Home
Search
Collections
Journals
About
Contact us
My IOPscience
Muon spin relaxation study on itinerant ferromagnet CeCrGe3 and the effect of Ti substitution on magnetism of CeCrGe3
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 016004 (http://iopscience.iop.org/0953-8984/27/1/016004) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 198.91.37.2 This content was downloaded on 21/02/2015 at 05:18
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 016004 (8pp)
doi:10.1088/0953-8984/27/1/016004
Muon spin relaxation study on itinerant ferromagnet CeCrGe3 and the effect of Ti substitution on magnetism of CeCrGe3 Debarchan Das1 , A Bhattacharyya2,3 , V K Anand4 , A D Hillier2 , J W Taylor2 , T Gruner5 , C Geibel5 , D T Adroja2,3 and Z Hossain1 1
Department of Physics, Indian Institute of Technology, Kanpur 208016, India ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot Oxon, OX11 0QX, UK 3 Highly Correlated Matter Research Group, Physics Department, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa 4 Helmholtz-Zentrum Berlin f¨ur Materialien und Energie, Hahn-Meitner Platz 1, D-14109 Berlin, Germany 5 Max-Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany 2
E-mail: [email protected] Received 24 September 2014, revised 3 November 2014 Accepted for publication 19 November 2014 Published 10 December 2014 Abstract
A Muon spin relaxation (µSR) study has been performed on the Kondo lattice heavy fermion itinerant ferromagnet CeCrGe3 . Recent investigations of bulk properties have revealed a long-range ordering of Cr moments at Tc = 70 K in this compound. Our µSR investigation between 1.2 K and 125 K confirm the bulk magnetic order which is marked by a loss in initial asymmetry below 70 K accompanied with a sharp increase in the muon depolarization rate. Field dependent µSR spectra show that the internal field at the muon site is higher than 0.25 T apparently due to the ferromagnetic nature of ordering. The effect of Ti substitution on the magnetism in CeCrGe3 is presented. A systematic study has been made on polycrystalline CeCr1−x Tix Ge3 (0 x 1) using magnetic susceptibility χ (T ), isothermal magnetization M(H ), specific heat C(T ) and electrical resistivity ρ(T ) measurements which clearly reveal that the substitution of Ti for Cr in CeCrGe3 strongly influences the exchange interaction and ferromagnetic ordering of Cr moments. The Cr moment ordering temperature is suppressed gradually with increasing Ti concentration up to x = 0.50 showing Tc = 7 K beyond which Ce moment ordering starts to dominate and a crossover between Cr and Ce moment ordering is observed with a Ce moment ordering Tc = 14 K for x = 1.0. The Kondo lattice behavior is evident from temperature dependence of ρ(T ) in all CeCr1−x Tix Ge3 samples. Keywords: muon spin relaxation, heavy fermion, quantum criticality, magnetic order (Some figures may appear in colour only in the online journal)
small fraction exhibits orders of magnitude enhancement of the conduction electron effective mass at low temperature, known as heavy fermion system and sometimes they even enter in the superconducting state alongside this enhanced conduction electron effective mass, known as heavy fermion superconductors (HFSC). Unlike the conventional s-wave superconductor where superconducting pairing is mediated by phonons, in HFSC superconducting pairing is believed to
1. Introduction
Strongly correlated electron systems have received a lot of attention in the condensed matter physics research community because of the wide range of interesting unusual magnetic and transport properties they exhibit which include heavy fermion behaviour, the Kondo effect, valance fluctuation, magnetic ordering and superconductivity (SC) [1, 2]. Among the vast number of existing intermetallic compounds, only a 0953-8984/15/016004+08$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
be mediated by magnetic interactions [3]. Heavy fermion and HFSC systems have continued to dominate the field of condensed matter research for the past several decades. Since the discovery of heavy fermion superconductivity in CeCu2 Si2 [4], Ce based intermetallic systems have become one of the most attractive research areas. Depending on the hybridization strength of the localized 4f electrons with itinerant conduction electrons, different unusual physical properties have been witnessed in these systems [5–11]. Moreover, intermetallic compounds containing Ce are of particular interest for studying quantum phase transition (QPT) or quantum critical point (QCP) as they can easily be tuned from the magnetic to the nonmagnetic state by doping or by applying external pressure [12–15]. Very recently a new class of rare-earth-based intermetallic system, RCrGe3 (R = rare earth), with hexagonal perovskite structure has been discovered which exhibits magnetic ordering of Cr moments [16]. Among these CeCrGe3 was reported to order ferromagnetically below 66 K [16]. Our investigations of physical properties of CeCrGe3 revealed Kondo lattice behaviour with an enhanced Sommerfeld coefficient γ = 130 mJ mol−1 K−2 reflecting a moderate heavy fermion behaviour in this compound [17]. Furthermore, we identified that it is the itinerant Cr moments which order ferromagnetically at Tc = 70 K. In order to gain further insight into the magnetic ordering in CeCrGe3 , we have performed a muon spin relaxation (µSR) experiment on this compound. The study of QCP in heavy fermion systems and in itinerant ferromagnetic systems is always a matter of interest as it enlightens the fascinating physics at QCP [18–22]. A QCP has been achieved using vanadium doping in LaCrGe3 [23]. This motivated us to extend our work in search of a quantum critical behaviour in CeCrGe3 by suppressing the Cr magnetic order. In our effort to suppress the ordering of itinerant Cr moments we substitute Ti for Cr. CeTiGe3 exhibits ferromagnetic ordering of localized Ce moments with Tc = 14 K [24]. Since the Ti-ions in CeTiGe3 carry no magnetic moment, the Ti substitution for Cr serves the purpose of suppressing the ordering of itinerant Cr moments. Here, in this report, we first address some points on the magnetic ordering in CeCrGe3 on the basis of our µSR study. Along with this we present a comprehensive study of low-temperature properties of CeCr1−x Tix Ge3 (0 x 1) investigated by means of magnetic susceptibility χ (T ), isothermal magnetization M(H ), specific heat C(T ) and electrical resistivity ρ(T ) measurements. The hexagonal perovskite structure (space group P63 /mmc) of the end point compounds CeCrGe3 (x = 0) [16, 17] and CeTiGe3 (x = 1) [24] is preserved for the doped (0 x 1) compounds. Our results manifest that with increasing x the total effective moment decreases systematically along with gradual decrease in the Curie temperature. We have been able to suppress the magnetic ordering of itinerant Cr moments down to 7 K for x = 0.50 above which localized Ce moment ordering starts to dominate and raises the ordering temperature to Tc = 14 K for x = 1.0.
