Dielectric and Spin-Glass Magnetic Properties of the A-Site Columnar-Ordered Quadruple Perovskite Sm2CuMn(MnTi3)O12

Belik, Alexei A.; Liu, Ran; Yamaura, Kazunari

doi:10.3390/ma15238306

Open AccessArticle

Dielectric and Spin-Glass Magnetic Properties of the A-Site Columnar-Ordered Quadruple Perovskite Sm₂CuMn(MnTi₃)O₁₂

by

Alexei A. Belik

^1,*

,

Ran Liu

^1,2,3 and

Kazunari Yamaura

^1,2

¹

International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba 305-0044, Ibaraki, Japan

²

Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku, Sapporo 060-0810, Hokkaido, Japan

³

Institute of Scientific and Industrial Research, Osaka University, Mihogaoka 8-1, Ibaraki 567-0047, Osaka, Japan

^*

Author to whom correspondence should be addressed.

Materials 2022, 15(23), 8306; https://doi.org/10.3390/ma15238306

Submission received: 11 October 2022 / Revised: 18 November 2022 / Accepted: 21 November 2022 / Published: 23 November 2022

(This article belongs to the Special Issue Synthesis, Structure and Properties of Metal Oxides)

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Abstract

Perovskite-type ABO₃ oxides show a number of cation-ordered structures, which have significant effects on their properties. The rock-salt-type order is dominant for B cations, and the layered order for A cations. In this work, we prepared a new perovskite-type oxide, Sm₂CuMn(MnTi₃)O₁₂, with a rare columnar A-site order using a high-pressure, high-temperature method at about 6 GPa and about 1700 K. Its crystal structure was studied with synchrotron powder X-ray diffraction. The compound crystallizes in space group P4₂/nmc (No. 137) at room temperature with a = 7.53477 Å and c = 7.69788 Å. The magnetic properties of the compound were studied with dc and ac magnetic susceptibility measurements and specific heat. Spin-glass (SG) magnetic properties were found with T_SG = 7 K, while specific heat, in the form of C_p/T, showed a strong, very broad anomaly developing below 20 K and peaking at 4 K. The dielectric constant of Sm₂CuMn(MnTi₃)O₁₂ was nearly frequency and temperature independent between 8 K and 200 K, with a value of about 50. Cu²⁺ doping drastically modified the magnetic and dielectric properties of Sm₂CuMn(MnTi₃)O₁₂ in comparison with the parent compound Sm₂MnMn(MnTi₃)O₁₂, which showed a long-range ferrimagnetic order at 34–40 K. The antisite disorder of Cu²⁺ and Mn²⁺ cations between square-planar and octahedral sites was responsible for the SG magnetic properties of Sm₂CuMn(MnTi₃)O₁₂.

Keywords:

quadruple perovskites; A-site columnar-ordered; antisite disorder; crystal structures; spin-glass

Graphical Abstract

1. Introduction

The properties of the perovskite-structure oxide material, ABO₃, are controlled by their chemical compositions and degrees of cation orderings [1,2]. There are perovskites with B-site cation orderings, A-site cation orderings, and both types of orderings. In the case of B-site ordering, the rock-salt-type order is dominant [3]. In the case of A-site ordering in ABO₃, the layered-type order is dominant [1,2,4], but there are other types of ordering [5,6]. There are also two special families of perovskites with A-site orderings: A-site-ordered quadruple perovskites, AA′₃B₄O₁₂ [7,8,9], and A-site columnar-ordered quadruple perovskites, A₂A′A″B₄O₁₂ [10]. Quadruple perovskites can have ordered arrangements of 3d transition metals at the A (in general) perovskite sites in addition to the B sites. The resulting B–B, A–B, and A–A exchange interactions can produce complex interaction patterns and frustration networks and result in competing magnetic ground states, a large number of magnetic transitions and unexpected magnetism [11].

