稀有金属(英文版) 2015,34(02),81-88

收稿日期：23 November 2012

基金：financially supported by the State Key Project of Fundamental Research of China (Nos. 2010CB923403 and 2011CBA00111);the National Natural Science Foundation of China (Nos. 11174290 and U1232142);the Hundred Talents Program of the Chinese Academy of Sciences (No. 2010A1175);

Dy_2-xY_xTi₂O₇: phonon vibration and magnetization with dilution

Hui Liu You-Ming Zou Shi-Le Zhang Ran-Ran Zhang Chang-Jin Zhang Yu-Heng Zhang

High Magnetic Field Laboratory, Chinese Academy of Sciences and University of Science and Technology of China

Abstract：

In this paper, the dilution effects of non-magnetic Y ions on spin-ice compound Dy2Ti2O7 by infrared and Raman spectra and magnetization measurements were investigated. An anomalous phonon softening with temperature decreasing is found in both the parent and diluted compounds, and Y doping can relax the softening of phonons except that of the IR mode near 233 cm-1, indicating a strong phonon–phonon coupling in the spin-ice material.The magnetization measurements reveal that the nonmagnetic impurities do not severely influence the spin-ice rules in the ground state when the level of dilution is not very high. However, a large amount of dilution enhance the disorder and break the spin-ice state because the collective spin-flip clusters are no longer available.

Keyword：

Dilution effect; Spin ice; Pyrochlore; Frustration;

Author： Chang-Jin Zhang e-mail: zhangcj@hmfl.ac.cn;

Received： 23 November 2012

1 Introduction

Competing or frustrated interactions are a very common feature of condensed matter systems. In some cases, the frustration can be so intense that it induces novel and complex phenomena, causing extensive degeneracy in the ground state of the system and preventing any ordering down to the absolute zero temperature [1]. For pyrochlore compounds, the spins reside on the vertices of cornersharing tetrahedral and there is a ferromagnetic coupling between the spins. As a result, the pyrochlore lattice can lead to full frustration in the case of strong single-ion Ising anisotropy along the [111] axes [2]. Therefore, pyrochlore oxide materials attracted significant attention from both experimental and theoretical physicists in the past two decades due to their remarkable low-temperature magnetic properties. Typical pyrochlore compounds have a structure of A₂B₂(O1)₆(O2), where A³⁺is a rare-earth ion and B⁴⁺is a transition metal ion. The atom A occupies the 16d and B occupies the 16c position and the oxygen atoms O1 and O2 occupy the 48f and 8b sites, respectively [3].

Among the pyrochlore oxide family, Ho₂Ti₂O₇,Ho₂Sn₂O₇, and Dy₂Ti₂O₇are identified as spin-ice materials in which the low-temperature behavior is closely analogous to that of water ice. In this kind of materials, the local spin correlations are characterized by the ice rules:two spins point in and two spins point out of every tetrahedron. For every tetrahedron, there are six possible combinations of spins under the two-in/two-out rule reflecting the global cubic symmetry. Since the ground state is highly degenerate, a static disordered state (the socalled ‘‘spin ice’’ state) is formed below 1 K in spite of the structural order of the system [4–6].

Dilution is expected to have a significant impact on such a strongly frustrated system. Study of the effects of the non-magnetic ions substitution on the spin ice is of considerable importance in exploring the spin-freezing mechanism and the spin dynamics. Recently, investigations of both diluted Ho and Dy spin ices revealed that the zeropoint entropy depended nonmonotonically on dilution [7].The magnetic correlations and relaxation processes in clean and diluted spin-ice materials were investigated and these results revealed the quantum process of spin relaxation and robustness of diluted spin ice [8–10]. Although there are some investigations in diluted spin ice, the formation and destruction of frustration are not very clear up to now.Thus, it is informative to study further in this field. In the present study, vibration modes as well as magnetization measurements were used to probe the dilution effects in Dy_2-xY_xTi₂O₇.

2 Experimental

Single crystals of Dy_2-xY_xTi₂O₇(x=0,0.1,0.4,1.0,1.4)were grown by the floating zone method[11].Before the single-crystal growth,polycrystalline feed rods were prepared.Polycrystalline samples Dy_2-xY_xTi₂O₇were prepared using high-purity Dy₂O₃,Y₂O₃,and Ti O₂chemicals by the standard solid-state reaction technique in air.Prior to weighing,both the rare-earth oxides were preheated at800°C for 12 h in order to remove the moisture.After grinding the stoichiometric powders sufficiently,the mixtures were sintered in high-density alumina crucibles at1,300°C for 72 h with several intermediate grindings.Then the powders were compressed in the form of cylindrical rods(6 mm in diameter and 10 cm in length)and sintered at 1,350°C for 12 h in air.The single crystals were grown in an infrared furnace equipped with four halogen lamps and elliptical mirrors under O₂gas flow to avoid oxygen deficiency(typical growth rate 4 mm h^-1).

