Complex magnetic phase diagram of ferromagnetic CeNiSb 3

Measurements of electrical resistivity at applied pressures up to 55 kbar have been carried out on single crystals of the ferromagnet CeNiSb 3 revealing a complex magnetic phase diagram. The ferromagnetism at ambient pressure at T c =6 K ﬁrst increases with pressure up to 25 kbar, then decreases slightly for P . 25 kbar. In the pressure range 35 kbar ł P ł 55 kbar, a second anomaly in the resistivity is found at T M 2 , below another higher temperature magnetic phase that is conjectured to be different than the ferromagnetism present at lower pressure. Changes in the physical properties such as the residual resistivity, and low temperature maximum in r mag s T d suggest a modiﬁcation of the electronic structure where the two magnetic phases coexist with one another above 35 kbar. The critical pressure for the suppression of the lower temperature phase is estimated to be P cmag 2 . 55 kbar, while the increase of both the T 2 coefﬁcient of the electrical resistivity A and residual resistivity r 0 is suggestive of a quantum critical point associated with the higher temperature magnetic phase at P c mag 1 , 60 kbar.

Measurements of electrical resistivity at applied pressures up to 55 kbar have been carried out on single crystals of the ferromagnet CeNiSb 3 revealing a complex magnetic phase diagram. The ferromagnetism at ambient pressure at T c = 6 K first increases with pressure up to 25 kbar, then decreases slightly for P Ͼ 25 kbar. In the pressure range 35 kbarഛ P ഛ 55 kbar, a second anomaly in the resistivity is found at T M2 , below another higher temperature magnetic phase that is conjectured to be different than the ferromagnetism present at lower pressure. Changes in the physical properties such as the residual resistivity, and low temperature maximum in mag ͑T͒ suggest a modification of the electronic structure where the two magnetic phases coexist with one another above 35 kbar. The critical pressure for the suppression of the lower temperature phase is estimated to be P c mag2 Ӎ 55 kbar, while the increase of both the T 2 coefficient of the electrical resistivity A and residual resistivity 0 is suggestive of a quantum critical point associated with the higher temperature magnetic phase at P c mag1 ϳ 60 kbar. The occurrence of exotic ground states in the vicinity to a second-order phase transition tuned to zero temperature, or quantum critical point ͑QCP͒, has attracted considerable attention in recent years. Pressure tuning of antiferromagnetic f-electron heavy-fermion compounds has been particularly fruitful in uncovering these emergent ordered phases near the quantum critical point as well as elucidating the unusual power law or logarithmic temperature dependences of the physical properties, or non-Fermi liquid ͑NFL͒ behavior, arising from the abundant quantum fluctuations in the vicinity of the QCP ͑for a recent review, see Ref. 1͒. For instance, a dome of superconductivity with T c max ϳ 0.4 K in CePd 2 Si 2 is found near an antiferromagnetic instability at a critical pressure P c = 28 kbar. 2 At P c , the normal state electrical resistivity is best described by a NFL power law T dependence − 0 = AT n with n = 1.2 in contrast to the T 2 behavior expected for a Fermi liquid. More recently, forms of order have been observed near a ferromagnetic ͑FM͒ QCP, such as the coexistence of superconductivity and FM order in UGe 2 , 3 a non-Fermi liquid ground state in the presence of ferromagnetism, 4 or the occurrence of a magnetic phase near the FM QCP in CeAgSb 2 . 5 It is therefore of interest to investigate f-electron systems near a ferromagnetic instability. To this end, we present measurements of electrical resistivity up to 55 kbar on ferromagnetic CeNiSb 3 .
CeNiSb 3 adopts the orthorhombic Pbcm structure comprised of alternating Ce, Ni-centered octahedra, buckled planar Sb layers. 6 It is one of the few Ce-based compounds to order ferromagnetically ͑T c =6 K͒. Magnetization measurements 7 indicate large magnetocrystalline anisotropy with an easy axis saturation magnetization M sat c = 1.55 B / Ce atom along the c direction, M sat b = 0.95 B /Ce atom, and a hard axis with M sat a ͑6 T͒ = 0.12 B / Ce atom along the a direction. Curie-Weiss fits to the magnetic susceptibility data yield an average effective moment ef f = 2.58 B , close to that expected for trivalent Ce ͑ ef f = 2.54 B ͒; the Curie-Weiss temperatures reveal strong ferromagnetic correlations along the c axis ͑ CW c =29 K͒ and antiferromagnetic correlations in the ab plane ͑ CW a = −156 K͒. Bulk ferromagnetism is confirmed by the large anomaly in the specific heat. Both the small value of the Sommerfeld coefficient ␥ ϳ 50 mJ/ mol K 2 and magnetic entropy released below the transition S mag Ӎ 4.4 J / mol K = ͑0.75͒Rln͑2͒ indicate a modest Kondo interaction within a crystal-field ͑CF͒ split doublet ground state of Ce in CeNiSb 3 . At high temperatures, a Schottky-like anomaly at ϳ70 K in the magnetic specific heat indicates excitations to an excited CF level; the magnetic entropy up to 300 K S mag ͑300 K͒Ӎ14 J / mol K is very close to the entropy expected for the full Ce J =5/2 Hund's rule multiplet Rln͑6͒ = 14.9 J / mol K.
