Specific heat of heavy fermion CePd2Si2 in high magnetic fields

We report specific heat measurements on the heavy fermion compound CePd2Si2 in magnetic fields up to 16 T and in the temperature range 1.4—16 K. A sharp peak in the specific heat signals the antiferromagnetic transition at TN ∼ 9.3 K in zero field. The transition is found to shift to lower temperatures when a magnetic field is applied along the crystallographic a-axis, while a field applied parallel to the tetragonal c-axis does not affect the transition. The magnetic contribution to the specific heat below TN is well described by a sum of a linear electronic term and an antiferromagnetic spin wave contribution. Just below TN , an additional positive curvature, especially at high fields, arises most probably due to thermal fluctuations. The field dependence of the coefficient of the low temperature linear term, γ0, extracted from the fits shows a maximum at about 6 T, at the point where an anomaly was detected in susceptibility measurements. The relative field dependence of both TN and the magnetic entropy at TN scales as [1 − (B/B0)] for B ‖ a, suggesting the disappearance of antiferromagnetism at B0 ∼ 42 T. The expected suppression of the antiferromagnetic transition temperature to zero makes the existence of a magnetic quantum critical point possible. The heavy fermion system CePd2Si2 has recently become a subject of considerable experimental and theoretical interest. This compound undergoes an antiferromagnetic transition at TN ∼ 9 K with a static moment of 0.6 μB at low temperature. Its spin configuration consists of ferromagnetic (110) planes with spins normal to the planes and alternating in directions along the spin axis. The existence of a quantum critical point at a pressure of about 30 kbar, where the antiferromagnetic transition temperature is suppressed to zero, was established a long time ago [1]. It is, however, only recently that Grosche et al [2] discovered the appearance of superconductivity in a small pressure range in the vicinity of the quantum critical point. This pioneering work gave rise to a new wave of interest in this compound. Recently, several experimental studies of CePd2Si2 were performed both at ambient and high pressure on different samples and using different experimental techniques [3, 4, 5, 6]. These works confirmed the emergence of superconductivity close to the critical pressure and gave an insight into the nature of the superconducting ground state. It has been also shown that non-Fermi liquid behavior at low temperature appears close to the critical pressure. Such behavior observed in resistivity, magnetization and specific heat measurements is a common trend in heavy fermion compounds in the vicinity of a magnetic instability induced by application of hydrostatic pressure. Letter to the Editor 2 A different way to tune a heavy fermion compound to a quantum critical point is by applying a high magnetic field. Field suppression of antiferromagnetism, like pressure, does not induce any disorder and, like pressure, opens up a new dimension in the phase diagram for study. Such a suppression of the magnetically ordered ground state by high magnetic field was found in CeCu5.2Ag0.8 [7], YbCu5−xAlx [8, 9], YbRh2Si2 [10] and CeCu5.2Au0.8 [11]. In all these cases, unusual non-Fermi liquid behavior was also found near the magnetic quantum critical point. There are, however, other systems, e.g. CePtSi0.4Ge0.6 [7], that show Fermi-liquid behavior upon field suppression of TN to zero. Two experimental investigations of CePd2Si2 at high magnetic field were recently reported. The first publication [12] reports magnetization measurements up to 28 T at 4.2 K with the magnetic field applied along both a and c crystallographic axes. No anomalies have been seen for either direction of the magnetic field. The other work [7] presents specific heat measurements at 0, 13 and 28.9 T on a polycrystalline sample. At 28.9 T, the antiferromagnetic transition was found to be broadened with both the peak in the specific heat and the transition midpoint suppressed to lower temperatures though the onset did not shift. This left the situation in this compound somewhat obscure, and no further high field investigations have been reported. We have, therefore, decided to reexamine the experimental situation in this material. We have performed specific heat measurements on a single crystal of CePd2Si2 in magnetic fields up to 16 T in the temperature range 1.4—16K. The specific heat measurements were performed on a single crystal of CePd2Si2, grown in a triarc furnace by the Czochralski method. Further details of the sample preparation are given elsewhere [13]. The sample, with a mass of 15mg, was mounted on a small sapphire plate. A carbon film with four contacts made of phosphor bronze was painted on the other side of the plate. The whole set-up including two thermometers and a heater was sealed inside a vacuum sample chamber. A carbon glass resistive thermometer was used to regulate the temperature inside the sample chamber. The temperature was measured by a Cernox thermometer calibrated in field. A thermal relaxation technique was used to measure the specific heat [14]. To extract the specific heat of the sample, the contribution of the sapphire, electrical wires and grease used as an adhesive was measured and subtracted. Magnetic fields up 16 T were generated by a superconducting coil. The temperature was varied from 1.4 to 16 K using a standard variable temperature insert (VTI). Figure 1 shows the zero-field specific heat. The data are in good agreement with previous measurements [13, 15]. The antiferromagnetic transition manifests itself by a sharp, almost step-like increase of the specific heat at 9.3 K. The magnetic contribution, Cmag, to the specific heat is obtained by subtracting the data of the nonmagnetic reference system LaPd2Si2 [16] (also shown in figure 1). At low temperature, LaPd2Si2 shows the classical behavior C = γrT + βrT 3 with γr = 6.0 mJ/molK 2 and βr = 0.267 mJ/molK . This is to be compared with C/T = 160 mJ/molK found for CePd2Si2 at 1.4 K, the lowest temperature of our measurements (see, however, the discussion below for fits of C/T as T → 0). Above the antiferromagnetic transition, Cmag/T increases with temperature decrease due to the Kondo spin fluctuations. Below TN , Cmag(T ) can be described in terms of spin fluctuations and an additional contribution from the antiferromagnetic