The structural and magnetic properties of the compound Tm₅Ge₄

Abstract

The compound Tm₅Ge₄ is the last one in the family of R₅Ge₄ (R = rare earth elements with magnetic moments) compounds (exclusive of Pm and Eu) whose magnetic properties are still unknown. We prepared high quality Tm₅Ge₄, and report the detailed crystal structure and magnetic properties. Tm₅Ge₄ crystallizes in the Sm₅Ge₄-type orthorhombic structure at room temperature, and orders antiferromagnetically at = 13 and T_N = 21 K. The paramagnetic Curie temperature of Tm₅Ge₄ is positive (θ_p = 16 K), and the effective magnetic moment (p_eff = 7.4 μ_B/Tm) is in good agreement with the theoretical value of 7.56 μ_B/Tm³⁺. The ac susceptibility of Tm₅Ge₄ shows obvious frequency dependence behaviors suggesting the existence of a ferromagnetic cluster in the antiferromagnetic substance. According to the magnetic hysteresis loop, the intrinsic coercivity of Tm₅Ge₄ is 2616 Oe at 2 K. Tm₅Ge₄ exhibits an oscillating magnetocaloric effect owing to a metamagnetic-like transformation induced by a critical magnetic field below 21 K.

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1. Introduction

The pseudobinary R₅(Si,Ge)₄ (R = rare earth elements) compounds form an extraordinary large family, and have received considerable attention due to their unique magnetic properties, e.g., giant magnetocaloric effect (MCE),^1,2 magnetostrictive effect,³ magnetoresistance effect,^4,5 and Griffiths-like phase behavior.^6–9 Depending on the different bonding types between the slabs (each slab represents half of the unit cell along the longest b-direction and is infinite in the a- and c-directions), R₅(Si,Ge)₄ compounds can form a Gd₅Si₄-type orthorhombic structure (space group: Pnma), a Gd₅Si₂Ge₂-type monoclinic structure (space group: P112₁/a), a Sm₅Ge₄-type orthorhombic structure (space group: Pnma) and a Tm₅Si₂Sb₂-type orthorhombic structure (space group: Ccmb).^10,11 Usually, the magnetic moments of rare earth atoms that belong to the same slab are aligned ferromagnetically (FM) in the c-direction. The direction of the moments may be reversed from one slab to another in the antiferromagnetic (AFM) structure, while the directions of the moments are the same in all slabs in the FM structure. Furthermore, the crystallography and magnetism in R₅(Si,Ge)₄ compounds are found to be closely related. The FM orderings usually appear when all slabs are interconnected (Gd₅Si₄-type structure), while AFM orderings can be observed in some compounds with a Sm₅Ge₄-type orthorhombic structure in which none of the slabs are interconnected. The paramagnetic (PM) states can exist when none (Sm₅Ge₄-type structure), one-half (Gd₅Si₂Ge₂-type structure), or all (Gd₅Si₄-type structure) of the slabs are interconnected.^10,11 For many R₅(Si,Ge)₄ compounds, magnetic phase transitions coupled with a crystal structure transformation are observed, and can be controlled by a magnetic field, temperature, pressure, as well as elemental substitution.^{1–3,12–14}

Among pseudobinary R₅Si_xGe_4−x compounds, the parent compounds R₅Ge₄ usually show very complex magnetic phase diagrams and interesting magnetic behaviors. So far, no proof indicates that Pm and Eu can combine with Ge to form 5:4-type compounds. Although the crystal structures of the Tm₅Ge₄ compound have been reported in past,^15,16 it is still the last one in the family of R₅Ge₄ compounds whose magnetic properties are unknown. R₅Ge₄ compounds often show some common features. Most of the R₅Ge₄ (R = rare earth elements with net magnetic moments) compounds crystallize in Sm₅Ge₄-type structures, and show an AFM order at low temperature.^{11,15,17–30} It is interesting that the ground states of R₅Ge₄ may be FM, but the development of the equilibrium FM ordering was inhibited by a kinetic arrest of the first-order AFM-FM transition.³¹ In addition, a first-order magnetostructural phase transition from AFM ordering (Sm₅Ge₄-type orthorhombic structure) to FM ordering (Gd₅Si₄-type orthorhombic structure) can be induced by the application of either a magnetic field, or hydrostatic pressure. Note that Ce₅Ge₄ and Yb₅Ge₄ are two exceptions. The Sm₅Ge₄-type Ce₅Ge₄ compound has FM ordering below 12 K,³² and the Gd₅Si₄-type Yb₅Ge₄ compound has AFM ordering below 3.2 K.³³

