⇦Chinese Physics Letters, 2020, Vol. 37, No. 6, Article code 067501 Tuning of Magnetic Properties of $\alpha$-RuCl$_{3}$ Single Crystal by Cr Doping * Yu-Jie Yuan (袁宇杰)1, Cheng-He Li (李承贺)2, Shang-Jie Tian (田尚杰)2, He-Chang Lei (雷和畅)2**, Xiao Zhang (张晓)1** Affiliations 1State Key Laboratory of Information Photonicsx and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China 2Department of Physics, and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China Received 21 January 2020, online 26 May 2020 *Supported by the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant Nos. 15XNLQ07, 18XNLG14, and 19XNLG17).
**Corresponding author. Email: hlei@ruc.edu.cn; zhangxiaobupt@bupt.edu.cn Citation Text: Yuan Y J, Li C H, Tian S J, Lei H C and Zhang X et al 2020 Chin. Phys. Lett. 37 067501    Abstract We study the influence of Cr doping on magnetic properties of $\alpha$-RuCl$_{3}$ single crystals in detail. With increasing Cr content, the $c$-axial lattice parameter increases gradually, implying that the Cr doping may weaken the interlayer interactions. The magnetism of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals evolves from a long-range AFM order to a possible spin-glass state with Cr doping. The appearance of a possible spin-glass state can be explained by the introduction of FM interaction by Cr$^{3+}$ ions, which competes with the AFM interaction between Ru$^{3+}$ ions. Moreover, the larger magnetic moment of Cr$^{3+}$ ion with $S= 3/2$ than Ru$^{3+}$ ion with $J_{\rm eff}= 1/2$ also results in a monotonic increase of the effective moment of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystal. DOI:10.1088/0256-307X/37/6/067501 PACS:75.50.Ee, 75.50.Lk, 75.40.Cx © 2020 Chinese Physics Society Article Text Recently, binary halides with interlayer van der Waals interaction have attracted tremendous interest because they exhibit various unusual physical properties such as two-dimensional magnetism,[1] quantum frustrated magnetism,[2] and interlayer charge disproportionation.[3] Among them, frustrated magnet $\alpha$-RuCl$_{3}$ as a candidate for quantum spin liquid (QSL) has been intensively investigated due to its exotic physical properties and potential applications in quantum computers.[2,4–6] In $\alpha$-RuCl$_{3}$ materials, a honeycomb lattice of Ru$^{3+}$ with effective moment $J_{\rm eff} =1/2$ is formed by the edge-sharing RuCl$_{6}$ octahedra. Unlike geometry frustration materials with 3$d$ transition metal elements where the Heisenberg interaction and frustrated lattice play important roles in the QSL, strong spin-orbit coupling (SOC) in the 4$d$ and 5$d$ electron systems can induce significantly anisotropic bond-dependent Ising interactions, i.e, exchange frustration. It could lead to a Kitaev QSL (KSQL) state.[7] Neutron scattering measurements have shown that the magnetic interactions in $\alpha$-RuCl$_{3}$ are closer to the Kitaev limit with possible Majorana spin excitations of a KQSL.[2,6] However, at low temperatures there is still a long-range zig-zag antiferromagnetic (AFM) order in the honeycomb layers with an AFM stacking between layers, which coexists with this KQSL state.[2,6,8–10] Recent studies indicate that external magnetic fields can change magnetic interaction effectively and suppress the long-range zig-zag AFM order, leading to the QSL state.[11–14] In contrast, although the application of pressure on $\alpha$-RuCl$_{3}$ melts the AFM state, it leads to the spin dimerization (valence bond state, VBS state) and the insulating behavior still persists even at very high pressure.[15,16] Doping is another effective method to tune physical properties of materials. For example, dopants can destroy long-range magnetic order and lead to the appearance of spin glass or VBS state in another QSL candidate of iridates $A_{2}$IrO$_{3}$ ($A$ = Li, Na).[17–19] For $\alpha$-RuCl$_{3}$, the doping of nonmagnetic Ir$^{3+}$ also suppresses the AFM ordering temperature and the quantum disordered state appears at high doping level, which could be related to the appearance of a dilute KQSL or a short-range correlated quasistatic order coexisting with dynamically fluctuating moments.