisotropy being naturally inherent to a layered hexagonal structure with distinctly different lattice parameters a and c (cf section 3.1). At low temperatures, both components of the magnetic susceptibility deviate from the modified Curie–Weiss behavior, likely because of gradual depopulation of the crystalline electric field levels with decreasing temperature. For the point symmetry of both Ce sites in the unit cell of Ce2 Co0.8 Si3.2 it is expected that the ground multiplet 2 F5/2 of each ion splits into three doublets. As can be inferred from the inset to figure 2, down to 0.46 K, which was the terminal temperature of our measurements, no features that might hint at any magnetic ordering were
Figure 2 shows the temperature dependences of the reciprocal molar magnetic susceptibility of single-crystalline Ce2 Co0.8 Si3.2 taken with a magnetic field of 0.1 T, applied parallel and perpendicular to the c axis of the hexagonal unit cell. At high temperatures, above about 150 K, both dependences are somewhat curvilinear and can be described by a modified Curie–Weiss law in the form χ = χ0 +
12 6 2 8 4 2 4 2 3 6 1 2 4 2
(1)
Taking into account the expected magnetic contribution due to 3d electrons of Co atoms [30], one may anticipate that the temperature independent term χ0 in the above expression should be close to the Pauli-type magnetic susceptibility χ0 ' 4 × 10−4 emu mol−1 of La2 CoSi3 [25]. With this assumption, equation (1) can be well fitted to the experimental data (see figure 2), and the resulting parameters are µ⊥ eff = k ⊥ 2.5 µB , θP = −130 K for B ⊥ c and µeff = 2.4 µB , 3
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Figure 3. Magnetic field variation of magnetization of Ce2 Co0.8 Si3.2 recorded at 0.46 K with the field applied along two characteristic directions. Solid lines describe power-law dependences.
Figure 4. Temperature variations of the electrical resistivity of Ce2 Co0.8 Si3.2 measured with the current flowing along and perpendicular to the c axis. The solid line emphasizes logarithmic behavior.
found. The paramagnetic character of the ground state in the compound studied is further indicated by the shape of the field variations of the magnetization isotherms taken at the lowest achievable temperature (figure 3) that is typical for Ce-based paramagnets. The magnetization data corroborate the magnetocrystalline anisotropy in Ce2 Co0.8 Si3.2 , with the magnetization component measured along the crystallographic c axis being smaller than that taken within the hexagonal plane. As displayed in figure 3, the magnetization isotherms can be approximated by a power-law function σ ∝ Bλ with λ = 0.7 and λ = 0.8 for the magnetic field applied perpendicular and parallel to the c axis, respectively. Furthermore, the low-temperature magnetic susceptibility can be described below about 10 K by a power-law expression χ ∝ T λ−1 with λ = 0.6 for B ⊥ c and λ = 0.8 for B k c (see the inset to figure 2). Such σ (B) and χ (T) dependences are quite unusual for Fermi liquids but expected for Griffiths phases [5, 6]. Thus, the magnetic characteristics of Ce2 Co0.8 Si3.2 are fully in line with the presence of sizable atomic disorder in the nonmagnetic-atom sublattice, as established from the x-ray diffraction data.
entire temperature range, the change in the magnitude of both ρ ⊥ (T) and ρ k (T) is small, leading to the residual resistivity ratio (RRR = ρ(300 K)/ρ(0.4 K)) being close to 1 for both current directions. This feature most likely results from the crystallographic disorder in the single crystal studied. Figure 5 presents the low-temperature dependences of the electrical resistivity of Ce2 Co0.8 Si3.2 measured in zero field and several external magnetic fields. As marked, at low temperatures the resistivity changes as ρ(T) ∝ T n , with the exponent n equal to 1.3 and 1.0 for ρ ⊥ and ρ k , respectively. The observed NFL behavior is significantly different from the quadratic temperature dependence expected for a Kondo lattice. Instead, it is fully compatible with the Griffiths phase scenario [5, 6], indicated also by the magnetic data (see above) and the heat capacity data (see below) of Ce2 Co0.8 Si3.2 . Somewhat unexpectedly, application of the magnetic field does not result in the Fermi liquid behavior but brings about an appearance of upturns in both components of the resistivity. In zero field, these features were probably masked by a strong low-temperature NFL-decrease of the resistivity. Since the magnetic field reduces the drop, the weak contribution to the resistivity leading to the low-temperature upturn is better seen. With increasing magnetic field strength, the local minima in ρ ⊥ (T) and ρ k (T) shift toward higher temperatures. Interestingly, similar features were recently observed for the single crystal of Ce2 Co0.4 Rh0.4 Si3.2 [35]. The resistivity behavior of both phases closely resembles that reported for U2 CoSi3 [36]. For latter case, it was interpreted in terms of a weak localization effect and strong electron–electron interactions in a system with significant structural disorder. It seems likely that a similar approach is appropriate also for the two Ce-based silicides.