Although the magnetic properties of the Tm₅Ge₄ compound are still unknown, the magnetic properties of the single crystal Tm₅Si₂Ge₂ (ref. 34) have been studied. Tm₅Si₂Ge₂ showed AFM ordering along the b-axis below ∼8 K with the FM coupled magnetic moments in the a–c plane.³⁴ The previous report had confirmed that the Tm₅Ge₄ compound could be fabricated by arc-melting, and crystallized in the Sm₅Ge₄-type orthorhombic structure.^15,16 However, it is not easy to obtain high quality Tm₅Ge₄ using an arc-melting method due to the high volatility of Tm and the impurity phases of Tm₁₁Ge₁₀ and Tm₅Ge₃ which have very close chemical compositions. The synthesis method needs to be further developed in order to guarantee a high quality sample of Tm₅Ge₄, and the magnetic properties of Tm₅Ge₄ need to be uncovered in order to gain a complete understanding of the magnetism of the family of R₅Ge₄ compounds.

In this work, we used an induction furnace to prepare high quality Tm₅Ge₄. The detailed crystal structure, magnetic properties, and phase transitions of Tm₅Ge₄ were investigated by X-ray powder diffraction (XRD), magnetic, and heat capacity measurements. We also measured the ac magnetic susceptibility and confirmed the existence of the magnetic cluster in Tm₅Ge₄.

2. Experimental details

A polycrystalline Tm₅Ge₄ sample was prepared by induction-melting of pure metals using a multi-step procedure. Tm metal was obtained from the Materials Preparation Center of the Ames Laboratory and its purity was exceeding 99.99 wt% with respect to all other elements in the periodic table.³⁵ Ge element was bought from a commercial vendor, and its purity was 99.9 wt%. An excess amount of Tm (2 at%) was added to compensate for the loss occurring due to evaporation during the induction-melting. The pure metals were sealed in a tantalum crucible (length 45 mm, diameter 9.5 mm) in a helium atmosphere. The mixture was melted at 2133 K for 7 min, cooled down to 1195 K (held for 1 h), further cooled down to 1123 K (held for 2 h), then cooled down to 973 K (held for 2 h) before finally powering off the induction furnace.

A single phase Tm₅Ge₄ sample with the Sm₅Ge₄-type orthorhombic structure (space group Pnma) was confirmed by an XRD study at room temperature performed on a Philips PANalytical powder diffractometer employing monochromatic Cu Kα₁ radiation. The lattice parameters were determined by performing Reitveld refinement using Rietica-LHPM.³⁶ The content of the minor phase Tm₅Ge₃ is ∼2 wt%. The dc and ac magnetization measurements were performed using a Quantum Design magnetic properties measurement system (MPMS) and physical properties measurement system (PPMS). A heat capacity measurement was conducted using the PPMS. The MCE (isothermal entropy change) was calculated from the heat capacity data by using where S is the total entropy change, T is the temperature, H is the magnetic field, and C is the heat capacity.

3. Results and discussion

The observed and calculated room-temperature XRD patterns of Tm₅Ge₄ are displayed in Fig. 1(a). The Sm₅Ge₄-type orthorhombic structure of the Tm₅Ge₄ compound is shown in Fig. 1(b). The refined structural parameters are summarized in Table 1. The refined lattice parameters are a = 7.4564(2) Å, b = 14.3234(5) Å, c = 7.5320(2) Å, and unit cell volume V = 804.4(4) ų, which are in agreement with the previous report.¹⁶ The distances between the Ge atoms of the slabs, as represented in Fig. 1(b), are 4.4 and 3.5 Å, respectively, indicating the presence of no chemical bond between the slabs.

Fig. 1 (a) The observed and calculated powder XRD patterns of Tm₅Ge₄. (b) The Sm₅Ge₄-type orthorhombic structure of Tm₅Ge₄.

