Heavy fermion behavior in PrRh2B2C: Excitonic mass enhancement
aa r X i v : . [ c ond - m a t . s t r- e l ] M a y APS/123-QED
Heavy Fermion behaviour in PrRh B C: An excitonic massenhancement
V. K. Anand ∗ and Z. Hossain Department of Physics, Indian Institute of Technology, Kanpur 208016, India
G. Chen, M. Nicklas, and C. Geibel
Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany (Dated: November 8, 2018)
Abstract
We report magnetic and transport properties of a new quaternary borocarbide PrRh B C, basedon magnetisation, resistivity and specific heat studies. This compound forms in LuNi B C-typetetragonal structure (space group
I4/mmm ) and does not exhibit magnetic ordering or supercon-ductivity down to 0.5 K. The crystal field analysis of specific heat data suggests a singlet groundstate in this compound. The high value of the Sommerfeld coefficient, γ ≈
250 mJ/mole K , to-gether with a singlet ground state suggests that the heavy fermion behaviour in PrRh B C resultsfrom the interaction of the conduction electrons with the low lying crystal field excitations. Nosignature of magnetic ordering or superconductivity is observed in PrRh B C under the applicationof pressure up to 23 kbar.
PACS numbers: 71.27.+a, 74.70.Dd, 71.70.Ch, 72.10.Di ∗ Electronic address: [email protected] ntroduction The heavy fermion systems have fascinated the condensed matter physicists with theexciting physics in the vicinity of quantum critical point. Most of the known heavy fermionsystems belong to Ce-, Yb- or U-based intermetallic compounds. Recently discovered Pr-based heavy fermion superconductor PrOs Sb [1] presents many unusual phenomena, suchas, two distinct superconducting phases, time reversal symmetry breaking, and point nodesat Fermi surface etc. [1, 2, 3, 4, 5] In contrast to the numerous Ce-based magneticallymediated heavy fermion superconductors, PrOs Sb is the only known Pr-based heavyfermion superconductor. Further, in contrast to the case of Ce-compounds where spin Kondoeffect leads to the heavy fermion behaviour, in Pr-compounds like PrInAg and PrFe P it is the quadrupolar Kondo effect which is suggested to be responsible for heavy fermionbehaviour. [6, 7]Another important mechanism for mass enhancement in Pr-compounds is the inelasticscattering of conduction electrons by the angular momentum associated with the crystalelectric field (CEF) levels, referred as excitonic mass enhancement. The theory of excitonicmass enhancement was proposed by White and Fulde [8] to explain the mass enhancementin elemental Pr itself and subsequently extended to rare earth systems with a CEF-splitnonmagnetic singlet ground state. [9] The true realization of heavy fermion behaviour dueto crystal field excitatons was found in PrOs Sb with a Sommerfeld coefficient γ ≈ . [5] Very recently we have seen evidence of excitonic mass enhancement inPr Rh Ge leading to moderate heavy fermion behaviour. [10] We present further evidencefor excitonic mass enahancement in PrRh B C in this paper. In addition to providing onemore example of Pr-based heavy fermion compound through our analysis of specific heat datawe attempt to provide a qualitative explanation of the unusual route to the heavy fermionstate in this compound. PrRh B C is a new member of the quaternary borocarbide familythat gives rise to the hope to provide a new route to high temperature superconductivityin boron based compounds which provided a unique playground to investigate the interplaybetween superconductivity and magnetism. We present in this paper electrical resistivity,magnetic susceptibility and specific heat data of a novel Pr-based quaternary compound.The reproducibility of the results has been checked by similar studies on a second batch ofsample. 2 xperimental
We prepared polycrystalline samples of PrRh B C and the nonmagnetic reference com-pound LaRh B C starting with high purity elements (99.99 % or better) in stoichiometriccomposition by the standard arc melting on water cooled copper hearth. During the arcmelting process samples were flipped and melted several times to improve the homogeneity.Arc melted samples were annealed for a week at 1200 o C under dynamic vacuum. Sampleswere characterized by copper K α X-ray diffraction and scanning electron microscopy. ASQUID magnetometer was used for magnetisation measurements. Heat capacity was mea-sured by relaxation method in a physical property measurement system (PPMS, QuantumDesign), and electrical resistivity was measured by the standard ac four probe techniques us-ing the AC-Transport option of PPMS. Electrical resistivity measurements under hydrostaticpressure were carried out in a double-layer piston-cylinder type pressure cell for pressuresup to 23 kbar. Silicone fluid served as pressure transmitting medium. The pressure wasdetermined at low temperatures by monitoring the pressure induced shift of the supercon-ducting transition temperature of lead. The narrow width of the transition confirmed thegood hydrostatic pressure conditions inside the pressure cell.
