Electronic correlations in $\mathrm{Fe}{\mathrm{Ga}}_3$ and the effect of hole doping on its magnetic properties

We investigate signatures of electronic correlations in the narrow-gap semiconductor $\mathrm{Fe}{\mathrm{Ga}}_3$ by means of electrical resistivity and thermodynamic measurements performed on single crystals of $\mathrm{Fe}{\mathrm{Ga}}_3$, ${\mathrm{Fe}}_{1-x}{\mathrm{Mn}}_x{\mathrm{Ga}}_3$, and $\mathrm{Fe}{\mathrm{Ga}}_{3-y}{\mathrm{Zn}}_y$, complemented by a study of the 4$d$ analog material $\mathrm{Ru}{\mathrm{Ga}}_3$. We find that the inclusion of sizable amounts of Mn and Zn dopants into $\mathrm{Fe}{\mathrm{Ga}}_3$ does not induce an insulator-to-metal transition. Our study indicates that both substitution of Zn onto the Ga site and replacement of Fe by Mn introduces states into the semiconducting gap that remain localized even at highest doping levels. Most importantly, using neutron powder diffraction measurements, we establish that $\mathrm{Fe}{\mathrm{Ga}}_3$ orders magnetically above room temperature in a complex structure, which is almost unaffected by the doping with Mn and Zn. Using realistic many-body calculations within the framework of dynamical mean field theory (DMFT), we argue that while the iron atoms in $\mathrm{Fe}{\mathrm{Ga}}_3$ are dominantly in an $S=1$ state, there are strong charge and spin fluctuations on short-time scales, which are independent of temperature. Further, the low magnitude of local contributions to the spin susceptibility advocates an itinerant mechanism for the spin response in $\mathrm{Fe}{\mathrm{Ga}}_3$. Our joint experimental and theoretical investigations classify $\mathrm{Fe}{\mathrm{Ga}}_3$ as a correlated band insulator with only small dynamical correlation effects, in which nonlocal exchange interactions are responsible for the spin gap of 0.4 eV and the antiferromagnetic order. We show that hole doping of $\mathrm{Fe}{\mathrm{Ga}}_3$ leads, within DMFT, to a notable strengthening of many-body renormalizations.

Figure 1

The relation between actual ($x_{\mathrm{m}}$) and nominal $x_{\mathrm{nom}}$ doping levels in Fe${}_{1-x}$Mn${}_x$Ga${}_3$ (black circles) and FeGa${}_{3-y}$Zn${}_y$ (red diamonds). Error bars indicate one standard deviation of the measured $x_{\mathrm{m}}$ values.

Figure 2

Lattice parameters $a$ and $c$ as functions of actual doping level ($x$) for Fe${}_{1-x}$Mn${}_x$Ga${}_3$ (black circles) and FeGa${}_{3-y}$Zn${}_y$ (red diamonds). Dashed lines are guides for the eye.

Figure 3

Magnetic susceptibility of single crystals of FeGa${}_3$ and RuGa${}_3$ measured in a magnetic field of 10 kOe applied in the tetragonal $ab$ plane (red circles) or along the $c$ axis (black circles). Thin solid lines indicate linear terms $aT$ in $\chi$($T$) for FeGa${}_3$ with $a=1.3\times {10}^{-8}$ emu/(K mol) and $a=1.9\times {10}^{-8}$ emu/(K mol) for $H\parallel ab$ and $H\parallel c$, respectively, and for RuGa${}_3$ with $a=0.7\times {10}^{-8}$ emu/(K mol) independent of the field direction. Dashed lines represent fits to the activated temperature dependence $\chi$($T$)$\propto$ exp[$-{\Delta }_{\mathrm{S}}$/(k${}_{\mathrm{B}}T$)] at $T\gtrsim 500$ K.

Figure 4

Results of neutron powder diffraction experiments for FeGa${}_3$. The main panel shows the Rietveld refinement (black) of the nuclear structure based on the neutron diffraction pattern (red) collected at 1.5 K. The difference curve is shown in green. The inset shows the low-angle range of the neutron diffraction patterns measured at 1.5 K (red) and at room temperature (blue), together with the x-ray powder diffraction data measured at 300 K on the same powder. Dashed vertical lines show the positions of nuclear peaks. The main magnetic peaks are indicated by arrows.

Figure 5

Specific heat $C_p$ of FeGa${}_3$ (black circles) modeled with a series of Einstein-type (solid line) and Debye-type (dotted line) lattice terms (see text). The blue dashed line represents the best fit of the assumed model to the experimental data. Dashed-dotted thin lines in panel (a) represent the “total” specific heat calculated based on the Debye model, assuming Debye temperatures of 300 K (red) and 400 K (black). A maximum in $C$/$T^3$($T$) dependence shown in panel (b) is the hallmark of the presence of Einstein modes. The inset in panel (b) shows $C_p$/$T$ at lowest temperatures plotted versus $T^2$. The red dashed line represents the fit to the experimental data using $C_p$/$T$($T^2$)=$\beta T^2$.

