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Magnetic and thermal property studies of RCrTeO6 (R=trivalent lanthanides) with layered honeycomb sublattices
Journal of Magnetism and Magnetic Materials 370 (2014) 13–17
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic and thermal property studies of RCrTeO6 (R¼trivalent lanthanides) with layered honeycomb sublattices G. Narsinga Rao a, R. Sankar a, I. Panneer Muthuselvam a, F.C. Chou a,b,c,n a
Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan c Taiwan Consortium of Emergent Crystalline Materials, National Science Council, Taipei 10622, Taiwan b
art ic l e i nf o
a b s t r a c t
Article history: Received 8 March 2014 Received in revised form 19 May 2014 Available online 2 July 2014
We have investigated the magnetic ordering of the RCrTeO6 (R¼ Y, La, Tb and Er) samples comprising Cr3 þ (S¼ 3/2). The X-ray diffraction structure analysis revealed that all samples are a hexagonal structure with the space group P 3. The magnetic susceptibility χ(T) and heat capacity CP(T) measurement results reveal that both short range and long range antiferromagnetic (AFM) orderings exist in non-magnetic rare earth R¼ Y and La compounds. For isostructural compounds of R¼ Tb and Er, CP(T) curves show long range ordering at the same temperature as non-magnetic R¼Y, which indicates that the super-super exchange of Cr spins dominates. For R elements of Tb and Er with large spins sitting between honeycomb sublattices composed of CrO6–TeO6 octahedra, the two sublattices of R and Cr appear to be independently magnetic. & 2014 Elsevier B.V. All rights reserved.
Keywords: Antiferromagnetic ordering Super–super exchange interaction Honeycomb lattice Heat capacity
1. Introduction Geometrically frustrated magnetic systems exhibit a variety of ground states depending on the spin size and the spin configuration [1,2]. The spin interactions of these systems cannot be simultaneously satisfied because of the connectivity of lattice. This opens up the possibility to have an unconventional magnetic order or even novel spin-liquid state without any long range spin order at low temperatures [1]. The honeycomb lattice Heisenberg antiferromagnetic (AFM) compounds have attracted much attention due to the existence of diverse novel magnetic ground states [3,4]. For example, Venderbos et al. found that the interplay between the superexchange interaction of localized spins and the double exchange interactions of itinerant spins on the non-frustrated honeycomb lattice leads to an unexpectedly rich phase diagram with exotic magnetic phases [5]. Recent experimental results of the honeycomb lattice compound Bi3Mn4O12(NO3) showed a spin-liquid behavior down to low temperature 0.4 K, which has been ascribed to the frustration effect due to the competition between AFM nearest and next nearest neighbor interactions [6–8]. The spin-1/2 honeycomb lattice InCu2/3V1/3O3 exhibits an AFM transition at 38 K with an estimated nearest neighbor exchange coupling constant 280 K [9]. On the other hand, Na3M2SbO6 (M¼Cu, Ni, and Co) compounds show different magnetic behaviors from spin gap (M¼Cu) to AFM order (M¼Ni and Co)
n Corresponding author at: Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan. E-mail address: [email protected] (F.C. Chou).
http://dx.doi.org/10.1016/j.jmmm.2014.06.057 0304-8853/& 2014 Elsevier B.V. All rights reserved.
[10,11]. For such a variety of magnetic ground state structures, honeycomb lattice with various types of spin systems offers new and interesting possibilities of low temperature properties. The PbSb2O6 structure is one of the typical mixed oxides with a honeycomb structure [12,13]. The mixed oxides of RCrTeO6, where R ¼trivalent lanthanides, have been proposed to be a superstructure of PbSb2O6 [14,15]. The unit cell of RCrTeO6 comprises two formula units and adopts the hexagonal structure with the space group P 3. All Cr and Te cations in RCrTeO6 have octahedral coordination with oxygen atoms. In this superstructure, the honeycomb layers are formed by edge-shared TeO6 and CrO6 octahedra as a sheet and stacked along the c-axis as shown in Fig. 1(a). The rare earth elements can be viewed to be sandwiched between (Cr/Te)O6 honeycomb layers. The (Cr/Te)O6 honeycomb lattice is depicted in Fig. 1(b). Except the structural studies, no other information related to the physical properties of this interesting class of materials are available in the literature. Here we present spin susceptibility and heat capacity measurement results on RCrTeO6 (R¼Y, La, Tb and Er) compounds and compare the impact of trivalent rare-earth elements which are sandwiched between (Cr/Te)O6 honeycomb layers.
2. Experimental details Polycrystalline samples of RCrTeO6 (R¼ trivalent lanthanides) were prepared by the solid state reaction method. R2O3 were heat treated at 900 1C for 12 h before mixing to remove the hydroxide
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G. Narsinga Rao et al. / Journal of Magnetism and Magnetic Materials 370 (2014) 13–17
Fig. 1. (a) Crystal structure of RCrTeO6 showing stacking of a alternative layers of rare earth (R1O6 and R2O6) and (Cr,Te)O6 octahedra (pink and yellow color). The small red colored sphere are oxygen atoms. (b) The honeycomb sheet topology of (Cr/Te)O6 in ab-plane. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
impurity. Stoichiometric proportions of high purity R2O3, Cr2O3, and TeO2 powders were mixed and heated at 600 1C for 12 h to ensure that all the tellurium was oxidized to the hexavalent state. The pre-heated powders were well ground and calcined at 700 1C for 12 h with a heating rate of 2 1C/min and cooled down to room temperature at the same rate. The calcined powders were pressed into pellets and sintered at 850 1C for 12 h. The preparation conditions are the same for all the samples. The structure and the phase purity of the samples were checked by powder X-ray diffraction (XRD) using the Cu–Kα radiation at room temperature. The field cooled (FC) and the zero field cooled (ZFC) magnetization were measured in a commercial Vibrating Sample Magnetometer (VSM, Quantum Design, USA) from 1.8 K to 300 K in the presence of different applied magnetic fields. The temperature dependence of average spin susceptibilities χ(T) is defined with MðTÞ=H based on the linear MðHÞ isotherms. The isothermal magnetization (M) data were also recorded at selected temperatures. The heatcapacity (CP) measurements were carried out by a relaxation method using commercial Physical Properties Measurement System (PPMS, Quantum Design, USA).
