Pressure influence on the valence and magnetic state of Yb ions in noncentrosymmetric heavy-fermion $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$

We present studies of neutron diffraction, electrical resistivity, magnetic susceptibility, magnetization, and specific heat of noncentrosymmetric $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$. At normal pressure, $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ is a moderate heavy-fermion compound with Kondo lattice. At 16 K we observe an anomaly in the temperature dependence of specific heat which is ascribed to an abrupt valence change of Yb ions. At pressures above 7 GPa, the valence change and the Kondo lattice state are suppressed, and near a temperature of 10 K we detect the appearance of magnetic order. Above 5 GPa, the temperature dependence of the resistivity behaves similarly to other compounds of the $\mathrm{Ce}\mathrm{Ni}{\mathrm{C}}_2$-type family, indicating the formation of charge density waves. This is attributed to the nesting properties of the Fermi surface (FS) found within the density functional $\mathrm{theory}+\mathrm{dynamical}$ mean field theory treatment. Our ab initio calculations also show that the valence of Yb in $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at normal conditions is 2.85, which increases with temperature and pressure. The FS of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ is anisotropic in shape in comparison with the 3D surface of $\mathrm{Yb}\mathrm{Co}{\mathrm{C}}_2$.

Figure 1

The refined XRPD pattern for $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at $T=295$ K and $P=0$ GPa (the obtained lattice parameters are listed in Table 1). The experimental points (blue dots), the calculated profiles (red line), and their differences (blue line) are shown. The bars in the lower part of the graph represent the calculated Bragg reflections that correspond to $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$. Inset: $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ crystal structure with the red, blue, and green balls corresponding to Yb, Co, and C ions, respectively.

Figure 2

The temperature dependencies of the magnetic susceptibility of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ measured in the external magnetic field $B=300$ Oe (blue line and dots) together with the Curie-Weiss fit above 150 K (red line) and the magnetic susceptibility of $\mathrm{Tm}\mathrm{Ni}{\mathrm{C}}_2$ measured in the external magnetic field $B=5$ Oe (green dots). Inset: The experimental magnetic susceptibility of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ together with the impurity corrected part (orange dots).

Figure 3

The isothermal magnetization of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ measured in the field range $H=0–9\mathrm{T}$ at $T=2$ and 40 K.

Figure 4

The temperature dependence of the electrical resistivity of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at $P=0$ GPa (blue points). The red line is a fit (see text for the details).

Figure 5

Temperature dependence of the heat capacity of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at $P=0$ GPa and $H=0$ T. The red line is a fit of the full heat capacity above the peak with ${\gamma }_{\mathrm{HT}}T+{\beta }_{\mathrm{HT}}{T}^3$ law, the green line is a fit of the full heat capacity below the peak by ${\gamma }_{\mathrm{LT}}T+{\beta }_{\mathrm{LT}}{T}^3$ law, and the yellow line is a fit of $C_{4f}$ heat capacity below 7 K by $\gamma T+D{T}^{3}ln(T/T_{\mathrm{sf}})$ law. Inset: Full heat capacity.

Figure 6

Temperature dependence of the heat capacity of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at different magnetic fields $H=0-9$ T and $P=0$ GPa.

Figure 7

Ambient-pressure small-angle scattering function $S\left(Q\right)$ of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at $T=5$ K (black points). The red (blue) lines are fits of Porod (Lorentzian) functions to the data, as described in the text.

Figure 8

The temperature dependence of the specific-heat jump $\mathrm{\Delta }{C}_{\mathrm{P}}/T$ of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at high pressures measured in Toroid high-pressure cell. Inset: The $C_{\mathrm{P}}/T$ jump versus pressure.

Figure 9

The temperature dependence of specific heat of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at high pressures measured in Bridgman anvils.

Figure 10

(a) Temperature dependence of the resistivity for $P=1.1-4.7$ GPa measured in Toroid high-pressure cell. The inset: Resistance maximum temperature versus pressure. (b) Temperature dependence of the derivative of the resistance for $P=4-18.5$ GPa. (c) Temperature dependence of the resistance for $P=5-18.5$ GPa measured in diamond anvil high-pressure cell. (d) The low temperature part of the resistance for $P=5-15.6$ GPa.

Figure 11

DMFT-calculated total (dashed blue lines) and $4f$-projected (pink lines) DOS for $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ (a) in comparison with $\mathrm{Yb}\mathrm{Co}{\mathrm{C}}_2$ (b). The Fermi energy (the vertical line) is set to zero. Insets: The enlarged parts of DOS near the Fermi energy.

Figure 12

DMFT-calculated band structure along high-symmetry $k$ path (left) and FS (right) of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$ at $T=300$ K. The FS was generated using the XCRYSDEN software [65].

Figure 13

DMFT-calculated band structure (left) and the FS (right) of $\mathrm{Yb}\mathrm{Co}{\mathrm{C}}_2$ at $T=300$ K.

Figure 14

The $P-T$ phase diagram of $\mathrm{Yb}\mathrm{Ni}{\mathrm{C}}_2$. Yellow region (PM), paramagnetic state with ${\mathrm{Yb}}^{3+}$; blue region (V-F), valence-fluctuating state of Yb ions with enhanced spin-fluctuations; magenta region (AFM), antiferromagnetic Yb; gray region (?), a possible coexistence of V-F and AFM phases; orange points ($T_{\mathrm{CDW}}$), CDW transition temperature (the orange line is a guide to the eye). Gray squares, red circles, and blue and green triangles are the temperatures of anomalies deduced from the measurements of resistance and specific heat.