Results and discussion
The powder X-ray diffraction (XRD) data of a polycrystalline sample of PrRh B C wereanalyzed by WINXPOW software and further refined by least squares Rietveld refinementmethod using the FULLPROF software (Fig. 1), the quality parameter χ being 2.82.PrRh B C forms in LuNi B C-type tetragonal structure (space group
I4/mmm ) with latticeconstants a = 3.855 ˚A, c = 10.257 ˚A and unit cell volume = 152.44 ˚A . The nonmagneticreference compound LaRh B C also crystallises in the same tetragonal structure with latticeconstants a = 3.896 ˚A, c = 10.247 ˚A and unit cell volume = 155.53 ˚A , which are in fairlygood agreement with the values reported. [11] From XRD and scanning electron microscope(SEM) image we estimate impurity phase(s) to be less than 3% of the main phase.The magnetic susceptibility data of PrRh B C is shown in Fig. 2 as a function of tem-perature. No anomaly is seen in the susceptibility down to 2 K. At higher temperatures thesusceptibility curve follows a Curie-Weiss behaviour χ = C/ ( T − θ p ). From the linear fit of3 IG. 1: (colour online) Powder X-ray diffraction pattern of PrRh B C recorded at room temper-ature. The solid line through the experimental points is the Rietveld refinement profile calculatedfor LuNi B C-type tetragonal
I4/mmm structural model. The lowermost curve represents thedifference between the experimental and model results. inverse susceptibility data at 1.0 T we obtained the effective moment µ eff = 3.59 µ B , whichis very close to the theoretically expected value of 3.58 µ B for Pr ion. The paramagneticCurie-Weiss temperature, θ p = -3.9 K. The inset of Fig. 2 shows the magnetic field depen-dence of isothermal magnetisation, M ( B ) of PrRh B C. The isothermal magnetization at2 K shows slight nonlinearity, most likely due to the crystal field effects (the kink in M ( B )near 2.7 T is an experimental artifact). The magnetisation does not reach the saturationvalue up to 5 T, it attains a value of 1.17 µ B at 5 T.The specific heat data of PrRh B C do not show any anomaly corresponding to a mag-netic or superconducting transition down to 0.5 K. However, a broad Schottky-type anomalycentered around 9 K is observed in the magnetic part of specific heat. The magnetic contri-bution to the specific heat, obtained by subtracting the specific heat of LaRh B C from thatof PrRh B C, assuming the lattice contribution to be approximately equal to the specificheat of LaRh B C is shown in Fig. 3. The experimentally observed feature of the magneticpart of the specific heat above 2 K could be reproduced by a crystal electric field (CEF)analysis with four levels: three singlets at 0 K, 14 K, 36 K and a doublet at 155 K. The solidline in Fig. 3 represents the fit with this CEF level scheme. The inset of Fig. 3 shows themagnetic contribution to the entropy of PrRh B C. The magnetic entropy attains a value4
50 100 150 200 250 30004080120160200 M ( B / P r) B (T) - ( m o l e / e m u ) T (K)
FIG. 2: Temperature dependence of inverse magnetic susceptibility of PrRh B C measured in afield of 1.0 T. The inset shows the field dependence of isothermal magnetisation at 2 K.
R ln5R ln4R ln3R ln2 S m ag ( J / m o l e K ) T (K) C m ag ( J / m o l e K ) T (K)
FIG. 3: Magnetic part of specific heat of PrRh B C as a function of temperature. Solid line showsthe fit to the CEF scheme as described in the text. Inset shows the temperature dependence ofmagnetic part of entropy. of Rln (2) at 10 K supporting the proposed CEF level scheme of a singlet ground state lyingbelow the first excited singlet at 14 K. From the specific heat data below 2 K we estimate alower bound to the value of Sommerfeld coefficient γ ≈
250 mJ/mole K . It is observed thatbelow 0.5 K C/T increases with decreasing temperature (inset of Fig. 4) while C keeps on5
50 100 150 200 250 30040455055606570 C / T ( m J / m o l e K ) T (K) ( c m ) T (K ) ( c m ) T (K)
FIG. 4: Temperature dependence of electrical resistivity of PrRh B C in the temperature range0.5 K – 300 K. The lower inset shows the electrical resistivity data below 5 K plotted as ρ vs. T . (measured on second sample). The solid line is a guide to eye. The upper inset shows the lowtemperature specific heat data below 2 K plotted as C/T vs. T . decreasing. Such a behaviour of specific heat suggests a gradual onset of heavy fermion stateand has some similarity with the C/T upturn in heavy fermion compounds YbNi B C [12]and YbRh Si . [13] However, we can not entirely exclude the possibility that sharp increaseof C/T might be related to the onset of phase transition at further lower temperatures.The electrical resistivity of PrRh B C shown in Fig. 4 exhibits metallic behaviour with ρ K = 68 µ Ω cm, residual resistivity ρ ≈ µ Ω cm and residual resistivity ratio RRR= ρ K / ρ ≈ B Cwhich we measured down to 0.5 K also shows metallic behaviour. A rapid drop is observed inresistivity of the La-based compound below 3 K possibly due to incipient superconductivity.The low temperature electrical resistivity data of PrRh B C fits well with ρ ( T ) = ρ + AT n with n ≈ A = 0.1 µ Ω cm/K n and is shown in the inset of Fig. 4 plottedas ρ vs. T . below 5 K. A T . temperature dependence of the electrical resistivity is acharacteristic of non-Fermi liquid behaviour as predicted by the spin fluctuation theory fora three dimensional system near an antiferromagnetic quantum critical point (AF-QCP).6owever in our compound because of the singlet ground state the departure from the Fermiliquid behaviour is more likely to be due to the presence of low-lying CEF levels. Further on,the residual resistivity is rather high which makes the power law exponent not so reliable.Therefore, we refrain from putting too much stress on the resistivity exponent and theassociated non-Fermi liquid nature and proximity of PrRh B C to an AF-QCP.We also calculated the value of Wilson ratio using the value of χ = 0.25 emu/mole at 2 Kand µ eff = 3.59 µ B together with γ ≈