3. Result and discussion The powder XRD pattern of the polycrystalline RCrTeO6 (R¼trivalent lanthanides) samples is shown in Fig. 2. The XRD patterns can be indexed to the hexagonal structure with the space group P 3 without any observable trace of impurity phase. The structural parameters were refined by the Rietveld technique with good quality refinement parameters (Rwp ¼ 8.75% and Rp ¼6.61%). The obtained values of the lattice parameters are depicted in Fig. 3 as a function of R3 þ ionic radius. Both the a and c parameters increase with the R3 þ ionic radius as expected. These parameters are in good agreement with those previously reported data [14]. The distances between chromium are larger along the c direction than in the ab-plane (Fig. 1(a)). In addition, partially substituted La/Y by Er samples also show the same hexagonal structure. The refined lattice parameters are decreased significantly with increasing Er content in the case of R ¼La, whereas in R ¼ Y a small decreasing is observed (Fig. 3). The decrease in the lattice parameters is consistent with the smaller ionic radius of Er3 þ (1.144 Å)
Fig. 2. Room temperature powder XRD pattern for RCrTeO6 (R ¼trivalent lanthanides). The symbols are experimental points, solid curve is the best fit from the Rietveld refinement. The vertical bars indicate the position of Bragg peaks and the bottom curve shows the difference between the observed and calculated intensities.
comparing to that of the ionic radius of La3 þ (1.300 Å) or Y3 þ (1.159 Å) [16]. The temperature dependence of magnetic susceptibility χ(T) and 1/χ(T) measured in an applied magnetic field of 10 kOe for RCrTeO6 (R¼La and Y) is shown in Fig. 4(a) and (b). No divergence between the zero field cooled (ZFC) and field cooled (FC) χ(T) curves has been found for both compounds through out the whole experimental temperature range. At low temperature, the χ(T) curves for R ¼ La and Y exhibit a rounded maximum at 10.2 K and
G. Narsinga Rao et al. / Journal of Magnetism and Magnetic Materials 370 (2014) 13–17
Fig. 3. Lattice parameters vs. R3 þ ionic radius for RCrTeO6. The error bars are smaller than data points.
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To analyze the χ(T) data quantitatively, the temperature dependence of χ is fitted with the Curie–Weiss expression χ(T)¼C/(T θ) in the high temperature (50–300 K) range (right axis of Fig. 4), which gives the Weiss temperature θ¼ 28.6 K and 32.4 K for R ¼La and Y, respectively. The observed effective magnetic moment per Cr3 þ ion is 3.79(3) μB (R¼ La) and 3.86(2) μB (R¼Y), which are in close agreement with the expected value of 3.87 μB for the Cr3 þ (S¼3/2) ions. The negative value of θ is indicative of AFM interactions between the Cr3 þ spins in these compounds. The ratio of jθj=T N 4 for R ¼Y and La indicates marginal frustration of Cr3 þ spins in the honeycomb arrangement. The χ(T) data for both compounds are described by the high temperature series expansion (HTSE) for an S ¼3/2 AFM satisfactorily [18]. Above 200 K, χ(T) data were fit well by the sixth order of HTSE (Fig. 4) with the same g factor 1.95 and the intralayer exchange interaction (J/kB) between Cr3 þ ions are found to be 58(2) K (R¼ La) and 40(3) K (R¼Y). Substitution of La3 þ ion with smaller ionic radius of Y3 þ ion leads to a contraction of honeycomb plane, and the shortened inter-Cr distance results in an increase in the antiferromagnetic exchange coupling interaction strength, as shown by the increased TN shown in the inset of Fig. 4(b). In order to obtain a better understanding of the magnetic ordering behavior, we have performed heat capacity measurements. The temperature dependence of the CP(T) curve for LaCrTeO6 is presented in Fig. 5(a) along with the lattice contribution CL(T). A clear λ-type peak is observed at TN. This is an evidence of longrange AFM order. This ordering temperature in turn appeared to be correlated with maximum in d(χT)/dT (inset of Fig. 4(a)). The absence of non-magnetic isomorphic sample of LaCrTeO6 does not allow a direct deduction of the CL from the CP, the CL above TN (20– 30 K) was approximated using a Debye T3 law instead (CP/T¼γ þ βT2). The extracted CL (βT3) is shown as a solid line in Fig. 5(a). The magnetic contribution of the heat capacity Cm was obtained by subtracting the CL from the measured CP data. The magnetic entropy R change (ΔS) was calculated by ΔS ¼ ðC m T 1 Þ dT. The variation of Cm/T and ΔS as a function of temperature for the LaCrTeO6 sample is depicted in Fig. 5(b). At TN, the inferred ΔS increases much less ð r 36%Þ than the full magnetic entropy associated with S¼ 3/2 Cr3 þ
