Magnetic phase diagram of the ferromagnetic Kondo-lattice compound CeAgSb 2 up to 80 kbar

Electrical resistivity and ac-calorimetric measurements reveal a complex magnetic phase diagram for single crystals of the ferromagnetic Kondo-lattice compound CeAgSb 2 at high pressures up to 80 kbar. The ferromagnetic order at T C 5 9.6 K at ambient pressure is completely suppressed at a critical pressure P C 5 35 kbar. Another magnetic transition, possibly antiferromagnetic, found above 27 kbar, attains a maximum value T N ; 6 K at 44 kbar and then appears to be completely suppressed by ; 50 kbar. Thermodynamic and transport measurements in the ferromagnetic state indicate an energy gap D; 30 K in the spin-wave excitation spectrum at ambient pressure which decreases to D; 10 K at P 5 30 kbar. No superconductivity is observed at ambient pressure above T ; 0.1 K, under applied pressure in the ferromagnetic state ( P 5 28.5 kbar), nor in the antiferromagnetic state ( P 5 33 2 46 kbar) above 0.3 K.


I. INTRODUCTION
Magnetically ordered heavy-fermion compounds are particularly interesting because they have revealed unusual states of matter that emerge as their magnetic phase transition is tuned to Tϭ0 K, a quantum-critical point ͑QCP͒, by an external parameter such as chemical substitution or pressure. Among these ground states found near the QCP are pressure-induced superconductivity coexisting with antiferromagnetism ͓e.g., CeRhIn 5 ͑Ref. 1͒ and CePd 2 Si 2 ͑Ref. 2͔͒, the coexistence of ferromagnetism and superconductivity ͑e.g., UGe 2 ͑Refs. 3 and 4͒ URhGe ͑Ref. 5͔͒, and non-Fermi-liquid ͑NFL͒ behavior, in which logarithmic or weak power-law behavior T dependencies of the physical properties at low temperatures do not follow those expected for a Fermi liquid. 6,7 The magnetic behavior of heavy-fermion compounds is determined qualitatively by a delicate balance between competing Ruderman-Kitel-Kasuya-Yosida ͑RKKY͒ and Kondo interactions which give rise to either a magnetically ordered ground state, antiferromagnetic ͑AFM͒ or ferromagnetic ͑FM͒ due to the oscillatory nature of the RKKY interaction, or a nonmagnetic ground state. The energy scales of these two interactions are governed by the hybridization strength ͉JN(E F )͉ between the localized f states and conduction-electron states, i.e., T RKKY ϰJ 2 N(E F ) and T K ϰexp(Ϫ1/͉JN(E F )͉), where J is the exchange coupling parameter and N(E F ) is the density of states at the Fermi level E F . For small values of ͉JN(E F )͉, the RKKY interaction dominates and the system orders magnetically. As ͉JN(E F )͉ increases, the magnetic ordering temperature T mag first increases, passes through a maximum when the Kondo and RKKY energies become comparable, then decreases rapidly as the Kondo interaction dominates.
This theoretical framework, proposed by Doniach some time ago, 8 has been applied to a number of Ce-and Yb-based heavy-fermion compounds with reasonable success. 9 At the quantum-critical point where the magnetic order is completely suppressed, i.e., JϭJ C , non-Fermi-liquid behavior is often observed, 6 while for JϾJ C , Fermi-liquid behavior is recovered. CeAgSb 2 is a rare example of a ferromagnetically ordered heavy-fermion compound and presents an opportunity to investigate the physical behavior near a ferromagnetic quantum-critical point. The family of RAgSb 2 compounds (RϭLa-Tm) crystallizes in the tetragonal ZrCuSi 2 -type crystal structure ͑space group P4/nmm) in which the R sites are crystallographically equivalent. 10 Aside from CeAgSb 2 , which has a Curie temperature T C ϭ9.6 K, 11 all other members of this family order antiferromagnetically at temperatures between T N ϭ 2 K and 11 K. [11][12][13] Neutron-diffraction experiments reveal that the Ce magnetic moments of CeAgSb 2 are aligned along the c axis with a value ϭ0.33 B /Ce, 13 in excellent agreement with the saturation moment sat ϭ0.37 B /Ce determined from magnetization measurements (H͉͉c). 12 This value of sat is smaller than the value expected in a crystal-field doublet ground state. The magnetic properties are quite anisotropic, with a saturation moment of sat ϭ1.1 B /Ce for HЌc. 12 These features are similar to those of the pressure-induced FM superconductor UGe 2 . 3 CeAgSb 2 can be considered a moderately heavy-fermion compound: above T C , the electronic specificheat coefficient ␥ϵC/Tϳ250 mJ/mol K 2 , which decreases to ␥ϳ65 mJ/mol K 2 as T→0 K. This electronic specific heat is consistent with thermopower and inelastic neutronscattering measurements, suggesting a Kondo temperature T K ϳ60 K. 14,15 The magnetic ordering temperature of CeAgSb 2 decreases with the application of high pressure, as was found in a magnetic-susceptibility study to 7 kbar ͑Ref. 15͒, and it is therefore a potential candidate for examining the behavior of superconductivity near a ferromagnetic quantum-critical point at higher pressures. In this paper, we report or our investigation of electrical resistivity at high pressure up to 80 kbar and ac-calorimetry measurements up to 50 kbar on single crystals of CeAgSb 2 .