The obtained crystals were characterized by powder X-ray diffraction (XRD) and X-ray single-crystal diffraction with Cu Kα radiation at room temperature. The principal axes were determined using the Laue diffraction patterns. The transmittance spectra at different temperatures were measured using a Fourier transform infrared spectrometer (FT-IR), and the Raman scattering measurements were performed using a micro-Raman instrument with a Kr⁺–Ar⁺mixed gas laser (λ= 514.5 nm) as an excitation source in a backscattering geometry. Aligned single crystals were used for magnetic measurements in a superconducting quantum interference device magnetometer. In this article, the magnetization data for a field applied along the [111] axis, which was an easy-axis direction for the spin-ice system Dy₂Ti₂O₇, was reported.

3 Results and discussion

Figure 1a gives the XRD patterns of a single crystal with the (hhh) reflections (the red curve) and Dy_2-xY_xTi₂O₇ powder samples. It is noticeable that the full width at half maximum for all the diffraction peaks shown in the single-crystal XRD pattern of Dy₂Ti₂O₇crystal is less than 0.10^o, indicating the high quality of the sample.To examine the purity of the prepared crystals, powder XRD measurements were further performed by grinding single crystals into powder for each component. From XRD patterns, all the samples are pure phase and the diffraction peaks can be well indexed with space group Fd-3m. Figure 1b shows the evolution of the lattice parameter.For Dy₂Ti₂O₇(x = 0) compound, the lattice constant of1.01248 nm is in good agreement with previous report[12]. With doping level increasing, the lattice parameter decreases monotonously along the trend expected for a system where larger Dy³⁺is gradually substituted by smaller Y³⁺.

In order to explore the doping effect of non-magnetic ions on structure, the vibration modes in the parent and diluted samples were investigated by means of infrared(IR) transmission and Raman scattering measurements as IR and Raman spectroscopies may provide very useful information on disorder, spin-phonon, and crystal field(CF) phonon interactions. According to a group theoretical analysis, a pyrochlore A₂B₂(O1)₆(O2) compound should have the vibrational phonon modes at the Brillouin zone center point with [13]

Fig. 1 Powder XRD patterns for Dy2-xYxTi2O7samples a and lattice constant of Y-doped samples b

Fig.2 Infrared transmission spectra for a Dy₂Ti₂O₇and b Dy YTi₂O₇at various temperatures

where A, E, and F are nondegenerate, double degenerate,and threefold degenerate modes, respectively. The subscript1 (2) represents symmetry (asymmetry) of the secondary axis perpendicular to the main axis and g (u) represents symmetry (asymmetry) of inversion-center operation.Among these 26 normal modes, only A_1g, E_g, and 4F_2gis Raman active, 7F_1uare infrared active, and one F_1uare acoustic. The rest of the modes are optically inactive.

The IR transmission spectra of Dy₂Ti₂O₇and Dy YTi₂O₇at various temperatures are shown in Fig. 2. As far as IR spectra for Dy₂Ti₂O₇are concerned, five phonon modes are observed in the measurements. The observed phonons in the spectra are denoted sequentially from low to high frequencies by F_1u(1) to F_1u(5). As for diluted sample Dy YTi₂O₇, the sixth mode F_1u*157 cm^-1appears, which is assigned to F_1u(6). It can be noticed that all the transmission peaks become prominent with temperature decreasing. In addition,F_1u(4) and F_1u(6) show discernible blueshifts while other modes show slight redshifts as the temperature decreases from 300.0 down to 4.5 K. That is to say, the center frequencies of F_1u(4) and F_1u(6) shift to higher frequencies,while the phonon peaks of F_1u(1), F_1u(2), F_1u(3), and F_1u(5)shift to lower frequencies with temperature decreasing. To our knowledge, for normal materials, with temperature decreasing, the anharmonic thermal motion would decrease,which results in a decrease in the lattice constant. Then the phonons should shift to higher frequencies and the linewidth becomes narrower. The modes F_1u(4) and F_1u(6) clearly demonstrate this effect. On the contrary, other IR modes exhibit the opposite behavior, which are consistent with a previous report [14]. To get the dilution effect, the percentage of change of wavenumbers is compared due to cooling, i.e.,?x4:5 K x300 K?=x300 K% for both the parent and diluted samples. For F_1u(4), the values are 1.34 % and 1.54 % for undoped and doped samples, respectively. As to F_1u(2),F_1u(3), and F_1u(5), the values are -4.20 %, -1.73 %, and-0.91 % for undoped sample, and -1.06 %, 0 %, -0.36 %for doped compound, respectively. However, with regard to F_1u(1), the values are -0.43 % and -2.48 % for the two compounds. Here, the positive values represent blueshifts,while the negative values show redshifts. It can be obtained that compared with those of Dy₂Ti₂O₇, the degree of hardening (blueshifts) in Y-doped sample is stronger, while the degree of softening (redshifts) is just the opposite except that of F_1u(1) *233 cm^-1, whose magnitude of redshift enhances, as presented in Fig. 2.