Fig. 4. The temperature dependence of magnetic susceptibility χ measured in an applied magnetic field of 10 kOe for RCrTeO6 (a) R¼ La, and (b) R¼ Y. The right axis shows the 1/χ versus T curves, solid lines are C–W fitting. The HTSE fitting is shown as a blue solid line above 200 K. In insets: expanded the transition region around TN, comparing the χ (open black square symbols), the first derivative of the product χT (solid red circles) for left axis and the heat capacity data (blue solid triangles) for right axis. The dashed lines mark the location of the peak in d(χT)/dT. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
11 K, respectively. The peak temperatures of the d(χT)/dT plot (known as Fisher's heat capacity [17]) coincide with the peak temperature shown in C P (T) (inset in Fig. 4(a)) to be TN 8:5 K and 10 K for R ¼La and Y, respectively, which are marked by vertical lines in the insets of Fig. 4. These results reveal that both short range and long range antiferromagnetic (AFM) orderings coexist in non-magnetic rare earth R ¼Y and La compounds. Since Cr3 þ (S¼ 3/2, 3d3) is the only magnetic ion contributes to the magnetic moment in these compounds. One would expect coupling between the Cr3 þ ions which are separated by the nonmagnetic Te6 þ octahedra in between Cr3 þ ions within the ab-plane (Fig. 1(a)). The interlayer exchange interactions (Cr–O–La1–O–Cr and Cr–O–La2–O–Cr of inter-Cr distance 5.983 Å) are expected to be weaker than the intralayer exchange interactions (Cr–O–Te–O–Cr of inter-Cr distance 5.159 Å). However, RCrTeO6 undergoes magnetic ordering at TN ¼ 8.5 K (R¼ La) and 10 K (R¼Y) owing to the weak inter-layer interaction.
Fig. 5. (a) The temperature dependence of the total heat capacity (CP) and phonon contribution (solid line) for LaCrTeO6. (b) The variation of Cm/T and ΔS as a function of temperature for the LaCrTeO6 and expected ΔS for Cr3 þ ion is indicated as a dashed line.
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Fig. 6. The typical χ(T) curves for the Y1 x Erx CrTeO6 samples (a) x ¼0.01 and (b) 0.05. The Curie–Weiss fitting χ(T) curve is shown as red solid line. Insets: expanded view of low temperature d(χT)/dT data (solid circles) and CP (solid squares). The blue dashed lines mark the location of the peak in CP. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
(R ln(2Sþ1)¼11.5 J/mole K), which indicates the persistence of short-range ordering above TN. It is expected that the substitution of Yttrium or Lanthanum by the magnetic rare earth will affect the Cr–Cr, R–R and R–Cr interactions due to strong paramagnetic signal of the R ¼Tb and Er ions. In order to shed more light on the magnetic ordering behavior, the partially substituted Er (x ¼0.01 and 0.05) in R1 x Erx CrTeO6 (R¼La and Y) has been investigated. Fig. 6 shows the typical temperature dependence of susceptibility for the Y1 x Erx CrTeO6 samples with x ¼0.01 and 0.05. The d(χT)/dT curve for x ¼0.01 shows a peak at 10.2 K, which coincides with that of TN from heat capacity measurements (inset of Fig. 6(a)). For x¼0.05 sample, the d(χT)/dT anomaly at TN has been masked by the strong paramagnetic signal from the rare-earth ions of large spins (inset of Fig. 6(b)). While CP(T) shows a peak corresponding to TN ¼10 K. Similar χ(T) behavior were also found in nonmagnetic doped Er1 x Lax CrTeO6 for both x¼ 0.01 and 0.05 samples (not shown here). The linearity of inverse χ over a wide range of T suggests that χ follows the Curie–Weiss law as shown in Fig. 6 as a solid line. The observed values of effective moments 4.12 μB and 4.66 μB are close to the expected values of 1% Er3 þ þ Cr3 þ ¼4.01 μB and 5% Er3 þ þ Cr3 þ ¼ 4.47 μB using the effective moments of 3.87 μB for Cr3 þ and 9.58 μB for Er3 þ . Fig. 7 shows the typical temperature dependence of χ(T) measured in an applied magnetic field of 10 kOe for RCrTeO6 (R¼Tb and Er). The red solid lines are C–W fitting results and blue solid curves are HTSE fitting results. Inset displays a comparison of the d(χT)/dT and CP(T) data around the magnetic transition for R ¼Tb and Er. The χ(T) for R ¼Tb, Dy, Ho and Er shows qualitative similar behavior, however, it reveals quite different magnetic behavior compare to that of the R ¼La and Y. The d(χT)/dT curves show monotonic increase with decreasing temperature down to 1.8 K without any evidence for a long-range order, whereas CP(T) curves exhibit long-range ordering at TN ¼ 10 K (inset in Fig. 7) for both compounds. The absence of anomaly in d(χT)/dT at TN is reflected on the χ(T) signal at low temperature dominated by the local moments of R3 þ ions. The linearity of χ 1 over a wide range of temperature suggests that χ follows the Curie–Weiss behavior, with observed moments 10.21 μB for R ¼Tb and 10.27 μB for R ¼Er,
Fig. 7. The temperature dependence of χ for RCrTeO6 (R ¼ Tb and Er), red solid lines are C–W fitting results. Inset: expanded view of low temperature d(χT)/dT data (solid circles) and CP (solid squares). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Table 1 The effective magnetic moments (μeff, experimental:, μcal, calculated) per formula unit and Curie–Weiss temperatures for R1 x Erx CrTeO6 (R ¼trivalent lanthanides, x¼ 0, 0.1 and 0.05).