Table 1 Crystallographic parameters of Tm₅Ge₄ at room temperature (RT)

	Atom	x/a	y/b	z/c	Boverall (Å^2)	Occupancy
Tm5Ge4@RT	Tm1(4c)	0.2045(6)	1/4	−0.0001(6)	0.336(7)	0.50
	Tm2(8d)	0.0250(4)	0.0988(2)	0.6812(4)	0.336(7)	1.00
	Tm3(8d)	0.3739(4)	0.1203(2)	0.3382(4)	0.336(7)	1.00
	Ge1(4c)	0.0727(1)	1/4	0.3856(1)	0.336(7)	0.50
	Ge2(4c)	0.3354(1)	1/4	0.6418(1)	0.336(7)	0.50
	Ge3(8d)	0.2175(9)	0.0463(4)	0.0263(9)	0.336(7)	1.00
Sm5Ge4-type	a = 7.4564(2) Å, b = 14.3234(5) Å, c = 7.5320(2) Å, V = 804.4(4) Å^3
(S. G. Pnma)	Rp = 12.08, Rwp = 15.23, Rexp = 4.04, χ^2 = 14.25

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As mentioned in the introduction, the Er₅Ge₄ compound adopts the Sm₅Ge₄-type structure,³⁰ and the Yb₅Ge₄ compound crystallizes in the Gd₅Si₄-type structure.³³ Nevertheless, both Er₅Ge₄ and Yb₅Ge₄ show AFM ordering.^30,33 Therefore, it is interesting to study the case of Tm₅Ge₄ in order to reveal the variation tendency of magnetic behaviors between Er₅Ge₄ and Yb₅Ge₄ compounds. The temperature dependence magnetizations of Tm₅Ge₄ measured in zero-field-cooled warming (ZFC), field-cooled cooling (FCC), and field-cooled warming (FCW) protocols are shown in Fig. 2. Unlike Er₅Ge₄ with only one AFM ordering,³⁰ Tm₅Ge₄ shows a peak at 21 K corresponding to AFM ordering temperature T_N and an additional peak at 13 K suggesting another possible AFM ordering temperature in a magnetic field of 50 Oe, as shown in Fig. 2(a). The hollow between two peaks appears at 18 K. Above the antiferromagnetic transition temperature, T_N = 21 K, the ZFC, FCC, and FCW curves are identical. However, significant differences, including irreversible thermomagnetic behavior, are observed below T_N (see inset of Fig. 2(a)). The insets of Fig. 2(a) and (b) enlarge the phase transition region ranging from 14 to 24 K and 13 to 24 K, respectively. Noticeable hysteresis between the FCC and FCW curves suggests that the transition observed near 18 K is a first-order phase transition.³⁷ The first-order nature of this transition was also identified by the heat capacity behavior. The inverse magnetic susceptibility of Tm₅Ge₄ obeys the Curie–Weiss law. The obtained paramagnetic Curie temperature θ_p is +16 K, and the effective magnetic moment p_eff is 7.4 μ_B/Tm which is in good agreement with the theoretical value of 7.56 μ_B/Tm³⁺. The positive θ_p indicates that ferromagnetic interactions are dominant in the ground state. This result is similar to that for Gd₅Ge₄ which is found to order antiferromagnetically at 127 K but with a positive paramagnetic Curie temperature of 94 K due to the competing exchange interactions present in this compound.³⁸ A magnetic field can drive the of Tm₅Ge₄ down to a lower temperature, reaching 8 K at 1 kOe and 5 K at 10 kOe, respectively. This behavior indicates that the magnetic ordering at is AFM. The peak at 21 K will disappear when the magnetic field is higher than 10 kOe. The thermal hysteresis behavior and peak cannot be observed in M–T curves any more in a 50 kOe magnetic field, and Tm₅Ge₄ changes into a FM state in that condition. Now we have obtained a whole picture of R₅Ge₄ compounds. R₅Ge₄ compounds (R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm) crystallize in a Sm₅Ge₄-type orthorhombic structure, while Yb₅Ge₄ crystallizes in a Gd₅Si₄-type orthorhombic structure. R₅Ge₄ compounds (R = Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb) exhibit AFM orderings, while Ce₅Ge₄ shows FM ordering.