Figure 6

Electrical resistivity $\rho$ for FeGa${}_3$ (black circles) and RuGa${}_3$ (red circles). Roman numbers I–IV denote four temperature regimes as described in the text. The inset shows the resistivity for FeGa${}_3$ in the temperature range 260–400 K (IV) on a logarithmic scale as a function of inverse temperature. The solid line represents the fit of the experimental data with Arrhenius law $\rho$($T$)$={\rho }_0$($T$)$\text{exp}$[$E_{\mathrm{g}}/$($2k_{\mathrm{B}}T$)], giving the activation gap $E_{\mathrm{g}}=0.4$ eV. The left small panel displays Arrhenius plots for the range II with solid lines indicating the best fits of the resistivity data to the Arrhenius expression $\rho$($T$)$={\rho }_0$($T$)$\text{exp}$[$E_{\mathrm{d}}/$($2k_{\mathrm{B}}T$)] at 24 K $<T<44$ K and 31 K $<T<83$ K, resulting in activation energies of $E_{\mathrm{d}}\approx 40$ and 20 meV for FeGa${}_3$ and RuGa${}_3$, respectively. The right small panel shows the resistivities at the lowest temperatures (I) plotted versus $T^{-1/4}$ to display the 3D VRH conduction among in-gap states. Solid lines indicate the best linear regression fits.

Figure 7

Electrical resistivity for FeGa${}_{3-y}$Zn${}_y$ ($y=0.02$; 0.04; 0.06) (a) and Fe${}_{1-x}$Mn${}_x$Ga${}_3$ ($x=0.014$; 0.034; 0.084; 0.087) (b) plotted together with the data for FeGa${}_3$ (brown solid lines). Panel (c) presents the resistivity of FeGa${}_{2.94}$Zn${}_{0.06}$ (black circles) together with fits using Arrhenius law $\rho$($T$)$\propto \text{exp}$[$E_{\mathrm{d}}/$($2k_{\mathrm{B}}T$)] for $T\gtrsim 100$ K (dashed violet line), 3D VRH conduction $\rho$($T$)$\propto \text{exp}$[($T_{\mathrm{M}}/T$)${}^{1/4}$] at 10 K$\gtrsim T\gtrsim 50$ K (dashed blue line), and based on the formula $\rho$($T$)$\propto \text{exp}$[($T_M$/$T$)${}^{1/2}$] (dashed red line) describing 3D VRH conduction of the Efros-Shklovskii type [63] associated with the opening of a small gap within the doping induced density of states at $T\gtrsim 10$ K. The temperature ranges in which the resistivities of FeGa${}_{3-y}$Zn${}_y$ and Fe${}_{1-x}$Mn${}_x$Ga${}_3$ follow the described temperature dependencies are indicated in panel (d). The points denote crossover temperatures estimated as the midpoints between the corresponding temperature ranges. The resistivities of FeGa${}_{3-y}$Zn${}_y$ and Fe${}_{1-x}$Mn${}_x$Ga${}_3$ for different $x$ and $y$ are plotted versus $T^{-1/4}$ in panels (e) and (g), respectively, and as functions of $T^{-1/2}$ in panels (f) and (h), respectively. Solid lines in panels (e), (f), (g), and (h) indicate the best regression fits. The inset in panel (c) shows values of the average activation gap obtained from the fits to the Arrhenius expression at highest temperatures as a function of the actual doping level $x$.

Figure 8

(a) Specific heat $C_p$/$T$ of Fe${}_{0.92}$Mn${}_{0.08}$Ga${}_3$ (black circles) together with the data of FeGa${}_3$ (red squares). The inset displays the low-temperature magnetic specific heat, with a fit of data based on the two-level Schottky model as described in the text. (b) Low temperature $C_p$/$T$($T$) for the series of Mn-doped FeGa${}_3$ together with the data for undoped FeGa${}_3$ (black empty circles). (c) $\Delta C_p$/$T$($T$) for the series of Fe${}_{1-x}$Mn${}_x$Ga${}_3$ ($x=0$; 1.8%; 6.6%; 8.4%; 10%) estimated as described in the text. The thin dashed vertical line indicates the position of the maxima in $\Delta C_p$/$T$($T$). The inset shows the values of the energy gap $\Delta$ derived from the fits based on the two-level Schottky model. (d) Values of the magnetic entropy at a temperature of 14 K for various doping levels of Mn (black circles) and Zn (red square). The dashed line corresponds to the entropy of $0.4Rln2$ per dopant. The dashed lines are guides for the eye.