n
Sample
μeff (μB)
μncal (μB)
θ (K)
LaCrTeO6 YCrTeO6 Y0.99Er0.01CrTeO6 Y0.95Er0.05CrTeO6 TbCrTeO6 ErCrTeO6
3.79 3.86 4.12 4.66 10.21 10.27
3.87 3.87 3.99 4.42 10.46 10.33
28.6 32.4 27.5 22.5 6.6 14.1
μcal ¼ ½xμ2R þ μ2Cr 1=2 .
which is consistent with non-interacting R3 þ and Cr3 þ . The fitted Curie–Weiss temperatures are θ 6.6 K and 14.1 K for R ¼ Tb and Er, respectively. The Curie–Weiss law fitted parameters are summarized in Table 1 for all the samples. These data suggest that the rare earth and Cr sublattices are independently magnetic, i.e., the TN near 10 K is due to the Cr3 þ spin ordering, and the Tb and Er elements of much larger spins do not order down to 2 K. Fig. 8(a) shows the temperature dependence of CP(T) curves for Y1 x Erx CrTeO6 , x ¼0.01, 0.05 and 1.0. The CP(T) curves exhibits a λ-type peak at 10 K, attributed to long-range magnetic ordering in all the samples. The value of CP(T) was found to increase with increasing Er-content. The transition temperature TN is independent of the Er content, which indicates that the super–super exchange Cr–O–Te–O–Cr interaction is dominating. The magnetic contribution to the heat capacity Cm and the corresponding change in entropy ΔS were estimated in the same way as discussed above in the case of R ¼ La compound. The variation of CP/T and ΔS as a function of temperature for x¼ 0.05 and 1.0 is depicted in Fig. 8(b). In these compounds, the magnetic transition is primarily due to the ordering of Cr3 þ ions which have a four-fold degenerated ground state. The recovered entropy at TN is 10.7 J/mole K, which is
G. Narsinga Rao et al. / Journal of Magnetism and Magnetic Materials 370 (2014) 13–17
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measurement results reveal that both short-range and long-range ordering co-exists in non-magnetic rare earth compounds (R ¼La and Y). The CP(T) results for Y1 x Erx CrTeO6 indicate that the transition temperature TN is independent of the Er content, which suggests that the exchange interaction among Cr3 þ spins within each layer is independent of the rare earth elements of large spins between layers. To fully understand the nature of the magnetic interactions, it is necessary to perform microscopic measurements such as neutron diffraction.
Acknowledgments FCC acknowledges the support provided by NSC-Taiwan under Project number NSC 102-2119-M-002-004. References Fig. 8. (a) The temperature dependence of the total heat capacity (CP) for Y1 x Erx CrTeO6 (x¼ 0.01, 0.05 and 1.0). (b) The variation of CP/T and ΔS as a function of temperature for the Y1 x Erx CrTeO6 and x¼ 0.05 and 1.0. The expected ΔS for Cr3 þ is indicated as a dashed line.
close to the expected value of Cr3 þ with magnetic entropy estimated to be ðR lnð2 32 þ 1Þ ¼ 11:5 J=mole KÞ. This implies that the observed magnetic entropy at TN does not include the Er3 þ ion contribution. The unordered Er3 þ ions will give a large contribution to the paramagnetic susceptibility at low temperature, which is consistent with the observed experimental data (see Figs. 6 and 7). At TN, the inferred ΔS increases less than the full magnetic entropy ð r 53%Þ, which indicates the persistence of short-range ordering above TN in x ¼0.05 sample. In the case of x¼1.0 (R¼Er) sample, the amount of entropy recovered at TN reached 93% of Cr3 þ ions contribution, which is higher than that of the nonmagnetic LaCrTeO6 ð r36%Þ compound. Usually this kind of large entropy released at TN is indicative of a long-range AFM ordering. Below 5 K, CPT 1 shows an upturn, which could be attributed to a nuclear Schottky contribution or Er spins order at even lower temperatures [19,20]. Our results reveal that both magnetic sublattices of Cr and R are magnetically independent throughout the measured temperature range in RCrTeO6. 4. Conclusions We have found that RCrTeO6 (R¼Y, La, Tb, Dy, Ho and Er) shows magnetic transition at low temperature. The χ(T), CP(T) and ΔS
[1] A.P. Ramirez, Ann. Rev. Mater. Sci. 24 (1994) 453. [2] D.C. Johnston, Handbook of Magnetic Materials, vol. 10, Elsevier, Amsterdam, 1997, p.1. [3] A. Kitaev, Ann. Phys. 321 (2006). [4] K. Takano, Phys. Rev. B 74 (2006) 140402 (R). [5] J.W.F. Venderbos, M. Daghofer, J. van den Brink, S. Kumar, Phys. Rev. Lett. 107 (2011) 076405. [6] O. Smirnova, M. Azuma, N. Kumada, Y. Kusano, M. Matsuda, Y. Shimakawa, T. Takei, Y. Yonesaki, N. Kinomura, J. Am. Chem. Soc. 131 (2009) 8313. [7] S. Okumura, H. Kawamura, T. Okubo, Y. Motome, J. Phys. Soc. Jpn. 79 (2010) 114705. [8] M. Matsuda, M. Azuma, M. Tokunaga, Y. Shimakawa, N. Kumada, Phys. Rev. Lett. 105 (2010) 187201. [9] V. Kataev, A. Mller, U. Lw, W. Jung, N. Schittner, M. Kriener, A. Freimuth, J. Magn. Magn. Mater. 