Tuning the ferromagnetic phase in the CDW compound SmNiC2 via chemical alloying

We report a study on tuning the charge density wave (CDW) ferromagnet SmNiC2 to a weakly coupled superconductor by substituting La for Sm. X-ray diffraction measurements show that the doped compounds obey Vegard’s law, where La (Lu) alloying expands (shrinks) the lattice due to its larger (smaller) atomic size than Sm. In the series Sm1−xLaxNiC2, CDW transition (TCDW = 148 K) for SmNiC2 is gradually suppressed, while the ferromagnetic (FM) ordering temperature (TC) at 17 K slightly increases up to x = 0.3. For x > 0.3, TC starts to decrease and there is no signature that could be related with the CDW phase. Electrical resistivity, magnetic susceptibility and specific heat measurements point toward the possible presence of a FM quantum critical point (QCP) near x = 0.92, where the TC is extrapolated to zero temperature. Superconductivity in LaNiC2 (Tsc = 2.9 K) is completely suppressed with small amount of Sm inclusion near the proposed FM critical point, indicating a competition between the two ordered phases. The tunable lattice parameters via chemical substitution (La,Lu) and the ensuing change among the ordered phases of ferromagnetism, CDW and superconductivity underscores that SmNiC2 provides a rich avenue to study the rare example of a FM QCP, where the broken symmetries are intricately correlated.

Recently, study on a quantum critical point (QCP) has attracted great interest because of the possibility of previously unknown phases of matter from the singular quantum fluctuations associated with the QCP 1 . There exist a plethora of reports on antiferromagnetic (AFM) QCP systems, but examples with a ferromagnetic (FM) QCP are rare [2][3][4] . The CDW ferromagnet SmNiC 2 shows a quasi-one-dimensional electronic structure, which leads to a CDW state from the Fermi surface nesting, e.g., Peierls instability 5 . Study on the effects of hydrostatic pressure in SmNiC 2 has suggested that singular quantum fluctuations may create novel quantum phases in a vicinity of the projected FM quantum critical point (QCP) near 3.8 GPa (ref. 6). These novel phases, however, hide the presence of the QCP, requiring an alternative approach to probe the nature of the candidate FM QCP. Recently, Kim et al. predicted that both hydrostatic and chemical pressure have similar effects in tuning the electronic states of SmNiC 2 (ref. 7).
Ternary rare-earth nickel carbides (RNiC 2 ) were first reported by Bodak 8 , which are formed in an orthorhombic Amm2 (space group #38) crystal structure with Ni and the rare-earth (R) metal chains being aligned along the crystallographic a-axis. This system is of particular interest because both CDW and long range magnetic ordering phases have been observed together. Among the RNiC 2 compounds only two -SmNiC 2 and LaNiC 2 -exhibit properties other than an AFM ground state. Magnetism in RNiC 2 originates from the lanthanide sublattice and displays an AFM ordering in most cases (R = Ce, Pr, Nd, Gd, Tb, Dy, Ho, Er, Tm) 9,10 . The exceptions, SmNiC 2 and LaNiC 2 , are a ferromagnet and a superconductor, respectively. We note that the crystal structure of LuNiC 2 has been reported 11 , but to our knowledge physical properties of this compound remain unknown.
In SmNiC 2 , the low-temperature synchrotron x-ray diffraction reveals that a CDW state with the wave vector q = (0.5, 0.52, 0) forms below 148 K and disappears below the Curie temperature 17.7 K, indicating destruction of the CDW due to appearance of the ferromagnetic ordering 12 . This is different from NdNiC 2 where a CDW is still observed below the Nèel temperature (in the AFM state) 13 . The coexistence of a CDW with superconductivity is also observed in Er 5 Ir 4 Si 10 and Lu 5 Ir 4 Si 10 (refs 14 and 15).