2. Experimental details
Polycrystalline samples of CeCr1−x Tix Ge3 were prepared by the arc-melting technique as described in [17]. High-purity elements (Ce and Ti: 99.9% Alfa-Aesar, Cr and Ge: 99.99% Sigma Aldrich) were used for this purpose. The samples were flipped after each melting and were remelted several times to ensure homogeneity. In order to remove the impurity phases the melted buttons were annealed in an evacuated quartz tube at 900◦ C for one week. The phase purities of the annealed samples were checked by powder x-ray diffraction (XRD) using Cu-Kα radiation. XRD data were analyzed by Rietveld refinement using FullProf software [25]. Compositional homogeneity was checked by performing metallographic examinations using scanning electron microscopy (SEM) and energy dispersive x-ray (EDX). The µSR measurements were carried out on the MUSR spectrometer with the detectors in a longitudinal configuration at the ISIS Muon Facility of the Rutherford Appleton Laboratory, United Kingdom [26]. The powdered sample was mounted on a high purity silver plate using diluted GE varnish and covered with kapton film which was cooled down to 1.2 K in a standard 4 He cryostat with He-exchange gas. Spinpolarized muon pulses were implanted into the sample and positrons from the resultant decay were collected in positions either forward or backward of the initial muon spin direction. The asymmetry is calculated by, Gz (t) =
[NF (t) − αNB (t)] [NF (t) + αNB (t)]
(1)
where NF (t) and NB (t) are the numbers of counts at the detectors in the forward and backward positions and α is a constant determined from calibration measurements made in the paramagnetic state with a small applied transverse magnetic field (20 Oe). Magnetic measurements were carried out using a commercial Vibrating Sample Magnetometer (VSM) attached with the physical property measurement system (PPMS, Quantum Design). The specific heat was measured by the relaxation method in a PPMS. Electrical resistivity measurements were carried out in the temperature range 4.2– 300 K using a standard four probe method in a closed cycle refrigerator (Oxford Instruments). 3. Results and discussion 3.1. Crystallography
Figure 1(a) shows the comparative powder XRD patterns of CeCr1−x Tix Ge3 samples for three representative doping concentrations x = 0, 0.5 and 1. The Rietveld refinement of XRD data confirmed the single phase nature of the samples and BaNiO3 -type hexagonal structure (space group P 63 /mmc). The lattice parameters obtained from the refinements are listed in table 1. A plot of lattice parameters (a and c) and unit cell volume (Vcell ) as a function of doping concentration x is shown in figure 1(b). From figure 1(b) we see that (a) and (c) as well 2
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
(a)
(b)
Figure 2. The time evolution of the muon spin relaxation for various
temperatures in zero field. The line is a least-squares fit to the data as described in the text.
Figure 1(c) shows the schematic views of the BaNiO3 type hexagonal perovskite crystal structure of CeT Ge3 (T = Cr, Ti). In this structure Ce atoms occupy 2d (1/3, 2/3, 3/4) site, T atoms occupy 2a (0, 0, 0) site and Ge atoms occupy 6h (r, 2r, 1/4) site with r ≈ 0.19. This structure consists of one-dimensional chains of face-sharing T -centered T Ge6 octahedra stacked along the c-axis and Ce atoms are situated at the center of anticuboctahedra coordinated by 12 Ge atoms [16]. While this hexagonal perovskite structure is common for chalcogenides and halides, it is considered quite unusual for intermetallic compounds.
(c)
3.2. µSR study on CeCrGe3
Figure 1. (a) The powder x-ray diffraction pattern of
CeCr1−x Tix Ge3 (shown only for x = 0, 0.5, 1) recorded at room temperature. Inset shows the relative shift of the (2 0 1) peak. (b) The variation of lattice parameters and unit cell volume as a function of doping x. (c) Structure of CeT Ge3 (T = Cr, Ti) viewed from different crystallographic directions as shown in the figure.
The time dependence of µSR asymmetry spectra of CeCrGe3 measured at various temperatures between 1.2 K T 125 K in zero field are shown in figure 2. The spectra show exponential type decay in the paramagnetic state as well as the magnetically ordered state. For T < Tc muon spin precession is not observable due to the fact that internal fields exceed the maximum internal field detectable on the µSR spectrometer due to the pulse width of the ISIS muon beam. We used simple Lorentzian decay plus constant background to fit our µSR spectra in 1.2 K T 125 K.
Table 1. Crystallographic data for CeCr1−x Tix Ge3 obtained from the structural Rietveld refinement of powder XRD data.
Structure Space group x
BaNiO3 -type Hexagonal P 63 /mmc a (Å)
c (Å)
Vcell (Å3 )
0 0.15 0.30 0.50 0.60 0.70 1
6.150 6.163 6.185 6.214 6.232 6.240 6.271
5.719 5.721 5.737 5.771 5.799 5.812 5.880
187.32 188.18 190.06 192.98 195.04 195.98 200.25
Gz (t) = A1 e−λt + Abg
(2)
where the initial amplitude of the exponential decay is A1 , λ is the muon depolarization rate and Abg is the background. The temperature dependence of these parameters is shown in figure 3. Below 75 K, as shown in figure 3(a) there is a loss of 2/3 the value of the initial asymmetry A1 from its high-temperature value, indicating the presence of a bulk magnetically ordered state in CeCrGe3 which agrees with the specific heat and magnetic susceptibility data [17]. The
as Vcell increase monotonically with increasing x which shows that there is a lattice expansion on account of negative chemical pressure brought by Ti substitution for Cr. 3
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
Figure 4. The time dependence of µSR asymmetry (µSR) spectra in the presence of the indicated applied longitudinal fileds at temperature T = 10 K.
Figure 3. The temperature T dependence of (a) the initial asymmetry A1 (b) the depolarization rate λ.
temperature dependence of the Lorentzian decay term is shown in figure 3(b). The muon depolarization rate was found to increase below 75 K, indicating a transition between the paramagnetic and ordered states. Furthermore, λ shows a weak anomaly below 8 K. The origin of this 8 K anomaly in λ is not clear. A weak anomaly was observed around 3 K in the heat capacity data of CeCrGe3 [17]. We recorded field dependence asymmetry spectra at 10 K as shown in figure 4. At 0.25 T asymmetry value is found to be 14.57% which is much less than zero field asymmetry value (29.3%) at 125 K. This indicated that internal field at the muon site is much greater than 0.25 T. 3.3. Magnetic properties of CeCr1−x Tix Ge3
To discern any magnetic phase transition occurring in the system we measured the temperature-dependent zero-fieldcooled (ZFC) magnetization of the CeCr1−x Tix Ge3 series in the temperature range of 2–300 K under an applied field of 0.1 T. The temperature dependence of the magnetic susceptibility χ(T ) of CeCr1−x Tix Ge3 is shown in figure 5 in the temperature range 2–150 K. As evident from the figure, the χ (T ) of CeCr1−x Tix Ge3 exhibits a sudden increase below a certain temperature which varies depending upon the doping (x), indicating a transition to a ferromagnetic state. The ordering temperature Tc is considered as the point of inflection of the χ(T ) yielding Tc ranging from 70–2.5 K depending upon the Ti doping. The transition temperatures of different samples have
Figure 5. (a) Zero-field-cooled (ZFC) dc magnetic susceptibility χ of CeCr1−x Tix Ge3 as a function of temperature T . Inset shows the susceptibility for x = 0.5, 0.6, 0.7 in a magnified scale. (b) Inverse susceptibility of the doped samples (x = 0.15–0.70).