250 mJ/mole K and obtained R w = 17 which is quitelarge. The high value of electronic specific heat coefficient γ together with the enhancedvalue of R w is a clear indication of strong correlations and heavy fermion behaviour in thiscompound. Since no Kondo-like behaviour is observed in ρ ( T ), the mechanism for the heavyfermion behaviour may be rooted in the low lying CEF splitting similar to that in the heavyfermion superconductor PrOs Sb . [1, 5] It was suggested by Fulde and Jensen [9] thatfor a system with CEF-split singlet ground state and low CEF splitting energy the inelasticscattering of conduction electrons with the excited levels of angular momentum of the 4 f electrons can result in an enhanced mass of the conduction electrons. After a rigoroustheoretical analysis they have shown that the enhanced mass due to the inelastic transitionbetween two levels i and j can be found by the expression [9], m ∗ m = 1 + ( g J − J sf N (0) 2 | < i | J | j > | ∆where J sf is the exchange integral coupling between the conduction electrons and the f electrons, and N(0) conduction electron density of states at the Fermi level. The matrixelement between i and j can be calculated using the CEF parameters. An inelastic neutronscattering experiment on PrRh B C is highly desired to know the exact CEF level schemeand evaluate the matrix elements. The CEF analysis of specific heat data clearly suggests aCEF-split singlet ground state with another singlet excited state at about 14 K and thereforean excitonic mass enhancement by the crystal field excitations leading to the heavy fermionbehaviour in PrRh B C.Using similar CEF analysis of magnetic specific heat data we have seen that PrPd B Calso has a singlet ground state lying below the first excited singlet at 50 K and a doublet at 80K. [14] However, the value of Sommerfeld coefficient γ ≈
16 mJ/mole K is much lower thanthat of PrRh B C, consistent with the theory of White and Fulde [8], the γ -value beinginversely proportional to the separation between the ground state and the excited state.7 ABLE I: The Sommerfeld coefficient γ , crystal field splitting energy ∆ and low temperaturesaturation value of magnetic susceptibility χ for few Pr-compounds having nonmagnetic singlet asground state.Compounds Ground First Splitting γ (mJ/ χ ( × − State Excited Energy mole K ) emu/mole)State ∆ (K) at 2 KPrRh B C singlet singlet 14 250 20.4Pr Rh Ge singlet singlet 12 81 10.6 [10]PrPd B C singlet singlet 50 16 3.8 [14]PrRhGe singlet doublet 70 10 3.8 [15] For a better insight of excitonic mass enhancement in Pr-compounds with nonmagneticsinglet ground state we present the values of Sommerfeld coefficient γ , crystal field splittingenergy ∆ and low temperature saturation value of magnetic susceptibility χ in Table I. Acomparison of γ and ∆ in these systems clearly reflect a systematic variation in their value,a smaller ∆ results in an increased γ and vice-versa. All these results establish the moregeneral nature of the mechanism of excitonic mass enhancement in Pr-compouds, and themass enhancement due to low lying crystal field excitations can even lead to the developmentof heavy fermion state as in our system PrRh B C.The application of pressure is expected to change the CEF level splitting energy andtherefore to influence the physical properties. We therefore made an effort to achieve astable ordered phase in PrRh B C by applying external pressure. In the resistivity studiesshown in Fig. 5 no significant effect (except a slight increase in magnitude of resistivity)of pressure was observed up to 23 kbar. Especially, the position of the anomaly around 10K attributed to the CEF effect is independent of pressure (the inflection point in dρ/dT characterizing the position of anomaly changes almost negligibly for the pressures of 0, 1.33and 2.24 GPa) indicating that the applied pressure of up to 23 kbar has no considerable effecton the CEF level splitting scheme. Furthermore, this pressure is not sufficient to stabilize anysuperconducting or magnetically ordered phase in PrRh B C. The insensitivity to externalpressure can be explained in the very rigid framework of the RNi B C structure as evidencedfrom a very high value of bulk modulus (e.g. YNi B C [16]).8
50 100 150 200 250 30030354045505560 ( c m ) T (K) ( c m ) T (K)
FIG. 5: (colour online) Electrical resistivity, ρ (T), of PrRh B C measured under the applicationof external pressures up to 23 kbar. Inset shows the extended view of low temperature resistivity.