With A = R = rare earth elements and Bi and A′ = A″ = B = Mn, interesting classes of perovskite manganites are formed, namely RMn₇O₁₂ [9] and RMn₃O₆ (in a short formula) [12]. They show several magnetic transitions with spin reorientations [9], and some members have incommensurate magnetic structures [13]. The Cu²⁺ doping of RMn₇O₁₂ and RMn₃O₆ has beneficial effects on their magnetic properties. in a sense that magnetic transition temperatures significantly increase, e.g., from about 80–87 K in RMn₇O₁₂ [13] to 360–400 K in RCu₃Mn₃O₁₂ [14], and from about 60–77 K in RMn₃O₆ [12] to 160–180 K in R₂CuMnMn₄O₁₂ [11,15]. In case of BiMn₇O₁₂ [9], Cu²⁺ doping results in complex structural behavior [16,17,18], complex magnetic behavior, and almost a linear rise of magnetic transition temperatures in BiCu_xMn_7–xO₁₂ [18] for 0.8 ≤ x ≤ 3 from about 30 K (for 0 < x < 0.8) to 360 K for x = 3 [19]. The beneficial effects of Cu²⁺ doping also took place in Y₂MnGaMn₄O₁₂, which shows spin-glass magnetic properties at 26 K [20], as Y₂CuGaMn₄O₁₂ exhibits long-range ferrimagnetic ordering at 115 K [21].

Sm₂MnMn(MnTi₃)O₁₂ is a member of the A-site columnar-ordered quadruple perovskites. The magnetic properties of Sm₂MnMn(MnTi₃)O₁₂ [22,23] were somewhat unexpected, as it shows a long-range ferrimagnetic ordering with T_C = 34–40 K and a well-defined M–H hysteresis loop with remnant magnetization of 2.3–2.4 μ_B/f.u. at 5 K. The concentration of 3d transition metals (Mn²⁺) at the B sites (25%) was below the percolation limit for the corner-shared octahedral network. Nevertheless, Mn²⁺ cations at the B sites were involved in the long-range ordering with a noticeable ordered magnetic moment [23]. Similar compounds without magnetic cations at the B sites (e.g., Ca₂MnMnTi₄O₁₂ [24] and NaRMnMnTi₄O₁₂ [25]) show antiferromagnetic (AFM) transitions at lower temperatures of about 12 K. Therefore, there should be a noticeable involvement of the A–A and A–B exchange interactions in Sm₂MnMn(MnTi₃)O₁₂ to stabilize the ferrimagnetic structure out of AFM one and to increase the magnetic transition temperature. In addition, Sm₂MnMn(MnTi₃)O₁₂ was the first example among A-site columnar-ordered quadruple perovskites, demonstrating relaxor-type dielectric properties with broad maxima on the temperature dependence of a dielectric constant near 220 K [22].

In this work, we investigated the effects of Cu²⁺ doping on the magnetic and dielectric properties of the parent Sm₂MnMn(MnTi₃)O₁₂ compound and prepared Sm₂CuMn(MnTi₃)O₁₂ using a high-pressure, high-temperature method. However, in this case, the magnetic properties of the parent compound were “degraded” by Cu²⁺ doping, as only spin-glass (SG) magnetic properties were observed below T_SG = 7 K. We attributed this degradation to antisite disorder. The relaxor-type dielectric properties of the parent compound disappeared, and Sm₂CuMn(MnTi₃)O₁₂ demonstrated a frequency and temperature independent dielectric constant between 10 K and 200 K, with a value of about 50.

2. Experimental

Sm₂CuMn(MnTi₃)O₁₂ was prepared using a high-pressure, high-temperature method using a belt-type high-pressure machine at 6 GPa and about 1700 K for 2 h in a Pt capsule. After annealing at 1700 K, the samples were quenched to room temperature (RT) by turning off the heating current, and the pressure was slowly released. Stoichiometric amounts of Sm₂O₃ (99.9%), CuO (99.9%), MnO (99.99%), and TiO₂ (99.9%) were used as an initial oxide mixture with the 1:1:2:3 ratio, respectively. Commercial Sm₂O₃, CuO, and TiO₂ chemicals were used. A single-phase MnO oxide was prepared from a commercial MnO₂ chemical by annealing at 1273 K for 4 h in a 20% H₂ + 80% Ar gas flow.