been summarized in table 2. In this context it is mentioned that for x > 0.5 the χ (T ) does not show the typical saturation behaviour which, we believe, can be seen at a temperature below our measurement limit 2 K. At high temperatures (above 4
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
Table 2. Ordering temperature Tc and the parameters obtained from
the modified Curie–Weiss fits of the paramagnetic state susceptibility of CeCr1−x Tix Ge3 . Doping (x)
Tc (K)
µeff (µB )
µ(Cr) eff (µB )
θp (K)
0 0.15 0.30 0.50 0.60 0.70
70 62 32 7 3.5 2.5
3.36 2.89 2.88 2.62 2.60 2.48
2.20 1.34 1.44 0.58 0.49 ≈0
67 56 31 − 4 −16 −21
ordering temperature) χ (T ) follows the modified Curie–Weiss behaviour, C χ (T ) = + χo (3) (T − θp ) where C is the Curie constant, θp is the Weiss temperature and χo is temperature-independent susceptibility. The effective paramagnetic moment µeff values calculated from the Curie constants and Weiss temperature θ p are summarized in table 2. Interestingly, the observation of a negative θ p for x 0.50 suggests the presence of antiferromagnetic correlations. Neutron diffraction study is called for to understand the magnetic structure of these compounds. In our previous report [17] we have already confirmed by means of XAS study that Ce in CeCrGe3 possesses a stable 3+ valance state with a theoretical value of µeff = 2.54 µB suggesting Ce contribution to the Curie constant (C) is CCe = 0.81 emu K mol−1 . By adopting an approach similar to what we used previously for CeCrGe3 [17, 27] we have determined the Cr contribution to the Curie constant, CCr , which gives effective moment value coming from Cr moments µ(Cr) eff as listed in table 2. For x = 0.60, Cr moments do not significantly contribute to the effective moment as the total effective moment is approximately the same as that of Ce3+ moments. We propose that for x 0.6 the localized Ce3+ moments start to dominate and order magnetically. It is evident from table 2 and figure 6 that the Ti doping concentration (x) behaves as the tuning parameter for the QCP in CeCr1−x Tix Ge3 system. Despite the fact that the Tc is not fully suppressed due to the ordering of Ce moments, the trend is quite evident from the plot of Tc (x) in figure 6. We tried to fit the dependence of Tc on x using Tc ∼ | xc − x |q with q as the fitting parameter. The Hertz–Millis–Moriya (HMM) model of quantum criticality [15, 28] predicts that for an FM QCP, the critical exponent q is 3/4 and 1 in three dimension and two dimension, respectively. We got the best fit to our data for q = 1.2 (figure 6) which is close to 1 suggesting a possible 2D behaviour of magnetic fluctuation. This needs to be verified using a neutron scattering experiment. Twodimensional feature of magnetic fluctuations may sometimes arise due to exchange anisotropies [15, 29, 30]. Figure 7 represents the magnetic isotherms M(H ) of CeCr1−x Tix Ge3 (for different x) measured at 2 K under applied field up to 5 T. For x > 0.5, M(H ) at 2 K does not increase rapidly to a saturated value which is characteristic of ferromagnetic ordering. Rather, it increases slowly and for fields up to 5 T it does not show any sign of saturation.
Figure 6. Dependence of Tc on the doping concentration x.
Figure 7. Isothermal magnetization M as a function of field H at 2 K for different doping concentration x.
This feature is seen in some ferromagnetic/canted magnetic state. It is mentioned in this context that we did not observe any saturation in χ (T ) down to 2 K for these concentrations. This suggests that the moments are not co-linearly aligned at 2 K. So, a M(H ) study at lower temperatures (∼1 K) would be worthwhile to have a conclusive idea about the ordering. In addition, neutron diffraction study will be important to get direct information on the magnetic structure. 3.4. Specific heat of CeCr1−x Tix Ge3
In order to confirm the magnetic transition near the critical regime we have performed the specific heat measurements in zero field and in different applied fields on CeCr1−x Tix Ge3 (for x = 0.5 and x = 0.6) samples. Figure 8(a) shows the specific heat C(T ) between 1.8 and 10 K. For x = 0.5, in the absence of any applied field we have observed an anomaly at 6.9 K which is close to the magnetic transition temperature (Tc = 7 K) as determined from the magnetization data (table 2). It is evident from the inset of figure 8(a) that this observed transition is easily smeared by a moderate applied field suggesting that 5
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
Table 3. A comparison of Sommerfeld coefficient γ values for different doping concentrations for CeCr1−x Tix Ge3 .
Doping (x)
γ (mJ mol−1 K−2 )
Reference
0.0 0.50 0.60 1.0
130 177 192 75
[14] This work This work [31]
that of CeCr1−x Tix Ge3 (for x = 0.5 and x = 0.6). The 4f entropy S4f which was determined by integrating the C4f /T versus T plot, is presented in figure 8(b). Furthermore, S4f nearly saturates close to R ln 2 = 5.76 J mol−1 K−1 suggesting a possible doublet ground state. However, even if we claim the transition around 3 K is originated due to the ordering of Ce moments, the 4f entropy does not recover much (only ∼14%) of R ln 2. A similar scenario has been found in the case of CeRhSi3 and CeIrSi3 where a reduced magnetic entropy at TN was found which was attributed to the Kondo effect [7]. 3.5. Electrical resistivity
The electrical resistivity ρ(T ) of CeCr1−x Tix Ge3 measured in the temperature range 4.2–300 K is normalized as ρ(T )/ρ(300) and presented in figure 9(a). Figures 9(b)–(f ) show the ρ(T ) of the individual doped samples over a magnified temperature scale (4.2–150 K). The resistivity profile is typical for Ce based heavy fermion compounds and reflects the formation of strongly correlated bands at low temperature. A sizable Kondo effect is evident from the electrical resistivity profile of CeCr1−x Tix Ge3 which exhibits Kondo-like behaviour i.e. broad maxima along with a logarithmic increase at high temperature (− ln T behaviour) and a sharp decrease in the low-temperature side of the peak. The logarithmic dependence at the high-temperature side is expected for Kondo scattering whereas the sharp decline at the low-temperature side reflects the coherence characteristic of the Kondo lattice [6–8, 32]. A relatively high value of resistivity for x = 0.15 can be attributed to the presence of micro cracks in the sample. In order to evaluate the magnetic contribution to the electrical resistivity ρm , we have subtracted the electrical resistivity of LaCrGe3 [17] (with the assumption that the lattice as well as Cr-magnetic contributions are the same in both the compounds) from that of CeCr1−x Tix Ge3 . As seen from figure 9(g) a sharp increase in ρm below 90 K is observed which seems to be an artificial effect of the subtraction process considering the fact that LaCrGe3 orders at Tc = 86 K. Despite the inaccuracy in the estimate of ρm below 90 K, the ρm data above 90 K are reliably estimated and clearly reflect the Kondo feature. In the high-temperature side ρm data are fitted with the expression (4) ρm = ρo − CK ln T
Figure 8. (a) Specific heat C of CeCr1−x Tix Ge3 (for x = 0.5 and
x = 0.6) as a function of temperature T . Inset: shows the C(T ) of CeCr0.5 Ti0.5 Ge3 under applied fields of 0 T, 0.2 T and 2 T. (b) Magnetic entropy S4f as a function of temperature. Inset: represents C/T versus T 2 plot with linear fitting.