Single crystals of CeNiSb 3 were grown in excess Sb flux. 8 The orthorhombic Pbcm structure was confirmed by powder x-ray diffraction. 6 Electrical resistivity measurements under pressure were carried out using both a Be/ Cu piston-cylinder clamped device and a profiled toroidal anvil clamped device 9 with anvils supplied with a boron-epoxy gasket and Teflon capsule, containing pressure-transmitting liquid, sample, and a pressure sensor. The pressure was determined from the variation of the superconducting transition of lead using the pressure scale of Eiling and Schilling. 10 The width of the Pb transition implied a pressure gradient of Շ0.5 kbar at the highest pressure. A standard four-probe technique was performed using an LR-700 Linear Research bridge operating at a current of 1 mA applied along the b axis of the crystal.
The electrical resistivity ͑T͒ of CeNiSb 3 at various applied pressures is displayed in Fig. 1. At ambient pressure, the resistivity is weakly temperature dependent above 150 K and reaches a minimum at ϳ30 K followed by a maximum at ϳ20 K, before decreasing rapidly in the ferromagnetic state. Upon subtraction of the nonmagnetic contribution of LaNiSb 3 , the magnetic scattering mag ϵ ͑CeNiSb 3 ͒ − ͑LaNiSb 3 ͒ exhibits a logarithmic temperature dependence above ϳ200 K, characteristic of Kondo systems, and two broad maxima ͑or shoulder͒ at T max1 ϳ 77 K and T max2 = 10.8 K s shown in inset ͑a͒ of Fig. 1. The low-T maximum in ͑T͒ is assumed to be related to the Kondo lattice coherence, 11 while the high temperature maximum at T max1 is associated with scattering from an excited crystal field level, consistent with the Schottky anomaly observed in specific heat measurements. Below 10 K, the ferromagnetic transition temperature first increases with applied pressure up to 31.3 kbar, then begins to decrease at higher pressure up to 35.6 kbar. At P = 39.5 kbar, a sharp kink in ͑T͒ at T M2 = 5 K signals the onset of a second phase transition below the upper one at T M1 = 7 K. The change in slope of ͑T͒ in between the two transitions for P ജ 39.5 kbar, suggests that the ferromagnetic phase transforms into a phase that is coexistent with the lower temperature phase. Both magnetic transitions are observed between 39.5 and 51.3 kbar and decrease with increasing pressure up to P = 55.2 kbar, at which point only the upper transition is found.
The evolution of the magnetic phase transitions of CeNiSb 3 with pressure is clearly illustrated by anomalies in the first derivative d / dT as shown in Fig. 2. If the relation between specific heat and d / dT is assumed to hold, 12 the ferromagnetic transition appears to be second-order up to 31.3 kbar, where the shape of the anomaly associated with this transition then changes at P = 39.5 kbar. The lower transition at T M2 is sharp and first-order-like up to 42.4 kbar, but then attains a broader shape more characteristic of a secondorder phase transition at P = 51.3 kbar; for P Ͼ 51.3 kbar, only an anomaly associated with the upper transition at T M1 is observed. Figure 3 shows the low temperature power law fits ͑ − 0 = AT n ͒ to the ͑P , T͒ data of CeNiSb 3 . The exponent n is about 3 up to the maximum in the Curie temperature at 25 kbar and exhibits a local minimum close to the pressure where there is coexistence of two magnetic phases in the range 35.6 kbarഛ P Շ 55 kbar. Fermi liquid behavior is recovered at pressures of 51.3 and 55.2 kbar. The generalized A coefficient of the power law fits increases by an order of magnitude between ambient pressure and P = 55.2 kbar; at this pressure, the empirical Kadowaki-Woods relation 13 ͓A / ␥ 2 =1ϫ 10 −5 ⍀ cm ͑mol K / mJ͒ 2 ͔ implies a heavy Fermi liquid ground state with ␥ ϳ 300 mJ/ mol K. 2 Fits of the data to activated behavior associated with a gap in the magnon dispersion 5 proved unsatisfactory for all pressures and only the data at the highest pressures of 51.3 and 55.2 kbar could be fit to a T 2 contribution ͓in agreement with the power law fits shown in Fig. 3͑b͔͒. Figure 4 provides a summary of our electrical resistivity measurements under pressure on CeNiSb 3 . At modest pressures, the Curie temperature first increases with increasing pressure, then decreases, passing through a maximum at 25 kbar. Features in the various physical properties ͓the abrupt jump in 0 , change in slope of A͑P͒, etc.͔ signal the onset of a second ͑lower͒ phase at T M2 at ϳ35 kbar. For 40 kbarഛ P Շ 55 kbar, there is evidence for two phase transitions in the ͑P , T͒ curves, which we postulate are magnetic in nature and different from the ferromagnetism present at lower pressure. It is likely that one or both of these phases are antiferromagnetic since PrNiSb 3 exhibits antiferromagnetic order at T N = 4.5 K and has a similar unit cell volume to that of CeNiSb 3 under pressure. 14 The increase of A and 0 at the highest pressures is suggestive of a quantum critical point at P c mag1 ϳ 60 kbar associated with the suppression of the upper magnetic phase at T M1 .