290–291 (2005) 310. [10] Y. Miura, R. Hirai, Y. Kobayashi, M. Sato, J. Phys. Soc. Jpn. 75 (2006) 084707. [11] L. Viciua, Q. Huangb, E. Morosana, H.W. Zandbergenc, N.I. Greenbauma, T. McQueena, R.J. Cava, J. Solid State Chem. 180 (2007) 1060. [12] A. Magneli, Ark. Kemi Min. Geol. 15B (1941). [13] R.J. Hill, J. Solid State Chem. 71 (1987) 12. [14] H.M. Kaspar, Mater. Res. Bull. 4 (1969) 33. [15] G. Blasse, A.D.M. De Pauw, J. Inorg. Nucl. Chem. 32 (1970) 2533. [16] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. Sect. A Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 32 (1976) 785. [17] M.E. Fisher, Philos. Mag. 7 (1962) 1731. [18] G.S. Rushbrook, P.J. Wood, Mol. Phys. 1 (1958) 257. [19] N. Hur, S. Park, P.A. Sharma, J.S. Ahn, S. Guha, S.-W. Cheong, Nature 429 (2004) 392. [20] T.J. Hayes, G. Balakrishnan, P.P. Deen, P. Manuel, L.C. Chapon, O.A. Petrenko, Phys. Rev. B 84 (2011) 174435.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic and thermal property studies of RCrTeO6 (R¼trivalent lanthanides) with layered honeycomb sublattices G. Narsinga Rao a, R. Sankar a, I. Panneer Muthuselvam a, F.C. Chou a,b,c,n a
Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan c Taiwan Consortium of Emergent Crystalline Materials, National Science Council, Taipei 10622, Taiwan b
art ic l e i nf o
a b s t r a c t
Article history: Received 8 March 2014 Received in revised form 19 May 2014 Available online 2 July 2014
We have investigated the magnetic ordering of the RCrTeO6 (R¼ Y, La, Tb and Er) samples comprising Cr3 þ (S¼ 3/2). The X-ray diffraction structure analysis revealed that all samples are a hexagonal structure with the space group P 3. The magnetic susceptibility χ(T) and heat capacity CP(T) measurement results reveal that both short range and long range antiferromagnetic (AFM) orderings exist in non-magnetic rare earth R¼ Y and La compounds. For isostructural compounds of R¼ Tb and Er, CP(T) curves show long range ordering at the same temperature as non-magnetic R¼Y, which indicates that the super-super exchange of Cr spins dominates. For R elements of Tb and Er with large spins sitting between honeycomb sublattices composed of CrO6–TeO6 octahedra, the two sublattices of R and Cr appear to be independently magnetic. & 2014 Elsevier B.V. All rights reserved.
Keywords: Antiferromagnetic ordering Super–super exchange interaction Honeycomb lattice Heat capacity
1. Introduction Geometrically frustrated magnetic systems exhibit a variety of ground states depending on the spin size and the spin configuration [1,2]. The spin interactions of these systems cannot be simultaneously satisfied because of the connectivity of lattice. This opens up the possibility to have an unconventional magnetic order or even novel spin-liquid state without any long range spin order at low temperatures [1]. The honeycomb lattice Heisenberg antiferromagnetic (AFM) compounds have attracted much attention due to the existence of diverse novel magnetic ground states [3,4]. For example, Venderbos et al. found that the interplay between the superexchange interaction of localized spins and the double exchange interactions of itinerant spins on the non-frustrated honeycomb lattice leads to an unexpectedly rich phase diagram with exotic magnetic phases [5]. Recent experimental results of the honeycomb lattice compound Bi3Mn4O12(NO3) showed a spin-liquid behavior down to low temperature 0.4 K, which has been ascribed to the frustration effect due to the competition between AFM nearest and next nearest neighbor interactions [6–8]. The spin-1/2 honeycomb lattice InCu2/3V1/3O3 exhibits an AFM transition at 38 K with an estimated nearest neighbor exchange coupling constant 280 K [9]. On the other hand, Na3M2SbO6 (M¼Cu, Ni, and Co) compounds show different magnetic behaviors from spin gap (M¼Cu) to AFM order (M¼Ni and Co)
n Corresponding author at: Center for Condensed Matter Sciences, National Taiwan University, Taipei 10617, Taiwan. E-mail address: [email protected] (F.C. Chou).
http://dx.doi.org/10.1016/j.jmmm.2014.06.057 0304-8853/& 2014 Elsevier B.V. All rights reserved.
[10,11]. For such a variety of magnetic ground state structures, honeycomb lattice with various types of spin systems offers new and interesting possibilities of low temperature properties. The PbSb2O6 structure is one of the typical mixed oxides with a honeycomb structure [12,13]. The mixed oxides of RCrTeO6, where R ¼trivalent lanthanides, have been proposed to be a superstructure of PbSb2O6 [14,15]. The unit cell of RCrTeO6 comprises two formula units and adopts the hexagonal structure with the space group P 3. All Cr and Te cations in RCrTeO6 have octahedral coordination with oxygen atoms. In this superstructure, the honeycomb layers are formed by edge-shared TeO6 and CrO6 octahedra as a sheet and stacked along the c-axis as shown in Fig. 1(a). The rare earth elements can be viewed to be sandwiched between (Cr/Te)O6 honeycomb layers. The (Cr/Te)O6 honeycomb lattice is depicted in Fig. 1(b). Except the structural studies, no other information related to the physical properties of this interesting class of materials are available in the literature. Here we present spin susceptibility and heat capacity measurement results on RCrTeO6 (R¼Y, La, Tb and Er) compounds and compare the impact of trivalent rare-earth elements which are sandwiched between (Cr/Te)O6 honeycomb layers.