Fig. 2 The ZFC, FCC and FCW temperature dependence of the magnetizations of Tm₅Ge₄ measured in different magnetic fields. (a) and (b) ZFC, FCC, and FCW curves measured in 50 Oe and 1 kOe, respectively. (c) and (d) ZFC and FCC curves measured in 10 kOe and 50 kOe, respectively. The insets of (a) and (b) enlarge the phase transition region ranging from 14 to 24 K and 13 to 24 K, respectively.

Fig. 3 presents the ac magnetic susceptibility at different frequencies under a zero dc magnetic field and a 5 Oe ac magnetic field. The real component of ac susceptibility shows a peak at 22.4 K which is corresponding to T_N (see Fig. 3(a)). No peak is observed at 13 K in the real component of ac susceptibility, but a peak appears at 8.8 K at 10 Hz which coincides with observed in the temperature dependence of magnetization at 1 kOe (see Fig. 2(b)). The peak at 8.8 K is almost unchanged till the frequency increases to 2997 Hz, but the magnitude reduces with the increase in frequency. The imaginary component of the ac magnetic susceptibility only shows a peak at 11 K (10 Hz) which increases and shifts upward to 12.8 K at 2997 Hz, as shown in Fig. 3(b). The notable frequency dependence of ac susceptibility observed below 22.4 K suggests the existence of a FM cluster embedded in the AFM substance. The spin-glass usually originates from the magnetic frustration or crystal disorder, and also can show the frequency dependence of ac susceptibility.^39–44 The frequency sensitivity K = ΔT_f/[T_fΔlog(2πf)] can be used to determine the presence of a spin-glass phase where T_f is the spin-glass transition temperature and f is the frequency of ac susceptibility.^39,41 K of Tm₅Ge₄ at (taken as the peak in M′′) is about 0.04 which is higher than the conventional spin-glass system (0.005–0.01).³⁹ Apparently, the possibility of spin-glass is excluded because there is no magnetic frustration or crystal disorder in the Tm₅Ge₄ compound.

Fig. 3 (a) The real components of ac magnetic susceptibility measured as a function of temperature and frequency on heating. (b) The imaginary components of ac magnetic susceptibility.

Fig. 4 shows the magnetic hysteresis loop and isothermal magnetization of Tm₅Ge₄. The magnetic hysteresis loop at 2 K is symmetric, as shown in Fig. 4(a). The intrinsic coercivity is 2616 Oe. Fig. 4(b) shows the isothermal magnetization from 3 K to 39 K. Tm₅Ge₄ shows complex behavior in the low magnetic field region due to the AFM orderings. The magnetizations increase on heating, then decrease with further increase in the temperature, and finally increase again with an increasing temperature. Taking into account the behaviors shown in the M–T and M–H curves, the Tm₅Ge₄ compound exhibits the metamagnetic-like transformation (AFM ↔ FM) in a critical magnetic field around 6 kOe at 3 K. The critical magnetic field will decrease on heating.

Fig. 4 (a) The magnetic hysteresis loops of Tm₅Ge₄ measured in ZFC conditions. The initial magnetization curves are marked in red color. (b) Isothermal magnetizations versus applied magnetic field where the magnetizations are measured under an increasing magnetic field.

Fig. 5(a) shows the heat capacity of Tm₅Ge₄ as a function of temperature and magnetic field. Unlike the complex magnetic properties, the heat capacity data show very simple behavior. The lambda-type anomaly, observed in a zero magnetic field around 21 K, corresponds to the AFM ordering temperature T_N which is observed at the same temperature in the low magnetic field dc magnetization data. The heat capacity behavior observed in nonzero magnetic fields is consistent with the isothermal magnetization of Tm₅Ge₄, and the lambda-type peak shifts slightly downward with the increasing magnetic field suggesting a metamagnetic-like transformation. The peak broadens and becomes smooth in a 20 kOe magnetic field. There is no anomaly observed at in the heat capacity curve suggesting the near zero energy difference between the AFM and FM states. The MCE feature also provides a useful tool to probe the phase transitions and magnetic states in complex magnetic systems.⁴⁵ Fig. 5(b) shows the total entropy change calculated from the heat capacity data. Tm₅Ge₄ shows oscillating MCE behavior, and the entropy change peaks for a magnetic field change ΔH = 20 kOe appear at 7 K (−1.4 J kg⁻¹ K⁻¹) and 17 K (1.0 J kg⁻¹ K⁻¹), respectively. The MCE of Tm₅Ge₄ is associated with the metamagnetic-like transformation induced by a magnetic field.

