Cite this Article
Cui Qi, Cai Yun-Qi, Li Xiang, Dun Zhi-Ling, Sun Pei-Jie, Zhou Jian-Shi, Zhou Hai-Dong, Cheng Jin-Guang. High pressure synthesis and characterization of the pyrochlore Dy2Pt2O7: A new spin ice material. Chinese Physics B, 2020, 29(4): 047502  
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High pressure synthesis and characterization of the pyrochlore Dy2Pt2O7: A new spin ice material
Cui Qi1, 2, Cai Yun-Qi1, 2, Li Xiang3, 4, Dun Zhi-Ling5, 6, Sun Pei-Jie1, 2, 7, Zhou Jian-Shi3, Zhou Hai-Dong5, Cheng Jin-Guang1, 2, 7, †
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
Materials Science and Engineering Program, Mechanical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement of Ministry of Education, School of Physics, Beijing Institute of Technology, Beijing 100081, China
Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996, USA
School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
Songshan Lake Materials Laboratory, Dongguan 523808, China

 

† Corresponding author. E-mail: jgcheng@iphy.ac.cn

Project supported by the National Key R&D Program of China (Grant No. 2018YFA0305700), the National Natural Science Foundation of China (Grant Nos. 11834016, 11874400, and 11921004), the Beijing Natural Science Foundation, China (Grant No. Z190008), the Key Research Program of Frontier Sciences of the Chinese Academy of Sciences (Grant No. QYZDB-SSW-SLH013), and the CAS Interdisciplinary Innovation Team. ZLD and HDZ acknowledge the support of Grant No. NSF-DMR-1350002. JSZ acknowledges the support of NSF DMR Grant No. 1729588.

Abstract

The cubic pyrochlore Dy2Pt2O7 was synthesized under 4 GPa and 1000 °C and its magnetic and thermodynamic properties were characterized by DC and AC magnetic susceptibility and specific heat down to 0.1 K. We found that Dy2Pt2O7 does not form long-range magnetic order, but displays characteristics of canonical spin ice such as Dy2Ti2O7, including (1) a large effective moment 9.64 μB close to the theoretical value and a small positive Curie–Weiss temperature θCW = +0.77 K signaling a dominant ferromagnetic interaction among the Ising spins; (2) a saturation moment ∼4.5 μB being half of the total moment due to the local 〈111〉 Ising anisotropy; (3) thermally activated spin relaxation behaviors in the low (∼1 K) and high (∼20 K) temperature regions with different energy barriers and characteristic relaxation time; and most importantly, (4) the presence of a residual entropy close to Pauling’ estimation for water ice.

PACS: ;75.10.Jm;;75.47.Lx;;75.30.-m;;75.30.Cr;
Keyword:;Dy2Pt2O7;;pyrochlore oxide;;spin ice;;high-pressure synthesis;
1. Introduction

Geometrically frustrated magnets can display rich and diverse phenomena, providing an excellent platform for experimental realizations of collective magnetism that was predicated theoretically.[1,2] The recognition of a spin ice state in the cubic pyrochlore compounds Ho2Ti2O7 and Dy2Ti2O7 represents such an example that successfully maps to the well-known water–ice problem.[3–6] In these pyrochlores, the magnetic rare-earth ions, Ho3+ or Dy3+, with a large magnetic moment of ∼ 10 μB reside on the vertices of the corner-sharing tetrahedra, forming a geometrically frustrated lattice. A uniaxial local crystalline electric field (CEF) around Ho3+ or Dy3+ results in a nearly perfect easy-axis anisotropy, forcing the rare-earth’ spin to point along the local 〈111〉 axis that joins the centers of two neighboring tetrahedra.[7,8] The combination of dipolar and magnetic exchange interactions favors ‘two-in, two-out’ spin configurations on each tetrahedron, which has been termed ‘spin ice’ in direct analogy to the ‘two-short, two-long’ proton bond disorder in water ice. The Pauling’ zero-point entropy SP = (R/2)ln(3/2), where R is the ideal gas constant, for water ice has also been confirmed in the spin ices having a macroscopically degenerate ground state.[5]