2. Experimental details Polycrystalline samples of RCrTeO6 (R¼ trivalent lanthanides) were prepared by the solid state reaction method. R2O3 were heat treated at 900 1C for 12 h before mixing to remove the hydroxide
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G. Narsinga Rao et al. / Journal of Magnetism and Magnetic Materials 370 (2014) 13–17
Fig. 1. (a) Crystal structure of RCrTeO6 showing stacking of a alternative layers of rare earth (R1O6 and R2O6) and (Cr,Te)O6 octahedra (pink and yellow color). The small red colored sphere are oxygen atoms. (b) The honeycomb sheet topology of (Cr/Te)O6 in ab-plane. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
impurity. Stoichiometric proportions of high purity R2O3, Cr2O3, and TeO2 powders were mixed and heated at 600 1C for 12 h to ensure that all the tellurium was oxidized to the hexavalent state. The pre-heated powders were well ground and calcined at 700 1C for 12 h with a heating rate of 2 1C/min and cooled down to room temperature at the same rate. The calcined powders were pressed into pellets and sintered at 850 1C for 12 h. The preparation conditions are the same for all the samples. The structure and the phase purity of the samples were checked by powder X-ray diffraction (XRD) using the Cu–Kα radiation at room temperature. The field cooled (FC) and the zero field cooled (ZFC) magnetization were measured in a commercial Vibrating Sample Magnetometer (VSM, Quantum Design, USA) from 1.8 K to 300 K in the presence of different applied magnetic fields. The temperature dependence of average spin susceptibilities χ(T) is defined with MðTÞ=H based on the linear MðHÞ isotherms. The isothermal magnetization (M) data were also recorded at selected temperatures. The heatcapacity (CP) measurements were carried out by a relaxation method using commercial Physical Properties Measurement System (PPMS, Quantum Design, USA).
3. Result and discussion The powder XRD pattern of the polycrystalline RCrTeO6 (R¼trivalent lanthanides) samples is shown in Fig. 2. The XRD patterns can be indexed to the hexagonal structure with the space group P 3 without any observable trace of impurity phase. The structural parameters were refined by the Rietveld technique with good quality refinement parameters (Rwp ¼ 8.75% and Rp ¼6.61%). The obtained values of the lattice parameters are depicted in Fig. 3 as a function of R3 þ ionic radius. Both the a and c parameters increase with the R3 þ ionic radius as expected. These parameters are in good agreement with those previously reported data [14]. The distances between chromium are larger along the c direction than in the ab-plane (Fig. 1(a)). In addition, partially substituted La/Y by Er samples also show the same hexagonal structure. The refined lattice parameters are decreased significantly with increasing Er content in the case of R ¼La, whereas in R ¼ Y a small decreasing is observed (Fig. 3). The decrease in the lattice parameters is consistent with the smaller ionic radius of Er3 þ (1.144 Å)
Fig. 2. Room temperature powder XRD pattern for RCrTeO6 (R ¼trivalent lanthanides). The symbols are experimental points, solid curve is the best fit from the Rietveld refinement. The vertical bars indicate the position of Bragg peaks and the bottom curve shows the difference between the observed and calculated intensities.
comparing to that of the ionic radius of La3 þ (1.300 Å) or Y3 þ (1.159 Å) [16]. The temperature dependence of magnetic susceptibility χ(T) and 1/χ(T) measured in an applied magnetic field of 10 kOe for RCrTeO6 (R¼La and Y) is shown in Fig. 4(a) and (b). No divergence between the zero field cooled (ZFC) and field cooled (FC) χ(T) curves has been found for both compounds through out the whole experimental temperature range. At low temperature, the χ(T) curves for R ¼ La and Y exhibit a rounded maximum at 10.2 K and
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Fig. 3. Lattice parameters vs. R3 þ ionic radius for RCrTeO6. The error bars are smaller than data points.