II. EXPERIMENTAL DETAILS
High-quality single crystals of CeAgSb 2 were grown in an Sb flux as described in Ref. 12. A starting composition of Ce 0.045 Ag 0.091 Sb 0.864 was used and the elements were placed in an alumina crucible and sealed in a quartz ampoule. The materials were heated to 1200°C and kept at that temperature for 12 hr, then slowly cooled to 670°C at 4°C hr Ϫ1 , at which point, excess Sb flux was removed in a centrifuge. Any remaining Sb flux was removed with dilute HCl. Typical dimensions of the platelike crystals were 5ϫ5ϫ2 mm.
Ambient-pressure magnetic measurements were performed in magnetic fields up to 5.5 T from 1.8 to 300 K using a Quantum Design superconducting quantum interference device magnetometer. Specific-heat measurements were carried out in a Quantum Design Physical Properties Measurement System from 0.3 K to 300 K. Three high-pressure cells were used for the electrical resistivity experiments at low temperatures: a clamped piston cylinder, a Bridgman anvil, 16 and a toroidal anvil cell. The latter is a profiled anvil system supplied with a boron-epoxy gasket and Teflon capsule, containing pressure-transmitting liquid, a sample, and a pressure sensor. 17 The pressure in all three cells was determined from the variation of the superconducting transition of lead using the pressure scale of Eiling and Schilling 18 and Bireckoven and Wittig. 19 The Bridgman pressure cell was comprised of a pyrophyllite gasket ͑internal diameter of 2.0 mm͒ and two steatite disks which served as the pressuretransmitting medium. A CeAgSb 2 sample was cut and polished to approximate dimensions of 220ϫ250ϫ30 m. The sample was placed between the two steatite disks in contact with a thin piece of Pb. Platinum wires ͑0.002-in diameter͒ were used for electrical contact out of the pyrophyllite gasket. The 10% and 90% values of the Pb transition in the Bridgman cell above 35 kbar were used as a rough measure of the pressure gradient caused by the solid pressuretransmitting media used in this apparatus; below about 35 kbar, the pressure gradient amounted to less than 1 kbar. Measurements at the University of California at San Diego ͑UCSD͒ from temperatures between 0.05 K and 3 K and 0.3 K and 300 K were performed in a 3 He cryostat and 3 He/ 4 He dilution refrigerator, respectively, using a LR-700 resistance bridge with excitation currents ranging from 100 A to 1 mA. Measurements between 1 K and 300 K were also carried out in a 4 He cryostat. In all cases, the current was applied along the a axis of the crystal.
Three samples of CeAgSb 2 were used in the study. One sample, labeled Los Alamos National Laboratory ͑LANL͒ 161, was used in electrical resistivity experiments in a toroidial cell up to ϳ50 kbar. A second sample from the same batch, labeled LANL 161a, was used in ac-calorimetric measurements in a toroidal cell. This sample was characterized by ambient-pressure magnetic-susceptibility measurements down to 2 K and heat-capacity measurements down to 0.4 K.
