Supplementary Materials of paper titled as “Electrical, Magnetic and Magneto-Electrical Properties in Quasi-two-dimensional K0.58RhO2 Single Crystals Doped with Rare-earth Elements”
In this supplementary material, we summarize the experimental details, compositions, crystal structures and some transport results of rare-earth element doped K0.58RhO2 single crystals to shorten the main text.
1. Experimental Procedure and Methods
The single crystals samples of K0.58RhO2 were grown by the self-flux method, which is similar to our previous report.1,2 The high-purity starting compositions Rh2O3, K2CO3 and rare-earth elemental compounds La2O3, Ho2O3, Sm2O3 and Dy2O3 powders were weighed carefully according to the mole ratio of 1: 25: 0.1. Then the mixture was heated to 1273 K and held for 12 hours to make the mixture uniformly. Then the temperature was decreased to 1153 K at the rate of -5 K/h, dropped to 973 K at the rate of -2 K/h and then cooling with the furnace. The polycrystalline potassium rhodate was also prepared using flux method. The difference from the previous crystal growth process is that the cooling rate is increased to -20 K/h to form the small and uniform crystals.
The composition of KxRhO2 crystals and rare-earth doped KxRhO2 crystals (as-grown single crystals and poly-crystals) were determined by the energy dispersive spectroscopy (EDS) in a scanning electron microscope (SEM) (FEI-Quantum) using a standard reference sample. The standard deviation is around 3% in the measured concentration. The analysis of actual composition of rare-earth element doped KxRhO2 crystals was made by inductively coupled plasma (ICP) atomic emission spectroscopy (AES) (ICP-AES) technique. In this paper we use five single-crystals with different rare-earth element contents and K contents. The potassium composition of the powder and crystalline sample of KxRhO2 was carefully checked by energy-dispersive spectroscopy (EDS). And the K content is around 0.58. The concentrations of rare-earth elements were determined by inductively coupled plasma (ICP) atomic emission spectroscopy (AES) (ICP-AES) technique. The measured concentrations of these samples are summarized in TableSI. Single crystal and poly-crystal X-ray diffraction (XRD) were carried out by a X-ray diffractometer (Philips PW 1710) using Cu Kα radiation, scanning rate of 1° per minute, and 2θ was scanned from 10° to 80°. The crystal structure was analyzed by Rietveld refinement, using the general structure analysis software package GSAS-EXPGUI.3 The electrical resistivity and Hall resistivity were measured by using the six-probe method and platinum as the electrical contact in PPMS system with temperature changed from 300 K to 2 K. The dc magnetization was measured by using a Quantum Design magnetic properties measurement system. And the magnetic field was perpendicular to the sample surface.
TableSI. Chemical compositions of single-crystal samples characterized in this paper.
Sample / Chemical compositionKxRhO2
La:KxRhO2
Sm:KxRhO2
Dy:KxRhO2
Ho:KxRhO2 / x=0.58
x=0.58, n(La): n(K)=0.202×10-4:1
x=0.58, n(Sm): n(K)= 2.96×10-4:1
x=0.58, n(Dy): n(K)= 1.67×10-4:1
x=0.58, n(Ho): n(K)= 2.73×10-4:1
2. The Crystal Structure of K0.58RhO2 and Rare-Earth Element -doped K0.58RhO2
In term of crystal structure, a rhodium atom and six oxygen atoms form rhodium-oxygen octahedron, and rhodium-oxygen octahedrons connected each other by edge sharing to form two-dimensional plane, then rhodium-oxygen octahedron layer and potassium ion layer stack alternately to form the crystal structure [Fig.S1(a)]. The resistance ratio between ab-plane and c-plane is as high as 300, which infers carriers itinerating mainly along the ab-plane. We can therefore treat KxRhO2 as the quasi-two-dimensional system.After the flux growth, we can easily separate the millimeter hexagonal crystals using the de-ionized water [see Fig. S1(b)]. Though the crystal structure of K0.63RhO2 and K0.49RhO2 has been