⇦Chinese Physics Letters, 2019, Vol. 36, No. 5, Article code 057501 Low-Temperature Properties of CePt$_{3}$P Tuned by Magnetic Field * Jian Chen (陈健)1**, Bai-Jiang Lv (吕柏江)2, Shi-Yi Zheng (郑实益)2, Yu-Ke Li (李玉科)3 Affiliations 1Zhejiang University of Water Resources and Electric Power, Hangzhou 310018 2Zhejiang Provincial Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027 3Department of Physics, Hangzhou Normal University, Hangzhou 310036 Received 19 December 2018, online 17 April 2019 *Supported by the Zhejiang Provincial Natural Science Foundation of China under Grant No LQ19A040006, and the Scientific Research Fund of Zhejiang Provincial Education Department under Grant No Y201840160.
**Corresponding author. Email: chenjian123@zju.edu.cn Citation Text: Chen J, Lv B J, Zheng S Y and Li Y K 2019 Chin. Phys. Lett. 36 057501    Abstract We present low-temperature magnetization, magnetoresistance and specific heat measurements on the Kondo lattice compound CePt$_{3}$P under applied magnetic fields up to 9.0 T. At zero field, CePt$_{3}$P exhibits a moderately enhanced Sommerfeld coefficient of electronic specific heat $\gamma_{\rm Ce}=86$ mJ/mol$\cdot$K$^{2}$ as well as two successive magnetic transitions of Ce 4$f$ moments: an antiferromagnetic ordering at $T_{\rm N1}=3.0$ K and a spin reorientation at $T_{\rm N2}=1.9$ K. The value of $T_{\rm N1}$ shifts to lower temperature as magnetic field increases, and it is ultimately suppressed around $B_{\rm c}\sim 3.0$ T at 1.5 K. No evidence of non-Fermi liquid behavior is observed around $B_{\rm c}$ down to the lowest temperature measured. Moreover, $\gamma$ decreases monotonously with increasing the magnetic field. On the other hand, the electrical resistivity shows an anomalous temperature dependence $\rho\propto T^{n}$ with the exponent $n$ decreasing monotonously from $\sim$2.6 around $B_{\rm c}$ down to $\sim$1.7 for $B=9.0$ T. The $T$–$B$ phase diagram constructed from the present experimental results of CePt$_{3}$P does not match the quantum criticality scenario of heavy fermion systems. DOI:10.1088/0256-307X/36/5/057501 PACS:75.20.Hr, 72.15.Qm, 74.62.-c © 2019 Chinese Physics Society Article Text The ground state of an intermetallic compound with correlated 4$f$-electrons is often determined by a competition between the inter-site RKKY interaction and the on-site Kondo screening. With increasing the hybridization between 4$f$ and conduction electrons, the magnetic moments associated with localized 4$f$ electrons are increasingly screened by the conduction electrons, resulting in a reduction in magnetic moments and finally being nonmagnetic.[1] A quantum critical point (QCP) can be approached by suppressing the phase transition temperature down towards $T\rightarrow 0$ K with an external controlling parameter ($P$, $x$, $B$) (pressure, composition or magnetic field). Among these nonthermal parameters, magnetic field is often considered as an ideal one because of its continuity.[2,3] Many antiferromagnetic (AFM) heavy fermion compounds with field-induced QCP have been identified and show non-Fermi liquid (NFL) behavior around QCP,[4–7] such as Ce-based CeAuSb$_{2}$,[8] CeNiGe$_{3}$,[9] Yb-based YbRh$_{2}$Si$_{2}$,[10] and YbAgGe.[11] CePt$_{3}$P, a member of $A$Pt$_{3}$P family with $A$=Ca, Sr and La, was firstly reported by our group recently.[12] These compounds crystallize in a tetragonal structure with space group $P4/nmm$ (No. 129) assembled by a sequence of $A$-Pt$_{6}$P-$A$ along the $c$-axis.