Another sample grown independently at UCSD ͑labeled UCSD͒ was used for resistivity measurements in the pistoncylinder and Bridgman cells. In general, both samples prepared at UCSD and LANL exhibited similar behavior, and differences between the two samples are discussed below.
ac-calorimetric measurements were performed on a single crystal of CeAgSb 2 with dimensions of 1ϫ1ϫ0.2 mm mounted in the torodial pressure cell using fluorinert as the pressure-transmitting medium. A small resistive heater was glued to one side of the sample and the temperature oscillations on the opposite side were probed by a Chromel-Constantan thermocouple and measured by a lock-in amplifier at a frequency twice that of the heater current. Further details of the ac-calorimetric method can be found in Refs. [20][21][22]. The frequency dependence of the thermocouple output voltage was inversely proportional to frequency in the range 1.5-20 Hz ͑at higher frequencies, temperature oscillations became too small to be measured precisely͒. An operating frequency of 3 Hz was chosen as a compromise between a higher signal level and sufficiently low heat losses to the surrounding environment. The frequency dependencies measured with the sample in the empty pressure cell and in the cell filled with fluorinert show that the amplitude of the thermocouple output voltage drops by ϳ50% at all frequencies due to heat losses to surrounding liquid. This effect produces a fictitious increase of the sample heat capacity, which should be, under the condition of small heat losses, simply inversely proportional to the amplitude T ac of temperature oscillations. [20][21][22] Thus, as an approximation, the 1/T ac curves have been shifted by a constant T ac * which was chosen to adjust the relative change of 1/T ac vs T from 5 to 18 K to be comparable to the ambient-pressure specific heat of CeAgSb 2 measured in a Quantum Design PPMS in this temperature range. After carrying out this procedure, the ratio of the peak value of 1/T ac at T C ϭ9.6 K to its value at 10.6 K is close to 3, while this ratio for specific heat measured in the PPMS is about 4.5. It is therefore concluded that this procedure provides at least a semiquantitative evaluation of C( P,T) from our measurements of 1/T ac vs T with an accuracy ϳ30%. The behavior of 1/T ac vs T at higher temperatures, between 20 K and 300 K, also reproduces the C(T) curve with this accuracy.

A. Ambient-pressure measurements
The temperature-dependent magnetic susceptibility ϵM /H of CeAgSb 2 for both H͉͉c and HЌc is shown in Fig.  1͑a͒. A sharp increase of (T) below 10 K indicates the onset of ferromagnetism. This is confirmed by magnetization ͑M͒ measurements at 2 K, as displayed in the inset of Fig.  1͑a͒, in which M quickly saturates to a value M sat ϳ0.4 B /Ce for H͉͉c. For HЌc, M (H) increases linearly up to Hϭ3 T, then saturates to a value M sat ϳ1.1 B /Ce; similar behavior has been observed previously. 12,23 Above 100 K, the magnetic susceptibility follows a Curie-Weiss law with an effective moment e f f ϭ2.46 B (2.48 B ) and a Curie-Weiss temperature CW ϭϪ55 K ͑5 K͒ for H͉͉c (HЌc).