Superconductivity in the first member of RNiC 2 family, LaNiC 2 with T sc = 2.9 K, was first reported by W. H. Lee, et al. almost two decades ago 8 . Superconducting critical temperature can be increased to 8 K in the solid slight broadening and splitting in the main reflection peaks for 0.2 ≤ x ≤ 0.6. An excellent Le Bail fit (R wp = 11.7, R exp = 8.65, χ 2 = 1.84) was obtained by assuming the presence of two phases with the same crystal structure and different lattice parameters as can be seen for Sm 0.8 La 0.2 NiC 2 (see Fig. 1c). This suggests that two distinct compounds Sm 1−x La x NiC 2 with slightly different La concentrations (x) are present for the intermediate composition range. The majority phase is the one with smaller x -the Sm-richer variant. Such behaviour is not observed for Lu-doped series. The refined lattice parameters for Sm 1−x La x NiC 2 are shown in Fig. S1 of the Supplementary Information. The a and c lattice parameters obey Vegard's law for the whole La concentration range, while the b parameter is almost constant up to x = 0.3 and linearly increases with further increasing La level. The rigid C-C dimers along the b direction are likely responsible for the negligible change in the b lattice constant for the lower La level 10 . The intermediate region, in which two phases with different La/Sm ratio are present, is shadowed on the diagram and the lattice parameters for the second, minority phase are shown by triangles.
The relative change (Δ L/L 0 ) of each lattice parameter vs. nominal concentration of La and Lu for Sm 1−x La x-NiC 2 and Sm 1−y Lu y NiC 2 is presented in Fig. 2. Δ L is the change of each lattice parameter compared to the lattice parameter (L 0 ) of the parent (SmNiC 2 ) compound. For example Δ a/a 0 was calculated from (a x − a 0 )/a 0 , where a x and a 0 are the a-axis lattice parameters for Sm 1−x La x NiC 2 and SmNiC 2 , respectively. With increase in x, the lattice parameter along the a-axis expands more rapidly than that along the b-and c-axis: as large as a 7% increase in the a-axis is observed, while less than 1% change occurs along the b-axis. In contrast, Lutetium doping (y) causes a decrease of the lattice parameters, which is most pronounced along the a-axis. Electrical Resistivity. Resistivity measurements were performed for Sm 1−x La x NiC 2 (0 ≤ x ≤ 1) and Sm 1−y Lu y NiC 2 (0 ≤ y ≤ 0.4) series. Temperature dependence of the normalized resistivity is shown in Fig. 3 for Sm 1−x La x NiC 2 , where resistivity values are normalized to those at 300 K for comparison. Depending on the La concentration, three features are observed. For the parent SmNiC 2 and slightly La doped (x < 0.3) Sm 1− x La x NiC 2 , a sharp inflection at high temperature is seen due to a charge density wave (CDW) formation. T CDW was assigned as the minimum of the temperature derivative of resistivity (dρ/dT). For the parent compound SmNiC 2 the obtained T CDW (= 148 K) is comparable with the previous reports 10, 28 . With increase in La content, the CDW transition temperature starts to decrease rapidly, reaches to 34 K for Sm 0.7 La 0.3 NiC 2 , and is not observed for x > 0.3. The increase in resistivity just below T CDW is due to a CDW gap opening on the Fermi surface. For SmNiC 2 resistivity reaches a maximum at about 120 K and decreases with further decrease of temperature. Another feature that is clearly visible for SmNiC 2 is a sharp drop in resistivity at 17.2 K (see Fig. 3(b)), which is caused by the ferromagnetic (FM) phase transition, as will be supported by magnetic measurements. Although such behaviour is typically seen for ferromagnetic compounds below the Curie temperature, one order of magnitude decrease of resistivity is rare and may originate from the destruction of the CDW state at the same temperature. When a CDW is present, ferromagnetism is robust. In fact, there is a slight increase in the Curie temperature from 17.2 K (SmNiC 2 ) to 17.8 K (Sm 0.25 La 0.75 NiC 2 ) with increasing x. For x > 0.3, the CDW transition is no longer observed and the Curie temperature starts to decrease with increasing La concentration, which suggests a strong correlation between the CDW and ferromagnetic phases. Figure 3(c) presents resistivity data for Sm 1−x La x NiC 2 system with high La concentration (x ≥ 0.9). A sharp superconductivity transition is observed for LaNiC 2 and Sm 0.02 La 0.98 NiC 2 with T sc = 3.4 K and 2 K, respectively. The samples with slightly lower x (0.97 and 0.95) do not show a transition to the zero-resistance superconducting state above 1.8 K, suggesting that the resistivity drop is due to filamentary nature of the SC phase. The rapid suppression of superconductivity is often observed in the presence of magnetic impurities that act as strong scattering centers to destroy superconducting Cooper pairs. One such example is La 1−x Gd x alloy, where only 1% of Gd alloying suppresses T sc from almost 6 K for La to 1 K for La 0.99 Gd 0.01 (ref. 29).