X-ray powder diffraction (XRPD) data were collected at RT with a RIGAKU MiniFlex600 diffractometer (CuKα radiation; a 2θ range of 8–100°; a step of 0.02°, and scan speed of 1°/min). The synchrotron XRPD data were collected at RT on the BL15XU beamline (the former NIMS beamline) of SPring-8 [26] between 2.04° and 60.23° at 0.003° intervals in 2θ with a wavelength of λ = 0.65298 Å. The data between 6° and 60.23° were used in the refinements as no reflections were observed and expected below 6°. The sample was inserted into a Lindemann glass capillary tube (inner diameter: 0.1 mm), which was rotated during the measurements. The Rietveld analysis of all XRPD data was performed using the RIETAN-2000 program [27].

Scanning electron microscopy (SEM) images and energy-dispersive X-ray (EDX) spectra were obtained on a Hitachi Miniscope TM3000 (operating at 15 kV).

SQUID magnetometers (Quantum Design, MPMS-XL-7T and MPMS3) were used for the magnetic measurements. Temperature dependence was measured between 2 and 400 K in applied fields of 100 Oe and 10 kOe under both zero-field-cooled (ZFC) and field-cooled on cooling (FCC) conditions on an MPMS-XL-7T. Magnetic-field dependence was measured at T = 2 K and 5 K between −70 and 70 kOe on MPMS3. Frequency dependent alternating current (ac) susceptibility measurements were performed on cooling with a Quantum Design MPMS3 instrument at different frequencies (f), different applied oscillating magnetic fields (H_ac), and different static dc field (H_dc). Relaxation curves were measured on MPMS3 using the following procedure: the sample was cooled down from 50 K to a measurement temperature at zero magnetic field, then a magnetic field of 100 Oe was applied, and magnetization was measured (as one scan within 2 s) as a function of time every 5 s.

Specific heat, C_p, was measured by cooling from 270 K to 2 K at zero magnetic field and from 150 K to 2 K at magnetic field of 90 kOe by a pulse relaxation method using a commercial calorimeter (Quantum Design PPMS).

The dielectric constant and dielectric loss were measured on a NOVOCONTROL Alpha-A High Performance Frequency Analyzer in a frequency range from 100 Hz to 665 kHz in a temperature range from 8 K to 330 K (on heating) at zero magnetic field.

3. Results and Discussion

The as-synthesized Sm₂CuMn(MnTi₃)O₁₂ contained a small amount of CuO impurity. In addition, the synchrotron XRPD pattern showed the presence of Pt impurity. However, Pt appeared from Pt capsules used in the synthesis and can be considered as an extrinsic impurity. The presence of a CuO impurity suggests that the main phase should be slightly Cu-deficient in comparison with the target composition. The morphology of the sample is shown in Figure 1. The particle sizes varied between about 10 and 50 μm. The Ti:Mn:Sm:Cu cation ratio determined with EDX was 3.24(8):2.02(5):1.96(4):0.77(7), respectively. These values were close to the nominal values within 3σ.

All of the reflections on the laboratory and synchrotron XRPD patterns (except CuO and Pt) could be indexed in a tetragonal system in space group P4₂/nmc (No. 137) (Figure 2). Sm₂CuMnMnTi₃O₁₂ was found to crystallize in the parent structure of the A-site columnar-ordered quadruple perovskites, A₂A′A″B₄O₁₂ [10]. Therefore, the structural data for the parent compound Sm₂MnMn(MnTi₃)O₁₂ [22,23] were taken as an initial starting model.