The specific heat C, plotted as C/T versus T, of CeAgSb 2 is shown in Fig. 1͑b͒, along with C/T of LaAgSb 2 and the 4 f contribution C 4 f /Tϵ͓C(CeAgSb 2 )ϪC(LaAgSb 2 )]/T. ͑The specific heat of LaAgSb 2 is well described by a Sommerfeld coefficient ␥ϭ1 mJ/mol K 2 and Debye temperature D ϭ238 K.͒ The ferromagnetic transition occurs at T C ϭ9.6 K; the magnetic entropy S mag ϭ͐(C 4 f /T)dT released below the transition amounts to S mag ӍRln2, indicating a doublet ground state of the Ce Jϭ5/2 multiplet in the tetragonal crystalline electric field ͑CEF͒. ͑A tetragonal CEF will split the Jϭ5/2 multiplet of Ce into three doublets.͒ Recent thermal-expansion 24,25 and specific-heat measurements 25 suggest the first and second CEF excited states to be at ⌬ 1 ϳ50 K and ⌬ 2 ϳ140 K above the ground state, in agreement with inelastic neutron-scattering measurements which reveal peaks at 5.1 meV and 12.4 meV. 26 The specificheat data presented here are consistent with this CEF energylevel scheme. Another specific-heat anomaly is present at T ϭ1.0 K ͓inset of Fig. 1͑b͔͒, but the tiny amount of entropy in this transition suggests that it is due to an impurity phase, excluding CeAg or CeSb 2 , which have ordering temperatures of 5 K and 15 K, respectively. A feature associated with this possible impurity phase is also observed in the electrical resistivity in CeAgSb 2 ͑LANL 161͒, but not in the sample prepared at UCSD, and is discussed below. The electronic specific-heat coefficient extrapolated to Tϭ0 K is ␥ϳ65 mJ/ mol K 2 , in good agreement with results obtained from polycrystalline samples. 27 In the ferromagnetic state, the 4 f contribution to the specific heat of CeAgSb 2 was fit by the expression describes the contribution 28 due to a FM spin-wave excitation spectrum with an energy gap ⌬ ͑with a constant B) and ␥T is the usual electronic term. Fits of the data to Eq. ͑1͒ between 0.4 K ϽTϽ8 K yield ␥ϭ100 mJ/mol K 2 and ⌬ ϭ18 K as shown in Fig. 2. Similar exponential gaplike behavior is observed in the electrical resistivity discussed below and also in thermal-expansion measurements which imply a somewhat smaller energy gap ⌬ϭ5.3 K below 10 K. 15

B. Electrical resistivity
The temperature dependence of the electrical resistivity (T) of CeAgSb 2 at ambient pressure ͑Fig. 3͒ is typical of a Kondo-lattice system. The resistivity exhibits a broad minimum around 200 K followed by a pronounced maximum at T max ϭ17.5 K. Similar behavior has been observed in other heavy-fermion systems, such as CeAgCu 4 , 29 CeRu 2 Ge 2 , 30 and CeCoIn 5 . 31 A sharp drop in (T) of CeAgSb 2 occurs at T C ϭ9.6 K at the onset of ferromagnetic order. Well below the magnetic transition, the resistivity approaches a value 0 ϳ0.2⍀ cm at 1 K. The residual resistivity ratio ͑RRR͒ ͓RRRϵ(300 K)/(1 K)͔ for both samples is quite large, RRR͑LANL 161͒ϭ480 and RRR͑UCSD͒ϭ285, indicating the high quality of the single crystals. Upon application of pressures up to 80 kbar, the overall shape of the ( P,T) curves does not change significantly; the maximum in the resistivity sharpens with pressure and shifts slightly, while the minimum flattens and moves to higher temperatures. Figure 4 shows the low-temperature behavior of the resistivity of CeAgSb 2 at various applied pressures. The kink in (T) at T C ϭ9.6 K at Pϭ0, corresponding to the Curie temperature, is suppressed to T C ϳ2.4 K at Pϭ32.6 kbar ͓Fig. 4͑a͔͒; the UCSD data yield a similar variation of T C with pressure ͓Fig. 4͑b͔͒, although the magnetic transitions are somewhat broader. The critical pressure for the suppression of ferromagnetism in CeAgSb 2 is estimated to be P C ϳ35 kbar. The evolution of T C with pressure is clearly visible as a jump in the temperature derivative of the resistivity d/dT as shown in Fig. 5 ͑LANL 161͒. If a close relationship between d/dT and the specific heat is assumed, 32 the ferromagnetic transition is second-order-like for PϽ27 kbar ͑Fig. 5͒ but sharpens considerably with increasing pressure for Pϭ27 Ϫ33 kbar, indicating a first-order-like FM transition. A difference between the cooling and heating (T) curves of ϳ30Ϫ100 mK below 2.2 K ͑at which point the thermal conductivity of the superfluid 4 He is essentially infinite͒ is also observed; however, the present experimental conditions preclude any definite conclusions to be drawn from this possible hysteresis. It is significant, however, that very close to P C ( Pϭ33.6 kbar in Fig. 5͒, d/dT becomes broad suggesting that the transition is driven to be second order as P→ P C , which is predicted theoretically for a clean itinerant ferromagnet. 33 A small change in slope of the (T) curves occurs at Tϳ1 K in CeAgSb 2 ͑LANL 161͒, corresponding to ordering of a possible impurity phase, and does not change significantly with pressure up to 44 kbar.