[13] The distorted antiperovskite Pt$_{6}$P octahedral unit alternates within the $ab$ plane, forming an antipolar pattern. The $z\rightarrow-z$ inversion operation is thus preserved. Noticeably, the $A$Pt$_{3}$P family shows superconductivity with a variation of $T_{\rm c}=8.4$, 6.6 and 1.5 K for $A$=Sr, Ca and La, respectively. The origin of the enhanced $T_{\rm c}$ in SrPt$_{3}$P is still an open issue, while a possible dynamic charge-density wave (CDW) is proposed by Chen et al.[14] Several theoretical works claimed that the CDW instability does not work in SrPt$_{3}$P.[15,16] The spin-orbit coupling (SOC) effect is reported to be prominent in LaPt$_{3}$P whereas is negligible in CaPt$_{3}$P and SrPt$_{3}$P.[14–16] However, Zocco et al. indicated that SOC could strongly renormalize the electron-phonon coupling of SrPt$_{3}$P and thus could enhance the electronic density of states near the Fermi level.[17] Different from the other $A$Pt$_{3}$P members with superconductivity, CePt$_{3}$P with localized moments of Ce$^{3+}$ exhibits the coexistence of AFM ordering, the Kondo effect and also the CEF interactions.[12] Two successive magnetic transitions are consistently observed as anomalies in $Td\chi/dT$, $C$ and $d\rho/dT$: an AFM ordering at $T_{\rm N1}=3.0$ K and a spin reorientation at $T_{\rm N2}=1.9$ K. The electronic Sommerfeld coefficient $\gamma_{\rm Ce}=86$ mJ/mol$\cdot$K$^2$ is enhanced by 4$f$–5$d$ hybridization. The Kondo effect is displayed as $\rho_{\rm mag}\sim -\log T$ in Ref.  [12]. The CEF effect is reflected as a slope change in $1/\chi(T)$ and a broad hump in $\rho(T)$. There is a field-induced metamagnetic transition (MMT) around $B_{\rm m}=3.0$ T at $T=2$ K. To tune the ground state and to gain further insight into the physical properties of CePt$_{3}$P, here we report the low-temperature magnetization, electrical resistivity, and specific heat measurements under applied magnetic fields up to 9.0 T. With increasing the applied magnetic field, both transition temperatures are gradually suppressed and tend to merge at $T=1.5$ K around $B_{\rm c}=3.0$ T. The $T$–$B$ phase diagram is constructed to show the evolutions of the magnetic ordering temperatures $T_{\rm N1}$ and $T_{\rm N2}$ with applied magnetic field. In the vicinity of $B_{\rm c}$, the behavior of specific heat and resistivity at low temperatures is analyzed in detail. The polycrystalline sample of CePt$_{3}$P was synthesized by two-step solid state reaction (see Ref.  [12] for details). The obtained CePt$_{3} $P sample is quite stable in air and thus ensures measurements of physical properties. The dc magnetization was measured up to 5.0 T and down to 1.9 K in a Quantum Design MPMS-5 superconducting quantum interference device (SQUID) magnetometer. The standard four-probe dc electrical resistivity $\rho(T)$ and heat capacity under zero field and applied magnetic field up to 9.0 T and 8.0 T, respectively, were measured in a Quantum Design PPMS-9 instrument using a $^3$He refrigerator down to 0.5 K.
cpl-36-5-057501-fig1.png
Fig. 1. Representative low-temperature magnetic susceptibility (a) and resistivity (b) of CePt$_{3}$P measured under zero and applied magnetic fields, respectively. The magnetic fields increase along the solid lines. The resistivity curves are shifted for clarity. Inset in (b): $d\rho(T)/dT$ for $B=2.5$ T. Arrows indicate a maximum and slope change in $d\rho/dT$.