this anomaly is associated with the magnetic transition in the system. In addition, an anomaly is observed near 3 K whose origin is not clear. The application of a magnetic field tends to smoothen this 3 K anomaly which suggests the anomaly is connected to a magnetic phase transition, possibly with Ce moments.For the parent compound CeCrGe3 too we have seen a clear anomaly at the same temperature (∼3 K) [17]. On the other hand, for x = 0.6 only one anomaly is observed at ∼3 K which is close to the Curie temperature (Tc = 3.5 K) determined from the magnetization measurement. It should be noted that the temperature of this anomaly is almost identical with that of the above-mentioned 3 K anomaly for x = 0.5. Linear fitting to C/T versus T 2 in the low temperature regime (Inset of figure 8(b)) gives us an idea about the possible values of Sommerfeld coefficient γ . We have obtained γ = 177 mJ mol−1 K−2 and 192 mJ mol−1 K−2 for x = 0.5 and 0.6 respectively. As listed in table 3 the γ values increase with increasing Ti substitution at the magnetic–nonmagnetic boundary. In order to evaluate the 4f contribution to the specific heat C4f , we have subtracted the heat capacity of LaCrGe3 from
where ρo is the sum of the residual resistivity and spin-disorder resistivity and CK is the Kondo coefficient. The − ln T dependence in the high-temperature (100–300 K) part reflects the Kondo effect from the excited multiplets of Ce3+ . 6
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
In addition to the µSR investigations, we have presented a detailed investigation of polycrystalline samples of CeCr1−x Tix Ge3 . The ordering temperature and the effective paramagnetic moment (µeff ) decrease systematically with increasing Ti doping concentration x. Remarkably, the result of the magnetization study on the doped samples suggests that the ordering of the itinerant Cr moments is suppressed for x = 0.6 and the ordering of the localized Ce moments starts to evolve for x 0.6. The intrinsic nature of magnetic transitions is confirmed by the specific heat measurements near the critical concentration (x = 0.5 and x = 0.6). A high value of the Sommerfeld coefficient is seen for x = 0.5 and 0.6 near the critical concentration as expected for Ce compounds situated near the magnetic–nonmagnetic boundary. In summary, CeCr1−x Tix Ge3 appears to be a rare example of a Ce based heavy fermion system where the ordering of itinerant Cr moments, having a strong coupling with the localized Ce moments, has been suppressed. A comparison of lattice parameters of CeCr1−x Tix Ge3 reveals that there is an expansion of unit cell volume across the series from CeCrGe3 to CeTiGe3 . Since both CeCrGe3 and CeTiGe3 form in the same crystal structure one would expect the Ce moment to order in CeCrGe3 as it does in CeTiGe3 , irrespective of the presence of Cr moment. However, despite the trivalent nature of cerium ions (Ce3+ ) in CeCrGe3 [17] no clear evidence of Ce moment long-range ordering is observed. We have carried out an inelastic neutron scattering study on CeCrGe3 . The neutron data did not reveal any clear sign of CEF excitations, which suggests that the Ce 4f-electrons are strongly hybridized with the conduction electrons. The absence of long-range ordering of Ce moments in CeCrGe3 can naively be connected to the lattice pressure brought by unit cell volume reduction with Cr. The decrease in lattice pressure with increasing Ti substitution for Cr might be linked with Ce-moment ordering for x > 0.6 in CeCr1−x Tix Ge3 . Acknowledgment
Discussion with Professor A M Strydom is gratefully acknowledged. This work is partially supported by the Council of Scientific and Industrial Research (CSIR), New Delhi (Grant No. 80(0080)/12/ EMR-II). A D Hillier and D T Adroja acknowledge financial assistance from CMPCSTFC grant number CMPC-09108. A Bhattacharyya would like to acknowledge FRC of UJ, NRF of South Africa and ISIS-STFC for funding support.
Figure 9. (a) Electrical resistivity ρ as a function of temperature T for CeCr1−x Tix Ge3 normalised as ρ(T )/ρ(300) in the temperature range 4.2 K to 300 K. (b)–(f ) ρ(T ) for 4.2 T 150 K. (g) Magnetic contribution to the electrical resistivity plotted on a semilogarithmic scale. Solid lines are fits to the equation ρm = ρo − CK ln T .
References
4. Conclusion
[1] [2] [3] [4]
Stewart G R 1984 Rev. Mod. Phys. 56 755 Steglich F 2005 J. Phys. Soc. Japan 74 167–77 Stockert O et al 2011 Nat. Phys. 7 119–24 Steglich F, Aarts J, Bredl C D, Lieke W, Meschede D, Franz W and Sch¨afer H 1979 Phys. Rev. Lett. 43 1892 [5] Pecharsky V K, Hyun O-B and Gschneidner K A Jr 1993 Phys. Rev. B 47 11839 [6] Yamamoto H, Ishikawa M, Hasegawa K and Sakurai J 1995 Phys. Rev. B 52 10136 [7] Muro Y, Eom D, Takeda N and Ishikawa M 1998 J. Phys. Soc. Japan 67 3601
The results of µSR study on the Kondo lattice heavy fermion itinerant ferromagnet CeCrGe3 have been presented which reveal bulk magnetic order below the transition temperature (Tc = 70 K) in good agreement with our previous report [17]. Muon spin precession is not observed as the internal field exceeds the maximum detectable internal field limit of the µSR spectrometer. Our µSR result corroborates that the internal field at muon site is much higher than 0.25 T. 7
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
[8] Hossain Z, Ohmoto H, Umeo K, Iga F, Suzuki T, Takabatake T, Takamoto N and Kindo K 1999 Phys. Rev. B 60 10383 [9] Petrovic C, Pagliuso P G, Hundley M F, Movshovich R, Sarrao J L, Thompson J D, Fisk Z and Monthoux P 2001 J. Phys.: Condens. Matter 13 L337 [10] Prasad A, Anand V K, Paramanik U B, Hossain Z, Sarkar R, Oeschler N, Baenitz M and Geibel C 2012 Phys. Rev. B 86 014414 [11] Paramanik U B, Anupam U B, Burkhardt U, Prasad R, Geibel C and Hossain Z 2013 J. Alloys Compounds 580 435 [12] Eom D, Ishikawa M, Kitagawa J and Takeda N 1998 J. Phys. Soc. Japan 67 2495 [13] Alzamora M, Fontes M B, Larrea J, Borges H A, Baggio-Saitovitch E M and Medeiros S N 2007 Phys. Rev. B 76 125106 [14] Honda F, Bonalde I, Shimizu K, Yoshiuchi S, Hirose Y, ¯ Nakamura T, Settai R and Onuki Y 2010 Phys. Rev. B 81 140507 [15] Kittler W, Fritsch V, Weber F, Fischer G, Lamago D, Andr´e G and L¨ohneysen H v 2013 Phys. Rev. B 88 165123 [16] Bie H, Zelinska O Y, Tkachuk A V and Mar A 2007 Chem. Mater 19 4613 [17] Das D, Gruner T, Pfau H, Paramanik U B, Burkhardt U, Geibel C and Hossain Z 2014 J. Phys.: Condens. Matter 26 106001 [18] Custers J, Gegenwart P, Wilhelm H, Neumaier K, Tokiwa Y, Trovarelli O, Geibel C, Steglich F, P´epin C and Coleman P 2003 Nature 424 524
[19] Coleman P and P´epin C 2002 Physica B 312–313 383 [20] Saxena S S et al 2000 Nature 406 587 [21] Huy N T, Gasparini A, de Nijs D E, Huang Y, Klaasse J C P, Gortenmulder T, de Visser A, Hamann A, G¨orlach T and L¨ohneysen H v 2007 Phys. Rev. Lett. 99 067006 [22] Gegenwart P, Si Q and Steglich F 2008 Nat. Phys. 4 186 [23] Lin X, Taufour V, Bud’ko S L and Canfield P C 2013 Phys. Rev. B 88 094405 [24] Manfrinetti P, Dhar S K, Kulkarni R and Morozkin A V 2005 Solid State Commun. 135 444 [25] Rodr´ıguez-Carvajal J 1993 Physica B 192 55 Program Fullprof 1996 LLB-JRC, Laboratoire L´eon Brillouin (France: CEA-Saclay) [26] King P J C, de Renzi R, Cottrell S P, Hillier A D and Cox S F J 2013 Phys. Scr. 88 068502 [27] Jackson D D, McCall S K, Karki A B and Young D P 2007 Phys. Rev. B 76 064408 [28] L¨ohneysen H v, Rosch A, Vojta M and W¨olfle P 2007 Rev. Mod. Phys. 79 1015 [29] Rosch A, Schr¨oder A, Stockert O and L¨ohneysen H v 1997 Phys. Rev. Lett. 79 159 [30] Stockert O, L¨ohneysen H v, Rosch A, Pyka N and Loewenhaupt M 1998 Phys. Rev. Lett. 80 5627 [31] Inamdar M, Thamizhavel A and Dhar S K 2014 J. Phys.: Condens. Matter 26 326003 [32] Takase A, Kojima K, Komatsubara T and Kasuya T 1980 Solid State Commun. 36 461