In the pressure range between 27 kbar and 33 kbar, a decrease in (T) is found at T mag ϳ4 K, indicating the presence of another phase transition in addition to the ferromagnetism, which also appears as a shoulder in d/dT ͑Fig. 5͒. This second magnetic phase is conjectured to be antiferromagnetic since the lattice parameters of CeAgSb 2 at P ϳ25 kbar ͑assuming a bulk modulus of ϳ1 Mbar͒ are close to those of PrAgSb 2 which has a Néel temperature T N ϭ6 K. 13 The first-order-like behavior between 27 kbar and 33 kbar could also be caused by the transition from an antiferromagnetic to a ferromagnetic state. Below P C , the Néel state is manifest as a shoulder in d/dT; but for Pу P C , the resistivity anomaly is more pronounced and d/dT at T N is a maximum near P C ͑see inset of Fig. 5͒ before decreasing at higher pressures. From these data, the Néel temperature of CeAgSb 2 is roughly constant for 27 kbarϽ PϽ P C , increases with increasing pressure to T N ϳ6 K at Pϭ44.1 kbar ͑inset of Fig. 5͒, then is rapidly suppressed above 45 kbar. accalorimetry measurements above 27 kbar provide further evidence for a second phase transition as discussed in Sec. III C. Measurements of CeAgSb 2 ͑UCSD͒ at ambient pressure did not reveal any signs of superconductivity down to T ϳ0.1 K where the resistivity became too small to detect within the capabilities of the experiment. In addition, no superconductivity was observed above 0.3 K in the ferromagnetic state ( Pϭ28.5 kbar) or in the antiferromagnetic state ( Pϭ33.2,40, and 46  as shown in Fig. 6͑a͒. In the ferromagnetic state, the temperature range of these fits is limited to 1 K рTр2 K, but the upper T range increases to 3-4 K in the AFM state. Both 0 and A exhibit a sharp maximum at Pϭ33.6 kbar ͓Figs. 7͑a͒ and 7͑b͔͒, increasing by two and three orders of magnitude compared to the ambient-pressure values, respectively. The results are consistent with previous measurements on CeAgSb 2 . 23 The maxima in 0 and A appear to be ubiquitous for heavy-fermion materials in the vicinity of the QCP. Re-cent work by Miyake and Maebashi 34 provides an explanation for the large increase in 0 near the QCP based on valence fluctuations; however, it is unclear whether this theory applies to CeAgSb 2 . At ambient pressure, the ratio of A to the square of the electronic specific-heat coefficient ␥ 2 yields A/␥ 2 ϭ1.7ϫ10 Ϫ5 ⍀ cm͑mol K/mJ͒ 2 , using ␥ ϭ 65 mJ/ mol K 2 and Aϭ0.071 ⍀ cm, in agreement with the Kadowaki-Woods relation. 35 Assuming the Kadowaki-Woods relation holds under applied pressure, as has been observed, for instance, in the ferromagnetic superconductor UGe 2 , 4,36 the Tϭ0 K Sommerfeld coefficient monotonically increases to ␥ϳ0.5 J/mol K 2 at Pϭ32.6 kbar before jumping to ␥ϳ1.3 J/mol K 2 at Pϭ33.6 kbar where A ϭ17.0 ⍀cm/K 2 .