To further investigate the temperature dependence of phonons and dilution effect on vibration modes, the Raman spectra of the parent and diluted samples were measured, as revealed in Fig. 3. The Raman spectra of Dy₂Ti₂O₇powder and Dy_1.9Y_0.1Ti₂O₇single crystal were cleaved and one-side polished with the surface parallel to the (111) plane.According to the researches for rare-earth titanates A₂Ti₂O₇[15, 16], the strongest band centered around 310 cm^-1shown in Fig. 3a, b actually consists of two modes: an F_2gmode(O1-A-O1 bending mode) and an E_gmode (O1-sublattice mode) recognized by Saha et al. [15]. Another intense band observed near 520 cm^-1is supposed to be A_1gand attributed to A-O1 stretching [16]. The locations of the remaining three F_2gmodes are not consistent yet. The bands near 200, 450, and580 cm^-1are assigned to the F_2gmodes, which are in good agreement with the theoretical calculations [13]. It should be noted that the F_2g*450 cm^-1and F_2g*580 cm^-1for Dy₂Ti₂O₇cannot be detected due to weak signal. However,they appear again in spectra of Dy_1.9Y_0.1Ti₂O₇, which indicates the selection rules in Raman spectra. Apart from these six Raman active modes, three weak modes are also observed at *410, *690, and *790 cm^-1, which are marked by the asterisks. The origin of these modes is not clear at present but the modes over 680 cm^-1can be attributed to high-frequency IR-active modes or second-order excitations, while the mode near 410 cm^-1may be due to the scattering effect of the powder sample [17, 18].

Fig.3 Raman spectra of a Dy₂Ti₂O₇polycrystal and b Dy_1.9Y_0.1Ti₂O₇single crystal at a few temperatures.Temperature dependence of modes c F_2g*200 cm^-1and d A_1g*520 cm^-1for undoped and doped samples

For both samples, as shown in Fig. 3c and d, an anomalous softening (redshift) of the modes F_2g*200 cm^-1and A_1g*520 cm^-1is observed with temperature decreasing, which is similar to those of IR modes. Besides, the magnitudes of the softening of phonons with temperature decreasing in the two samples are compared using linear-fitting method. It is noticed that the slope of doped sample k₂is smaller than that of undoped sample k₁, suggesting that doping decreases the magnitude of phonon softening, which is also analogous to that of IR modes except F_1u(1).

The change in wavenumber of a phonon Dxican be given by [17–20]

where(△ω)_lattcorresponds to the change in the ionic binding energies due to lattice expansion;(△ω)_anhcorresponds to the intrinsic anharmonic contribution,i.e.,an harmonic wave number shift at constant volume;(△ω)_el-phis due to coupling of phonons and charge carries,and(△ω)_sp-phaccounts for the spin-phonon contribution.To our knowledge,(△ω)_el-phcan be negligible due to the insulation of pyrochlore titanates.Saha et al.[18]found that in both the magnetic Dy₂Ti₂O₇and the non-magnetic Lu₂Ti₂O₇,the magnitude of phonon softening is comparable,so(△ω)_sp-phwould not contribute to the change of frequency and it can also be negligible.For(△ω)_latt,the lattice term should lead to an increase of all wavenumbers with temperature decreasing,which is the‘‘regular’’behavior.So we unambiguously believe that the‘‘anomalous’’phonon shifts stem from(△ω)_anh.In other words,the anharmonic phonon–phonon coupling that comes from the real part of the self energy of a phonon decaying into two or three phonons induces this anomalous phonon softening.Also,as the mass number of Y atom is much smaller than that of Dy,the binding energy of atoms in a diluted component is smaller than that of the parent sample.As a result,the coefficient of volume expansion of a doped sample is larger,thus the contribution of(△ω)_lattdue to lattice expansion in Eq.(2)is more obvious in doped systems.In this case,one expects to obtain that the doping leads to the enhanced hardening and relaxed softening of phonons.However,from Figs.2 and 3,it can be seen that all the phonons follow this rule except the IR mode F_1u(1)whose softening is strengthened by Y doping.This confirms that there is a strong effect of phonon–phonon coupling presented by(△ω)_anhthat cannot be weakened by latticeexpansion effect which produces(△ω)_latt.It should be noted that the phonons of Y-doped sample show blueshifts due to the shrink of lattice constant,which is obvious and understandable.Other dopants such as larger or magnetic ions may play a different role.