The temperature-dependent molar magnetic susceptibility of CePt$_{3}$P, $\chi(T)=M/H$, measured under various applied magnetic fields is plotted in Fig. 1(a). For zero magnetic field, there are two anomalies at low temperatures corresponding to two successive magnetic transitions: an AFM ordering at $T_{\rm N1}=3.0$ K and a spin reorientation at $T_{\rm N2}=1.9$ K. As the external magnetic field increases, $T_{\rm N2}$ drops down below 1.9 K and cannot be detected within our measurement limit, while $T_{\rm N1}$ shifts to lower temperatures and drops to 2.35 K at $B=2.5$ T. At higher fields, $\chi(T)$ does not reveal any signature of magnetic phase transition but shows a tendency towards saturation at low temperatures instead. Representative temperature-dependent resistivity $\rho(T)$ curves of CePt$_{3}$P are shown in Fig. 1(b). For $B=0$, no trace of superconducting transition is observed at the lowest temperature measured ($\sim$0.5 K). Instead, CePt$_{3}$P shows magnetic ordered ground state, of which the AFM transition manifests itself in the $d\rho(T)/dT$ curve as a clear slope change at $T_{\rm N1}=3.0$ K and a precipitous drop at $T_{\rm N2}=1.9$ K.[12] With increasing magnetic field, $T_{\rm N2}$ is slightly suppressed while $T_{\rm N1}$ shifts down to lower temperatures. The inset of Fig. 1(b) plots $d\rho(T)/dT$ for $B=2.5$ T, in which two anomalies can be seen around $\sim$2.65 K as a slope change and $\sim$1.85 K as a maximum, corresponding to $T_{\rm N1}$ and $T_{\rm N2}$, respectively. Here $T_{\rm N1}$ is suppressed around $B=3.0$ T and at higher fields ($\geq$4.0 T), no signature of magnetic transition can be differentiated.
cpl-36-5-057501-fig2.png
Fig. 2. Low-temperature specific heat of CePt$_{3}$P divided by temperature, $C/T$, versus $\log T$ measured under various applied magnetic fields. Arrows show the onset of AFM ordering temperatures $T_{\rm N1}$ (see text). Inset: $C/T$ as a function of applied magnetic field at $T=0.58$ K.
The temperature-dependent specific heat of CePt$_{3}$P is plotted as $C(T)/T$ in a semi-logarithmic scale in Fig. 2 under representative applied magnetic field. For zero magnetic field, $C/T$ shows a pronounced $\lambda$-shape peak at $T_{\rm N1}=3.0$ K, implying a second-order magnetic phase transition. A slight slope change is also observed around $T_{\rm N2}=1.9$ K. As magnetic field increases, $T_{\rm N1}$ shows a pronounced suppression and cannot be distinguished from specific heat measurement. The determined AFM phase transition temperatures from $C(T)/T$ are indicated by arrows in Fig. 2, which are consistent with the values determined from magnetic susceptibility $\chi(T)$ and transport data $\rho(T)$. For $B=4.0$ T, $C(T)/T$ exhibits a broad maximum centered around 2.3 K, implying a crossover from AFM to paramagnetic (PM) state. At higher magnetic fields, this maximum, a Schottky-like anomaly, broadens further and shifts to higher temperatures as presented in Fig. 2. This indicates that the magnetic entropy is removed at higher temperatures for larger applied magnetic fields.[18] Similar examples are also found in a number of Kondo lattice systems under magnetic fields. Note that $C(T)/T$ at low temperatures displays no clear signature of NFL behavior for any field measured.[2,3] The electronic specific-heat coefficient $\gamma$ reflects the effective mass of Ce-4$f$ electrons. To evaluate the change of $\gamma$, the evolution of the specific heat with applied magnetic field is measured at $T=0.58$ K, plotted as $C/T$ versus $B$ in the inset of Fig. 2. Although $\gamma$ at low fields cannot be simply defined as $C/T$ because of the AFM order, ($C/T-\gamma_{\rm Ce}$) at low temperature acts as a rough estimate. One can see that $C/T$ drops monotonously with increasing the magnetic field within the measured range. Moreover, the estimated $\gamma$ value in PM state decreases to $\sim$90 mJ/mol$\cdot$K$^{2}$ for $B=8.0$ T, indicating that an applied magnetic field can weaken the hybridization of Ce-4$f$ with conduction electrons in CePt$_3$P.
cpl-36-5-057501-fig3.png
Fig. 3. (a) Magnetization isotherms of CePt$_{3}$P at $T=2$, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 6 and 10 K. (b) Electrical resistivity of CePt$_{3}$P versus magnetic field at $T=1.5$, 1.75, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.75, 4, 5 and 6 K. The dashed line marks the MMT transitions. Inset in (a): $dM(B)/dB$ at $T=2$, 2.25, 2.5, 2.75, 3 and 3.25 K.