The electrical resistivity of CeAgSb 2 in the ferromagnetic state can be fit over a much wider temperature range by the expression by including, besides the Fermi-liquid T 2 term, the contribution due to an energy gap in the magnon dispersion relation. 37 In Eq. ͑4͒, D involves the electron-magnon and the spin-disorder scattering and ⌬ is the magnitude of the gap. Fits to Eq. ͑4͒ are shown in Fig. 6 ͓ 0 has been fixed to the value obtained from Eq. ͑3͒ discussed above͔. The T 2 coefficient A increases by nearly an order of magnitude at Pϳ30 kbar, similar to the results obtained from the T 2 fits described above, whereas, the gap energy decreases from ⌬ ϳ30 K at ambient pressure to ⌬ϳ 10 K at Pϳ30 kbar ͓Fig. 7͑c͔͒. Ambient-pressure specific-heat measurements yield a similar value of ⌬ as discussed above. The fit results obtained from the ( P,T) measurements of CeAgSb 2 ͑UCSD͒ are in quantitative agreement with those of CeAgSb 2 ͑LANL 161͒, however, the sharp maxima of 0 and A found in the LANL data ͑Fig. 7͒ are not observed. One possible reason for this discrepancy is that the critical pressure in CeAgSb 2 ͑UCSD͒ is slightly higher than in CeAgSb 2 ͑LANL 161͒ causing the sharp maxima in A and 0 to fall in between the data at Pϭ33.2 kbar and 40 kbar. At the highest pressure of Pϭ77 kbar, a fit of the data to Eq. ͑3͒ was not successful; however, the data could be fit by the power-law expression Ϫ 0 ϭAЈT n over a limited temperature range 1.0 K рT р2.3 K, yielding AЈϭ34 ⍀ cm/K n and nϭ0.8. Further measurements in this pressure range are in progress to determine if this non-Fermi-liquid behavior persists to lower temperatures. Figure 8 displays the inverse of the temperature oscillations 1/T ac vs T obtained at different pressures up to 36.5 kbar. The right vertical axis shows the scale for the approximate heat-capacity values after performing the calibration procedure described in Sec. II to the ambient-pressure C(T) data. The peak in the specific heat due to the ferromagnetic ordering at T C shifts to lower temperatures with increasing pressure. The height and shape of the peak are similar at 1 bar and 6.8 and 16.6 kbar. The transition temperatures at 27 kbar ͑not shown͒ and 31.2 kbar are nearly the same and close to 4 K, which corresponds well to the appearance of a shoulder at 4 K in the d/dT curves. The specific-heat jump at these two pressures is smaller than at 16.6 kbar and the transitions appear to be somewhat broader. At higher pressures, the peak height increases again at 34.2 kbar ͑not shown͒ and 36.5 kbar where the ͑AFM͒ magnetic transition shifts to higher temperatures, resembling the pressure dependence of the anomalies associated with antiferromagnetism in the d/dT curves. The shape of the heat-capacity peak is more symmetric at these two highest pressures and differs from that at low P where ferromagnetic order sets in. We are unable to observe any sharpening of the magnetic transitions in these specific-heat measurements above 27 kbar due to a first-order AFM to FM transition, the proximity to the QCP, or the presence of two transitions in the coexistence region, primarily because the ac-calorimetric method is not well suited for studies of first-order transitions; 21 the accalorimetry method only detects the reversible part and hence, the latent heat associated with the first-order transition will be less than the true value if some part of the system is irreversible. The magnetic entropy associated with both the ferromagnetic and possible antiferromagnetic transitions is approximately equal. This suggests that the second pressureinduced magnetic transition ͑AFM͒ is a bulk effect.

IV. DISCUSSION
The pressure-temperature ( P-T) phase diagram of CeAgSb 2 obtained from analysis of resistivity and specificheat data at high pressure is depicted in Fig. 9͑a͒. Three main regions are indicated, corresponding to a high-temperature paramagnetic ͑PM͒ state, a ferromagnetic ͑FM͒ state, and a presumably antiferromagnetic ͑AFM͒ state. The ferromagnetism at T C ϭ9.6 K at ambient pressure is completely suppressed at an estimated critical pressure P C ϳ35 kbar. As shown by the solid curve in Fig. 9͑a͒, the P dependence of the Curie temperature follows a power law T C ϰ͉PϪ P C ͉ ␤ with P C ϭ35(1) kbar and ␤ has the mean-field value 0.5(1).
There is evidence for the coexistence of a ferromagnetic phase and another magnetic phase ͑AFM͒ between 28 and 33 kbar, suggesting a tricritical point at Pϭ27 kbar. Once the ferromagnetism is suppressed, the Néel temperature increases from T N ϳ4 K at Pϭ35 kbar to ϳ6 K at 44.1 kbar, the highest pressure of the LANL 161 measurements. Experiments on CeAgSb 2 ͑UCSD͒ reveal a similar evolution of the Curie temperature with pressure and an initial increase of T N above 33 kbar ͓Fig. 9͑a͔͒. The Néel temperature drops to a value T N ϳ0.5 K at Pϭ46(6) kbar in this sample, suggesting that the critical pressure for the complete suppression of this magnetic phase is ϳ50 kbar. This estimate is consistent with a linear fit to ⌬( P) ͓Fig. 7͑c͔͒ which shows that ⌬ →0 K at ϳ47 kbar. A recent investigation 23 of the electrical resistivity of CeAgSb 2 under pressure of up to 42 kbar reveals a somewhat different phase diagram than the one presented here ͑Fig. 9͒. In this study, Nakashima and co-workers 23 found a similar suppression of ferromagnetism, with P C ϭ33 kbar and ␤ϭ0.38, but no evidence for the second phase transition between 27 kbar р PϽ50 kbar perhaps due to quasihydrostatic conditions in their pressure cell. However, the decrease in at ϳ1 K at Pϭ36 kbar and 42 kbar ͑e.g., Fig. 3 of Ref. 23͒ may be related to this second high-pressure phase transition rather than the onset of superconductivity as the authors suggest.