[20,21] In contrast to nonmagnetic element doping, the studies on the effects of magnetic dopants are scarce. In this Letter, we present a detailed study on the physical properties of Cr doped RuCl$_{3}$ single crystals. We find that Cr doping results in the monotonic increase of effective magnetic moment of Ru$^{3+}$/Cr$^{3+}$ site and the sign change of Weiss temperature from negative to positive, implying that the magnetic interaction evolves from AFM interaction to ferromagnetic (FM) one. Moreover, a possible spin-glass (SG) state appears in Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ ($0.143 \leq x \leq 0.761$) single crystals once the AFM order states in both end members are suppressed. Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals were grown using the chemical vapor transport method. First, the commercial RuCl$_{3}$ and CrCl$_{3}$ powders were dehydrated at 473 K for 12 h in a dynamic vacuum. Then, RuCl$_{3}$ and CrCl$_{3}$ powders were mixed with the different ratios and put into a silica tube with length of 20 cm. The tube was evacuated down to 10$^{-2}$ Pa and sealed under vacuum. The source zone was raised to 873–973 K, and the growth zone was raised to 773–873 K. The growth period was about seven days, and then the furnace was cooled naturally. The shiny black plate-like single crystals of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ can be obtained. Room-temperature x-ray diffraction (XRD) patterns were collected using a Bruker D8 x-ray diffractometer with Cu $K_{\alpha}$ radiation ($\lambda= 0.15418$ nm) at room temperature. The elemental analysis was performed using energy-dispersive x-ray spectroscopy (EDX) analyses. Magnetization measurements were performed in a Quantum Design magnetic property measurement system (MPMS3).
cpl-37-6-067501-fig1.png
Fig. 1. (a) XRD patterns of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals. The Miller indexes from the monoclinic $C2/m$ are displayed. (b) Evolution of diffraction peak position 2$\theta$ for (001) index and the evaluated lattice constant $c$ with Cr content $x$. The inset shows a typical photograph for the single crystal.
Figure 1(a) exhibits the XRD patterns of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals. These XRD patterns can be well indexed by the (00$l$) reflections of honeycomb structure with space group $C2/m$, indicating that the surface of crystals is perpendicular to the $c$ axis. As shown in Fig. 1(b), with increasing Cr content, the diffraction peaks for (001) shift to lower angles (Fig. 1(b)). Correspondingly, the estimated $c$-axial lattice parameter increases gradually. This trend is opposite in contrast to the Ir-doped Ru$_{1-x}$Ir$_{x}$Cl$_{3}$ with the rhombohedral.[21] The $c$-axial lattice parameter of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ exhibits an almost linear dependence on the actual Cr content determined from the EDX measurement, perfectly following Vegard's law. It confirms that the Cr enters into the Ru site indeed without any solubility limit and the atom distributions in the doped crystals should be homogeneous. It has to be noted that the ionic radius of Cr$^{3+}$ (75.5 pm) is smaller than that of Ru$^{3+}$ (82 pm) with octahedral coordination.[22] Thus, the expanded $c$-axial lattice with Cr doping cannot be ascribed to the evolution of ionic radius and it implies that the interlayer interaction may be weakened by introducing Cr$^{3+}$ ions. The Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystal shows a plate-like shape (inset of Fig. 1(b)), consistent with the single crystal XRD patterns and the layered structure of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$. Temperature dependence of zero-field-cooling (ZFC) and field-cooling (FC) magnetization curves $M(T)$ at $\mu_{0}H = 0.1$ T parallel to the $c$ axis are shown in Figs. 2(a) and 2(b). It can be seen in the low Cr doped region ($x\leq 0.039$), there are drops in the FC and ZFC $M(T)$ curves below 10 K and both the curves overlap each other very well in the whole temperature region (main panel and insets of Fig. 2(a)). It indicates that the samples with low Cr doping level have AFM ground states. For undoped RuCl$_{3}$, it has an in-plane zig-zag AFM order but the ZFC $\chi(T)$ curve exhibits a significant drop at $T_{\rm N}\sim 7$ K and a weak kink around 14 K. The former transition is associated with a trilayer ABC antiferromagnetic stacking and the latter corresponds to a bilayer AB periodicity, which may become more obvious when there are a high density of stacking faults.