Interplay of structure and magnetism in ${\mathrm{LuFe}}_4{\mathrm{Ge}}_2$ tuned by hydrostatic pressure

$\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ crystallizes in the $\mathrm{Zr}{\mathrm{Fe}}_4{\mathrm{Si}}_2$-type structure, hosting chains of Fe tetrahedra giving rise to geometric frustration and low dimensionality. The compound orders antiferromagnetically at around 36 K accompanied by a simultaneous structural transition from a tetragonal phase to an orthorhombic phase. The hydrostatic pressure dependence of the magnetic and structural transitions is investigated using electrical transport, AC magnetic susceptibility, AC calorimetry, $\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$, muon-spin relaxation ($\mu \mathrm{SR}$), and x-ray-diffraction measurements. External pressure suppresses the first-order transition to the antiferromagnetic phase (AFM1) around 1.8 GPa. The structural transition is largely unaffected by pressure and remains between 30 to 35 K for pressures up to 2 GPa. A second antiferromagnetic phase (AFM2) is observed at higher pressures. The transition from the paramagnetic to the AFM2 phase is of second-order nature and appears to be connected to the structural transition. The magnetic volume fraction obtained from $\mu \mathrm{SR}$ and $\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$ measurements reveal that the entire sample undergoes magnetic ordering in both magnetic phases. In addition, similar low-temperature muon-precession frequencies in AFM1 and AFM2 phases point at similar ordered moments and magnetic structures in both phases. Our results further indicate enhanced magnetic fluctuations in the pressure-induced AFM2 phase. The experimental observations together with density functional theory calculations suggest that the magnetic- and structural-order parameters in $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ are linked by magnetic frustration, causing the simultaneous magnetostructural transition.

Figure 1

(a) Crystal structure of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ viewed along the $c$ axis. In the low-temperature orthorhombic phase ($Pnnm$), the Fe sites split in to two sites marked as Fe1 and Fe2 [14]. (b) The chainlike arrangement of edge-shared Fe tetrahedra viewed along the $b$ axis.

Figure 2

(a) Temperature dependence of the DC magnetic susceptibility $\chi$ of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$. The inverse susceptibility ${\chi }^{-1}\left(T\right)$ is plotted on the right axis along with a Curie-Weiss fit to the data (red curve) in the temperature interval between 100 and 300 K. (b) Temperature dependence of the electrical resistivity $\rho \left(T\right)$ (left axis) and the temperature derivative $d\rho \left(T\right)/dT$ (right axis). (c) Heat-capacity $C_p$ of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ as a function of temperature. The upper inset displays the thermal hysteresis in $C_p\left(T\right)$ obtained from the analysis of heating and cooling parts of the thermal-relaxation cycle. The lower inset shows $C_p/T$ vs $T^2$ where the straight line is a fit to the data for $2\mathrm{K}\le T\le 20$ K using $C_p\left(T\right)=\gamma T+\beta T^3$.

Figure 3

(a) Electrical resistivity of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ as a function of temperature for several applied pressures. The inset: Resistivity isotherms as a function of pressure. The arrows indicate the phase boundary to a pressure-induced phase. (b) Temperature derivative of electrical resistivity $d\rho /dT$ vs $T$ for several pressures. Various anomalies are marked by symbols. (c) Temperature dependence of the real part of the AC magnetic susceptibility (${\chi }^{\prime }$) of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ for selected applied pressures (data shifted vertically). The pressure dependence of the anomalies are traced by the dashed lines and additional low-temperature anomalies at higher pressures are marked by $*$ and # symbols.

Figure 4

(a) Temperature dependence of the magnetic-volume fraction $V_{\mathrm{mag}}$ of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ obtained using $\mu \mathrm{SR}$ at different pressures. The solid lines are fits to the data using a phenomenological equation provided in the text. (b) Temperature dependence of the muon-spin precession frequency under different applied pressures. (c) $V_{\mathrm{mag}}$ obtained from time-domain ${}^{57}\mathrm{Fe}\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$ spectroscopy under several pressures. (b) Energy-domain ${}^{57}\mathrm{Fe}\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$ spectra measured at $p=2.9$ GPa, $T=3$ K, and an external magnetic field of 6 T. The solid lines are fits to the spectra by exact line-shape site analysis using recoil software.

Figure 5

Representative peaks in the x-ray diffraction patterns of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ at different temperatures and applied pressures. The structural transition from the tetragonal to the orthorhombic phase is evidenced by the splitting of the diffraction peak around $2\theta \approx 15.5^{\circ }$.

Figure 6

(a) $T-p$ phase diagram of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$. The transition temperatures obtained from $\rho \left(T\right)$ (circle), ${\chi }^{\prime }\left(T\right)$ (square), $\mu \mathrm{SR}$ (star), and $\mathrm{M}\ddot{\mathrm{o}}\mathrm{ssbauer}$ (sphere) data are indicated. The $*$ and # symbols stand for the low-temperature anomalies observed in $\rho \left(T\right)$ and ${\chi }^{\prime }\left(T\right)$ data. (b) Thermal hysteresis in $C\left(T\right)$, measured using an AC-calorimetry technique under pressure, confirms the first-order nature of the transition at $T_{N1}$. The arrow points at a very weak feature at $T_{N2}$. (c) $\mathrm{MR}\left(B\right)=\left[\rho \right(B)-\rho (B=0\left)\right]/\rho (B=0)$ of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ measured at $T=2$ K.

Figure 7

Total and partial density of states of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ for (a) the nonmagnetic tetragonal and (b) the antiferromagnetic orthorhombic cases. The Fermi level is at zero energy. Panel (c) shows the dependence of the lattice distortion (in percentages) on the Fe magnetic moment for different exchange correlation potentials.

Figure 8

Powder XRD pattern of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ obtained at ambient pressure and room temperature. The solid red line is a Rietveld refined fit of the experimental data. The Bragg positions are indicated by green vertical bars, and the bottom solid blue line indicates the difference between the experimental and the calculated intensities.

Figure 9

(a) MR($B$) of $\mathrm{Lu}{\mathrm{Fe}}_4{\mathrm{Ge}}_2$ measured at $T=2$ K for different pressures. The inset shows an enlarged view of the low-pressure curves. (b) Normalized resistivity $\rho /{\rho }_{300\mathrm{K}}$ as a function of field at 2 K for several pressures.