There is growing evidence that the CeTSb 3 and CeTSb 2 ferromagnets are unstable to new forms of magnetic order. In CeNiSb 3 , the change in shape of the ͑T͒ curves for P ജ 40 kbar and the presence of a second magnetic phase at T M2 suggests the emergence of a new phase at T M1 descendent from the ferromagnetism at lower pressure. The appear- ance ͑or disappearance͒ of these two phases seems not to be related to a change in the crystal field ground state as the feature at T max1 decreases only slightly upon the application of 60 kbar. In addition, the smooth evolution of the coherence feature at T max2 indicates the occurrence of the new phases are not associated with a drastic change in the electronic structure. A complex magnetic T-P phase diagram is also revealed in the heavy-fermion ferromagnet CeAgSb 2 . 5 In this material, ferromagnetism at T c =10 K at P = 0 kbar is suppressed at P c = 35 kbar. In a narrow pressure range ͑ϳ5 kbar͒ below P c , a first order transition occurs between a ͑presumed͒ antiferromagnetic state ͑T N ϳ 5 K͒ and the ferromagnetic phase. A sharp maximum in the A coefficient of the T 2 behavior and also 0 at P c is the only evidence of quantum criticality; any low-T NFL behavior is likely obscured by the antiferromagnetism at T N ϳ 2 -4 K in this pressure range. In contrast to CeNiSb 3 , a distinct feature in the low-T maximum in the ͑T͒ curves at T max is found close to P c in CeAgSb 2 . Preliminary measurements on CeZnSb 2 indicate ferromagnetism at T C ϳ 6 K coexisting with a spin glass phase at lower temperature up to 60 kbar. 15 The unusual magnetic phase diagrams of all three of the Ce-based ferromagnets indicate the competition between the Ruderman-Kittel-Kasuya-Yosida ͑RKKY͒ interaction, which promotes magnetic order, and the Kondo effect, which suppresses magnetic order, is more complex than originally proposed by Doniach 16 and is influenced by such factors as magnetocrystalline anisotropy and crystal field effects.
In summary, measurements of electrical resistivity under pressure on CeNiSb 3 reveal a complex magnetic phase diagram. Ferromagnetism in this material is only slightly suppressed for P Ͼ 35 kbar before a second phase transition is found at T M2 below another higher temperature magnetic phase. Changes in the physical properties such as the residual resistivity, and coherence maximum in mag ͑T͒ suggest a modification of the electronic structure upon entering this two phase region above 35 kbar. The critical pressure for the suppression of the lower temperature phase is estimated to be P c mag2 Ӎ 55 kbar, while the increase of both the T 2 coefficient of the electrical resistivity A and residual resistivity 0 is suggestive of a quantum critical point associated with the higher temperature magnetic phase at P c mag1 ϳ 60 kbar.
Work at Los Alamos was performed under the auspices of the U.S. DOE. V.A.S. acknowledges the support of Russian FIG. 3. ͑a͒ − 0 vs T for P ഛ 39.5 kbar on a log-log scale of CeNiSb 3 . Each of the curves have been shifted vertically by one decade from the curve below it for clarity. ͑b͒ − 0 vs T for 46.6 kbarഛ P ഛ 55.2 kbar. The lines in ͑a͒ and ͑b͒ are power law fits to the data yielding the exponent n indicated beside each curve where the uncertainty in the last digit is indicated by the number in the parentheses. The deviations from the power law behavior at ϳ4 K of the data at 1 bar and 25.6 kbar are an experimental artifact.
FIG. 4. Power law exponent n, coefficient A, residual resistivity 0 , features in the magnetic contribution to the resistivity T max1 and T max2 , and magnetic ordering temperatures T c , T M1 , T M2 vs P in ͑a͒-͑d͒, respectively. The lines are guides to the eye.