Insight into the physics of the $5f$-band antiferromagnet ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ from the pressure dependence of crystal structure and electrical resistivity

A resistivity study of a single crystal of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ has been performed at ambient pressure and under hydrostatic pressure up to $p=3.3\mathrm{GPa}$. It revealed Fermi-liquid behavior accompanied by spin excitations with an energy gap $\mathrm{\Delta }=30\text{–}55\mathrm{K}$ in the whole pressure range. The Néel temperature varies with pressure in a nonmonotonous way. It increases at the rate $d{T}_{\mathrm{N}}/dp=+0.6\mathrm{K}/\mathrm{GPa}$, and later, after passing through the maximum at ≈3 GPa, it starts to decrease quickly. High-pressure x-ray diffraction indicated that an orthorhombic distortion of the tetragonal structure takes place around the pressure of this $T_{\mathrm{N}}$ maximum. The computational study based on the density functional theory illustrates that the loss of magnetism in ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ with pressure is primarily due to $5f$-band broadening, which results from the collapse of the U spacing within the U-U dimers.

Figure 1

(a) The undercut lamella connected to the parent crystal by a thin bridge. (b) The lamella placed on a substrate with prefabricated electric contact pads. (c),(d) Shape of the microscale device used for measurement. $V$ and $I$ are contacts for voltage and current, respectively. Panel (c) shows the current path, while (d) shows the voltage terminals.

Figure 2

Temperature dependence of electrical resistivity of the ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ single crystal in the form of bulk and microdevice for different current directions.

Figure 3

Temperature dependence of electrical resistivity of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ in the vicinity of the Néel temperature for different current directions in magnetic fields $H$//[001] up to 8 T.

Figure 4

Field dependence of the resistivity of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ at $T=4\mathrm{K}$ (left) and 24.5 K (right). The current directions are indicated in the legend. The magnetic field was applied along the [001] direction. The dashed lines for both current directions correspond to the $\rho \sim H^2$ fit. Notice the axis breaks.

Figure 5

Temperature dependence of electrical resistivity for $i//\left[001\right]$ with the fit to the function (3) (red line), together with its individual components (dashed lines).

Figure 6

Pressure effect on the zero-field resistivity of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ for $i$//[001]. The inset shows the vicinity of the inflection point.

Figure 7

Temperature dependence of electrical resistivity ρ($T$) in selected pressures for the two current directions. The lower curves correspond to $i$//[001], the upper ones to $i//\left[110\right]$. The solid lines represent the result of the curve fitting by Eq. (2).

Figure 8

Pressure dependence of parameters (${\rho }_0$, $A$, and $\mathrm{\Delta }$) used to fit the temperature dependence of resistivity of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ at various pressures. The lines in the graphs are the eye-guides.

Figure 9

Pressure dependence of the Néel temperature of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ derived from the zero-field resistivity. The inset shows the temperature dependence of the dρ/dT derivatives at the selected pressures for $i//\left[110\right]$ in the vicinity of the ordering temperature of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$. The minima on these derivatives have been used for tracking the $T_{\mathrm{N}}\left(p\right)$ dependence.

Figure 10

XRD patterns of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ taken at zero pressure (left) and at 10 GPa (right) using Mo radiation. The red line represents the fit. The peak positions are marked by the ticks at the baseline. The red ticks indicate the positions of lines belonging to the gasket.

Figure 11

Pressure variations of XRD patterns of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ (Mo radiation). The black dashed lines mark the peaks of the tetragonal structure. The red dashed lines represent the pressure dependence of the additional peaks originating from splitting due to a reduction of symmetry.

Figure 12

Pressure dependence of lattice parameters and unit cell volume of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ at room temperature. The lines represent linear fits used to determine the linear and bulk compressibilities mentioned in the text.

Figure 13

Comparison of the ground-state crystal structure of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ (left) with the orthorhombic structure at $p=8\mathrm{GPa}$ (right). The U-positions were first taken from ${\mathrm{Nd}}_2{\mathrm{Ni}}_2\mathrm{In}{\mathrm{H}}_6$ (red) and then relaxed in LSDA calculations, giving the equilibrium U-position (green).

Figure 14

Variations of the electronic structure of $\mathrm{U}{\mathrm{Ni}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ at ambient pressure and $p=8\mathrm{GPa}$, the latter with the orthorhombic distortion, obtained in fully relativistic non-spin-polarized calculations. For details, see the full text.

Figure 15

Increase of total energy if a magnetic moment is prescribed in the high-pressure phase of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$—comparison of the starting and relaxed phase from Fig. 13. The inset shows the energy vs volume dependence for the high-pressure phase obtained using the GGA-PBE calculations. $V_0$ is the experimental equilibrium volume. $E_0$ was set arbitrarily.

Figure 16

Volume variations of the spin, orbital, and total magnetic moments of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$. The circles represent the case of isotropic compression, the squares show compression only in $a$, and the diamonds show additional small $c$-axis compression. For the latter two cases, the $a$-axis compression corresponds to the low-pressure tetragonal phase extrapolated to high pressures of $p\approx 14\mathrm{GPa}$, chosen to make the tendencies more pronounced.

Figure 17

(a) Variations of magnetic anisotropy energy for the same types of lattice compression as given in Fig. 16. (b) Related energy differences between AFM-G and FM structures. (c) Energy difference between AFM-A and AFM-G structures. AFM-A corresponds to the ferromagnetic coupling of U moments along the $c$-axis and $+-+-$ coupling within one unit cell. The decrease of spin moments for high pressures means inexorably also a drop of critical temperatures of magnetic ordering. The increase of $T_{\mathrm{N}}$, observed at lower pressures, cannot be directly confronted with calculations. In reality, the reduced moments can be over a limited compression range compensated by enhanced effective intersite exchange coupling.