Fig. 5 (a) The heat capacity of Tm₅Ge₄ measured as a function of temperature and magnetic field. (b) The entropy change calculated by heat capacity data in ΔH = 20 kOe magnetic field.

4. Conclusions

The Tm₅Ge₄ compound crystallizes in the Sm₅Ge₄-type orthorhombic structure, and shows complex AFM ordering at T_N = 21 K and = 13 K. The AFM ordering will change into FM ordering in a 50 kOe magnetic field. The ac susceptibility measurements confirm the AFM ordering, and show obvious frequency dependence behaviors suggesting the existence of a FM cluster. The magnetic hysteresis loop shows a symmetric characteristic, and the intrinsic coercivity at 2 K is as large as about 2616 Oe. According to the specific heat measurements, a small and lambda-like peak is observed at 21 K confirming the AFM ordering temperature T_N. The Tm₅Ge₄ compound exhibits a metamagnetic-like transformation when the magnetic field exceeds a critical value leading to an obvious oscillating MCE.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant no. 51471150, 51301116) and Program for Innovative Research Team in University of Ministry of Education of China (IRT13R54). Work at the Ames Laboratory was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering. The research was performed at the Ames Laboratory operated for the U.S. Department of Energy by Iowa State University under Contract no. DE-AC02-07CH11358.