In contrary to La alloying, the low-T normalized resistivity of SmNiC 2 is enhanced by Lu alloying (see Fig.  S2 in the Supplementary Information). The slope of the resistivity (dρ/dT) at high temperatures decreases with  (Fig. 4a) shows a rapid increase with decreasing temperature below 17 K and saturates between 0.5 to 1.2 emu/Sm mol for different La concentrations at low temperatures. At this moment, it is difficult to point out a correlation between the saturated moments and alloying concentrations because the samples are in a polycrystalline form. The FM transition temperature determined by the minimum of the temperature derivative of susceptibility (dχ/dT), as shown in Fig. 4b, is in good agreement with the Curie temperature T C = 17.2 K from the resistivity measurement. Ferromagnetism in Sm 1−x La x NiC 2 is robust. T C initially increases with La concentration, reaches a maximum of 18 K at x = 0.25, and then decreases with further increasing La level, showing a small dome shape in the T-x phase diagram. It is interesting to note that the ferromagnetic phase persists up to the nominal La concentration x = 0.86: a ferromagnetic transition at as low as 2.5 K was observed for the composition x = 0.86 in the series Sm 1−x La x NiC 2 . In order to confirm the ferromagnetic state and precisely estimate the Curie temperature, the Arrott plot analysis was performed. A series of isothermal magnetisation curves in the immediate vicinity of the Curie temperature were measured. In a plot of H/M vs M 2 , the isotherm which passes through the origin gives the best estimate of Curie temperature because H/M = βM 2 at T = T C (ref. 30). The Arrott plot presented in Fig. 5 shows that the ferromagnetic transition temperature for Sm 0.2 La 0.8 NiC 2 is 5.5 K, very close to T C = 5.3 K estimated for the same sample from the minimum of dχ/dT. Using the Arrott plot, T C = 3.5 K was estimated for Sm 0.14 La 0.86 NiC 2 (not shown here).
A molar magnetic susceptibility at 300 K for the Sm 1−x La x NiC 2 series is shown in Fig. S3 of the Supplementary Information, which linearly decreases with increasing La concentration. As expected, the extrapolated line reaches zero at LaNiC 2 . The same experimental data normalized per Sm-mol is almost independent of x and is about χ(300K) = 1.8 × 10 −3 emu/Sm-mol, indicating that La is successfully substituted for Sm.
According to H. Onodera et al., spontaneous magnetization (M) along the a-axis of the single crystal (~0.32 μ B ) is smaller than 0.72 μ B for Sm 3+ , while it is negligible along the b-and c-axis 9 . The fact that we have obtained 0.19 μ B at 2 K could be ascribed to the polycrystalline form of the measured sample. Such a small value has been explained by the mixed valence state of Sm 2+ and Sm 3+ ions or crystalline electric field (CEF) effects. A mixed valent state is common in Sm containing compounds. Above the ferromagnetic transition temperature the entire series did not follow the Curie-Weiss behaviour, which might be pertinent to the mixed valent state of Sm ions. It is imperative to study the exact nature of magnetic interactions present in SmNiC 2 by measurements like neutron diffraction to gain a deep insight on the valence of Sm ions.