reported as space group P63mmc (No.194),2,4 the structure of our sampleswerestudied carefully. In order to refine the crystal structure of our crystal (K0.58RhO2), we consider the space groups from the cobaltate, which have many similarities in crystal structure. K4Co7O14 and K0.60CoO2 belong to space group P63m(No.176) and P63mmc (No.194), respectively.5 The two space groups have been tried in our powder X-ray diffraction data. Fig. S1(c) shows powder X-ray diffraction pattern (XRD) result and refinement one of K0.58RhO2. It substantiates that the space group P63mmc is better than P63m. And the lattice constants of a = 0.30664 nm and c = 1.22866 nm are different from those of a = 0.30645 nm, c = 1.35284 nm in K0.63RhO2 and a = 0.30647 nm, c = 1.3600 nm in K0.49RhO2. The reason of the differences might be due to the obvious (0 0 L) plane preferential peaks of their samples used for the structural refinement. Fig. S1(d) demonstrates the typical X-ray diffraction pattern of the grown un-doped K0.58RhO2 single-crystal sample, which shows the diffraction peaks labeled as (0 0 L). This confirms that the crystals are mainly grown along the ab-plane. The similar X-ray diffraction patterns are observed in rare-earth doped K0.58RhO2 single crystals.
Fig.S1.(a) The schematic of atomic structure of KxRhO2. (b) The photo of the grown KxRhO2 crystal from the flux shows typical size. (c) The Rietveld refinement of the XRD of polycrystalline K0.58RhO2.(d) The XRD of the grown K0.58RhO2single crystal.
3. Some Results of Un-doped and La-doped K0.58RhO2Single Crystals
In Fig. S2 (a) and (b) depict the temperature-dependent-resistanceρab of un-doped and La-doped K0.58RhO2 single crystals. We can clearly seethemetallic behaviour of these two samples. And there is normal positive magnetoresistance in these two samples with the application of magnetic field.
Fig. S2 (a) and (b) are temperature-dependent resistance of un-doped and La-doped K0.58RhO2 single crystals under the application of different magnetic field, respectively. Magnetic field is parallel to c-axis.
Fig. S3 (a) and (b) show the dependence between magnetic-field and Hall resistance. Linear magnetic dependence behaviors are observed in un-doped and nonmagnetic-atom La doped samples in the magnetic field ranged from 0 Oe to 80 kOe. The values of the slope RH in these curves are positive and about 2×10-3 cm3/C, which infers the type of carrier is hole.
Fig. S3 (a) and (b) are the dependence between magnetic field and Hall resistance of un-doped and La-doped K0.58RhO2 single crystals.
4. The Relationships between Magnetoresistance and Magnetic Hysteresis Loops in Ho, Dy and Sm-doped K0.58RhO2Single Crystals
Fig. S4 shows magnetoresistances and hysteresis loops for Ho, Dy and Sm-doped K0.58RhO2 single crystals.They all show the similar corresponding relationships between magnetoresistance and magnetic hysteresis loops.We can find the strong correlation between MR and M/Ms. When M/Ms = 1 or -1, it represents ferromagnetic domain regions align and the resistance shows the lowest value. When M/Ms = 0, all the ferromagnetic domain regions arrange randomly and the resistance demonstrates the largest value.
Fig. S4 (a)(c) (e) Magnetoresistances are measured in 2 K for Ho, Dy and Sm, respectively. (b) (d) (f)and the magnetic hysteresis loops forHo, Dy and Sm-doped K0.58RhO2 single crystals in 2 K, respectively.
5.The Temperature-Dependent Carrier Concentration of Five Samples
Fig. S5 shows.Using the slopes of Hall voltage measured at 8 T as nominated value, we can extract temperature-dependent nominated carrier concentration. One can see that nominated carrier concentration of non-doped, La, Sm and Ho doped samples are weakly dependent on temperature, while these of Dy-doped sample even change the signs at about 20 K.
Fig. S5The temperature-dependentcarrier concentration of five doped and non-doped K0.58RhO2samples.
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