8
Search
Collections
Journals
About
Contact us
My IOPscience
Muon spin relaxation study on itinerant ferromagnet CeCrGe3 and the effect of Ti substitution on magnetism of CeCrGe3
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 016004 (http://iopscience.iop.org/0953-8984/27/1/016004) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 198.91.37.2 This content was downloaded on 21/02/2015 at 05:18
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 016004 (8pp)
doi:10.1088/0953-8984/27/1/016004
Muon spin relaxation study on itinerant ferromagnet CeCrGe3 and the effect of Ti substitution on magnetism of CeCrGe3 Debarchan Das1 , A Bhattacharyya2,3 , V K Anand4 , A D Hillier2 , J W Taylor2 , T Gruner5 , C Geibel5 , D T Adroja2,3 and Z Hossain1 1
Department of Physics, Indian Institute of Technology, Kanpur 208016, India ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot Oxon, OX11 0QX, UK 3 Highly Correlated Matter Research Group, Physics Department, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa 4 Helmholtz-Zentrum Berlin f¨ur Materialien und Energie, Hahn-Meitner Platz 1, D-14109 Berlin, Germany 5 Max-Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany 2
E-mail: [email protected] Received 24 September 2014, revised 3 November 2014 Accepted for publication 19 November 2014 Published 10 December 2014 Abstract
A Muon spin relaxation (µSR) study has been performed on the Kondo lattice heavy fermion itinerant ferromagnet CeCrGe3 . Recent investigations of bulk properties have revealed a long-range ordering of Cr moments at Tc = 70 K in this compound. Our µSR investigation between 1.2 K and 125 K confirm the bulk magnetic order which is marked by a loss in initial asymmetry below 70 K accompanied with a sharp increase in the muon depolarization rate. Field dependent µSR spectra show that the internal field at the muon site is higher than 0.25 T apparently due to the ferromagnetic nature of ordering. The effect of Ti substitution on the magnetism in CeCrGe3 is presented. A systematic study has been made on polycrystalline CeCr1−x Tix Ge3 (0 x 1) using magnetic susceptibility χ (T ), isothermal magnetization M(H ), specific heat C(T ) and electrical resistivity ρ(T ) measurements which clearly reveal that the substitution of Ti for Cr in CeCrGe3 strongly influences the exchange interaction and ferromagnetic ordering of Cr moments. The Cr moment ordering temperature is suppressed gradually with increasing Ti concentration up to x = 0.50 showing Tc = 7 K beyond which Ce moment ordering starts to dominate and a crossover between Cr and Ce moment ordering is observed with a Ce moment ordering Tc = 14 K for x = 1.0. The Kondo lattice behavior is evident from temperature dependence of ρ(T ) in all CeCr1−x Tix Ge3 samples. Keywords: muon spin relaxation, heavy fermion, quantum criticality, magnetic order (Some figures may appear in colour only in the online journal)
small fraction exhibits orders of magnitude enhancement of the conduction electron effective mass at low temperature, known as heavy fermion system and sometimes they even enter in the superconducting state alongside this enhanced conduction electron effective mass, known as heavy fermion superconductors (HFSC). Unlike the conventional s-wave superconductor where superconducting pairing is mediated by phonons, in HFSC superconducting pairing is believed to
1. Introduction
Strongly correlated electron systems have received a lot of attention in the condensed matter physics research community because of the wide range of interesting unusual magnetic and transport properties they exhibit which include heavy fermion behaviour, the Kondo effect, valance fluctuation, magnetic ordering and superconductivity (SC) [1, 2]. Among the vast number of existing intermetallic compounds, only a 0953-8984/15/016004+08$33.00
1
© 2015 IOP Publishing Ltd Printed in the UK
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
be mediated by magnetic interactions [3]. Heavy fermion and HFSC systems have continued to dominate the field of condensed matter research for the past several decades. Since the discovery of heavy fermion superconductivity in CeCu2 Si2 [4], Ce based intermetallic systems have become one of the most attractive research areas. Depending on the hybridization strength of the localized 4f electrons with itinerant conduction electrons, different unusual physical properties have been witnessed in these systems [5–11]. Moreover, intermetallic compounds containing Ce are of particular interest for studying quantum phase transition (QPT) or quantum critical point (QCP) as they can easily be tuned from the magnetic to the nonmagnetic state by doping or by applying external pressure [12–15]. Very recently a new class of rare-earth-based intermetallic system, RCrGe3 (R = rare earth), with hexagonal perovskite structure has been discovered which exhibits magnetic ordering of Cr moments [16]. Among these CeCrGe3 was reported to order ferromagnetically below 66 K [16]. Our investigations of physical properties of CeCrGe3 revealed Kondo lattice behaviour with an enhanced Sommerfeld coefficient γ = 130 mJ mol−1 K−2 reflecting a moderate heavy fermion behaviour in this compound [17]. Furthermore, we identified that it is the itinerant Cr moments which order ferromagnetically at Tc = 70 K. In order to gain further insight into the magnetic ordering in CeCrGe3 , we have performed a muon spin relaxation (µSR) experiment on this compound. The study of QCP in heavy fermion systems and in itinerant ferromagnetic systems is always a matter of interest as it enlightens the fascinating physics at QCP [18–22]. A QCP has been achieved using vanadium doping in LaCrGe3 [23]. This motivated us to extend our work in search of a quantum critical behaviour in CeCrGe3 by suppressing the Cr magnetic order. In our effort to suppress the ordering of itinerant Cr moments we substitute Ti for Cr. CeTiGe3 exhibits ferromagnetic ordering of localized Ce moments with Tc = 14 K [24]. Since the Ti-ions in CeTiGe3 carry no magnetic moment, the Ti substitution for Cr serves the purpose of suppressing the ordering of itinerant Cr moments. Here, in this report, we first address some points on the magnetic ordering in CeCrGe3 on the basis of our µSR study. Along with this we present a comprehensive study of low-temperature properties of CeCr1−x Tix Ge3 (0 x 1) investigated by means of magnetic susceptibility χ (T ), isothermal magnetization M(H ), specific heat C(T ) and electrical resistivity ρ(T ) measurements. The hexagonal perovskite structure (space group P63 /mmc) of the end point compounds CeCrGe3 (x = 0) [16, 17] and CeTiGe3 (x = 1) [24] is preserved for the doped (0 x 1) compounds. Our results manifest that with increasing x the total effective moment decreases systematically along with gradual decrease in the Curie temperature. We have been able to suppress the magnetic ordering of itinerant Cr moments down to 7 K for x = 0.50 above which localized Ce moment ordering starts to dominate and raises the ordering temperature to Tc = 14 K for x = 1.0.