Figure 4 plots the temperature dependence of magnetic susceptibility of the Dy_2-xY_xTi₂O₇(x = 0, 0.4, 1.4) samples from 2 K to 300 K. All the magnetic measurements were performed with applied magnetic field of 1 9 10^-2T. It is found that the magnetic susceptibility v above 2 K increases monotonically with temperature decreasing as expected for a paramagnetic system with no spin freezing, and there is no difference between the zero-field-cooling (ZFC) and fieldcooling (FC) measurements. The inverse susceptibility data were fitted using the Curie–Weiss law [21]

where C is the Curie constant, θ is the Curie–Weiss temperature, and B is a temperature independent Van Vleck contribution. The model was used to fit the high-temperature (above 100 K) experimental data.

For the parent sample, the fitted data give an effective paramagnetic moment and a Curie–Weiss temperature -0.84 K. The negative Curie–Weiss temperature is presumably due to antiferromagnetic (AFM)exchange coupling. Bramwell et al. [22] suggested that in Dy₂Ti₂O₇there is an extremely large demagnetizing field correction that reduces the observed value of Curie–Weiss temperature in a manner that depends on the shape of the sample. For spherical samples, the correction is about 1.4 K,which adjusts the estimated Curie–Weiss temperature to0.56 K when applied to our sample. This is close to the value of 0.84 K for the crystal derived from hydrothermal synthesis [16]. The small positive Curie–Weiss temperature indicates the dominance of very weak ferromagnetic (FM)interaction between Dy^3?spins. It is the FM interaction that gives rise to the ‘‘ice rule’’ constraint. It should be noted that the net FM interaction between Dy spins is a combination of AFM exchange interaction and FM dipolar coupling. It is also gotten l_eff? 10:23l_B, h = 0.36 K for Dy_1.6Y_0.4Ti₂O₇and l_eff? 10:27l_B, h = 1.86 K for Dy_0.6Y_1.4Ti₂O₇by using the same way. It is found that the calculated effective moment per ion for all samples studied was consistent with J = 15/2 Dy^3?, where J is the total angular momentum of Dy^3?. With Y doping increasing, the Curie–Weiss temperature becomes a large negative value. Thus, it can be concluded that the Y substitution for Dy enhances the disorder,which can break the ice-rule ordering, corresponding to the increased zero-point entropy in diluted compounds [7]. This is reasonable because dilution will weaken the local fields felt by each Dy spin, so the degeneracy of ground state increases, resulting in the enhanced disorder in the system.

Fig. 4 Temperature dependence of magnetic susceptibility of Dy2-xYxTi2O7(x = 0, 0.4, 1.4) samples from 2 to 300 K. Inset being corresponding inverse magnetic susceptibility

In order to investigate the influence of the non-magnetic dopant on the frustration in Dy₂Ti₂O₇at very low temperatures, magnetization measurements were performed below 2 K. The results are shown in Figs. 5 and 6. From Fig. 5, a pergence can be seen between the ZFC and FC magnetization at T = 0.66 K for Dy₂Ti₂O₇, T = 0.63 K for Dy_1.9Y_0.1Ti₂O₇, and T = 0.64 K for Dy_1.6Y_0.4Ti₂O₇,respectively. This implies that the systems present a disordered state of spin freezing associated with the ice rules.Besides, the percentage differences between the ZFC and FC data decrease with doping so that in x = 1.0 and x = 1.4 samples, it can be hardly observed any difference between the two curves. That is to say, there is no spin-ice state in highly diluted samples. One might expect that the ice rules are relaxed due to the vacancies introduced by Y in each tetrahedron. The present results, however, show that the spin ice still exists when x = 0.4, in agreement with the result that Y dilution does not alter the neutronscattering patterns significantly even with x = 1.0 [10, 23].Also, studies of doped spin ice by replacing Ho or Dy with Y, and stuffed spin-ice materials, suggest that the spin-ice state is present even when the doping content is as high as40 % [24]. In other words, the non-magnetic defects do not strongly influence the long-range dipolar interactions in the ground state when the level of dilution is not very high,supporting that the spin-ice state is robust against dilution[10, 23, 25, 26].