The isothermal field-dependent magnetization $M(B)$ and resistivity $\rho(B)$ shed further light on the low-temperature magnetic states of CePt$_{3}$P, as shown in Fig. 3. At the lowest temperature $T=2.0$ K, $M(B)$ linearly increases below 2.0 T, undergoes a weak field-induced MMT around $B_{\rm m}=3.0$ T and then shows a relatively slight increase without saturation up to 5.0 T. With increasing temperature, the MMT shifts to lower fields and is no longer observed for $T\geq3.0$ K. This MMT is clearly indicated as a peak in the $dM/dB$ analysis, as seen from inset of Fig. 3(a). On the other hand, $\rho(B)$ for 1.5 K$\leq T\leq$3.0 K reveals a clear slope change corresponding to MMT, but shows a monotonous decrease for $T>T_{\rm N1}$ up to 8.0 T. The MMT derived from $\rho(B)$ curves shifts to lower fields as temperature increases, as the dashed line shown in Fig. 3(b). Note that no hysteresis is observed in the $M(B)$ curve down to 2.0 K, nor in the magnetoresistance curve $\rho(B)$ at 1.5 K. Such absence of hysteresis around MMT is not rare for CePt$_{3}$P but also reported in the single-crystalline samples CeAuSb$_{2}$[8] and YbNiSi$_{3}$.[19] In Fig. 4 the phase transition temperatures and fields of CePt$_{3}$P determined from magnetization, resistivity and specific heat measurements are plotted in the $T$–$B$ plane, where symbols are extracted from $d\rho(T)/dT$, $d\chi\cdot T/dT$ and $dM(B)/dB$ analyses, together with anomalies in $\rho(B)$ and $C(T)$. The value of $T_{\rm N1}$ gradually shifts to lower temperature under applied fields up to $\sim$3.0 T, namely the critical field $B_{\rm c}$. It is assumed that a magnetic field of $\sim$3.1 T may suppress the phase transition completely making the phase diagram similar to the cases of field-induced QCP in several heavy fermion systems.[10,11,20,21] One can see from the phase diagram that the phase transitions determined from temperature sweeps track well those values determined from field sweeps measurements. Nevertheless, single crystals are highly desired to investigate the magnetic anisotropy.
cpl-36-5-057501-fig4.png
Fig. 4. The $B$–$T$ phase diagram of CePt$_{3}$P. Different symbols correspond to the phase lines obtained from different thermodynamic and transport measurements: open circle-$\rho(T)$, filled circle-$\rho(B)$, open square-$\chi(T)$, filled square-$M(B)$ and filled triangle-$C(T)$ for $T_{\rm N1}$.
cpl-36-5-057501-fig5.png
Fig. 5. (a) Low-temperature electrical resistivity of CePt$_{3}$P around the critical field $B_{\rm c}$ at $B=2.5$, 3.0 and 3.5 T, respectively. The curves are shifted along the longitude direction for clarity. (b) Resistivity as a function $T^{n}$ at the selective magnetic fields. Red solid lines are the linear fit to $AT^{n}$ below 1.8 K. Exponent $n$ (c) and coefficient $A$ (d) as a function of magnetic field.