Heat Capacity Measurements. Heat capacity C p (T) of the polycrystalline SmNiC 2 (black dots) and
LaNiC 2 (blue solid line) is plotted as a function of temperature in Fig. 6(a). At the highest temperature, C p (at 300 K) reaches approximately 80% of the value expected by Dulong-Petit law 3nR value ~100 J mol −1 K −1 , suggesting that the Debye temperature for SmNiC 2 exceeds 300 K. A small anomaly at around 153K (inset b) is likely caused by the CDW ordering, although this temperature is 5 K higher than a CDW temperature estimated from the resistivity and magnetization measurements. A huge anomaly is visible at low temperature and details are presented in Fig. 6(c). In the zero-field data, a λ -shape transition occurs at T C = 17 K, which is in agreement with the Curie temperature estimated by resistivity and magnetization techniques. With increasing magnetic field, the transition is broadened and split into two peaks, indicating an additional field-induced phase transition. A simple subtraction of the LaNiC 2 specific heat from the SmNiC 2 specific heat yields the temperature dependence of the magnetic specific heat (not shown). The integrated entropy, presented in Fig. 6(d), is close to Rln4 at about 150 K, comparable to the CDW transition temperature for SmNiC 2 . The magnetic entropy recovered at T C ( = 17.1 K) accounts for 80% of Rln2, the entropy expected for the doublet ground state of the J = 5/2 multiplet for Sm 3+ (4f 6 ). Incomplete recovery of the entropy at T C could be ascribed to either the fluctuating valence between Sm 3+ and Sm 2+ or the Kondo screening effects of Sm 4f spins by the itinerant electrons.  Heat capacity data (C p /T) for La-rich samples is selectively presented on a semi-logarithmic scale in Fig. 7. A sharp SC transition for LaNiC 2 (open circles) is visible at 2.9 K in Fig. 7(a). When Sm is alloyed in LaNiC 2 , the SC jump in the specific heat is quickly suppressed and there is no signature for the SC transition down to 1.8 K, the lowest measured temperature, for 3% Sm concentration (x = 0.97). With further increasing Sm concentration, the  low-temperature specific heat divided by temperature (C/T) increases with decreasing temperature and shows a peak at 14% Sm concentration due to the FM ordering, where the brown vertical line marks the Curie temperature estimated from the Arrott plot of magnetization. Even though the lowest measured temperature is limited to 1.8 K, the singular enhancement in C/T is clearly visible as Sm concentration approaches 10%, indicating the possible presence of a FM quantum critical point at that concentration. Figure 7(b,c) magnifies the specific heat of LaNiC 2 near the SC transition temperature. The normal-state specific heat measured at μ 0 H = 3 T, shown by open squares in Fig. 7b, was fitted to C p = γ T + β T 3 , where the first and second terms represent electronic and lattice contributions, respectively. The fit to these data allows us to estimate γ = 7.3(1) mJ mol −1 K −2 , and β = 0.088(5) mJ mol −1 K −4 . The simple Debye model connects the β coefficient and the Debye temperature Θ D through Θ D = (12π 4 nR/5β ) 1/3 = 445 K, where R = 8.314 J mol −1 K −1 and n is the number of atoms per formula unit (n = 4 for LaNiC 2 ). This value is slightly lower than reported Θ D = 456 K for YNiC 2 (ref. 31) and can be explained by a simple mass relationship: larger La mass than Y should result in lower Θ D .
From an equal entropy construction shown by the solid lines in Fig. 7c, superconducting critical temperature was obtained to be T sc = 2.9 K, which is lower than that from the resistivity measurement (T sc = 3.4 K). The ratio between the specific heat jump (Δ C) at T c and the Sommerfeld coefficient (γ ), Δ C/γ T sc , is 1.33, which is close to the BCS predicted value of 1.42 for a weakly coupled superconductor.

Discussion
It is interesting to note that the CDW phase is driven by the one-dimensional (1D) anisotropy along the a-axis in the electronic structure 7 . The 1D anisotropy increases with chemical or physical pressure mainly because the Ni (or Sm) chain along the a-axis is affected the most (either compressed or expanded). The phase diagram for the series Sm 1−x La x NiC 2 is shown in Fig. 8. The results from both transport and magnetic measurements are used to plot the phase diagram. In the top panel of Fig. 8, the unit cell volume is plotted against x and y, which evidently shows that both Sm 1−x La x NiC 2 and Sm 1−y Lu y NiC 2 follow Vegard's law. In the bottom plot of Fig. 8, we can see a slight increase in T CDW with the inclusion of Lu in the lattice due to a positive chemical pressure, while there occurs a decrease in T CDW with increase in La due to a negative chemical pressure in the lattice. The CDW transition is getting suppressed from 148 K (x = 0) to 34 K (x = 0.3) with La doping concentration x and completely destroyed for x > 0.3. When a CDW is present, there is a slight increase in the FM Curie temperature from 17.2 K to 17.8 K (which is confirmed from both transport and magnetic measurements). Recently B-doped SmNiC 2 reported a similar increase in T C from 17.5 K to 23.1 K until the CDW is present 32 . Once a CDW is suppressed in Sm 1−x La x NiC 2 , however, the Curie temperature starts to decrease and is suppressed down to 2.5 K at x = 0.86. Inset of the bottom panel magnifies the temperature-La concentration phase diagram near the pure LaNiC 2 , where solid lines are guides to eyes. Both T C and T sc could be extrapolated to zero Kelvin at x = 0.92, underscoring the possibility of a FM QCP that was proposed by the singular enhancement in the low-T specific heat. Electrical resistivity measurements show that the first-order FM transition in SmNiC 2 changes to the second order or a weakly first order for higher La concentration, suggesting that the disorder introduced by La substitution may be important to the realization of the FM QCP in SmNiC 2 (see Fig. S4 in the Supplementary Information). In the case of Lu doped SmNiC 2 , T C is strongly suppressed from 17.5 K to 8.8 K for y = 0.4. As shown in Fig. S2 in the Supplementary Information, however, the disparate resistivity behaviour near T C for y = 0.4 demands further investigation on the precise nature of magnetic ordering for different Lu doped level.
