High magnetic field properties in ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ with antiferromagnetic and spin-glass states

We report experimental studies on ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ focusing on properties related to antiferromagnetism in ${\mathrm{Ru}}_2\mathrm{CrSi}$ and spin glass (SG) in ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$. By measuring the temperature dependence of magnetization $M\left(T\right)$, specific heat $C\left(T\right)$, electrical resistivity $\rho \left(T\right)$, and muon spin relaxation ($\mu \mathrm{SR}$), we observed that ${\mathrm{Ru}}_2\mathrm{CrSi}$ exhibited an antiferromagnetic (AF) transition at a temperature $T_N$ of $\sim 13$ K, and ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$ showed SG properties that could be interpreted as successive SG transitions, where the spin-freezing occurred at temperature $T_g$, and below that strong irreversibility in $M\left(T\right)$ and a gradual peak of $M\left(T\right)$ at $T^{*}(>T_g)$ appeared. When the data for $0\le x\le 0.1$ were compared, by substituting Fe the AF order was rapidly destroyed and it appeared to change to two anomalies at $T^{*}$ and $T_g$. With increasing $x$, there was a slight change in $T_g$ from $T_N$ for $x=0$; however, $T^{*}$ increased, suggesting that the AF and the SG states are closely related. Furthermore, the results of specific heat, resistivity, and magnetization in high fields were presented and compared. For ${\mathrm{Ru}}_2\mathrm{CrSi}$ in specific heat under high magnetic fields up to 14 T, the peak shape around $T_N$ and the $T_N$ value were constant. The resistivity and magnetization in pulsed fields suggested that $T_N$ of ${\mathrm{Ru}}_2\mathrm{CrSi}$ was constant up to over 50 T. These results demonstrated the unusual robustness of the AF transition to magnetic fields. In ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$, unusual hysteresis in magnetoresistance was observed in static and pulsed magnetic fields, although their appearances differed. These hystereses were considered a manifestation of the curious properties of the SG state with strong irreversibility.

Figure 1

(a) Temperature dependence of the magnetization $M\left(T\right)$ at a magnetic field of 1 T of ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ ($0\le x\le 0.05$). Irreversibility between zero-field cooling (ZFC) and field cooling (FC) is observed. (b) Typical temperature dependences of the resistivity normalized by that at 300 K, $\rho \left(T\right)/{\rho }_{300}$ of ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ ($0\le x\le 0.3$).

Figure 2

(a) Specific heat $C\left(T\right)$ of ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ ($x=0$, 0.01, and 0.1). The dotted line shows the estimated lattice contribution (see the text). (b) Magnetic specific heat divided by $T$, $C_m\left(T\right)/T$, $C_m\left(T\right)$ is obtained by subtracting the lattice contribution. The inset is an expanded view at low temperatures. An absence of a linear term and a $T^2$ dependence of $C_m\left(T\right)$ at low temperatures are observed. (c) Magnetic entropy $S_m$ obtained by integrating (b).

Figure 3

Specific heat, as a form of $C/T-T$, of the ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ [$x=$ (a) 0 and (b) 0.1] under magnetic fields of 0, 5, 10, and 14 T. For both samples at any fields up to 14 T, no influence of magnetic field is observed.

Figure 4

(a) Time spectra of the asymmetry in $\mu \mathrm{SR}$ of ${\mathrm{Ru}}_2\mathrm{CrSi}$ at longitudinal field $B_{\mathrm{LF}}=0.01$ T at various temperatures. Solid lines are fit to a single exponential function [Eq. (3)]. (b) Temperature dependence of the initial asymmetry $A$ and the relaxation rates $\lambda$ after zero-field cooling.

Figure 5

Magnetization of ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ ($x=0$, 0.1, 0.3, and 0.5) in pulsed fields up to $B=72$ T at 4.2 K.

Figure 6

Magnetization of ${\mathrm{Ru}}_2\mathrm{CrSi}$ in pulsed fields at temperatures $4.2\le T\le 20$ K.

Figure 7

(a) Magnetoresistance ratio $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ of ${\mathrm{Ru}}_2\mathrm{CrSi}$ at $T=1.8$ K in static magnetic fields. (b) $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ of ${\mathrm{Ru}}_2\mathrm{CrSi}$ in pulsed fields at temperatures of $1.4\le T\le 20$ K. (c) Temperature dependence of resistivity for different values of magnetic field constructed from the $\rho \left(B\right)$ data in pulsed fields at different temperatures, shown in (b). Solid circles show the data of $\rho \left(T\right)$ at $B=0$ measured directly for this sample with varying temperature.