In the structural analysis, we first assumed ideal cation distributions (that is, Sm at the A site, Cu at the square-planar A′ site, Mn at the tetrahedral A″ site, and 0.75Ti + 0.25Mn at the octahedral B site) and refined the occupation factors (g) together with all of the other structural and nonstructural parameters (except g(B): one cation occupation factor should always be fixed to avoid significant correlations among the refined g parameters). In addition, in the structural analysis, we always assumed that Ti⁴⁺ cations were located at the B site, as Ti⁴⁺ cations strongly prefer octahedral sites [28].

The refined g values were as follows: g(Sm–A) = 0.9167(16), g(Cu–A′) = 0.914(7), and g(Mn–A″) = 1.047(7). These values suggest that the ideal cation distribution was not realized, and there were some antisite disorders. The g(Cu–A′) value suggested that this site should contain lighter elements that could only be Mn (with the above assumption on Ti). When only Mn was placed at the square-planar A′ site, the occupation factor was g(Mn–A′) = 1.112(8), meaning that heavier elements should also be at this site. Because it was difficult to precisely refine the distribution of Mn and Cu with X-ray diffraction, we introduced a virtual atom: MC = 0.5Mn + 0.5Cu. The precise distribution of Mn and Cu could only be determined with neutron diffraction. The disordering of cations at the Cu site was also observed as in many cases of such perovskites [21,22,25,29].

The refined structural parameters and primary bond lengths and angles in Sm₂CuMn(MnTi₃)O₁₂ are listed in Table 1 and Table 2. The experimental, calculated, and difference synchrotron patterns are shown in Figure 3. The crystal structure of Sm₂CuMn(MnTi₃)O₁₂ is illustrated in the inset of Figure 3.

Our model suggested that a small fraction of Cu²⁺ cations should be located at the B site. Indirect evidence for the location of Cu²⁺ cations at the octahedral site can be seen from the resulting Ti/MC–O bond lengths. In the parent and related compounds, R₂MnMn(MnTi₃)O₁₂ (R = Nd, Sm, Eu, and Gd), the Ti/Mn–O bond lengths were about 1.99, 2.01, and 2.01 Å (from both the synchrotron [22,29] and neutron [23] diffraction data), resulting in an octahedral distortion parameter, Δ, of about 0.2 × 10^–4. On the other hand, in Sm₂CuMn(MnTi₃)O₁₂, the Ti/MC–O bond lengths were about 1.95, 1.99, and 2.02 Å resulting in Δ of about 2.0 × 10^–4. This rise in the octahedral distortion could be caused by the presence of a small amount of Jahn–Teller active Cu²⁺ cations at this site.

Magnetic susceptibility curves, χ versus T, of Sm₂CuMn(MnTi₃)O₁₂ under applied magnetic fields of 0.1 kOe and 10 kOe are shown on Figure 4. There was a divergence between the 100 Oe ZFC and FCC curves at 7 K and a relatively sharp maximum on the 100 Oe ZFC curve at 7 K. A divergence between the ZFC and FCC curves almost disappeared under 10 kOe. These features are typical for spin-glass transitions [30,31,32]. Isothermal magnetization, M versus H, curves demonstrated an extended S-type shape with very weak and narrow hysteresis (Figure 5). Almost no hysteresis was observed at 5 K because 5 K was close to its T_SG = 7 K; on the other hand, the hysteresis was noticeably wider at a lower temperature of 2 K. Such M versus H curves are also typical for spin glasses [30,31,32].

The inverse magnetic susceptibilities (χ⁻¹ versus T) followed the Curie–Weiss law at high temperatures (Figure 4). To obtain the effective magnetic moment and the Curie–Weiss temperature, we performed fits between 250 and 345 K using the 10 kOe FCC curves (the fit and fitting parameters are summarized on Figure 4). The experimental effective magnetic moment was close to the expected one (8.803 μ_B; in the calculations we used 1.5 μ_B for Sm³⁺ [33]). The negative Curie–Weiss temperature shows that the main magnetic interactions were antiferromagnetic in nature. The ratio between the Curie–Weiss temperature (−81.5 K) and T_SG (the so-called frustration ratio) was about 11, indicating a strong degree of magnetic frustration. We note that CuO was in an antiferromagnet with transition temperatures of 213 K and 230 K. Therefore, CuO impurity should not affect the reported magnetic properties at low temperatures.