In heavy-fermion/Kondo-lattice systems, a crossover occurs from a high-temperature local moment regime to a to 60 kbar. ͓The T C ( P) data of CeAgSb 2 ͑UCSD͒ have been normalized by a factor 0.97 to match the ambient pressure T C to that of the LANL 161 data.͔ The Curie temperature T C ͑squares͒ and Néel temperature T N ͑circles͒ are determined from anomalies in d/dT. The magnetic ordering temperature T mag ͑triangles͒ is determined from ac-calorimetry measurements. The solid line is a fit of the Curie temperature to T C ϰ͉PϪ P C ͉ ␤ discussed in the text. ͑b͒ T max vs P. The dashed lines in both panels are guides for the eye. strongly interacting Fermi-liquid regime at low T as the conduction electrons hybridize with the localized f electrons, giving rise to a maximum in the resistivity at T max . The temperature scale of this maximum in (T) is a rough measure of the Kondo temperature T max ϰT K and is also related to the renormalized energy scale of the low-T Fermi-liquid properties which are manifest, for instance, in the T 2 behavior of the resistivity ͓(T)ϳAT 2 ͔, i.e., T max ϰA Ϫ1/2 . For Cebased heavy-fermion compounds, T max is expected to increase with pressure since the exchange coupling parameter increases with P (dJ/dPϾ0). If the material has a magnetic ground state, the magnetic ordering temperature is eventually suppressed with applied pressure due to the increased strength of the Kondo interaction over the RKKY interaction. The magnetic phase diagram of CeAgSb 2 is more complex than that of a typical Kondo-lattice compound. The appearance of a new magnetic phase under pressure and the coexistence of this magnetic phase with ferromagnetism over a narrow pressure range are in contrast to the behavior of heavy-fermion compounds such as CeIn 3 and CePd 2 Si 2 in which the single magnetic ordering temperature is suppressed with P. 2 The nominally ferromagnetic structure at Hϭ0 and Pϭ0 in CeAgSb 2 , with a linear H dependence of the magnetization below Hϭ3 T followed by saturation with M sat ϳ1.1 B /Ce above 3 T, suggests a more complex magnetic structure that may be easily influenced by magnetic field and pressure. As the Kondo effect increases the exchange parameter J with pressure, the Curie temperature is suppressed to Tϭ0 K at which point strong fluctuations produce a sharp maximum in A and 0 . These fluctuations associated with the FM critical point also influence the Néel temperature giving rise to a minimum in T N ( P) close to P C ϳ 35 kbar. These results are in striking contrast to the behavior of another heavy fermion compound CeRu 2 Ge 2 which exhibits the coexistence of antiferromagnetism (T N ϭ8.5 K, at ambient pressure͒ and ferromagnetism (T C ϭ 7.4 K͒. 30 In CeRu 2 Ge 2 , there is no divergence in A or 0 at the FM critical point; moreover, there is no anomaly in T N ( P) at which the Curie temperature is suppressed to Tϭ0 K. 38,39 The increase in J with additional P in CeAgSb 2 , reflected in the increase of T max above 40 kbar, apparently also causes the eventual suppression of the AFM state at ϳ 50 kbar.