FM ordering persists up to x = 0.92 in LaNiC 2 -SmNiC 2 system, where the dilution of Sm local moments by La substitution exceeds the percolation limit 33 . Once a CDW is destroyed, the relationship in LaNiC 2 -SmNiC 2 solid solution is almost similar to La-Gd alloy system, where the SC transition temperature of La elemental metal decreases rapidly with increasing Gd content and is completely suppressed at 0.9 at% Gd. La-Gd alloy containing just 3% Gd becomes ferromagnetic at 1.3 K (ref. 29). However, Gd in Y did not show any FM until 10 at% Gd 34 . With the introduction of other rare earths in binary alloys the Neel and Curie points are generally lowered. We have also synthesized other rare earth substitution such as Y alloying to SmNiC 2 . For 20% Y concentration, the CDW is completely destroyed and the Curie temperature is also dropped to 10 K (not shown here).

Conclusions
We have successfully synthesized SmNiC 2 solid solution with La (or Lu) and investigated the tuneable behaviour from the CDW ferromagnet to the weakly coupled superconductor. La alloying in SmNiC 2 expands the lattice parameters (negative pressure), while Lu alloying shrinks the lattice parameters (positive pressure). The CDW transition temperature (T CDW = 148 K) in Sm 1−x La x NiC 2 decreases with increasing La inclusion x because of the poor Fermi surface nesting conditions from the La alloying. La (or Lu) alloying also dilutes the density of Sm local moments because there is no f electron in the substituent, therefore suppressing the FM phase. The Curie temperature, however, does not decrease monotonically with La concentration, but shows a maximum near x = 0.3, underscoring that the CDW and ferromagnetic phases compete against each other. Superconductivity is observed only for La rich compounds (x > 0.92), where the SC transition temperature (T sc = 3.4 K) for LaNiC 2 is quickly suppressed with increasing Sm contents and to zero Kelvin near 8% Sm concentration. When combined with the fact that both Curie temperature and SC transition temperature is suppressed to zero Kelvin near x c = 0.92, the singular enhancement of the low-T specific heat at the critical concentration x c points toward the presence of a ferromagnetic quantum critical point (QCP). We note that disorder introduced by the La substitution may be conducive to the realization of the FM QCP in SmNiC 2 (ref. 35). More study is in progress to elucidate the nature of the candidate QCP.

Methods
The series of compounds Sm 1−x La x NiC 2 (0 ≤ x ≤ 1) and Sm 1−y Lu y NiC 2 (0 ≤ y ≤ 0.4) were synthesized by the arc-melting technique, using constituent elements of purity 99.9% or higher. The weight loss after arc melting was less than 1%, indicating that the nominal concentration is close to the actual alloying level. Since WDS analysis corroborates this conclusion, the nominal concentration was used throughout this manuscript. The arc-melted samples were annealed at 1173K for ten days in a sealed evacuated quartz tube. The annealed samples were quenched in NaCl-ice water mixture. Structural characterization was performed by the powder x-ray diffraction (PXRD) method using a Rigaku diffractometer with Cu Kα radiation. The lattice parameters of the samples were determined by LeBail profile refinements of PXRD carried out using the FULLPROF software 27 . Resistivity measurements were performed using a standard four probe technique employing a Quantum Design Physical Property Measurement System (PPMS). The contacts were made by spot welding of platinum wires on the sample surface. Heat capacity was measured in temperature range 1.9 K < T < 300 K at fields up to 9 T by using the thermal relaxation technique (PPMS system). Magnetic measurements were carried out using a Quantum Design Magnetic Property Measurement System (MPMS).