2. Experimental details
Polycrystalline samples of CeCr1−x Tix Ge3 were prepared by the arc-melting technique as described in [17]. High-purity elements (Ce and Ti: 99.9% Alfa-Aesar, Cr and Ge: 99.99% Sigma Aldrich) were used for this purpose. The samples were flipped after each melting and were remelted several times to ensure homogeneity. In order to remove the impurity phases the melted buttons were annealed in an evacuated quartz tube at 900◦ C for one week. The phase purities of the annealed samples were checked by powder x-ray diffraction (XRD) using Cu-Kα radiation. XRD data were analyzed by Rietveld refinement using FullProf software [25]. Compositional homogeneity was checked by performing metallographic examinations using scanning electron microscopy (SEM) and energy dispersive x-ray (EDX). The µSR measurements were carried out on the MUSR spectrometer with the detectors in a longitudinal configuration at the ISIS Muon Facility of the Rutherford Appleton Laboratory, United Kingdom [26]. The powdered sample was mounted on a high purity silver plate using diluted GE varnish and covered with kapton film which was cooled down to 1.2 K in a standard 4 He cryostat with He-exchange gas. Spinpolarized muon pulses were implanted into the sample and positrons from the resultant decay were collected in positions either forward or backward of the initial muon spin direction. The asymmetry is calculated by, Gz (t) =
[NF (t) − αNB (t)] [NF (t) + αNB (t)]
(1)
where NF (t) and NB (t) are the numbers of counts at the detectors in the forward and backward positions and α is a constant determined from calibration measurements made in the paramagnetic state with a small applied transverse magnetic field (20 Oe). Magnetic measurements were carried out using a commercial Vibrating Sample Magnetometer (VSM) attached with the physical property measurement system (PPMS, Quantum Design). The specific heat was measured by the relaxation method in a PPMS. Electrical resistivity measurements were carried out in the temperature range 4.2– 300 K using a standard four probe method in a closed cycle refrigerator (Oxford Instruments). 3. Results and discussion 3.1. Crystallography
Figure 1(a) shows the comparative powder XRD patterns of CeCr1−x Tix Ge3 samples for three representative doping concentrations x = 0, 0.5 and 1. The Rietveld refinement of XRD data confirmed the single phase nature of the samples and BaNiO3 -type hexagonal structure (space group P 63 /mmc). The lattice parameters obtained from the refinements are listed in table 1. A plot of lattice parameters (a and c) and unit cell volume (Vcell ) as a function of doping concentration x is shown in figure 1(b). From figure 1(b) we see that (a) and (c) as well 2
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
(a)
(b)
Figure 2. The time evolution of the muon spin relaxation for various
temperatures in zero field. The line is a least-squares fit to the data as described in the text.
Figure 1(c) shows the schematic views of the BaNiO3 type hexagonal perovskite crystal structure of CeT Ge3 (T = Cr, Ti). In this structure Ce atoms occupy 2d (1/3, 2/3, 3/4) site, T atoms occupy 2a (0, 0, 0) site and Ge atoms occupy 6h (r, 2r, 1/4) site with r ≈ 0.19. This structure consists of one-dimensional chains of face-sharing T -centered T Ge6 octahedra stacked along the c-axis and Ce atoms are situated at the center of anticuboctahedra coordinated by 12 Ge atoms [16]. While this hexagonal perovskite structure is common for chalcogenides and halides, it is considered quite unusual for intermetallic compounds.
(c)
3.2. µSR study on CeCrGe3
Figure 1. (a) The powder x-ray diffraction pattern of
CeCr1−x Tix Ge3 (shown only for x = 0, 0.5, 1) recorded at room temperature. Inset shows the relative shift of the (2 0 1) peak. (b) The variation of lattice parameters and unit cell volume as a function of doping x. (c) Structure of CeT Ge3 (T = Cr, Ti) viewed from different crystallographic directions as shown in the figure.
The time dependence of µSR asymmetry spectra of CeCrGe3 measured at various temperatures between 1.2 K T 125 K in zero field are shown in figure 2. The spectra show exponential type decay in the paramagnetic state as well as the magnetically ordered state. For T < Tc muon spin precession is not observable due to the fact that internal fields exceed the maximum internal field detectable on the µSR spectrometer due to the pulse width of the ISIS muon beam. We used simple Lorentzian decay plus constant background to fit our µSR spectra in 1.2 K T 125 K.
Table 1. Crystallographic data for CeCr1−x Tix Ge3 obtained from the structural Rietveld refinement of powder XRD data.
Structure Space group x
BaNiO3 -type Hexagonal P 63 /mmc a (Å)
c (Å)
Vcell (Å3 )
0 0.15 0.30 0.50 0.60 0.70 1
6.150 6.163 6.185 6.214 6.232 6.240 6.271
5.719 5.721 5.737 5.771 5.799 5.812 5.880
187.32 188.18 190.06 192.98 195.04 195.98 200.25
Gz (t) = A1 e−λt + Abg
(2)
where the initial amplitude of the exponential decay is A1 , λ is the muon depolarization rate and Abg is the background. The temperature dependence of these parameters is shown in figure 3. Below 75 K, as shown in figure 3(a) there is a loss of 2/3 the value of the initial asymmetry A1 from its high-temperature value, indicating the presence of a bulk magnetically ordered state in CeCrGe3 which agrees with the specific heat and magnetic susceptibility data [17]. The
as Vcell increase monotonically with increasing x which shows that there is a lattice expansion on account of negative chemical pressure brought by Ti substitution for Cr. 3
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
Figure 4. The time dependence of µSR asymmetry (µSR) spectra in the presence of the indicated applied longitudinal fileds at temperature T = 10 K.
Figure 3. The temperature T dependence of (a) the initial asymmetry A1 (b) the depolarization rate λ.
temperature dependence of the Lorentzian decay term is shown in figure 3(b). The muon depolarization rate was found to increase below 75 K, indicating a transition between the paramagnetic and ordered states. Furthermore, λ shows a weak anomaly below 8 K. The origin of this 8 K anomaly in λ is not clear. A weak anomaly was observed around 3 K in the heat capacity data of CeCrGe3 [17]. We recorded field dependence asymmetry spectra at 10 K as shown in figure 4. At 0.25 T asymmetry value is found to be 14.57% which is much less than zero field asymmetry value (29.3%) at 125 K. This indicated that internal field at the muon site is much greater than 0.25 T. 3.3. Magnetic properties of CeCr1−x Tix Ge3
To discern any magnetic phase transition occurring in the system we measured the temperature-dependent zero-fieldcooled (ZFC) magnetization of the CeCr1−x Tix Ge3 series in the temperature range of 2–300 K under an applied field of 0.1 T. The temperature dependence of the magnetic susceptibility χ(T ) of CeCr1−x Tix Ge3 is shown in figure 5 in the temperature range 2–150 K. As evident from the figure, the χ (T ) of CeCr1−x Tix Ge3 exhibits a sudden increase below a certain temperature which varies depending upon the doping (x), indicating a transition to a ferromagnetic state. The ordering temperature Tc is considered as the point of inflection of the χ(T ) yielding Tc ranging from 70–2.5 K depending upon the Ti doping. The transition temperatures of different samples have
Figure 5. (a) Zero-field-cooled (ZFC) dc magnetic susceptibility χ of CeCr1−x Tix Ge3 as a function of temperature T . Inset shows the susceptibility for x = 0.5, 0.6, 0.7 in a magnified scale. (b) Inverse susceptibility of the doped samples (x = 0.15–0.70).