Notes and references

1. V. K. Vitalij and K. A. Gschneidner Jr, Phys. Rev. Lett., 1997, 78, 4494.
2. V. K. Vitalij and K. A. Gschneidner Jr, Appl. Phys. Lett., 1997, 70, 3299.
3. L. Morellon, P. A. Algarabel, M. R. Ibarra, J. Blasco, B. Garcia-Landa, Z. Arnold and F. Albertini, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 58, R14721.
4. L. Morellon, J. Stankiewicz, B. Garcia-Landa, P. A. Algarabel and M. R. Ibarra, Appl. Phys. Lett., 1998, 73, 3462.
5. E. M. Levin, V. K. Pecharsky and K. A. Gschneidner Jr, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 60, 7993.
6. F. Casanova, S. de Brion, A. Labarta and X. Batlle, J. Phys. D: Appl. Phys., 2005, 38, 3343.
7. C. Magen, P. A. Algarabel, L. Morellon, J. P. Araujo, C. Ritter, M. R. Ibarra, A. M. Pereira and J. B. Sousa, Phys. Rev. Lett., 2006, 96, 167201.
8. Z. W. Ouyang, V. K. Pecharsky, K. A. Gschneidner Jr, D. L. Schlagel and T. A. Lograsso, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 094404.
9. J. D. Zou, J. Liu, Y. Mudryk, V. K. Pecharsky and K. A. Geschneidner Jr, J. Appl. Phys., 2013, 114, 063904.
10. K. A. Gschneidner Jr, V. K. Pecharsky and A. O. Tsokol, Rep. Prog. Phys., 2005, 68, 1479.
11. V. K. Pecharsky and K. A. Gschneidner Jr, Pure Appl. Chem., 2007, 79, 1383.
12. C. Magen, L. Morellon, P. A. Algarabel, M. R. Ibarra, Z. Arnold, J. Kamarad, T. A. Lograsso, D. L. Schlagel, V. K. Pecharsky, A. O. Tsokol and K. A. Gschneidner Jr, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 024416.
13. L. Morellon, P. A. Algarabel, C. Magen, M. R. Ibarra and Y. Skorokhod, J. Phys.: Condens. Matter, 2004, 16, 1623.
14. A. M. G. Carvalho, C. S. Alves, A. de Campos, A. A. Coelho, S. Gama, F. C. G. Gandra, P. J. von Ranke and N. A. Oliveira, J. Appl. Phys., 2005, 97, 10M320.
15. G. S. Smith, A. G. Tharp and Q. Johnson, Acta Crystallogr., 1967, 22, 940.
16. V. N. Eremenko, K. A. Meleshevich, Y. I. Buyanov and P. S. Martsenyuk, Powder Metall. Met. Ceram., 1989, 28, 543.
17. G. S. Smith, Q. Johnson and A. G. Tharp, Acta Crystallogr., 1967, 22, 269.
18. F. Holtzberg, R. J. Gambino and T. R. McGuire, J. Phys. Chem. Solids, 1967, 28, 2283.
19. H. F. Yang, G. H. Rao, W. G. Chu, G. Y. Liu, Z. W. Ouyang and J. K. Liang, J. Alloys Compd., 2002, 339, 189.
20. G. H. Rao, Q. Huang, H. F. Yang, D. L. Ho, J. W. Lynn and J. K. Liang, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 69, 094430.
21. P. Schobinger-Papamantellos and A. Niggli, J. Phys. Chem. Solids, 1981, 42, 583.
22. J. M. Cadogan, D.H. Ryan, Z. Altounian, H. B. Wang and I. P. Swainson, J. Phys.: Condens. Matter, 2002, 14, 7191.
23. V. K. Pecharsky and K. A. Geschneidner Jr, J. Alloys Compd., 1997, 260, 98.
24. P. Schobinger-Papamantellos, J. Phys. Chem. Solids, 1978, 39, 197.
25. C. Ritter, L. Morellon, P. A. Algarabel, C. Magen and M. R. Ibarra, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 65, 094405.
26. W. Tian, A. Kreyssig, J. L. Zarestky, L. Tan, S. Nandi, A. I. Goldman, T. A. Lograsso, D. L. Schlagel, K. A. Gschneidner Jr, V. K. Pecharsky and R. J. McQueeney, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 134422.
27. V. V. Ivtchenko, V. K. Pecharsky and K. A. Geschneidner Jr, Adv. Cryog. Eng., 2000, 46, 405.
28. N. K. Singh, D. Paudyal, Y. Mudryk, V. K. Pecharsky and K. A. Gschneidner Jr, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 094115.
29. C. Ritter, C. Magen, L. Morellon, P. A. Algarabel, M. R. Ibarra, A. M. Pereira, J. P. Araujo and J. B. Sousa, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 104427.
30. A. O. Pecharsky, K. A. Gschneidner Jr, V. K. Pecharsky, D. L. Schlagel and T. A. Lograsso, Phys. Rev. B: Condens. Matter Mater. Phys., 2004, 70, 144419.
31. S. B. Roy, M. K. Chattopadhyay, P. Chaddah, J. D. Moore, G. K. Perkins, L. F. Cohen, K. A. Gschneidner Jr and V. K. Pecharsky, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 74, 012403.
32. R. Nirmala, A. V. Morozkin, J. Lamsal, W. B. Yelon and S. K. Malik, J. Appl. Phys., 2010, 107, 09E308.
33. K. Ahn, A. O. Tsokol, Yu. Mozharivskyj, K. A. Gschneindner Jr and V. K. Pecharsky, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 054404.
34. J. H. Kim, S. J. Kim, C. I. Lee, M. A. Jung, H. J. Oh, J.-S. Rhyee, Y. Jo, H. Mitani, H. Miyazaki, S.-I. Kimura and Y. S. Kwon, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 104401.
35. Materials Preparation Center, Ames Laboratory US-DOE, Ames, IA, USA, http://www.mpc.ameslab.gov.
36. B. Hunter, Rietica-A Visual Rietveld Program, International Union of Crystallography Commission on Powder Diffraction Newsletter, no. 20 (Summer, 1998), http://www.rietica.org.
37. M. Khan, Y. Mudryk, K. A. Gschneidner Jr and V. K. Pecharsky, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 064421.
38. E. M. Levin, K. A. Gschneidner Jr and V. K. Pecharsky, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 65, 214427.
39. J. A. Mydosh, Spin Glass: An Experimental Introduction, Taylor & Francis, London, 1993.
40. D. N. H. Nam, K. Jonason, P. Nordblad, N. V. Khiem and N. X. Phuc, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 4189.
41. M. K. Singh, W. Prellier, M. P. Singh, R. S. Katiyar and J. F. Scott, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 144403.
42. F. Wang, J. H. Kim and Y. J. Kim, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 024419.
43. M. H. Phan, N. A. Frey, M. Angst, J. de Groot, B. C. Sales, D. G. Mandrus and H. Srikanth, Solid State Commun., 2010, 150, 341.
44. E. Ilker and A. N. Berker, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2014, 89, 042139.
45. P. Lampen, N. S. Bingham, M. H. Phan and H. Srikanth, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 144414.

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