[10] With Cr doping, the AFM ordering temperature $T_{\rm N}$ becomes lower monotonically (Fig. 2(c)), implying that Cr doping suppresses the long-range in-plane zig-zag AFM ordering of RuCl$_{3}$. On the other hand, for the crystals with higher Cr content ($x> 0.039$), a bifurcation behavior between the FC and ZFC $M(T)$ curves can be observed clearly. It suggests that the long-range AFM order disappears and a possible SG state may appear. With increasing the doping level of Cr further, the SG transition temperature $T_{\rm g}$ (corresponding to the peak position of the ZFC $M(T)$ curve) first increases and reaches the maximum value ($\sim $6.04 K) at $x\sim 0.418$. Then the $T_{\rm g}$ decreases gradually but still can be observed even when $x= 0.692$ (Fig. 2(c)). For the sample with $x= 0.761$, the $T_{\rm g}$ sharply increases again. It has to be mentioned that pure CrCl$_{3}$ shows a long-range A-type antiferromagnetism (intralayer ferromagnetic (FM) interaction and interlayer AFM interaction) with $T_{\rm N}\sim 14$ K.[23] Therefore, the competition of in-plane AFM and FM interactions would be the origin of SG state in Ru$_{1-x}$Cr$_{x}$Cl$_{3}$. In addition, it can be seen that with Cr doping, the absolute values of $M(T)$ increases quickly, especially at low temperature, implying that the local moment is enhanced significantly. In the high-temperature region, i.e., above 100 K, temperature dependence of magnetic susceptibility $\chi(T)$ can be fitted very well by using the Curie–Weiss law $\chi(T)=C/(T-\theta)$, where $C$ is the Curie constant and $\theta$ is the Curie–Weiss temperature (inset of Fig. 2(b) for some samples). First, the value of $\theta$ exhibits a monotonic change with Cr doping, changing from negative to positive when increasing $x$ (Fig. 2(d)). It implies that the Cr doping introduces the FM interaction along the $c$-axis gradually. When close to RuCl$_{3}$ side, the dominant in-plane AFM interaction is consistent with the zig-zag long-range AFM order in RuCl$_{3}$.[2,6,8–10] Moreover, the much larger $\theta$ ($\sim $60–140 K) than $T_{\rm N}$ suggests the strong magnetic frustration in this system. The introduced FM interaction by Cr doping decreases the absolute value of $\theta$ and destroys the long-range AFM magnetic order. Then, the SG state appears because of the competition of AFM and FM interactions. Especially, the maximum value of $T_{\rm g}$ appears exactly when the sign change of $\theta$ is observed at $x= 0.418$, where the strength of AFM and FM should be comparable. Further increasing Cr content results in the increase of positive $\theta$, suggesting the dominance of FM interaction. Correspondingly, the $T_{\rm g}$ starts to decrease in general. Finally the long-range A-type AFM order emerges in undoped CrCl$_{3}$.[23] On the other hand, the effective magnetic moment $\mu_{\rm eff}$ can be calculated from $C$ ($=N\mu_{0}\mu_{\rm eff}^2/3k_{_{\rm B}}$, where $N$, $\mu_{0}$, and $k_{_{\rm B}}$ is the total number of Ru and Cr ions, the vacuum permeability, and the Boltzmann constant, respectively). It also shows a similar monotonic increase to $\theta$ with Cr doping (Fig. 2(d)). For undoped RuCl$_{3}$, the $\mu_{\rm eff}$ is about 2.301 $\mu_{_{\rm B}}$/f.u., consistent with results in the literature.[8] However, it is larger than the spin-only value of 1.73 $\mu_{_{\rm B}}$ for the low-spin state of Ru$^{3+}$ ion ($S= 1/2$), suggesting a significant contribution from the orbital moment. It is a common feature in many magnetic materials.[24] With Cr doping, the increased $\mu_{\rm eff}$ can be explained well by the larger local moment of Cr$^{3+}$ ion ($\mu_{\rm eff}= 3.87 \mu_{_{\rm B}}$ for spin-only $S= 3/2$) than Ru$^{3+}$ ion. When approaching CrCl$_{3}$, the value of $\mu_{\rm eff}$ (3.835 $\mu_{_{\rm B}}$/f.u. for $x= 0.761$) is close to the above spin-only value of 3.87$\mu_{_{\rm B}}$ for Cr$^{3+}$ ion, implying the quenching of orbital moment gradually.