The complexity of magnetic interactions in CeAgSb 2 is reflected in the pressure dependence of T max as shown in Fig.  9͑b͒. T max initially decreases with increasing pressure and exhibits a local minimum at ϳ20 kbar before assuming the expected monotonic increase at pressures above 40 kbar. A similar initial decrease of T max with P occurs in the Ce-based heavy-fermion compound CeRhIn 5 . 1 A sharp minimum of T max is found close to the FM QCP at P C ϭ35 kbar. The maximum in the T 2 coefficient A and the minimum of T max occur at the same pressure Pϭ33.6 kbar and their behavior is qualitatively consistent with the two quantities being related to the Kondo temperature T max ϰA Ϫ1/2 ϰT K . The Néel temperature is also suppressed at Pϭ33.6 kbar and increases when T max increases again above 40 kbar. It is quite unusual to have such a low value of T max Ӎ10 K; in particular, the value of T max is very close to the magnetic ordering temperature over an extended pressure range. It is conceivable that the evolution of T max ( P) is influenced by quantum-critical fluctuations in the vicinity of the quantum critical point. Another possible interpretation is that variation of T max with P could be due to the influence of a low-lying crystalline electric field level above the ground state of comparable magnitude to T max ϳ10 K. While there is evidence of a CEF level at ⌬ 1 ϳ50 K, 25,26 the expected low-T anomalies in the electrical resistivity and specific heat as this CEF level changes with pressure are not observed. Moreover, a second, broad maximum in at ϳ75 K at Pϭ46 kbar and ϳ100 K at P ϭ77 kbar ͓Fig. 3͑b͔͒ and the increase of the minimum in at T min ϳ150 K ( Pϭ1 bar͒ with increasing pressure indicate an increase of ⌬ 1 with pressure. In CeAgSb 2 , the Curie temperature follows a power-law P dependence ͓T C ϰ͉PϪ P C ͉ ␤ , ␤ϭ0.5(1)] and is suppressed at a critical pressure P C ϭ35(1) kbar. In addition, a divergence of the T 2 coefficient of (T), A, is observed in the vicinity of P C , suggesting the presence of a quantumcritical point. Phenomenological spin-fluctuation models [40][41][42] or fluctuations of an order parameter of a second-order phase transition at Tϭ0 K 43 have been proposed to explain the non-Fermi-liquid behavior often observed near a QCP. The predictions of these models for a ferromagnetic quantum-critical point in three ͑two͒ dimensions, i.e., (T)ϰT n with nϭ5/3 ͑4/3͒, a Curie temperature which varies as T C ϰ͉PϪ P C ͉ ␤ with ␤ϭ3/4 ͑1͒, and a divergence of A at P C have been applied to d-electron systems such as MnSi and ZrZn 2 with reasonable success, 2,44 but with less success in the f-electron systems. The variation of T C with P in CeAgSb 2 is more consistent with three-dimensional ͑3D͒ spin fluctuations (␤ϭ3/4) than 2D fluctuations (␤ϭ1); however, an NFL power-law T dependence of is not observed in the present measurements close to the QCP, but may be obscured by the second phase transition above 27 kbar. Further experiments are in progress to examine the behavior of CeAgSb 2 near the suppression of the AFM transition at ϳ50 kbar and possible NFL behavior at higher pressures.

V. CONCLUSIONS
The magnetic phase diagram of the Kondo-lattice material CeAgSb 2 has been investigated at high pressures to 80 kbar and low temperatures by means of electrical resistivity and ac-calorimetry measurements. The ferromagnetism is suppressed at a critical pressure P C ϭ35 kbar, while a new magnetic phase ͑possibly antiferromagnetic͒ appears above 27 kbar. The ordering temperature of this second phase reaches a maximum value T N ϳ6 K at 44 kbar before being suppressed at an estimated critical pressure of ϳ50 kbar. Superconductivity is not observed in the pressure range Pϭ28 Ϫ46 kbar down to Tϭ0.3 K. While there is some evidence of critical phenomena, namely, a divergence of the T 2 coefficient of the electrical resistivity A, no sign of non-Fermiliquid behavior is found near the ferromagnetic quantumcritical point, possibly due to the presence of the antiferromagnetic phase. It is interesting that a nonsuperconducting but ordered phase emerges near the ferromagnetic QCP. If, indeed, this high-pressure magnetic phase in CeAgSb 2 is found to be antiferromagnetic, as we believe it is, it suggests that finite-q excitations can exist near a FM QCP and perhaps play a role in mediating Cooper pairing even in nominally ferromagnetic systems.