The low-temperature magnetic properties of a pyrochlore spin ice are mainly controlled by the magnetic exchange (Jnn) and the dipole–dipole interaction (Dnn) of the nearest-neighbor spins. For these pyrochlore spin ice materials, Jnn is usually antiferromagnetic, while Dnn is ferromagnetic and can be calculated as , where rnn is the nearest-neighbor rare-earth distance. Dnn is estimated to be ∼ 2.35 K for Ho2Ti2O7 and Dy2Ti2O7. The physics of pyrochlore spin ices can be largely captured by the dipolar spin ice model (DSIM) proposed by den Hertog and Gingras.[9] In the theoretical phase diagram based on DSIM,[9] the spin ice state is stable for Jnn/Dnn > −0.91, and a Q = 0 antiferromagnetically ordered state is favored for Jnn/Dnn < −0.91. Since Jnn is more sensitive to rnn than Dnn, by synthesizing Ho2Ge2O7 and Dy2Ge2O7,[10,11] which have smaller lattice parameter in comparison to the corresponding titanates and stannates, our previous studies have successfully modified the ratio of Jnn/Dnn. The lowest value of −0.73 is achieved in Dy2Ge2O7,[11] which is still located inside the spin ice regime. A further enhancement of Jnn is needed in order to achieve a transition from spin ice to a Q = 0 state.

Besides the chemical pressure effects caused by the size of B-cation in Ln2B2O7 (Ln = rare earth), our recent studies on the platinum-based pyrochlores Ln2Pt2O7 have revealed an additional effect of the nonmagnetic Pt4+ ions,[12,13] i.e., the spatially more extended Pt-5d orbitals and thus the enhanced Pt 5d–O 2p hybridizations can modify the CEF and influence the exchange interactions. In comparison with Gd2B2O7 (B = Ge, Ti, Sn), the antiferromagnetic transition temperature of Gd2Pt2O7 is substantially enhanced because the empty Pt-eg orbitals provide extra superexchange pathways.[13] Thus, we expect an alternative routine to modify Jnn/Dnn in the Pt-based Ising pyrochlores.

In this work, we have prepared the pyrochlore compound Dy2Pt2O7 under high pressure, and characterized its magnetic and thermodynamic properties via magnetic susceptibility and specific heat measurements down to 0.1 K. We find that Dy2Pt2O7 does not exhibit any long-rang magnetic order at low temperature, but displays canonical spin ice characteristics, including the thermally activated spin dynamics and the presence of Pauling’ zero-point entropy. By comparing the low-temperature magnetic specific heat to DSIM, we obtain a ratio of Jnn/Dnn = −0.56 for Dy2Pt2O7. Our results demonstrate that Dy2Pt2O7 is a new spin ice compound with enhanced superexchange interaction Jnn.

2. Experimental details

The sample preparations and characterizations in the present study are similar to those performed in our previous work.[12] The cubic pyrochlore Dy2Pt2O7 sample was prepared under 4 GPa and 1000 °C by using a Kawai-type multianvil module (Max Voggenreiter GmbH). The resultant high-pressure products were first washed with warm aqua regia to remove a small amount of platinum metal and unreacted Dy2O3; the obtained powders were then pressed into pellets and subjected to heat treatment at 900 °C for 10 h to facilitate the measurements of the bulk physical properties.

Phase purity of the obtained powder and pellet samples was examined by powder x-ray diffraction (XRD) at room temperature. Structural parameters were extracted from the XRD patterns via Rietveld refinement with the FullProf program. DC magnetic susceptibility was measured with a commercial magnetic property measurements system (MPMS-III, Quantum Design) in the temperature range from 1.8 K to 300 K under an external magnetic field of μ0H = 0.1 T. AC magnetic susceptibility measurements in the temperature range 2 K < T < 50 K were performed in a physical property measurement system (PPMS, Quantum Design). AC susceptibility measurements from 70 mK to 2 K were carried out in an Oxford dilution refrigerator with the mutual induction method; an excitation current of ∼ 1 mA with frequencies ranging from 117 Hz to 1517 Hz was applied to the primary coil during the measurements. Specific-heat data down to 0.1 K were collected by the PPMS with a dilution refrigerator insert.

3. Results and discussion
3.1. Structure characterizations

Figure 1 (a) shows the powder XRD pattern of Dy2Pt2O7, which is confirmed to be single phase with the pyrochlore structure. The XRD pattern can be refined well with a cubic pyrochlore structure defined by the Fd-3m (No. 227) space group with the Dy atom at 16d (1/2,1/2,1/2), the Pt atom at 16c (0,0,0), the O1 atom at 48f (x,1/8,1/8), and the O2 atom at 8b (3/8,3/8,3/8) site, respectively. The obtained lattice constant a = 10.1913(1) Å for Dy2Pt2O7 is in excellent agreement with the previously reported value of 10.202 Å.[14] In addition, the lattice constant a scales linearly with the ionic radius (IR) of the B4+ ions for the series of Dy2B2O7 (B = Sn, Pt, Ti, Ge), as depicted in Fig. 1(b).