3.3. Electrical resistivity The temperature variations of the electrical resistivity of Ce2 Co0.8 Si3.2 , ρ ⊥ (T) and ρ k (T), measured with the electrical current flowing perpendicular and parallel to the hexagonal c axis, respectively, are shown in figure 4. At room temperature, both components of the resistivity have rather large magnitudes, being ρ ⊥ = 255 µ cm and ρ k = 235 µ cm. With decreasing temperature the ρ ⊥ component increases in a logarithmic manner, most likely due to the Kondo effect, undergoes through a broad maximum near 80 K, and then drops down to 246 µ cm measured at 0.4 K. In turn, ρ k is nearly temperature independent down to about 100 K, and at lower temperatures smoothly decreases, reaching a value of 206 µ cm at 0.4 K. Generally, over the
3.4. Heat capacity Figure 6 presents the low-temperature dependences of the specific heat over temperature ratio of single-crystalline Ce2 Co0.8 Si3.2 , measured in different magnetic fields applied 4
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
Figure 5. Low-temperature dependences of the electrical resistivity of Ce2 Co0.8 Si3.2 measured with the current flowing perpendicular to (upper panel) and along (lower panel) the c axis in several magnetic fields applied in the c direction and within the basal plane, respectively. Solid lines are power-law fits described in the text.
Figure 6. Low-temperature variations of the specific heat of Ce2 Co0.8 Si3.2 measured with several magnetic fields applied along (upper panel) and perpendicular to (lower panel) the hexagonal c axis. The solid lines emphasize a power-law dependence.
feature of unclear origin may be observed at the lowest temperatures. At 0.4 K, the C/T value decreases from −2 measured in zero field down to about 200 mJ mol−1 Ce K −1 −2 150 mJ molCe K found in B = 9 T. Remarkably, in such a strong magnetic field, a Fermi liquid behavior with nearly constant C/T is seen at the lowest temperatures. In contrast, for B k c (see the lower panel of figure 6), the magnetic field effect is much smaller, namely even in a field of 9 T a clear upturn in C/T is still observed, and the C/T ratio −2 is reduced only to about 167 mJ mol−1 Ce K . The different response mimics the magnetocrystalline anisotropy seen in the magnetic data, where the crystallographic c axis was the direction of smaller field-dependent magnetization and smaller temperature-dependent magnetic susceptibility.
within the ab plane and along the c axis of the hexagonal unit cell. In zero magnetic field, no phase transition is seen on C/T(T), which proves that the studied compound remains intrinsically paramagnetic down to 0.4 K, and the measured sample was free of any magnetic impurities (here we recall that contamination by cerium oxide affected the previous heat capacity study on polycrystalline material of Ce2 CoSi3 [25]). The observed increase in the C/T ratio with decreasing temperature resembles the behavior reported for the solid solution Ce2−x Lax CoSi3 with x ≥ 0.25 [25]. Analytically, C/T(T) diverges as a power of the temperature C/T ∝ T λ−1 with the exponent λ = 0.6. The latter value is equal to that obtained for the low-temperature χ (T) variation measured with the magnetic field oriented perpendicular to the hexagonal c axis (see section 3.2). Furthermore, the behavior of the specific heat of Ce2 Co0.8 Si3.2 is consistent with the theoretical prediction for Griffiths phases [5, 6], and entirely in line with the magnetization and resistivity data. Upon applying a magnetic field perpendicular to the c axis (see the upper panel of figure 6), the NFL upturn in C/T(T) becomes systematically suppressed with increasing field. At the dependence measured in a field of 2 T, a tiny
4. Conclusions The cerium silicide Ce2 Co0.8 Si3.2 crystallizes with the AlB2 -related crystal structure, in which the lattice parameter a is doubled with respect to the parent subcell, while the parameter c is equal to that of the AlB2 -type subcell. The physical properties of the compound strongly reflect atomic disorder in its unit cell. Down to 0.4 K, no magnetic 5
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