spin waves [13]. We have integrated Cmag/T to obtain the magnetic entropy. Since the lowest temperature of our measurements was 1.4 K, we extrapolated the data below 1.4 K using the empirical temperature dependence C = γT + βT 3 discussed Letter to the Editor 3 below. The calculated magnetic entropy is shown in the inset of figure 1. The entropy at the transition temperature reaches about 75% of R ln 2, the value expected for a doublet ground state [13]. This is not necessarily surprising and is likely to imply that the ordered moment in the antiferromagnetic phase is somewhat compensated by the Kondo interactions. At 22 K, the highest temperature of the zero-field measurement, the magnetic entropy reaches 95% of R ln 2. When a magnetic field is applied parallel to the crystallographic a-axis, the transition gradually moves to lower temperatures remaining, however, as sharp as in zero field as shown in figure 2. Conversely, a magnetic field of 14 T applied along the tetragonal c-axis was not found to affect the transition temperature (see the inset of figure 2). This implies the existence of strong magnetic anisotropy between the basal plane and the tetragonal c-axis of the compound. Such anisotropy is consistent with the magnetic structure of the material with its spins aligned in the basal plane. This anisotropy explains the result of a previous report obtained on a polycrystal [7], where at 29 T, the transition was found to be much broader with the peak in C/T suppressed to about 5 K but without any shift of the onset. Indeed, in the case of a polycrystal, the part of the sample more or less aligned with the field along the c-axis shows no change and that is why the onset of the transition does not move. On the other hand, the other field directions suppress the transition which leads both to a shift of the specific heat peak and the transition broadening. We have tried to fit the data below TN by the commonly used empirical fitting functions Cmag = γT + A exp(−∆/T ) for a spin gap [17] and Cmag = γT + βT 3 for antiferromagnetic spin waves [13]. While both of them fit well the low temperature part of the data, neither of them succeeded in providing a satisfactory fit over the whole temperature range. We found, however, that the magnetic contribution to the specific heat is well described by a model composed of a linear electronic contribution as above, γ0T , plus a term that accounts for the contribution from antiferromagnetic spin waves with the dispersion relation ω = √ ∆2 +Dk2 [18]: Cmag = γ0T+α∆ T e [1+(39/20)(T/∆)+(51/32)(T/∆)](1) Here ∆ is the spin-wave gap, and α is related to the spin-wave stiffness D by α ∝ D. As shown in figure 3 for B = 0 and 16 T, the above equation yields a good fit to the data, except for a small temperature range just below TN , which was ignored when fitting the data. The failure of the fit over this small temperature range is due to the existence of a positive curvature just below TN . This curvature becomes gradually stronger with field as can be seen in figure 3. We associate this curvature with thermal fluctuations that are expected to play a role in the vicinity of the transition, and to become stronger in magnetic field. The field dependence of the low temperature electronic contribution to the specific heat extracted from the fits is shown in figure 4. As one can see, the low temperature Sommerfield coefficient, γ0, passes through a maximum at about 6 T before starting to decrease monotonically. This maximum matches a clear anomaly observed in susceptibility measurements when the magnetic field was also applied along the crystallographic a-axis [19]. The anomaly can be associated with a spinflop process. Indeed, the behavior of γ0 in magnetic field we find here is very similar to that of the coefficient A of the T 2 term of the resistivity found by McDonough and Julian in CePb3 around a spin-flop transition [20]. Note that the coefficient A also reflects the many-body enhancement, the ratio A/γ0 having an universal value in heavy fermion systems, as pointed out by Kadowaki and Woods [21]. Letter to the Editor 4 The field-dependent values of TN have been determined by an equal-entropy construction with an ideal step transition. Figure 5 shows the field dependence of the transition temperature and the magnetic entropy at TN . Both follow a simple scaling relation [1 − (B/B0)]. Here B0 corresponds to the field necessary to suppress the antiferromagnetic order, and is found to be (41.5±0.6)T. This scaling relation explains quantitatively why no anomalies were observed in the magnetization measurements up to 28T at T = 4.2K [12]. According to the above formula, at T = 4.2K the transition should occur at about 31 T for B ‖ a, while in [12] the highest applied field was only 28T. The same scaling behavior was found for another heavy fermion system URu2Si2 [22], where the value of B0 was found to be in relatively good agreement with the results obtained from resistivity, thermal expansion and magnetization measurements. In conclusion, we have shown that the antiferromagnetic transition in CePd2Si2 shifts to lower temperatures in magnetic fields applied in the basal plane. The absence of influence of the magnetic field parallel to the tetragonal c-axis on the transition temperature points to the existence of a strong magnetic anisotropy, which is a common trend for heavy fermion compounds. Analysis of the field dependence of TN and the magnetic entropy suggests the suppression of the antiferromagnetic ground state at about 42T, rising the possibility of the existence of a quantum critical point at this field. This might make this compound a new member of a growing family of heavy fermion antiferromagnets which can be tuned by a magnetic field through the magnetic quantum critical point, where the Néel temperature vanishes. This prediction calls for further experiments at higher, probably pulsed fields. The magnetic specific heat below TN is best described by the sum of an electronic contribution and antiferromagnetic spin waves. The fit, however, breaks down just below TN where thermal fluctuations give rise to a positive curvature. The low temperature coefficient of the electronic term of the specific heat extracted from the fits is found to have a maximum at about 6 T. This suggests the existence of a magnetic transition, presumably a spin-flop, the idea being also supported by the results of the magnetization measurements [19].