Fig. 1. (a) Room-temperature powder XRD pattern of Dy2Pt2O7 and the results of the Rietveld refinement. (b) Lattice parameter a (left) and the Curie–Weiss temperature θCW (right) as a function of the ionic radius of the B4+ ions in the series of Dy2B2O7 (B = Sn, Pt, Ti, Ge).
3.2. DC magnetic susceptibility

The magnetic properties of Dy2Pt2O7 were first characterized by DC magnetization measurements in the temperature range from 1.8 K to 300 K. Figure 2(a) displays the DC magnetic susceptibility χ(T) and its inverse χ−1(T) measured under μ0H = 0.1 T after zero-field-cooled (ZFC) and field-cooled (FC) processes from room temperature. No sign of long-range magnetic ordering was observed down to 1.8 K. A Curie–Weiss (CW) fitting has been applied to χ−1(T) in the temperature range 10–50 K, i.e., χ−1(T) = (T–θCW)/C, which yields an effective moment μeff = 9.62 μB per Dy3+ and a CW temperature θCW = +0.77 K for Dy2Pt2O7. The obtained μeff is very close to the theoretical value of 9.55 μB for free Dy3+ ion with J = 15/2, and the small positive θCW signals a net ferromagnetic interaction between the Ising spins located on the vertices of the corner-shared tetrahedra.[15] As seen in Fig. 1(b), the positive θCW decreases roughly linearly with decreasing IR of B4+ and approaches to zero for the Ge-based pyrochlore. Such a monotonic variation of θCW versus IR(B4+) suggests that the nearest-neighbor distance, rnn, remains the dominant factor that governs the balance between the antiferromagnetic Jnn and the ferromagnetic Dnn between the nearest-neighbor Ising spins.

Fig. 2. (a) Temperature dependence of the DC magnetic susceptibility χ(T) and its inverse χ−1(T) for Dy2Pt2O7. The solid line represents the Curie–Weiss fitting curve and the fitting parameters are given in the figure. (b) The isothermal magnetization curves M(H) measured at T = 2 K and 5 K for Dy2Pt2O7.

The isothermal magnetization M(H) curves measured in fields up to 5 T at 2 K and 5 K are shown in Fig. 2(b) for Dy2Pt2O7. As seen in the classical spin ices, a typical ferromagnetic behavior is observed and the saturation moment reaches ∼ 4.5 μB per Dy3+, which is about half of the total moment available at each site due to the local 〈111〉 Ising magnetic anisotropy and the powder averaging.[16] From these DC magnetic measurements on Dy2Pt2O7, we find nearly identical behaviors as those well-characterized classical spin ices Dy2B2O7 (B = Sn, Ti, Ge). Below we further provide the AC magnetic susceptibility and thermodynamics evidences in support of the spin-ice behavior for Dy2Pt2O7.

3.3. AC magnetic susceptibility

Figure 3 shows the AC magnetic susceptibility of Dy2Pt2O7 in the temperature range (a)–(c) below 2 K and (d)–(f) above 2 K. For T < 2 K, the real χ′(T) and the imaginary part χ″(T) are normalized by their maximum values. As can be seen in Figs. 3(a) and 3(b), χ′(T) in the frequency range from 117 Hz to 1317 Hz drops quickly below ∼ 1.6 K, and χ″(T) displays a broad shoulder at a slightly lower temperature. Both χ′(T) and χ″(T) are frequency dependent and the shoulder shifts to higher temperatures upon increasing frequency. Such a slow spin dynamics is typical for classical spin ices and has been attributed to the formation of spin-ice configurations.[17,18] Due to the ambiguity of the maximum in χ″(T), here we define the maximum of dχ′/dT as a characteristic temperature T1 whose frequency dependence can be fitted with an Arrhenius formula, f = f01exp(–Ea1/κBT1), Fig. 3(c), yielding an activation energy K and a characteristic relaxation time s.

Fig. 3. The real part χ′(T) and the imaginary part χ″(T) of the AC magnetic susceptibility for Dy2Pt2O7 in the temperature range (a), (b) below 2 K and (d), (e) above 2 K. (c) and (f) The linear fit to the Arrhenius plot of the characteristic temperatures T1 and T2, respectively.

