Effects of antiferro-ferromagnetic phase coexistence and spin fluctuations on the magnetic and related properties of NdCuSi

After the discovery of giant magneto-resistance (GMR) effect in certain artificial magnetic metallic multilayers, extensive theoretical and experimental studies on this phenomenon in a variety of materials have been carried out because of its importance in fundamental physics and practical applications such as magnetoresistive read heads and field sensing devices.^1–5 The dramatic change in resistivity in multilayers arises because of the change in the spin polarized transport current when the AFM coupled layers are forced into a FM alignment by the application of an external field.⁶ In addition to artificial multilayers, certain bulk compounds such as magnetic perovskites,⁷ granular alloys,⁸ and intermetallics^6,9–11 are also known to exhibit large MR. Many of these systems can be considered as natural multilayers as they have layered structure with magnetic ions confined to certain layers. However, it is interesting to note that some bulk compounds, which do not crystallize in the layered structure, also show considerable MR.^9,11 Large MR in these compounds arises due to the spin-dependent scattering of charge carriers and may be associated with field induced magnetic phase transition, structural transformation, or volume change. Similarly, MCE is also seen to be large in systems which show co-existence of the two magnetically different phases.

In this paper, we study magnetic and related properties of NdCuSi, which belong to the RTX family (where R = rare earth element, T = 3d/4d/5d transition metal ion, and X is nonmagnetic ion). Observation of many interesting magnetic and related properties in the compounds of this family has drawn the attention of researchers.¹² Some compounds in this family are found to show large MCE and has the potential to be used as magnetic refrigerants at low temperatures.^11–18 It is reasonable to expect large MR also in these compounds. In certain compounds of this family, interesting MCE and MR behavior has been observed, which is attributed to the coexistence of AFM-FM phases. For example, NdCuAl, which is iso-structural to NdCuSi, shows features attributed to such a coexistence.¹⁹ 

In the absence of any significant moment on the transition metal, the exchange interaction in almost all RTX compounds (except RMnX) is the indirect RKKY interaction. Therefore, the magnetic structure is usually collinear or canted. In some cases, the R-R distance is such that there is FM coupling between certain sites and AFM coupling between certain other sites. Because of this, generally, the ordering temperatures (T_C or T_N) are low in this series. Furthermore, in these compounds, competition between exchange interactions and crystal field effect often results in complex magnetic structures and unusual magnetic properties. Hence, from fundamental as well as application points of view, it is of importance to probe the MR and MCE properties in this family of compounds and correlate these properties with the magnetic properties. It has been observed that compounds of the RCuSi series are isostructural and crystallize in the hexagonal crystal structure. It has reported that two types of structures are possible for the RCuSi series; one is Ni₂ In type (SG = P6₃/mmc) and the other is AlB₂ type (SG = P6/mmm).^20–23 It is also known that most of the compounds in this series are antiferromagnetic. CeCuSi is an exception as it is ferromagnetic below 15.5 K.²⁴ Some compounds of this series are found to be promising because of large MCE in them. For example, DyCuSi¹⁷ and HoCuSi¹⁸ are found to exhibit giant MCE with isothermal magnetic entropy changes (−ΔS_M) of 24 and 33.1 J/kg K, respectively, for a field change of 50 kOe at low temperatures. In view of these, we have investigated the magnetic and related properties of NdCuSi using a variety of techniques.

Polycrystalline compound of NdCuSi was prepared by arc melting of the constituent elements with purity better than 99.9% in a water cooled copper hearth under argon atmosphere. The arc melted ingot was annealed for 10 days at 850 °C. The phase purity of annealed sample was examined by the analysis of x-ray diffraction (XRD) pattern taken from X’Pert Pro diffractometer at room temperature. Neutron diffraction measurements were carried out on the E6 diffractometer at HZB, Germany. Magnetization M(T,H), heat capacity C(T), and electrical resistivity ρ(T, H) measurements were carried out using a physical property measurement system (quantum design). Thermal relaxation method was used to carry out the heat capacity measurement. The magneto-transport measurements were carried out on a home-made system, by employing standard four probe technique, with an excitation current of 100 mA parallel to the magnetic field.

The Rietveld refinement of room temperature powder XRD pattern shows the hexagonal crystal structure with the space group P6₃/mmc (SG#194). The goodness of the fit was revealed by the χ² value of 2.3. The unit cell volume was found to be 120.19 Å.³ A careful analysis of the XRD pattern shows that 96% phase is of ZrBeSi type structure. A weak reflection from impurity phase (Cu₁₅Si₄) is observed, which indicates that a minor decomposition of NdCuSi powder may have occurred during grinding. The impurity peak is indicated by * in the XRD pattern (Fig. 1). The lattice parameters obtained from the Rietveld refinement are found to be a = b = 4.21(3) Å, c = 7.83(2) Å. These parameters are very close to the reported values.²¹ The XRD pattern, along with the refinement, is shown in Fig. 1.