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To analyze the χ(T) data quantitatively, the temperature dependence of χ is fitted with the Curie–Weiss expression χ(T)¼C/(T θ) in the high temperature (50–300 K) range (right axis of Fig. 4), which gives the Weiss temperature θ¼ 28.6 K and 32.4 K for R ¼La and Y, respectively. The observed effective magnetic moment per Cr3 þ ion is 3.79(3) μB (R¼ La) and 3.86(2) μB (R¼Y), which are in close agreement with the expected value of 3.87 μB for the Cr3 þ (S¼3/2) ions. The negative value of θ is indicative of AFM interactions between the Cr3 þ spins in these compounds. The ratio of jθj=T N 4 for R ¼Y and La indicates marginal frustration of Cr3 þ spins in the honeycomb arrangement. The χ(T) data for both compounds are described by the high temperature series expansion (HTSE) for an S ¼3/2 AFM satisfactorily [18]. Above 200 K, χ(T) data were fit well by the sixth order of HTSE (Fig. 4) with the same g factor 1.95 and the intralayer exchange interaction (J/kB) between Cr3 þ ions are found to be 58(2) K (R¼ La) and 40(3) K (R¼Y). Substitution of La3 þ ion with smaller ionic radius of Y3 þ ion leads to a contraction of honeycomb plane, and the shortened inter-Cr distance results in an increase in the antiferromagnetic exchange coupling interaction strength, as shown by the increased TN shown in the inset of Fig. 4(b). In order to obtain a better understanding of the magnetic ordering behavior, we have performed heat capacity measurements. The temperature dependence of the CP(T) curve for LaCrTeO6 is presented in Fig. 5(a) along with the lattice contribution CL(T). A clear λ-type peak is observed at TN. This is an evidence of longrange AFM order. This ordering temperature in turn appeared to be correlated with maximum in d(χT)/dT (inset of Fig. 4(a)). The absence of non-magnetic isomorphic sample of LaCrTeO6 does not allow a direct deduction of the CL from the CP, the CL above TN (20– 30 K) was approximated using a Debye T3 law instead (CP/T¼γ þ βT2). The extracted CL (βT3) is shown as a solid line in Fig. 5(a). The magnetic contribution of the heat capacity Cm was obtained by subtracting the CL from the measured CP data. The magnetic entropy R change (ΔS) was calculated by ΔS ¼ ðC m T 1 Þ dT. The variation of Cm/T and ΔS as a function of temperature for the LaCrTeO6 sample is depicted in Fig. 5(b). At TN, the inferred ΔS increases much less ð r 36%Þ than the full magnetic entropy associated with S¼ 3/2 Cr3 þ
Fig. 4. The temperature dependence of magnetic susceptibility χ measured in an applied magnetic field of 10 kOe for RCrTeO6 (a) R¼ La, and (b) R¼ Y. The right axis shows the 1/χ versus T curves, solid lines are C–W fitting. The HTSE fitting is shown as a blue solid line above 200 K. In insets: expanded the transition region around TN, comparing the χ (open black square symbols), the first derivative of the product χT (solid red circles) for left axis and the heat capacity data (blue solid triangles) for right axis. The dashed lines mark the location of the peak in d(χT)/dT. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
11 K, respectively. The peak temperatures of the d(χT)/dT plot (known as Fisher's heat capacity [17]) coincide with the peak temperature shown in C P (T) (inset in Fig. 4(a)) to be TN 8:5 K and 10 K for R ¼La and Y, respectively, which are marked by vertical lines in the insets of Fig. 4. These results reveal that both short range and long range antiferromagnetic (AFM) orderings coexist in non-magnetic rare earth R ¼Y and La compounds. Since Cr3 þ (S¼ 3/2, 3d3) is the only magnetic ion contributes to the magnetic moment in these compounds. One would expect coupling between the Cr3 þ ions which are separated by the nonmagnetic Te6 þ octahedra in between Cr3 þ ions within the ab-plane (Fig. 1(a)). The interlayer exchange interactions (Cr–O–La1–O–Cr and Cr–O–La2–O–Cr of inter-Cr distance 5.983 Å) are expected to be weaker than the intralayer exchange interactions (Cr–O–Te–O–Cr of inter-Cr distance 5.159 Å). However, RCrTeO6 undergoes magnetic ordering at TN ¼ 8.5 K (R¼ La) and 10 K (R¼Y) owing to the weak inter-layer interaction.
Fig. 5. (a) The temperature dependence of the total heat capacity (CP) and phonon contribution (solid line) for LaCrTeO6. (b) The variation of Cm/T and ΔS as a function of temperature for the LaCrTeO6 and expected ΔS for Cr3 þ ion is indicated as a dashed line.
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Fig. 6. The typical χ(T) curves for the Y1 x Erx CrTeO6 samples (a) x ¼0.01 and (b) 0.05. The Curie–Weiss fitting χ(T) curve is shown as red solid line. Insets: expanded view of low temperature d(χT)/dT data (solid circles) and CP (solid squares). The blue dashed lines mark the location of the peak in CP. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
(R ln(2Sþ1)¼11.5 J/mole K), which indicates the persistence of short-range ordering above TN. It is expected that the substitution of Yttrium or Lanthanum by the magnetic rare earth will affect the Cr–Cr, R–R and R–Cr interactions due to strong paramagnetic signal of the R ¼Tb and Er ions. In order to shed more light on the magnetic ordering behavior, the partially substituted Er (x ¼0.01 and 0.05) in R1 x Erx CrTeO6 (R¼La and Y) has been investigated. Fig. 6 shows the typical temperature dependence of susceptibility for the Y1 x Erx CrTeO6 samples with x ¼0.01 and 0.05. The d(χT)/dT curve for x ¼0.01 shows a peak at 10.2 K, which coincides with that of TN from heat capacity measurements (inset of Fig. 6(a)). For x¼0.05 sample, the d(χT)/dT anomaly at TN has been masked by the strong paramagnetic signal from the rare-earth ions of large spins (inset of Fig. 6(b)). While CP(T) shows a peak corresponding to TN ¼10 K. Similar χ(T) behavior were also found in nonmagnetic doped Er1 x Lax CrTeO6 for both x¼ 0.01 and 0.05 samples (not shown here). The linearity of inverse χ over a wide range of T suggests that χ follows the Curie–Weiss law as shown in Fig. 6 as a solid line. The observed values of effective moments 4.12 μB and 4.66 μB are close to the expected values of 1% Er3 þ þ Cr3 þ ¼4.01 μB and 5% Er3 þ þ Cr3 þ ¼ 4.47 μB using the effective moments of 3.87 μB for Cr3 þ and 9.58 μB for Er3 þ . Fig. 7 shows the typical temperature dependence of χ(T) measured in an applied magnetic field of 10 kOe for RCrTeO6 (R¼Tb and Er). The red solid lines are C–W fitting results and blue solid curves are HTSE fitting results. Inset displays a comparison of the d(χT)/dT and CP(T) data around the magnetic transition for R ¼Tb and Er. The χ(T) for R ¼Tb, Dy, Ho and Er shows qualitative similar behavior, however, it reveals quite different magnetic behavior compare to that of the R ¼La and Y. The d(χT)/dT curves show monotonic increase with decreasing temperature down to 1.8 K without any evidence for a long-range order, whereas CP(T) curves exhibit long-range ordering at TN ¼ 10 K (inset in Fig. 7) for both compounds. The absence of anomaly in d(χT)/dT at TN is reflected on the χ(T) signal at low temperature dominated by the local moments of R3 þ ions. The linearity of χ 1 over a wide range of temperature suggests that χ follows the Curie–Weiss behavior, with observed moments 10.21 μB for R ¼Tb and 10.27 μB for R ¼Er,
Fig. 7. The temperature dependence of χ for RCrTeO6 (R ¼ Tb and Er), red solid lines are C–W fitting results. Inset: expanded view of low temperature d(χT)/dT data (solid circles) and CP (solid squares). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)
Table 1 The effective magnetic moments (μeff, experimental:, μcal, calculated) per formula unit and Curie–Weiss temperatures for R1 x Erx CrTeO6 (R ¼trivalent lanthanides, x¼ 0, 0.1 and 0.05).