Conclusion
We present clear evidence of heavy fermion behaviour in the new quaternary borocarbidePrRh B C. The mechanism for the electronic mass enhancement in this case is not the usualKondo effect but it is due to the low-lying crystal field excitations. In this compound theground state is a singlet separated from the first excited state only by about 10 K. Our effortto induce magnetism or superconductivity using hydrostatic pressure did not succeed. Thisis attributed to extremely rigid frame of the borocarbide structure as evidenced from highbulk modulus of YNi B C. Acknowledgement
We acknowledge CSR Indore (India) for providing access to low temperature measure-ments using PPMS. [1] E. D. Bauer, N. A. Frederick, P. -C. Ho, V. S. Zapf, and M. B. Maple, Phys. Rev. B ,100506(R) (2002).
2] K. Izawa, Y. Nakajima, J. Goryo, Y. Matsuda, S. Osaki, H. Sugawara, H. Sato, P. Thalmeier,and K. Maki, Phys. Rev. Lett. , 117001 (2003).[3] Y. Aoki, A. Tsuchiya, T. Kanayama, S. R. Saha, H. Sugawara, H. Sato, W. Higemoto, A. Koda,K. Ohishi, K. Nishiyama, and R. Kadono, Phys. Rev. Lett. , 067003 (2003).[4] Elbert E. M. Chia, M. B. Salamon, H. Sugawara, and H. Sato, Phys. Rev. Lett. , 247003(2003).[5] E. A. Goremychkin, R. Osborn, E. D. Bauer, M. B. Maple, N. A. Frederick, W. M. Yuhasz,F. M. Woodward, and, J. W. Lynn, Phys. Rev. Lett. , 157003 (2004).[6] A. Yatskar, W. P. Beyermann, R. Movshovich, and P. C. Canfield, Phys. Rev. Lett. , 3637(1996).[7] H. Sugawara, T. D. Matsuda, K. Abe, Y. Aoki, H. Sato, S. Nojiri, Y. Inada, R. Settai, andY. ¯Onuki, Phys. Rev. B , 134411 (2002).[8] R. M. White, and P. Fulde, Phys. Rev. Lett. , 1540 (1981).[9] P. Fulde, and J. Jensen, Phys. Rev. B , 4085 (1983).[10] V. K. Anand, Z. Hossain, and C. Geibel, Phys. Rev. B , 184407 (2008).[11] R. J. Cava, T. Seigrist, B. Batlogg, H. Takagi, H. Eisaki, S. A. Carter, J. J. Krajewski, andW. F. Peck, Jr., Phys. Rev. B , 12966 (1994).[12] A. Yatskar, N. K. Budraa, W. P. Beyermann, P. C. Canfield, and S. L. Bud’ko, Phys. Rev. B , R3772 (1996).[13] O. Trovarelli, C. Geibel, S. Mederle, C. Langhammer, F. M. Grosche, P. Gegenwart, M. Lang,G. Sparn, and F. Steglich, Phys. Rev. Lett. , 626 (2000).[14] V. K. Anand, A. Chaudhuri, S. K. Dhar, C. Geibel, and Z. Hossain, Physica C , 785(2007).[15] V. K. Anand, Z. Hossain, and C. Geibel, Solid State Commun. , 335 (2008).[16] S. Meenakshi, V. Vijayakumar, R. S. Rao, B. K. Godwal, S. K. Sikka, P. Ravindran, Z. Hossain,R. Nagarajan, L. C. Gupta, and R. Vijayaraghavan, Phys. Rev. B , 3377 (1998)., 3377 (1998).