Figure 8

(a) Magnetoresistance ratio $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ of ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$ under a static field. The arrows show the order of varying magnetic field. The measurements start initially in a zero-field-cooling (ZFC) condition, and ${\rho }_0$ is the value of $\rho \left(0\right)$ when $B$ returns to zero from 9 T. $B_i$ is the magnetic field where the initial $\rho \left(B\right)$ curve after ZFC, indicated by the arrow 1, meets the loop of $\rho \left(B\right)$ in the subsequent sequence. (b) $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ of ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ as a function of magnetic field with $x=0.06$, 0.3, and 0.5 at 2 K, measured under a static magnetic field up to 9 T with the field sequence shown in (a) after ZFC.

Figure 9

(a) Magnetoresistance ratio $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ of ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$ under a static field at $T=1.3$ K after ZFC from 0 to 18 T and decreasing $B$ back to 0 T for longitudinal and transverse configurations. The inset shows an expanded view around 0 T. The arrows show the order of varying magnetic field: first increasing $B$ after ZFC and decreasing $B$ back to 0 T. (b) $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ of ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$ under a static field at $T=0.5$ K in varying $B$ back and forth for $-10\le B\le 10$ T from 0 T after ZFC. The arrows show the order of varying magnetic field. The inset shows an expanded view around $B=0$ T.

Figure 10

(a) Electrical resistivity of ${\mathrm{Ru}}_{1.9}{\mathrm{Fe}}_{0.1}\mathrm{CrSi}$ under pulsed fields of $B=56$ T as a function of magnetic field $B$ at temperatures between 1.4 and 30 K. The curves are offset by equal amounts for clarity. The inset shows the magnetoresistance ratio (MRR) $\mathrm{\Delta }\rho \left(B\right)/{\rho }_0$ at 1.4 and 20 K. The magnitude of MRR hardly changes below 30 K. For the data at 1.4 K, the open circle shows the starting point and the arrows show the time ordering of $B$. Crosses show MR for a smaller pulsed field of 7.8 T at 1.4 K. For $T\lesssim 3$ K, an unusual hysteresis appears, forming a figure-8. (b) MRR of ${\mathrm{Ru}}_{1.7}{\mathrm{Fe}}_{0.3}\mathrm{CrSi}$ under pulsed fields of $B=45$ T at temperatures between 1.3 and 30 K.

Figure 11

Magnetic field vs temperature ($B-T$) magnetic phase diagram for ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ ($x=0$, 0.02, and 0.1). The antiferromagnetic (AF) transition $T_N$ of ${\mathrm{Ru}}_2\mathrm{CrSi}$ determined by magnetization (open circles), specific heat (solid circles), electrical resistance (crosses), and magnetoresistance in a pulsed field (MR), as described in Fig. 7 (broken line), is shown. The inset is the $B-T$ phase diagram extending to a high field of 55 T, where the almost upright phase boundary of the AF transition determined by MR is shown. Characteristic temperatures of the spin-glass behavior, $T_g$ and $T^{*}$ in magnetic fields, for $x=0.1$ and 0.02 are plotted. Open diamonds show $B_i$ for $x=0.1$ determined from Figs. 8 and 9, and the solid line shows the expected dependence $\mathrm{\Delta }{T}^{3/2}={[T_g\left(0\right)-T_g\left(B\right)]}^{3/2}$ for the AT transition.

Figure 12

Temperature vs Fe concentration ($T-x$) diagram for ${\mathrm{Ru}}_{2-x}{\mathrm{Fe}}_x\mathrm{CrSi}$ ($0\le x\le 0.5$). The solid diamond shows the antiferromagnetic (AF) transition $T_N$ for $x=0$. The AF phase exists only for near $x=0$. Characteristic temperatures of spin-glass behavior, $T_g$ [onset of strong irreversibility in $M\left(T\right)$] and $T^{*}$ [maximum of $M\left(T\right)$], at a low field of $B=0.005$ T are shown by open circles and triangles. Below $T_g$ the spin-glass state with strong irreversibility (SG) exists, and for $T_g<T\lesssim T^{*}$ the inhomogeneous magnetic state with weak irreversibility (WI) exists. The ferromagnetic transition $T_C$ is shown by the solid square ($T_C$ for $x=0.5$ is 190 K).