been summarized in table 2. In this context it is mentioned that for x > 0.5 the χ (T ) does not show the typical saturation behaviour which, we believe, can be seen at a temperature below our measurement limit 2 K. At high temperatures (above 4
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
Table 2. Ordering temperature Tc and the parameters obtained from
the modified Curie–Weiss fits of the paramagnetic state susceptibility of CeCr1−x Tix Ge3 . Doping (x)
Tc (K)
µeff (µB )
µ(Cr) eff (µB )
θp (K)
0 0.15 0.30 0.50 0.60 0.70
70 62 32 7 3.5 2.5
3.36 2.89 2.88 2.62 2.60 2.48
2.20 1.34 1.44 0.58 0.49 ≈0
67 56 31 − 4 −16 −21
ordering temperature) χ (T ) follows the modified Curie–Weiss behaviour, C χ (T ) = + χo (3) (T − θp ) where C is the Curie constant, θp is the Weiss temperature and χo is temperature-independent susceptibility. The effective paramagnetic moment µeff values calculated from the Curie constants and Weiss temperature θ p are summarized in table 2. Interestingly, the observation of a negative θ p for x 0.50 suggests the presence of antiferromagnetic correlations. Neutron diffraction study is called for to understand the magnetic structure of these compounds. In our previous report [17] we have already confirmed by means of XAS study that Ce in CeCrGe3 possesses a stable 3+ valance state with a theoretical value of µeff = 2.54 µB suggesting Ce contribution to the Curie constant (C) is CCe = 0.81 emu K mol−1 . By adopting an approach similar to what we used previously for CeCrGe3 [17, 27] we have determined the Cr contribution to the Curie constant, CCr , which gives effective moment value coming from Cr moments µ(Cr) eff as listed in table 2. For x = 0.60, Cr moments do not significantly contribute to the effective moment as the total effective moment is approximately the same as that of Ce3+ moments. We propose that for x 0.6 the localized Ce3+ moments start to dominate and order magnetically. It is evident from table 2 and figure 6 that the Ti doping concentration (x) behaves as the tuning parameter for the QCP in CeCr1−x Tix Ge3 system. Despite the fact that the Tc is not fully suppressed due to the ordering of Ce moments, the trend is quite evident from the plot of Tc (x) in figure 6. We tried to fit the dependence of Tc on x using Tc ∼ | xc − x |q with q as the fitting parameter. The Hertz–Millis–Moriya (HMM) model of quantum criticality [15, 28] predicts that for an FM QCP, the critical exponent q is 3/4 and 1 in three dimension and two dimension, respectively. We got the best fit to our data for q = 1.2 (figure 6) which is close to 1 suggesting a possible 2D behaviour of magnetic fluctuation. This needs to be verified using a neutron scattering experiment. Twodimensional feature of magnetic fluctuations may sometimes arise due to exchange anisotropies [15, 29, 30]. Figure 7 represents the magnetic isotherms M(H ) of CeCr1−x Tix Ge3 (for different x) measured at 2 K under applied field up to 5 T. For x > 0.5, M(H ) at 2 K does not increase rapidly to a saturated value which is characteristic of ferromagnetic ordering. Rather, it increases slowly and for fields up to 5 T it does not show any sign of saturation.
Figure 6. Dependence of Tc on the doping concentration x.
Figure 7. Isothermal magnetization M as a function of field H at 2 K for different doping concentration x.
This feature is seen in some ferromagnetic/canted magnetic state. It is mentioned in this context that we did not observe any saturation in χ (T ) down to 2 K for these concentrations. This suggests that the moments are not co-linearly aligned at 2 K. So, a M(H ) study at lower temperatures (∼1 K) would be worthwhile to have a conclusive idea about the ordering. In addition, neutron diffraction study will be important to get direct information on the magnetic structure. 3.4. Specific heat of CeCr1−x Tix Ge3
In order to confirm the magnetic transition near the critical regime we have performed the specific heat measurements in zero field and in different applied fields on CeCr1−x Tix Ge3 (for x = 0.5 and x = 0.6) samples. Figure 8(a) shows the specific heat C(T ) between 1.8 and 10 K. For x = 0.5, in the absence of any applied field we have observed an anomaly at 6.9 K which is close to the magnetic transition temperature (Tc = 7 K) as determined from the magnetization data (table 2). It is evident from the inset of figure 8(a) that this observed transition is easily smeared by a moderate applied field suggesting that 5
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
Table 3. A comparison of Sommerfeld coefficient γ values for different doping concentrations for CeCr1−x Tix Ge3 .
Doping (x)
γ (mJ mol−1 K−2 )
Reference
0.0 0.50 0.60 1.0
130 177 192 75
[14] This work This work [31]
that of CeCr1−x Tix Ge3 (for x = 0.5 and x = 0.6). The 4f entropy S4f which was determined by integrating the C4f /T versus T plot, is presented in figure 8(b). Furthermore, S4f nearly saturates close to R ln 2 = 5.76 J mol−1 K−1 suggesting a possible doublet ground state. However, even if we claim the transition around 3 K is originated due to the ordering of Ce moments, the 4f entropy does not recover much (only ∼14%) of R ln 2. A similar scenario has been found in the case of CeRhSi3 and CeIrSi3 where a reduced magnetic entropy at TN was found which was attributed to the Kondo effect [7]. 3.5. Electrical resistivity
The electrical resistivity ρ(T ) of CeCr1−x Tix Ge3 measured in the temperature range 4.2–300 K is normalized as ρ(T )/ρ(300) and presented in figure 9(a). Figures 9(b)–(f ) show the ρ(T ) of the individual doped samples over a magnified temperature scale (4.2–150 K). The resistivity profile is typical for Ce based heavy fermion compounds and reflects the formation of strongly correlated bands at low temperature. A sizable Kondo effect is evident from the electrical resistivity profile of CeCr1−x Tix Ge3 which exhibits Kondo-like behaviour i.e. broad maxima along with a logarithmic increase at high temperature (− ln T behaviour) and a sharp decrease in the low-temperature side of the peak. The logarithmic dependence at the high-temperature side is expected for Kondo scattering whereas the sharp decline at the low-temperature side reflects the coherence characteristic of the Kondo lattice [6–8, 32]. A relatively high value of resistivity for x = 0.15 can be attributed to the presence of micro cracks in the sample. In order to evaluate the magnetic contribution to the electrical resistivity ρm , we have subtracted the electrical resistivity of LaCrGe3 [17] (with the assumption that the lattice as well as Cr-magnetic contributions are the same in both the compounds) from that of CeCr1−x Tix Ge3 . As seen from figure 9(g) a sharp increase in ρm below 90 K is observed which seems to be an artificial effect of the subtraction process considering the fact that LaCrGe3 orders at Tc = 86 K. Despite the inaccuracy in the estimate of ρm below 90 K, the ρm data above 90 K are reliably estimated and clearly reflect the Kondo feature. In the high-temperature side ρm data are fitted with the expression (4) ρm = ρo − CK ln T
Figure 8. (a) Specific heat C of CeCr1−x Tix Ge3 (for x = 0.5 and
x = 0.6) as a function of temperature T . Inset: shows the C(T ) of CeCr0.5 Ti0.5 Ge3 under applied fields of 0 T, 0.2 T and 2 T. (b) Magnetic entropy S4f as a function of temperature. Inset: represents C/T versus T 2 plot with linear fitting.