Figure 9

Inverse magnetic susceptibilities for FeGa${}_{3-y}$Zn${}_y$ ($y=0.006$; 0.01; 0.02; 0.04; 0.046; 0.06) (a) and Fe${}_{1-x}$Mn${}_x$Ga${}_3$ ($x=0.032$; 0.043; 0.044; 0.061; 0.065; 0.066; 0.085; 0.087) (b) after subtracting a constant term ${\chi }_0$ as obtained from fits using a modified Curie law (see details in text). The insets in panels (a) and (b) show the values of the product $\chi T$ as functions of temperature for the field of $H=70$ kOe obtained after subtracting the temperature-independent terms ${\chi }_0$. Arrows indicate the direction of the increase in measured doping level. Panel (c) depicts the values of the effective magnetic moment per formula unit obtained from the fits as a function of the doping level $x$ for FeGa${}_{3-y}$Zn${}_y$ (red diamonds) and Fe${}_{1-x}$Mn${}_x$Ga${}_3$ (black circles). The values of the effective moment recalculated per dopant are shown in panel (d), together with a dashed line indicating an effective moment of 1.73 ${\mu }_{\mathrm{B}}$, as expected for $S=\frac{1}{2}$.

Figure 10

(a) Magnetic susceptibility of Fe${}_{0.92}$Mn${}_{0.08}$Ga${}_3$ measured in various magnetic fields applied either along the $c$ axis (empty circles) or along the [110] direction (full squares). Arrows point in the direction of the increasing magnetic field applied along the $c$ axis. For $H\parallel$ [110], $\chi$($T$) is only weakly field dependent. The inset shows $\chi$($T$) measured in $H=1$ kOe applied along the $c$ axis in a log-log plot. The dashed line represents the fit to the data at $T\lesssim 5$ K using $\chi$($T$)$\sim T^{-\alpha }$. (b) Magnetization measured for Fe${}_{0.92}$Mn${}_{0.08}$Ga${}_3$ in a magnetic field applied along the $c$ axis at indicated temperatures. The inset shows the $M$($H$) curves plotted in a standard Arrott representation.

Figure 11

Values of the magnetic susceptibility for Fe${}_{1-x}$Mn${}_x$Ga${}_3$ (black) and FeGa${}_{3-y}$Zn${}_y$ (red) measured at 2 K in a magnetic field applied either along the [110] direction (circles) or along the $c$ axis for $H=1$ kOe (triangles). Dashed lines are guides for the eye.

Figure 12

Neutron powder diffraction patterns for Fe${}_{0.95}$Mn${}_{0.05}$Ga${}_3$, obtained at temperatures of 1.5 K (black) and 15 K (red), together with the data for undoped FeGa${}_3$ collected at 1.5 K. The main magnetic peaks are indicated by arrows.

Figure 13

Magnetic susceptibility of Fe${}_{0.91}$Mn${}_{0.09}$Ga${}_3$ (red circles) measured at temperatures above $\sim$300 K in a magnetic field of 10 kOe on a set of randomly oriented crystals, together with the data for FeGa${}_3$ (black circles) calculated as explained in the text. Dashed line represents the fit to a model described in the text.

Figure 14

Left panel shows LDA+DMFT spectral functions calculated at $T=116$ K (solid lines) for FeGa${}_3$ (black) and for RuGa${}_3$ (red) compared to the LDA results (dashed line). Right panel presents probability of atomic states of the DMFT impurity at $T=116$ K, decomposed in number of particles $N$ ($x$ axis) and spin state $S$, as indicated.

Figure 15

LDA+DMFT effective masses for doped and undoped FeGa${}_3$ as obtained from the energy derivative of the self-energy. Orbital components that account for the majority of spectral weight for the valence (conduction) states are denoted “$t_{2\mathrm{g}}$” in black (“$e_{\mathrm{g}}$” in red).

Figure 16

(a) LDA+DMFT local spin susceptibility as functions of temperature (solid lines) for FeGa${}_{2.955}$Zn${}_{0.045}$ (blue), FeGa${}_{2.925}$Zn${}_{0.075}$ (green), and FeGa${}_3$ (black) together with fits (dashed lines) to either the modified Curie law or to the activation law $\chi$($T$)$={\chi }_0+\text{exp}$[$-{\Delta }_{\mathrm{S}}$/($k_{\mathrm{B}}T$)] with a spin gap ${\Delta }_{\mathrm{S}}=0.21$ eV. The inset displays Pauli susceptibilities computed from the spectral function for the two simulated Zn-doping levels in the same units. (b) LDA+DMFT spectral functions (solid lines) for FeGa${}_{2.925}$Zn${}_{0.075}$ at different temperatures compared to those for FeGa${}_3$ at 77 K (dashed line). An offset (multiples of 2 st. eV${}^{-1}$f.u.${}^{-1}$) was added to each curve so that all the presented curves can be easily viewed and compared. The $A$($E$) curve for FeGa${}_3$ was shifted on the energy scale by $-0.365$ eV to facilitate visual comparison of its shape with the calculated $A$($E$) for FeGa${}_{2.955}$Zn${}_{0.045}$.