Multiple charge density wave states and magnetism in ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ against the background of its nonmagnetic analog ${\mathrm{LaPt}}_2{\mathrm{Si}}_2$

Results of structural, magnetic, thermodynamic, and electron transport measurements on single-crystalline ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ are reported. Temperature variations of crystal structure show two different charge density wave states. The structure modulation with the propagation vector ${\mathit{q}}_{\mathbf{1}}=(0.323,0,0)$ arises below $T=300$ K. An additional modulation, with propagation vector ${\mathit{q}}_{\mathbf{2}}=(0.163,0.163,0.500)$, appears below $T=50$ K in a first-order phase transition. This situation was found analogous to isostructural ${\mathrm{LaPt}}_2{\mathrm{Si}}_2$ with similar (but not identical) propagation vectors and characteristic temperatures. Nd magnetic moments order antiferromagnetically at $T_N=1.5$ K. Temperature dependence of electrical resistivity for current j applied along the $a$, $b$, and $c$ axes is strongly affected by the first-order transition, inducing a Fermi surface gapping.

Figure 1

X-ray powder diffraction patterns of crushed ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ single crystal collected at $T=5$ and 300 K. The observed experimental data are shown by green and red symbols, while the solid blue and black lines through the data represent the results of the structure refinement by using the Rietveld analysis. The respective difference between experimental and calculated data and the vertical bars indicating the positions of Bragg reflections are shown at the bottom. Inset (a) shows the Laue diffraction pattern with a view along the $a$ axis. Inset (b) shows the SEM micrograph obtained from the surface of single-crystalline ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ used for the EDX analysis.

Figure 2

Temperature dependence of the lattice parameters $a$ and $c$, the $c/a$ ratio, and the unit cell volume of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ determined for the powder (crushed) and single crystal samples. The inset shows the anomalous behavior of the $c$-lattice parameter in the vicinity of $T=50$ K.

Figure 3

Reciprocal space map around the (2 4 0) diffraction at $T=300$, 225, and 10 K for ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$. The scattering plane corresponds to the basal plane. The black dot shows the position of q = (1/3, 0, 0). Red and green circles marks broad and sharp contribution. The black line segment correspond to the $1^{\circ }$ mosaicity.

Figure 4

Reciprocal space map around the (2 4 0) diffraction at $T=300$, 225, and 10 K for ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$. The scattering plane corresponds to the basal plane. The black dot shows the position of q = (0, 1/3, 0). Red and green circles marks broad and sharp contribution.

Figure 5

(a) Temperature dependence of integrated intensity of the $q_{\mathbf{1}}$ satellites. (b) Temperature dependence of $q_{1k}$ and $q_{1h}$ position of satellites in the basal plane.

Figure 6

Evolution of the reconstructed sections (h k 0) and (h h l) of reciprocal space as a function of temperature for ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$. Satellite reflections indexed by the modulation vectors $q_{\mathbf{1}}$ = $0.323{\mathit{a}}^{\mathbf{*}}$ and $q_{\mathbf{1}}\text{'}$ = $0.323{\mathit{b}}^{*}$, respectively, from the twin domains 1 and 2, are evidenced in the (h k 0) reciprocal section below $T=300$ K. Additional satellite reflections indexed by the modulation vectors $q_{\mathbf{2}}$ = $0.163{\mathit{a}}^{\mathbf{*}}$ + $0.163{\mathit{b}}^{*}$ + 0.500$c$${}^{*}$ and $q_{\mathbf{2}}\text{'}$ = 0.163$a$${}^{*}-$ $0.163{\mathit{b}}^{*}$ + 0.500$c$${}^{*}$, respectively, from the twin domains 1 and 2, appear below $T=100$ K in the (h h l) reciprocal section.

Figure 7

Evolution of the reconstructed sections (h k 0) and (h h l) of reciprocal space as a function of temperature for ${\mathrm{LaPt}}_2{\mathrm{Si}}_2$. Satellite reflections indexed by the modulation vectors $q_{\mathbf{1}}$ = $0.360{\mathit{a}}^{\mathbf{*}}$ and $q_{\mathbf{1}}\text{'}$ = $0.360{\mathit{b}}^{*}$, respectively, from the twin domains 1 and 2, are evidenced in the (h k 0) reciprocal section below $T=260$ K. Additional satellite reflections indexed by the modulation vectors $q_{\mathbf{2}}$ = $0.187{\mathit{a}}^{\mathbf{*}}$ + $0.187{\mathit{b}}^{*}$ + 0.500$c$${}^{*}$ and $q_{\mathbf{2}}\text{'}$ = 0.187$a$${}^{*}-$ $0.187{\mathit{b}}^{*}$ + 0.500$c$${}^{*}$, respectively, from the twin domains 1 and 2, appear below $T=$ 115 K in the (h h l) reciprocal section.

Figure 8

Temperature dependence of the magnetic susceptibility $\chi (T$) of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ measured in magnetic field of 0.5 T applied along the $a$ and $c$ axes. Inset displays the temperature dependence of the inverse magnetic susceptibility ${\chi }^{-1}(T$). The red solid lines represent the Curie-Weiss fits.

Figure 9

Isothermal magnetization curves as a function of an applied magnetic field along the $a$ and $c$ axes of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ at $T=1.8$, 10, and 50 K.

Figure 10

Temperature dependence of the specific heat $C$${}_p(T$) of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ measured using subsequent cooling and warming cycles. The solid line illustrates the best fit of the high-$T$ $C$${}_p(T$) data using Eq.(1) with parameters given in the text. Inset (a) highlights the presence of thermal irreversibility effect around 57 K and indicates the first-order phase transition. Inset (b) shows low-$T$ dependence of $C$${}_p(T$) with emphasized low temperatures characteristic features. Inset (c) illustrates the temperature dependence of the ratio $C$${}_p(T$)/$T{}^3$.

Figure 11

Low-$T$ dependencies of $C$${}_p(T$) of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ measured in various values of applied magnetic fields and its non-4f-electron isostructural analog ${\mathrm{LaPt}}_2{\mathrm{Si}}_2$ in zero field on a semilogarithmic plot. For ${\mathrm{LaPt}}_2{\mathrm{Si}}_2$, the dashed line represents a fit using the simplified Debye model extrapolated for estimating the magnetic part of $C$${}_p(T$) below 2 K. The 4f-electron contribution to the specific heat $C$${}_{4f}$ (open blue circles), obtained by subtracting $C$${}_p(T$) data of the reference La compound, from that of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ is also shown on a log-$T$ scale.

Figure 12

The 4f-electron derived magnetic specific heat of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ as a function of temperature (left-hand axis), and the associated magnetic entropy $S_{4f}$ which is shown using a bold line referring to the right-hand axis. The solid line superimposed onto $C$${}_{4f}(T$) data represents a simulation of a contribution of the lowest CEF excitation, not assuming anything particular about the complete CEF scheme using model described in the text.

Figure 13

Temperature dependence of the electrical resistivity $\rho (T$) of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ single crystal for current j applied along the $a$, $b$, and $c$ axes measured in cooling (filled symbols) and heating (open symbols) runs. Inset shows the hysteretic behavior in ${\rho }_a(T$), ${\rho }_b(T$), and ${\rho }_c(T$).

Figure 14

Temperature dependences of electrical resistivity for j $\parallel$ $c$ axis (left-hand axis) and specific heat (right-hand axis) of ${\mathrm{NdPt}}_2{\mathrm{Si}}_2$ below $T=20$ K with emphasized low-$T$ characteristic features, including the anomaly at the phase transition at $T_N$.