Antiferromagnetism and hidden order in isoelectronic doping of ${\text{URu}}_2{\text{Si}}_2$

We present muon spin rotation $\left(\mu \mathrm{SR}\right)$ and susceptibility measurements on single crystals of isoelectronically doped ${\mathrm{URu}}_{2-x}{\mathrm{T}}_x{\mathrm{Si}}_2$ (T = Fe, Os) for doping levels up to 50%. Zero field (ZF) $\mu \mathrm{SR}$ measurements show long-lived oscillations demonstrating that an antiferromagnetic state exists down to low doping levels for both Os and Fe dopants. The measurements further show an increase in the internal field with doping for both Fe and Os. Comparison of the local moment-hybridization crossover temperature from susceptibility measurements and our magnetic transition temperature shows that changes in hybridization, rather than solely chemical pressure, are important in driving the evolution of magnetic order with doping.

Figure 1

(a) ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$ magnetization data measured in a field of $H=0.1T\parallel c$ for $x=0.02$ (black circles), 0.1 (blue squares), 0.2 (red triangles), and 0.3 (green diamonds). (b) Temperature derivative of the data shown in (a) arrows on plot (b) show the measured transition temperatures.

Figure 2

(a) ${\mathrm{URu}}_{2-x}{\mathrm{Os}}_x{\mathrm{Si}}_2$ magnetization data measured in a field of $H=0.1T\parallel c$ for $x=0.1$ (red circles), 0.2 (black squares), and 0.4 (blue triangles). (b) Temperature derivative of the data shown in (a). Arrows on plot (b) show the measured transition temperatures.

Figure 3

${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2\mu \mathrm{SR}$ Data measured at $T=2$ K in zero applied external field with the muon spins initially perpendicular to the $c$-axis for (a) $x=0.02$ (black circles), 0.1 (blue squares), 0.2 (red triangles), and 0.3 (green diamonds) and (b) $x=0.6$ (cyan circles), $x=0.8$ (purple squares), and $x=1$ (orange triangles). Solid lines in (a) show fits to Eq. (1) and those in (b) show fits to Eq. (2).

Figure 4

Fitting parameters for the $\mu \mathrm{SR}$ data of ${\mathrm{URu}}_{2-x}{\mathrm{Fe}}_x{\mathrm{Si}}_2$ measured in zero applied field with the muon spins perpendicular to the $c$-axis. (a) Average internal field $B_{\mathrm{av}}=0.5(B+RB)$ for dopings $x=0.02$ (black circles), 0.1 (blue squares) 0.2 (red triangles) and 0.3 (green diamonds). (b) Internal field $B$ for dopings $x=0.6$ (cyan circles), 0.8 (purple squares) and 1 (orange triangles). (c) Magnetic volume fraction for dopings $x=0.02$ (black circles), 0.1 (blue squares) 0.2 (red triangles) and 0.3 (green diamonds). (d) Magnetic volume fraction for dopings $x=0.6$ (cyan circles), 0.8 (purple squares) and 1 (orange triangles).

Figure 5

${\mathrm{URu}}_{2x-}{\mathrm{Os}}_x{\mathrm{Si}}_2\mu \mathrm{SR}$ data and fitting in zero external field measured with muon spins initially perpendicular to the $c$ axis for $x=0.1$ (red circles), 0.2 (black squares), and 0.3 (blue triangles). (a) $\mu \mathrm{SR}$ data measured at 5 K, (b) Fourier transform of ${\mathrm{URu}}_{1.9}{\mathrm{Os}}_{0.1}{\mathrm{Si}}_2$ (red line) data measured at 5 K and ${\mathrm{URu}}_{1.8}{\mathrm{Fe}}_{0.1}{\mathrm{Si}}_2$ (green line) data measured at 2 K, and (c) magnetic volume fraction $F$ (d) internal field $B$. Solid lines in (d) correspond to fits to Eq. (2).

Figure 6

Comparison of the transition temperatures measured by susceptibility to those measured by $\mu \mathrm{SR}$ for Fe doped samples (red squares) and Os doped samples (blue circles). The solid black line shows the expected 1:1 correspondence.

Figure 7

Measured internal fields as a function of effective chemical pressure for Fe doped (red squares) and Os doped (blue circles), and as a function of applied hydrostatic pressure for pure ${\mathrm{URu}}_2{\mathrm{Si}}_2$ (black triangles) from Ref. [11]. Error bars are not shown as in all cases they would lie within the symbols.

Figure 8

High temperature susceptibility data showing the broad maxima that appears for (a) Fe doped samples, $x=0.04$ (black circles), 0.1 (blue squares), 0.2 (red triangles), and 0.3 (green diamond) and (b) Os doped samples, $x=0.1$ (red circles), 0.2 (black squares), and 0.4 (blue triangles). (c) A plot of $T_N$ from susceptibility vs the temperature of this susceptibility maxima for Fe doped (red squares), Os doped (blue circles), and pure ${\mathrm{URu}}_2{\mathrm{Si}}_2$ (black triangle).