Temperature dependences of the dc magnetic susceptibility (χ) and the inverse magnetic susceptibility are shown in Fig. 2. A magnetic transition at 3.1 K is clearly observed in the upper inset of Fig. 2. The lower inset shows the magnetic susceptibility in semi-log scale at 30 and 50 kOe. It can be noted from the latter inset that the application of field suppresses and broadens the peak at 3.1 K, which indicates that the field influences the antiferromagnetic behavior of the compound. At 50 kOe field, the nature of the susceptibility plot looks like that of a ferromagnetic material.

The Curie-Weiss law fit (χ⁻¹ = (T − θ_p)/C_m where C_m is the molar Curie constant and θ _p is the paramagnetic Curie temperature) yields the effective magnetic moment (μ_eff) of 3.87 μ_B/f.u. and θ_p of −11 K. The value of μ_eff is close to the free Nd³⁺ ion moment. Neutron diffraction patterns have been recorded in zero field, at different temperatures to determine the magnetic structure. Analysis of the neutron diffraction pattern at 10 K confirms that the compound crystallizes in the hexagonal structure with P6₃/mmc (194) space group. In this structure, Nd occupies 2(a) (0 0 0), Cu 2(c) (1/3 2/3 $1 4$⁠), and Si 2(d) (1/3 2/3 $3 4$⁠) Wyckoff positions. Fig. 3(a) shows the refined diffraction pattern at 10 K. A few unindexed reflections were observed, which are attributed to the impurity phase (Cu₁₅Si₄). On reducing the temperature below 3 K, weak superlattice reflections were observed, in addition to the enhancement in the intensity of the fundamental reflections. The former indicates the AFM nature of the compound, while the latter suggests the presence of FM phase. Therefore, neutron data indicate the coexistence of AFM and FM phases in this compound. The magnetic structure was, therefore, refined by taking into account the coexistence of the two magnetic phases. The superlattice reflections could be indexed with the propagation vector, k = (1/2, 1/2, 0). The basis vectors for the magnetic structure were determined using BASIREPS program.²⁵ For this propagation vector, there are four possible representations (IR). Among these, only one IR supports both AFM and FM ordering, leading to a canted AFM structure. This set of basis vectors, however, does not describe the data. Therefore, a canted AFM structure is ruled out in this sample. Fig. 3(b) shows a section of the diffraction pattern indicating the superlattice reflections and a fit to the magnetic model. The orientation of the Nd moments is restricted to the ab plane. In this structure, FM planes are antiferromagnetically coupled between the planes, which propagate along the face diagonal (Fig. 3(b)). The refined value of the AFM moment on Nd at 1.6 K is found to be 1.33 μ_B. It can be noted that the moment deduced from the neutron diffraction data is lower than the expected moment for Nd ion. The reduction in the magnetic moment may arise due to the crystalline electric field (CEF). Such a reduction is also observed in some other compounds of RTX family (e.g., NdCuGe, NdRuSi, and ErRuSi).²⁶ 

The variations with temperature of the Nd³⁺ moment in the AFM and FM phases are shown in Fig. 4. Both the ferromagnetic and the antiferromagnetic phases appear to have the same transition temperature.

Fig. 5(a) displays the field dependence of magnetization in the temperature range of 2-20 K for fields up to 50 kOe. The rapid increase of M(H) at low fields and the non-saturating behavior at high fields together with the narrow hysteresis at 2 K reveal the presence of coexisting ferromagnetic and antiferromagnetic phases, in agreement with the neutron diffraction data.

In order to probe the magnetic properties further, the heat capacity measurement was carried out in the temperature range of 2-100 K and at 0, 10, 20, 50 kOe fields [see figure in the supplementary material].³⁶ The zero field heat capacity data show a λ-like peak at the onset of magnetic ordering and confirm the second order magnetic transition. On application of a magnetic field, the peak gets broadened and shifts to higher temperatures. This behavior is normally observed in ferromagnetic materials. It, therefore, suggests that both the ferromagnetic and antiferromagnetic phases are strongly influenced by the magnetic field. However, in the absence of neutron diffraction data in the presence of field, we are unable to comment on the exact influence of the field on the magnetic structure of the compound.

The estimation of magnetocaloric effect has been done from the magnetization (M-H-T) data as well as from the heat capacity (C-H-T) data. Isothermal magnetic entropy change (ΔS_M) has been calculated utilizing the procedure given in Ref. 27. Generally, it has been observed that the ferromagnetic materials show positive MCE, while the antiferromagnets show negative MCE. The temperature dependence of −ΔS_M, estimated from M-H-T and C-H-T data for various field changes in NdCuSi, is shown in Fig. 5(b). It can be seen that this compound shows positive MCE in the entire temperature range, which indicates the dominant FM phase at high enough fields. The peak in −ΔS_M is around T_N, whose magnitude increases with increase in field and attains a maximum value of 11.1 J/kg K for a field change of 50 kOe. This value is comparable to that of other members of RTX family as well as some other rare earth compounds.^27–30 The field dependence of MCE is shown in the inset of Fig. 5(b). It has been observed that the compound shows quadratic dependence of MCE with field, which reveals the presence of spin fluctuations in the paramagnetic regime.¹¹ 