n
Sample
μeff (μB)
μncal (μB)
θ (K)
LaCrTeO6 YCrTeO6 Y0.99Er0.01CrTeO6 Y0.95Er0.05CrTeO6 TbCrTeO6 ErCrTeO6
3.79 3.86 4.12 4.66 10.21 10.27
3.87 3.87 3.99 4.42 10.46 10.33
28.6 32.4 27.5 22.5 6.6 14.1
μcal ¼ ½xμ2R þ μ2Cr 1=2 .
which is consistent with non-interacting R3 þ and Cr3 þ . The fitted Curie–Weiss temperatures are θ 6.6 K and 14.1 K for R ¼ Tb and Er, respectively. The Curie–Weiss law fitted parameters are summarized in Table 1 for all the samples. These data suggest that the rare earth and Cr sublattices are independently magnetic, i.e., the TN near 10 K is due to the Cr3 þ spin ordering, and the Tb and Er elements of much larger spins do not order down to 2 K. Fig. 8(a) shows the temperature dependence of CP(T) curves for Y1 x Erx CrTeO6 , x ¼0.01, 0.05 and 1.0. The CP(T) curves exhibits a λ-type peak at 10 K, attributed to long-range magnetic ordering in all the samples. The value of CP(T) was found to increase with increasing Er-content. The transition temperature TN is independent of the Er content, which indicates that the super–super exchange Cr–O–Te–O–Cr interaction is dominating. The magnetic contribution to the heat capacity Cm and the corresponding change in entropy ΔS were estimated in the same way as discussed above in the case of R ¼ La compound. The variation of CP/T and ΔS as a function of temperature for x¼ 0.05 and 1.0 is depicted in Fig. 8(b). In these compounds, the magnetic transition is primarily due to the ordering of Cr3 þ ions which have a four-fold degenerated ground state. The recovered entropy at TN is 10.7 J/mole K, which is
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measurement results reveal that both short-range and long-range ordering co-exists in non-magnetic rare earth compounds (R ¼La and Y). The CP(T) results for Y1 x Erx CrTeO6 indicate that the transition temperature TN is independent of the Er content, which suggests that the exchange interaction among Cr3 þ spins within each layer is independent of the rare earth elements of large spins between layers. To fully understand the nature of the magnetic interactions, it is necessary to perform microscopic measurements such as neutron diffraction.
Acknowledgments FCC acknowledges the support provided by NSC-Taiwan under Project number NSC 102-2119-M-002-004. References Fig. 8. (a) The temperature dependence of the total heat capacity (CP) for Y1 x Erx CrTeO6 (x¼ 0.01, 0.05 and 1.0). (b) The variation of CP/T and ΔS as a function of temperature for the Y1 x Erx CrTeO6 and x¼ 0.05 and 1.0. The expected ΔS for Cr3 þ is indicated as a dashed line.
close to the expected value of Cr3 þ with magnetic entropy estimated to be ðR lnð2 32 þ 1Þ ¼ 11:5 J=mole KÞ. This implies that the observed magnetic entropy at TN does not include the Er3 þ ion contribution. The unordered Er3 þ ions will give a large contribution to the paramagnetic susceptibility at low temperature, which is consistent with the observed experimental data (see Figs. 6 and 7). At TN, the inferred ΔS increases less than the full magnetic entropy ð r 53%Þ, which indicates the persistence of short-range ordering above TN in x ¼0.05 sample. In the case of x¼1.0 (R¼Er) sample, the amount of entropy recovered at TN reached 93% of Cr3 þ ions contribution, which is higher than that of the nonmagnetic LaCrTeO6 ð r36%Þ compound. Usually this kind of large entropy released at TN is indicative of a long-range AFM ordering. Below 5 K, CPT 1 shows an upturn, which could be attributed to a nuclear Schottky contribution or Er spins order at even lower temperatures [19,20]. Our results reveal that both magnetic sublattices of Cr and R are magnetically independent throughout the measured temperature range in RCrTeO6. 4. Conclusions We have found that RCrTeO6 (R¼Y, La, Tb, Dy, Ho and Er) shows magnetic transition at low temperature. The χ(T), CP(T) and ΔS
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