Fig. 5 Temperature dependence of magnetization of Dy2-xYxTi2O7samples from 0.5 to 1.0 K: a x = 0, b x = 0.1, c x = 0.4, d x = 1.0,and e x = 1.4

Fig. 6 Filed dependence of magnetization of samples at 0.5 K. Inset being hysteresis of magnetization: a x = 0, b x = 0.1, c x = 0.4,d x = 1.0, and e x = 1.4

In order to get a deep insight on the spin freezing, the field dependence of magnetization were measured at T = 0.5 K. The results are shown in Fig. 6. The saturation moment is essentially unchanged with dilution, demonstrating that dilution does not alter the anisotropy of the system. In other words, the rare-earth-metal moments retain their Ising-like nature in the diluted samples, which is consistent with a previous report [8]. It should be noted that the x = 0.4 sample does not present saturation even when the field goes up to 3 T, probably because of the enormous sensitivity to the precise orientation of the sample, the large demagnetizing factor, and non-equilibrium effects at very low temperature. Remarkably, the magnetization study of the parent sample reveals that there is a plateau in the range of 0.3 T ＜ H＜ 0.8 T, suggesting that the system is magnetized into an intermediate state which is still governed by ice rules (two-in/two-out state).This is a macroscopically degenerate phase, known as Kagome? ice, where one of the four spins on each tetrahedron has a component of moment antiparallel to the field[27, 28]. Moreover, a sufficiently high magnetic field (for example, ＞1 T) breaks the ice rules and drives the system into the ordered state. This moment value corresponds to the fully saturated one-in/three-out (or three-in/one-out)state of the pyrochlore lattice along [111] direction. In this case, the ground-state degeneracy is removed by applying magnetic field, suggesting that the plateau in the intermediate field range is followed by a spin flip. This transition is similar to a liquid–gas phase transition and the excitations included are considered to be magnetic monopoles [29].With dilution increasing, the Kagome? ice state disappears,while the ordered state appears again.

The emergence of the plateau is closely associated with the formation of the spin-ice state which is proved by the appearance of magnetization hysteresis below the transition temperature (the pergence between ZFC and FC data), as shown in the insets of Fig. 6. With doping content increasing, the hysteresis becomes weak. Also, the irreversibility loop becomes weaker with temperature increasing, and the loop is closed completely at 1 K.Similar irreversibility was also reported previously [6]. The irreversibility and plateau in magnetization can be ascribed to the slow dynamics of the spin ice [30]. Although the origin is not very clear, the hysteresis may possibly be related to the clustering phenomenon.

Finally, we make some discussion on why low-level dilution still keeps the ice rules, but high-level dilution breaks the ice rules. The excitations in spin ice are those of low energy, involving the collective spin-flip clusters [31].If the doping level is not very high, the low-energy spectrum is not changed much, though the local ice rules might be violated due to impurities. In this case, the spins still freeze collectively and form spin-ice ground state. Thus,the ground state is very similar in both the doped and undoped systems. Moreover, if the magnetic lattice is highly diluted, the local fields felt by each Dy spin will be reduced such that these spin-flip clusters are no longer available, thus the system can be described by simple single-spin physics [23]. In other words, the enhanced disorder induced by dilution breaks the spin-ice rules, so the system cannot enter the spin-ice ground state any more.

4 Conclusion

In summary, the dilution effects of non-magnetic ions Y on vibration modes and magnetization in spin-ice Dy₂Ti₂O₇were studied. Both the parent and diluted samples show anomalous phonon softening with temperature decreasing.The phonon softening is relaxed in Y-doped samples except that of an IR mode near 233 cm^-1, indicating a strong phonon–phonon coupling in this highly frustrated material. The magnetization data show that the non-magnetic dilution enhances the disorder, which breaks the icerules ordering. In the low doping region, the compounds still keep the ice rules, indicating the spin-ice state is robust against dilution. Moreover, if the doping level increases such that the collective spin-flip clusters in spin ice are no longer available, the spin-ice rules will be broken.