To further understand the low-temperature state of CePt$_{3}$P under applied magnetic field, it is necessary to analyze the magnetotransport and thermodynamic data in detail. The arrow in Fig. 5(a) indicates the onset of AFM order $T_{\rm N1}$, which corresponds to a round anomaly. As the magnetic field increases from 2.5 to 3.0 T, the AFM order is gradually suppressed and cannot be differentiated above 3.5 T. Low-temperature resistivity measured under applied magnetic fields was fitted with a power law equation $\rho(T)=\rho_0+AT^{n}$ from 1.8 K down to the base temperature ($\sim$0.5 K), by the red solid lines shown in Fig. 5(b). The fitting parameters of coefficient $A$ and exponent $n$ are plotted in Figs. 5(c) and 5(d), respectively. The exponent $n$ drops quickly from $\sim$2.6 for $B=3.0$ T down to $\sim$1.9 for $B=7.0$ T and then tends to saturate around 1.7 up to $B=9.0$ T. The coefficient $A$ shows a broad maximum around $B=6.0$ T. In contrast to field-induced QCP in CeAuSb$_{2}$,[8] YbRh$_{2}$Si$_{2}$,[10] and YbAgGe,[11] the expected NFL behavior with $n\approx 1.0$ and a divergent coefficient are not exhibited in CePt$_{3}$P in the vicinity of the magnetic phase boundary $B_{\rm c}$. This may arise due to a weak hybridization between Ce-4$f$ and conduction electrons and the possible first order nature of the phase transition near $B_{\rm c}$.[9] It is possible that $n$ may approach 1.0 for $T < 0.5$ K and a field-induced QCP may come out in a narrow field range around $B=6.0$ T at lower temperatures. This conclusion cannot be reached from the present data and further low-temperature experiments are therefore called for to explore the existence of the field-induced QCP in CePt$_{3}$P. Note that the $n>2$ deviation from fermi-liquid behavior is also reported in CeNiGe$_{3}$[9] and YbNiSi$_{3}$.[19] In these Kondo lattice compounds, the anomalous metallic resistivity behavior in the paramagnetic state is reflected as $\rho(T)\propto T^{n}$, with $n=3$ for CeAuSb$_{2}$[8] and $n>2$ for CeNiGe$_{3}$[9] and YbNiSi$_{3}$[19] at low temperatures. Different from CePt$_{3}$P, these compounds show similar $T$–$B$ phase diagrams with two MMTs, emerging when $T_{\rm N}$ is lowered by applied magnetic field. In summary, magnetization, transport and thermodynamic measurements of CePt$_{3}$P reveal a $T$–$B$ phase diagram which reflects the evolutions of antiferromagnetic ordering temperature $T_{\rm N1}$ with the applied magnetic field: $T_{\rm N1}$ can be suppressed by magnetic field of $B_{\rm c}\sim 3.0$ T to 1.5 K. Unlike several heavy fermion systems with a field-induced QCP, no clear signature of non-Fermi liquid behavior can be observed at the lowest temperatures in the vicinity of $B_{\rm c}$. The Sommerfeld coefficient $\gamma$ decreases monotonously with increasing the magnetic field without divergency around $B_{\rm c}$. However, at higher fields, an anomalous temperature dependence of resistivity, $\rho\propto T^{n}$, with the exponent $n$ smaller than 2.0, is observed. A field-induced QCP in CePt$_{3}$P cannot be excluded from the present results and more experiments down to much lower temperatures ($ < $0.5 K) are highly desired to further complete the $T$–$B$ phase diagram. We thank Qimiao Si, Jianhui Dai and Yongkang Luo for useful discussions. References Non-Fermi-liquid behavior in d - and f -electron metalsAddendum: Non-Fermi-liquid behavior in d - and f -electron metalsFermi-liquid instabilities at magnetic quantum phase transitionsQuantum Criticality: Competing Ground States in Low DimensionsHow do Fermi liquids get heavy and die?Locally critical quantum phase transitions in strongly correlated metalsThe Kondo lattice and weak antiferromagnetismMagnetic field-tuned quantum critical point in CeAuSb 2 Tuning low-temperature physical properties of CeNiGe 3 by magnetic fieldMagnetic-Field Induced Quantum Critical Point in Y b R h 2 S i 2 Magnetic field induced non-Fermi-liquid behavior in YbAgGe single crystalsAntiferromagnetic Kondo lattice compound CePt3PStrong Coupling Superconductivity at 8.4 K in an Antiperovskite Phosphide Sr Pt 3 P First-principles calculations of the electronic and phonon properties of A Pt 3 P ( A = Ca, Sr, and La): Evidence for a charge-density-wave instability and a soft phononElectron and Phonon Band-Structure Calculations for the Antipolar SrPt 3 P Antiperovskite Superconductor: Evidence of Low-Energy Two-Dimensional PhononsElectron-phonon superconductivity in A Pt 3 P ( A = Sr , Ca, La) compounds: From weak to strong couplingLattice dynamical properties of superconducting SrPt 3 P studied via inelastic x-ray scattering and density functional perturbation theoryInterpretation of Kondo experiments in a magnetic fieldMagnetic-field tuning of the low-temperature state of Yb Ni Si 3 The break-up of heavy electrons at a quantum critical pointField-induced non-Fermi-liquid resistivity of stoichiometric YbAgGe single crystals
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