Another distinct feature in the AC susceptibility of Dy-pyrochlore spin ices is the presence of a high-temperature peak around 15 K.[17–20] Similar behaviors are also observed in Dy2Pt2O7, Figs. 3(d) and 3(e). For f ≥ 333 Hz, we observe a clear drop in χ′(T) and a corresponding maximum in χ″(T) at temperature T2, which starts at ∼ 18 K and moves to higher temperatures with increasing frequency. Similarly, a linear fitting to the Arrhenius plot of lnf versus 1/T2, Fig. 3(f), gives the activation energy K and the characteristic relaxation time s, which are also consistent with the reported values of Ea = 210 K and τ0 = 1.39 × 10−9 s for the polycrystalline Dy2Ti2O7.[20] Since the energy barrier Ea2 ∼ 300 K is close to the energy scale set by the first excited CEF level from the ground state doublet, the spin relaxation processes are thermally activated for T ≥ T2.

3.4. Specific heat

Figure 4(a) shows the low-temperature specific heat C(T) of Dy2Pt2O7, which displays a Schottky-like peak centered at about 1.1 K. Both the peak position ∼ 1 K and the magnitude ∼ 3 J⋅(mol-Dy)−1⋅K−1 are very similar to those of the classical Dy-pyrochlore spin ices, Dy2B2O7 (B = Sn, Ti, Ge).[11] The magnetic contribution Cm was obtained by subtracting from the measured total specific heat Ctotal the lattice contribution Clat, which was taken from the specific heat of isostructural, nonmagnetic Lu2Pt2O7. As shown in Fig. 4(a), the magnetic entropy obtained via integrating Cm/T over the investigated temperature range approaches a constant value of ∼ 4.2 J⋅(mol-Dy)−1⋅ K−1, which falls considerably short of the expected value of Rln2 ≈ 5.76 J⋅(mol-Dy)−1·K−1 for Dy3+ with a ground Karmers doublet. The resultant residual entropy 1.56 J⋅(mol-Dy)−1⋅ K−1 is close to the Pauling’ zero-point entropy SP = (R/2)ln(3/2) = 1.68 J⋅(mol-Dy)−1⋅ K−1, providing an important evidence for the spin-ice state in Dy2Pt2O7.[5]

Fig. 4. (a) Specific heat C(T) of Dy2Pt2O7. The C(T) of isostructural, nonmagnetic Lu2Pt2O7 was used as the lattice contribution Clat. The magnetic contribution Cm was obtained by subtracting Clat from the measured total Ctotal. The entropy S was evaluated by integrating Cm/T over the investigated temperature range. (b) Comparison of the magnetic specific heat Cm of Dy2B2O7 (B = Sn, Pt, Ti, Ge) pyrochlores.
3.5. Discussion

Based on these above characterizations, we can conclude that Dy2Pt2O7 is a new spin ice characterized by: (i) a large effective moment 9.64 μB close to the theoretical value, and a small positive Curie–Weiss temperature θCW = +0.77 K signaling a dominant ferromagnetic interaction among the Ising spins; (ii) a saturation moment ∼ 4.5 μB being half of the total moment due to the local 〈111〉 Ising anisotropy; (iii) thermally activated spin relaxation behaviors in the low (∼ 1 K) and high (∼ 20 K) temperature regions with different energy barriers and characteristic relaxation time; and most importantly, (iv) the presence of a residual entropy close to Pauling’ estimation for water ice.

Although it is not unexpected that Dy2Pt2O7 displays typical behaviors of canonical spin ice, the effects of non-magnetic Pt4+ are noteworthy. For this purpose, we have compared the Cm of Dy2Pt2O7 with those of Dy2B2O7 (B = Sn, Ti, Ge) in Fig. 4(b). For those latter spin ices, it has been shown that the Cm peak shifts to lower temperatures and its height also increases upon reducing the ionic radius of B4+ ions or rnn.[11] This is consistent with the prediction of DSIM due to the enhancement of Jnn with respect to Dnn.[9] If considering only the lattice parameter or rnn, the Cm peak of Dy2Pt2O7 should locate in between those of Dy2Sn2O7 and Dy2Ti2O7. However, as shown in Fig. 4(b), the Cm peak of Dy2Pt2O7 is higher than that of Dy2Sn2O7 and Dy2Ti2O7, and the Cm peak also occurs at a lower temperature than the other two. Based on the prediction of DSIM[9] and Dnn ≈ 2.29 K for Dy2Pt2O7, the Cm peak temperature Tpeak = 1.13 K corresponds to a Jnn/Dnn = −0.56, which predicts Jnn = −1.28 K and Jeff = Jnn + Dnn = 1.01 K. These values are also listed in Table 1. For comparison, Dy2Ti2O7 has Jnn/Dnn = −0.49, Jnn = −1.15 K, and Jeff = 1.20 K.[11] Because the ionic radius of Pt4+ (0.625 Å ) is larger than that of Ti4+ (0.605 Å ), the observed larger |Jnn| and |Jnn/Dnn| in Dy2Pt2O7 than those of Dy2Ti2O7 suggest that other factors beyond the chemical pressure effect should play a role in determining the low-temperature magnetic properties of Dy2Pt2O7. As in the case of Gd2Pt2O7,[13] we attribute the enhanced |Jnn| in Dy2Pt2O7 to the extra superexchange pathways through the empty eg orbitals of Pt4+ via Dy–O–Pt–O–Dy. This contribution becomes prominent in Dy2Pt2O7 having the spatially more extended Pt 5d orbitals.