phase transition is seen in the magnetic susceptibility, electrical resistivity, and heat capacity characteristics, hence proving that Ce2 Co0.8 Si3.2 remains paramagnetic down to the lowest temperatures. Furthermore, below about 10 K, distinct non-Fermi liquid features occur in all the bulk properties examined. With decreasing temperature the magnetic susceptibility and the specific heat over temperature ratio diverge in a power-law manner, whereas the electrical resistivity varies quasi-linearly. Moreover, the magnetization isotherms measured at 0.4 K are proportional to a power of the magnetic field strength. All these findings, and even the particular exponents in the power-law variations, are consistent with the theoretical predictions for Griffiths phases, which form because of crystallographic disorder in the system. For Ce2 Co0.8 Si3.2 , the presence of atomic disorder provides a straightforward explanation of the observed large values of the residual resistivity, small changes in the electrical resistivity with temperature, and the occurrence of some low-temperature minima in the resistivity measured in external magnetic fields. The effects of structural disorder may strongly influence the formation of the ground state, which is most likely governed by f-ligand hybridization, typical for Ce-based intermetallics. In Ce2 Co0.8 Si3.2 the latter interaction seems fairly strong, and brings about the enhanced electronic contribution to the specific heat, the large values of the paramagnetic Curie temperature, and the logarithmic temperature variation of the electrical resistivity. It is worth recalling here that the original aim of the present work was to examine the ground state properties of the stoichiometric phase Ce2 CoSi3 . The surplus amount of Si at the expense of Co in the single crystal grown appeared unintentionally. Curiously, a very similar result was obtained in our recent study of the solid solution between Ce2 CoSi3 and Ce2 RhSi3 , where the crystal Ce2 Co0.4 Rh0.4 Si3.2 was synthesized instead of the intended alloy Ce2 Co0.6 Rh0.4 Si3 [35]. The coincidence in the composition of these crystals may be accidental but it might also hint at somewhat higher thermodynamic stability of the ‘Ce2 CoSi3 ’ phases, in which Co cobalt atoms are replaced by Si atoms, at least at the applied experimental conditions of Czochralski growing process of both materials. It should be emphasized that the observed deviations from the ideal 2:1:3 stoichiometry are entirely consistent with several reports on the Ce–T–Si isothermal sections [31, 37–41], where the extended homogeneity ranges of the cerium silicides crystallizing with the AlB2 -type or related structures are indicated as Ce2 T1−x Si3+x . As regards the physical behavior of such materials, it may critically depend on their actual exact composition. The obvious effect of inherent crystallographic disorder is on the transport properties, but also the magnetic ground state can be fairly sensitive to structural defects, as proved for example for the so-called nonmagnetic-atom-disorder spin-glasses (NMAD SG). Prominent representatives of the latter group of systems are numerous U-based U2 TSi3 silicides with the AlB2 -type unit cells [42–48], and amidst them also the Co-bearing counterpart to the compound studied in the present work [36]. Naturally, small differences in the composition may account
for the diverse physical properties reported earlier for polycrystalline samples of ‘Ce2 CoSi3 ’. Obviously, very careful determination of the actual composition and crystal structure of the Ce2 TSi3 and U2 TSi3 phases is a prerequisite condition for reliable interpretation and understanding of their fairly complex low-temperature physical behaviors.
Acknowledgments The authors are grateful to L Gulay for his assistance in the crystal growth process and J St˛epie´n-Damm, A Gagor, ˛ and W Walerczyk for x-ray measurements. This work was supported by the Ministry of Science and Higher Education within research project No. IP 2011 054471. The authors thank Wrocław Center for Networking and Computing for access to the MATLAB license (grant no. 92).