cpl-37-6-067501-fig2.png
Fig. 2. (a) and (b) Temperature dependence of magnetization $M(T)$ for Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals at $\mu_{0}H= 0.1$ T for $H\Vert c$. The insets in (a) show the $M(T)$ curves for the samples with $x= 0$ (left panel) and 0.018 (right panel). The inset in (b) shows the fitting results of magnetic susceptibility $\chi(T)$ using the Curie–Weiss law in the high-temperature region (solid lines) for the samples with $x= 0.039$–0.418. (c) The variation of $T_{\rm N}$ and $T_{\rm g}$ with Cr content $x$. (d) Fitted values of $\theta$ and $\mu _{\rm eff}$ as a function of $x$.
cpl-37-6-067501-fig3.png
Fig. 3. (a) Temperature dependence of the $M(T)$ for crystals with $x= 0.143$. (b) $T_{\rm g}$ as a function of Cr content $x$ at various magnetic fields for $H\Vert c$. (c) and (d) Field dependence of magnetization $M(\mu_{0}H)$ at 1.8 K and 300 K for $H\Vert c$. The inset of (c) shows the enlarged parts of $M(\mu_{0}H)$ for $x$ between 0.261 and 0.619 at low field region.
In order to further clarify the origin of glassy magnetic behaviors in Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals, the temperature dependences of ZFC and FC $M(T)$ at different magnetic fields parallel to the $c$ axis are measured. Figure 3(a) shows the results for crystal with $x= 0.143$ and with increasing field, the $T_{\rm g}$ shifts to lower temperature. Such behavior has been observed in all the samples with SG state transitions (Fig. 3(b)). These results are consistent with the classical SG behavior,[25] in contrast to the behaviors of some cluster SG (the assemblies of interacting FM magnetic clusters) systems where the peak of $M(T)$ shifts to higher temperatures with increasing field due to the growth of clusters.[26] At high field of $\mu_{0}H= 5$ T, the ZFC and FC $M(\mu_{0}H)$ curves coincide with each other in the whole measuring temperature range, indicating the full suppression of the SG state at this field. Figure 3(c) shows the field dependence of magnetization $M(\mu_{0}H)$ at $T= 1.8$ K for Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals. On the other hand, it can be seen that all the $M(\mu_{0}H)$ curves have S-shapes with weak hysteresis at low field region. This is different from the traditional linear behavior for the AFM state, but similar to the behaviors of other SG systems.[27,28] It also reveals that the FM interaction is introduced by Cr doping in Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals. Moreover, the magnetization at 5 T is still not saturated, implying the coexistence of AFM interaction with the FM one in the samples with SG state. On the other hand, at higher doping levels, the hysteresis is more obvious and becomes strongest with highest coercive field ($\sim $0.3 T) when $x$ is between 0.261 and 0.418. It is consistent with the appearance of maximum $T_{\rm g}$ near this doping level, implying the maximized competition of AFM and FM interactions. With further increasing $x$, the hysteresis becomes weaker again with a decreased coercive field. It may be due to the soft interlayer FM interaction combined with the interlayer AFM interaction, as in pure CrCl$_{3}$.[23] At $T= 300$ K ($>$$T_{\rm g}$), all of $M(\mu_{0}H)$ curves for the whole series exhibit a linear behavior without any hysteresis (Fig. 3(d)), in agreement with the paramagnetic state at this temperature. The slope of the $M(\mu_{0}H)$ curve increases with $x$, reflecting the enhanced magnetic moment of Cr$^{3+}$ ion when compared to Ru$^{3+}$ ion. It is consistent with the $M(T)$ results shown in Fig. 2. In summary, we have grown a series of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals using the chemical vapor transport method. It is found that Cr doping increases the interlayer distance monotonically. More importantly, with Cr doping, the long-range AFM order is suppressed gradually, accompanied with a possible SG state appearing in Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystals when $x> 0.039$. Such an SG state persists even at very high Cr doping level ($x= 0.761$). Such behavior originates from the introduction of FM interaction by Cr$^{3+}$ ions, which leads to the competition of AFM and FM interactions in the doped samples. The highest SG transition temperature emerges when the sign of Curie–Weiss temperature is changed at $x= 0.418$, where the competition between the AFM and FM interactions should be strongest. In addition, the effective moment of Ru$_{1-x}$Cr$_{x}$Cl$_{3}$ single crystal increases with Cr doping because of the larger magnetic moment of Cr$^{3+}$ ion than the low-spin state Ru$^{3+}$ ion. The results suggest an efficient method of adjusting the magnetism for spin-based devices. 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