Table 1.

Lattice parameter and selected magnetic parameters for the Dy-pyrochlore spin ices Dy2B2O7 (B = Ge, Ti, Pt, Sn).

.
4. Conclusion

In summary, we have synthesized the cubic pyrochlore Dy2Pt2O7 under 4 GPa and 1000 °C, and confirmed it to be a new classical spin ice as Dy2Ti2O7. The magnetic specific heat of Dy2Pt2O7 signals a moderate enhancement of |Jnn|, but the ratio Jnn/Dnn = −0.56 remains located in the spin ice regime as predicted by DSIM. Our work demonstrates that the Jnn/Dnn can be effectively tuned by replacing the B-site cation of Ising pyrochlores. But further explorations are needed to realize a transition from spin ice to an antiferromagnetically ordered state by varying Jnn/Dnn in a larger range as predicated by the DSIM.

Reference
[1] Ramirez A P 1994 Annu. Rev. Mater. Sci. 24 453
[2] Greedan J E 2001 J. Mater. Chem. 11 37
[3] Harris M J Bramwell S T McMorrow D F Zeiske T Godfrey K W 1997 Phys. Rev. Lett. 79 2554
[4] Bramwell S T Gingras M J P 2001 Science 294 1495
[5] Ramirez A P Hayashi A Cava R J Siddharthan R Shastry B S 1999 Nature 399 333
[6] Castelnovo C Moessner R Sondhi S L 2012 Annu. Rev. Condens. Matter Phys. 3 35
[7] Rosenkranz S Ramirez A P Hayashi A Cava R J Siddharthan R Shastry B S 2000 J. Appl. Phys. 87 5914
[8] Jana Y M Sengupta A Ghosh D 2002 J. Mag. Mag. Mater. 248 7
[9] den Hertog B C Gingras M J P 2000 Phys. Rev. Lett. 84 3430
[10] Zhou H D Bramwell S T Cheng J G Wiebe C R Li G Balicas L Bloxsom J A Silverstein H J Zhou J S Goodenough J B Gardner J S 2011 Nat. Commun. 2 478
[11] Zhou H D Cheng J G Hallas A M Wiebe C R Li G Balicas L Zhou J S Goodenough J B Gardner J S Choi E S 2012 Phys. Rev. Lett. 108 207206
[12] Cai Y Q Cui Q Li X Dun Z L Ma J Dela Cruz C R Jiao Y Y Liao J Sun P J Li Y Q Zhou J S Goodenough J B Zhou H D Cheng J G 2016 Phys. Rev. 93 014443
[13] Li X Cai Y Q Cui Q Lin C J Dun Z L Matsubayashi K Uwatoko Y Sato Y Kawae T Lv S J Jin C Q Zhou J S Goodenough J B Zhou H D Cheng J G 2016 Phys. Rev. 94 214429
[14] Hoekstra H R Gallagher F 1968 Inorg. Chem. 7 2553
[15] Tang Z Li C Z Yin D Zhu B P Wang L L Wang J F Xiong R Wang Q Q Shi J 2006 Acta Phys. Sin. 55 6532 in Chinese
[16] Fukazawa H Melko R G Higashinaka R Maeno Y Gingras M J P 2002 Phys. Rev. 65 054410
[17] Matsuhira K Hinatsu Y Sakakibara T 2001 J. Phys.: Conden. Matter 13 L737
[18] Snyder J Ueland B G Slusky J S Karunadas H Cava R J Schiffer P 2004 Phys. Rev. 69 064414
[19] Shi J Tang Z Zhu B P Huang P Ying D Li C Z Wang Y Wen H 2007 J. Mag. Mag. Mater. 310 1322
[20] Snyder J Ueland B G Slusky J S Karunadas H Cava R J Mizel A Schiffer P 2003 Phys. Rev. Lett. 91 107201