References [1] Doniach S 1977 Valence Instabilities and Related Narrow Band Phenomena (New York: Plenum) [2] Stewart G R 2001 Rev. Mod. Phys. 73 797 [3] Löhneysen H v, Rosch A, Vojta M and Wölfle P 2007 Rev. Mod. Phys. 79 1015 [4] Miranda E and Dobrosavljevi´c V 2005 Rep. Prog. Phys. 68 2337 [5] Castro Neto A H, Castilla G and Jones B A 1998 Phys. Rev. Lett. 81 3531 [6] Castro Neto A H and Jones B A 2000 Phys. Rev. B 62 14975 [7] Rojas D P, Rodríguez Fernández J, Espeso J I, Gómez Sal J C, da Silva J C, Gandra F G, dos Santos A O and Medina A N 2010 J. Magn. Magn. Mater. 322 3192 [8] Szlawska M and Kaczorowski D 2012 Phys. Rev. B 85 134423 [9] Hwang J S, Lin K J and Tien C 1996 Solid State Commun. 100 169 [10] Chevalier B, Lejay P, Etourneau J and Hagenmuller P 1984 Solid State Commun. 49 753 [11] Das I and Sampathkumaran E V 1994 J. Magn. Magn. Mater. 137 L239 [12] Leciejewicz J, Stüsser N, Szytuła A and Zygmunt A 1995 J. Magn. Magn. Mater. 147 45 [13] Nakano T, Sengupta K, Rayaprol S, Hedo M, Uwatoko Y and Sampathkumaran E V 2007 J. Phys.: Condens. Matter 19 326205 [14] Kase N, Muranaka T and Akimitsu J 2009 J. Magn. Magn. Mater. 321 3380 ´ [15] Szlawska M, Kaczorowski D, Slebarski A, Gulay L and St˛epie´n-Damm J 2009 Phys. Rev. B 79 134435 [16] Saha S R, Sugawara H, Matsuda T D, Aoki Y, Sato H and Sampathkumaran E V 2000 Phys. Rev. B 62 425 [17] Szlawska M and Kaczorowski D 2011 Phys. Rev. B 84 094430 [18] Majumdar S, Sampathkumaran E V, Brando M, Hemberger J and Loidl A 2001 J. Magn. Magn. Mater. 236 99 [19] Majumdar S, Sampathkumaran E V, Berger St, Della Mea M, Michor H, Bauer E, Hemberger J and Loidl A 2002 Solid State Commun. 121 665 ´ [20] Szytuła A, Hofmann M, Penc B, Slaski M, Majumdar S, Sampathkumaran E V and Zygmunt A 1999 J. Magn. Magn. Mater. 202 365 [21] Sampathkumaran E V 2003 Acta Phys. Pol. B 34 999 [22] Li D X, Shiokawa Y, Nimori S, Haga Y, Yamamoto E, ¯ Matsuda T D and Onuki Y 2003 Physica B 329–333 506 [23] Yubuta K, Yamamura T, Li D X and Shiokawa Y 2009 Solid State Commun. 149 238 [24] Gordon R A, Warren C J, Alexander M G, DiSalvo F J and Pöttgen R 1997 J. Alloys Compounds 248 24 6
J. Phys.: Condens. Matter 26 (2014) 016004
M Szlawska and D Kaczorowski
[38] Bodak O I, Kalychak Y M and Gladyshevskii E I 1974 Izv. Akad. Nauk SSSR Neorg. Mater. 10 450 [39] Gribanov A V, Seropegin Y, Tursina A I, Bodak O I, Rogl P and Noël H 2004 J. Alloys Compounds 383 286 [40] Lipatov A, Gribanov A, Grytsiv A, Rogl P, Murashova E, Seropegin Y, Giester G and Kalmykov K 2009 J. Solid State Chem. 182 2497 [41] Lipatov A, Gribanov A, Grytsiv A, Safronov S, Rogl P, Rousnyak J, Seropegin Y and Giester G 2010 J. Solid State Chem. 183 829 [42] Kaczorowski D and Noël H 1993 J. Phys.: Condens. Matter 5 9185 [43] Kaczorowski D and Pöttgen R 1993 J. Alloys Compounds 201 157 [44] Chevalier B, Pöttgen R, Darriet B, Gravereau P and Etourneau J 1996 J. Alloys Compounds 233 150 [45] Yubuta K, Yamamura K and Shiokawa Y 2006 J. Phys.: Condens. Matter 18 6109 [46] Li D X, Shiokawa Y, Homma Y, Uesawa A, Dönni A, ¯ Suzuki T, Haga Y, Yamamoto E, Homma T and Onuki Y 1998 Phys. Rev. B 57 7434 [47] Li D X, Dönni A, Kimura Y, Shiokawa Y, Homma Y, ¯ Haga Y, Yamamoto E, Honma T and Onuki Y 1999 J. Phys.: Condens. Matter 11 8263 [48] Szlawska M, Kaczorowski D and Reehuis M 2010 Phys. Rev. B 81 094423
[25] Majumdar S, Mahesh Kumar M, Mallik R and Sampathkumaran E V 1999 Solid State Commun. 110 509 [26] Majumdar S, Mahesh Kumar M, Mallik R and Sampathkumaran E V 2000 Physica B 281/282 367 [27] Majumdar S and Sampathkumaran E V 2000 Phys. Rev. B 62 8959 [28] Patil S, Iyer K K, Maiti K and Sampathkumaran E V 2008 Phys. Rev. B 77 094443 [29] Majumdar S and Sampathkumaran E V 2001 J. Magn. Magn. Mater. 223 247 [30] Patil S, Pandey S K, Medicherla V R R, Singh R S, Bindu R, Sampathkumaran E V and Maiti K 2010 J. Phys.: Condens. Matter 22 266602 [31] Bodak O I and Gladyshevskii E I 1970 Izv. Akad. Nauk SSSR Neorg. Mater. 6 1186 [32] Sheldrick G M 2008 Acta Crystallogr. A 64 112 [33] Pöttgen R, Gravereau P, Darriet B, Chevalier B, Hickey E and Etourneau J 1994 J. Mater. Chem. 4 463 [34] Gladyshevskii R E, Cenzual K and Parthé E 1992 J. Alloys Compounds 189 221 [35] Szlawska M and Kaczorowski D 2013 J. Phys.: Condens. Matter 25 255601 [36] Szlawska M, Gnida D and Kaczorowski D 2011 Phys. Rev. B 84 134410 [37] Bodak O I, Mis’kiv M G, Tyvanchuk A T, Kharchenko O I and Gladyshevskii E I 1973 Izv. Akad. Nauk SSSR Neorg. Mater. 9 864
7