The electrical resistivity study of a material plays an important role in its understanding because of its sensitivity to the electronic structure as well as the magnetic nature. In the case of NdCuSi, the resistivity measurement was carried out in zero as well as in 20 and 50 kOe fields, in the temperature range of 2-150 K and is shown in Fig. 6(a). The resistivity data show linear nature and positive temperature coefficient of resistivity in the paramagnetic regime. The inset in Fig. 6(a) shows the low temperature, zero field resistivity data in an expanded scale. The T_N is marked with an arrow. It is worth noting from the inset that the compound changes its resistivity behavior in the temperature range of 3.1-8.6 K, where it shows negative temperature coefficient of resistivity with a maximum at 3.1 K (T_N). The main panel of Fig. 6(a) shows a considerable decrease in resistivity on the application of field below the antiferromagnetic ordering temperature, which indicates that the resistivity is strongly field dependent near T_N. Moreover, the anomaly seen in the zero field resistivity data near T_N gets suppressed with field and completely disappears at 50 kOe. The decrease in resistivity with field leads to a large negative magnetoresistance in this compound.

Generally, there is a decrease in the resistivity near a magnetic transition due to the decrease in the disorder of moments in the magnetically ordered regime. However, in the present case, we get an anomalous behavior near the ordering temperature. The resistivity shows a minimum above the magnetic ordering temperature and an increase at lower temperatures. The anomalous behavior near T_N suggests that some other effects are likely to be present in this compound. Charge carrier scattering by critical spin fluctuations and the formation of antiferromagnetic superzone gaps (which arise due to new Brillouin zone boundaries as a consequence of additional magnetic periodicity) are usually known to cause this kind of anomalous behavior.^31,32 It has been observed that generally spin fluctuations get suppressed below T_N.³¹ Many reports^31–35 show that scattering of carriers by critical spin fluctuations takes place above the ordering temperature and hence there is an increase in the resistivity above T_N (on cooling), while superzone gap effect occurs at or just below T_N. The present case shows an increase in resistivity above T_N. Therefore, a careful observation of these facts rules out the presence of magnetic superzone gap effects in this compound.^31–34 Therefore, the anomalous behavior above T_N is attributed mainly to the carrier scattering by critical spin fluctuations, which is seen to influence the field dependence of MCE as well.

The MR has been estimated from the field dependence of electrical resistivity using the relation, MR = Δρ/ρ₀, where Δρ = ρ(H, T) − ρ(0, T) and ρ₀ = ρ(0, T) is the zero field resistivity. Fig. 6(b) shows the change in MR with temperature and field. One can see from this figure that the magnitude of MR is negligible in the paramagnetic region and increases with decrease in temperature. MR reaches the maximum values of −31.6% and −36.4% at 3.1 K (T_N) for fields of 20 and 50 kOe. The MR value of 36.4% appears to be the largest reported value among various RTX compounds. The large negative MR is attributed to the co-existence of ferro- and antiferromagnetic phases. The antiferromagnetic component decreases on the application of field, which in turn reduces the carrier scattering and results in large negative MR.

The most interesting point noted from MR vs. H plots is that the MR is negative and shows approximately a H² dependence well above 2T_N (i.e., 10 K). There is a deviation from the quadratic dependence at higher fields. The same behavior was also observed in GdPd₂Si³⁴ and arises due to the existence of strong spin fluctuations above the ordering temperature. The MR vs. H data at 1.5 K do not show this dependence because at this temperature, the spin fluctuation almost dies out, as can be seen from the zero field resistivity data.

Based on the results of neutron diffraction, magnetization, heat capacity, and MCE, it is proposed that NdCuSi shows co-existence of antiferro- and ferromagnetic phases, which gives rise to large negative MR and positive MCE. Furthermore, from transport and magneto-transport data, it is clear that the application of field suppresses the spin fluctuations and consequently gives rise to large negative MR. The large negative MR and MCE in this compound could make it suitable for magnetic sensors and magnetic refrigeration at low temperatures.

In summary, we find that NdCuSi crystallizes in the hexagonal crystal structure and shows coexistence of antiferromagnetic and ferromagnetic phases, confirmed by magnetic and neutron diffraction data. Temperature dependence of electrical resistivity shows a pronounced anomaly at the ordering temperature, which is attributed to the spin fluctuations. The compound also shows large negative magnetoresistance of ∼36% at 50 kOe and ∼32% at 20 kOe, below the ordering temperature. The suppression of critical spin fluctuations by the applied field results in the large, low field magneto-resistance. The MCE estimated from the magnetization data is found to be 11.1 J/kg K at 50 kOe. The quadratic dependence of MR and MCE on the field also suggests the role of spin fluctuations.

S.G. thanks CSIR, New Delhi for granting the fellowship and D. Buddhikot for his help in the resistivity measurements. The authors acknowledge Dr. R. Rawat (UGC-DAE Consortium for Scientific Research, Indore) for the magnetoresistance measurements.