this anomaly is associated with the magnetic transition in the system. In addition, an anomaly is observed near 3 K whose origin is not clear. The application of a magnetic field tends to smoothen this 3 K anomaly which suggests the anomaly is connected to a magnetic phase transition, possibly with Ce moments.For the parent compound CeCrGe3 too we have seen a clear anomaly at the same temperature (∼3 K) [17]. On the other hand, for x = 0.6 only one anomaly is observed at ∼3 K which is close to the Curie temperature (Tc = 3.5 K) determined from the magnetization measurement. It should be noted that the temperature of this anomaly is almost identical with that of the above-mentioned 3 K anomaly for x = 0.5. Linear fitting to C/T versus T 2 in the low temperature regime (Inset of figure 8(b)) gives us an idea about the possible values of Sommerfeld coefficient γ . We have obtained γ = 177 mJ mol−1 K−2 and 192 mJ mol−1 K−2 for x = 0.5 and 0.6 respectively. As listed in table 3 the γ values increase with increasing Ti substitution at the magnetic–nonmagnetic boundary. In order to evaluate the 4f contribution to the specific heat C4f , we have subtracted the heat capacity of LaCrGe3 from
where ρo is the sum of the residual resistivity and spin-disorder resistivity and CK is the Kondo coefficient. The − ln T dependence in the high-temperature (100–300 K) part reflects the Kondo effect from the excited multiplets of Ce3+ . 6
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
In addition to the µSR investigations, we have presented a detailed investigation of polycrystalline samples of CeCr1−x Tix Ge3 . The ordering temperature and the effective paramagnetic moment (µeff ) decrease systematically with increasing Ti doping concentration x. Remarkably, the result of the magnetization study on the doped samples suggests that the ordering of the itinerant Cr moments is suppressed for x = 0.6 and the ordering of the localized Ce moments starts to evolve for x 0.6. The intrinsic nature of magnetic transitions is confirmed by the specific heat measurements near the critical concentration (x = 0.5 and x = 0.6). A high value of the Sommerfeld coefficient is seen for x = 0.5 and 0.6 near the critical concentration as expected for Ce compounds situated near the magnetic–nonmagnetic boundary. In summary, CeCr1−x Tix Ge3 appears to be a rare example of a Ce based heavy fermion system where the ordering of itinerant Cr moments, having a strong coupling with the localized Ce moments, has been suppressed. A comparison of lattice parameters of CeCr1−x Tix Ge3 reveals that there is an expansion of unit cell volume across the series from CeCrGe3 to CeTiGe3 . Since both CeCrGe3 and CeTiGe3 form in the same crystal structure one would expect the Ce moment to order in CeCrGe3 as it does in CeTiGe3 , irrespective of the presence of Cr moment. However, despite the trivalent nature of cerium ions (Ce3+ ) in CeCrGe3 [17] no clear evidence of Ce moment long-range ordering is observed. We have carried out an inelastic neutron scattering study on CeCrGe3 . The neutron data did not reveal any clear sign of CEF excitations, which suggests that the Ce 4f-electrons are strongly hybridized with the conduction electrons. The absence of long-range ordering of Ce moments in CeCrGe3 can naively be connected to the lattice pressure brought by unit cell volume reduction with Cr. The decrease in lattice pressure with increasing Ti substitution for Cr might be linked with Ce-moment ordering for x > 0.6 in CeCr1−x Tix Ge3 . Acknowledgment
Discussion with Professor A M Strydom is gratefully acknowledged. This work is partially supported by the Council of Scientific and Industrial Research (CSIR), New Delhi (Grant No. 80(0080)/12/ EMR-II). A D Hillier and D T Adroja acknowledge financial assistance from CMPCSTFC grant number CMPC-09108. A Bhattacharyya would like to acknowledge FRC of UJ, NRF of South Africa and ISIS-STFC for funding support.
Figure 9. (a) Electrical resistivity ρ as a function of temperature T for CeCr1−x Tix Ge3 normalised as ρ(T )/ρ(300) in the temperature range 4.2 K to 300 K. (b)–(f ) ρ(T ) for 4.2 T 150 K. (g) Magnetic contribution to the electrical resistivity plotted on a semilogarithmic scale. Solid lines are fits to the equation ρm = ρo − CK ln T .
References
4. Conclusion
[1] [2] [3] [4]
Stewart G R 1984 Rev. Mod. Phys. 56 755 Steglich F 2005 J. Phys. Soc. Japan 74 167–77 Stockert O et al 2011 Nat. Phys. 7 119–24 Steglich F, Aarts J, Bredl C D, Lieke W, Meschede D, Franz W and Sch¨afer H 1979 Phys. Rev. Lett. 43 1892 [5] Pecharsky V K, Hyun O-B and Gschneidner K A Jr 1993 Phys. Rev. B 47 11839 [6] Yamamoto H, Ishikawa M, Hasegawa K and Sakurai J 1995 Phys. Rev. B 52 10136 [7] Muro Y, Eom D, Takeda N and Ishikawa M 1998 J. Phys. Soc. Japan 67 3601
The results of µSR study on the Kondo lattice heavy fermion itinerant ferromagnet CeCrGe3 have been presented which reveal bulk magnetic order below the transition temperature (Tc = 70 K) in good agreement with our previous report [17]. Muon spin precession is not observed as the internal field exceeds the maximum detectable internal field limit of the µSR spectrometer. Our µSR result corroborates that the internal field at muon site is much higher than 0.25 T. 7
J. Phys.: Condens. Matter 27 (2015) 016004
D Das et al
[8] Hossain Z, Ohmoto H, Umeo K, Iga F, Suzuki T, Takabatake T, Takamoto N and Kindo K 1999 Phys. Rev. B 60 10383 [9] Petrovic C, Pagliuso P G, Hundley M F, Movshovich R, Sarrao J L, Thompson J D, Fisk Z and Monthoux P 2001 J. Phys.: Condens. Matter 13 L337 [10] Prasad A, Anand V K, Paramanik U B, Hossain Z, Sarkar R, Oeschler N, Baenitz M and Geibel C 2012 Phys. Rev. B 86 014414 [11] Paramanik U B, Anupam U B, Burkhardt U, Prasad R, Geibel C and Hossain Z 2013 J. Alloys Compounds 580 435 [12] Eom D, Ishikawa M, Kitagawa J and Takeda N 1998 J. Phys. Soc. Japan 67 2495 [13] Alzamora M, Fontes M B, Larrea J, Borges H A, Baggio-Saitovitch E M and Medeiros S N 2007 Phys. Rev. B 76 125106 [14] Honda F, Bonalde I, Shimizu K, Yoshiuchi S, Hirose Y, ¯ Nakamura T, Settai R and Onuki Y 2010 Phys. Rev. B 81 140507 [15] Kittler W, Fritsch V, Weber F, Fischer G, Lamago D, Andr´e G and L¨ohneysen H v 2013 Phys. Rev. B 88 165123 [16] Bie H, Zelinska O Y, Tkachuk A V and Mar A 2007 Chem. Mater 19 4613 [17] Das D, Gruner T, Pfau H, Paramanik U B, Burkhardt U, Geibel C and Hossain Z 2014 J. Phys.: Condens. Matter 26 106001 [18] Custers J, Gegenwart P, Wilhelm H, Neumaier K, Tokiwa Y, Trovarelli O, Geibel C, Steglich F, P´epin C and Coleman P 2003 Nature 424 524
[19] Coleman P and P´epin C 2002 Physica B 312–313 383 [20] Saxena S S et al 2000 Nature 406 587 [21] Huy N T, Gasparini A, de Nijs D E, Huang Y, Klaasse J C P, Gortenmulder T, de Visser A, Hamann A, G¨orlach T and L¨ohneysen H v 2007 Phys. Rev. Lett. 99 067006 [22] Gegenwart P, Si Q and Steglich F 2008 Nat. Phys. 4 186 [23] Lin X, Taufour V, Bud’ko S L and Canfield P C 2013 Phys. Rev. B 88 094405 [24] Manfrinetti P, Dhar S K, Kulkarni R and Morozkin A V 2005 Solid State Commun. 135 444 [25] Rodr´ıguez-Carvajal J 1993 Physica B 192 55 Program Fullprof 1996 LLB-JRC, Laboratoire L´eon Brillouin (France: CEA-Saclay) [26] King P J C, de Renzi R, Cottrell S P, Hillier A D and Cox S F J 2013 Phys. Scr. 88 068502 [27] Jackson D D, McCall S K, Karki A B and Young D P 2007 Phys. Rev. B 76 064408 [28] L¨ohneysen H v, Rosch A, Vojta M and W¨olfle P 2007 Rev. Mod. Phys. 79 1015 [29] Rosch A, Schr¨oder A, Stockert O and L¨ohneysen H v 1997 Phys. Rev. Lett. 79 159 [30] Stockert O, L¨ohneysen H v, Rosch A, Pyka N and Loewenhaupt M 1998 Phys. Rev. Lett. 80 5627 [31] Inamdar M, Thamizhavel A and Dhar S K 2014 J. Phys.: Condens. Matter 26 326003 [32] Takase A, Kojima K, Komatsubara T and Kasuya T 1980 Solid State Commun. 36 461
8