To confirm the spin-glass nature of the sample, we measured ac magnetic susceptibility curves (Figure 6 and Figure 7). We note that no dependence of the χ′ and χ″ values on the applied H_ac field was observed (inset of Figure 6). We indeed observed typical features of spin-glasses: peak positions were frequency-dependent and shifted to higher temperatures with increasing frequency; in addition, peak intensity was suppressed on the χ′ versus T curves and enhanced on the χ″ versus T curves with increasing frequency. All of these features are typical for spin glasses [30,31,32]. In addition, the shape of the χ′ versus T and the χ″ versus T curves was also typical for spin glasses. The criterion, which quantifies the relative change of the spin-glass temperature per frequency decade and is defined as ΔT_SG/[T_SGΔlog(f)], was about 0.023 for Sm₂CuMn(MnTi₃)O₁₂ (with T_SG = 7.2 K at f = 2 Hz and T_SG = 7.6 K at f = 500 Hz). This value is often observed in different spin-glass materials [30,31,32].

Sm₂CuMn(MnTi₃)O₁₂ shows time-dependent magnetic properties below T_SG, namely magnetization relaxation (Figure 8). Above T_SG, no noticeable relaxation of magnetization was detected. Time-dependent magnetic properties, such as relaxation, are typical features of spin-glass systems. Relaxation below T_SG was fitted by the stretched exponential function, f(t) = M₀ − M_SG × exp[−(t/t_r)^β] [30], and the resultant parameters are listed on Table 3. The most important parameter is the mean relaxation time, t_r, and it decreases monotonically with increasing temperature.

The specific heat data showed a noticeable magnetic contribution to the total specific heat below about 20 K, where it could be clearly seen as a rise in C_p/T values below 20 K (Figure 9). No λ-type anomaly was detected in the C_p versus T curve (inset of Figure 9, a green curve). Instead, a broad anomaly was seen in the C_p versus T curve, which gave a broad peak centered at 4 K in the C_p/T versus T curve. Therefore, specific heat measurements confirmed the absence of long-range magnetic ordering. A magnetic field of 90 kOe slightly suppressed the peak near 4 K and moved the magnetic entropy into the 14–40 K range.

The temperature dependence of the dielectric constant and dielectric loss is shown in Figure 10. The dielectric constant was nearly temperature and frequency-independent between 8 and 200 K. Above about 200 K, a sharp rise in the dielectric constant was observed, where the magnitude of the rise depended on frequency. This behavior typically originates from the Maxwell–Wagner contribution due to increased conductivity. No broad anomalies were observed in Sm₂CuMn(MnTi₃)O₁₂ in comparison with the parent compound Sm₂MnMn(MnTi₃)O₁₂. This fact shows that Cu²⁺ doping drastically modified the dielectric properties as well, in addition to the magnetic properties. We note that Pt impurity was only observed in a powder sample, which could contain parts from the surface. The surfaces of a pellet used for dielectric measurements were polished. Therefore, Pt impurity should not present in a pellet and affect dielectric measurements.

Spin-glass magnetic properties were also observed in Sm₂MnZn(MnTi₃)O₁₂ at T_SG = 6.5 K, with a significant antisite disorder [34]. This fact shows that antisite structural disorder should play a major role in the modification of magnetic properties of the parent Sm₂MnMn(MnTi₃)O₁₂ compound, not the nature of dopant cations (magnetic as Cu²⁺ or non-magnetic as Zn²⁺). Both Sm₂CuMn(MnTi₃)O₁₂ and Sm₂MnZn(MnTi₃)O₁₂ demonstrated similar low-temperature specific heat features (Figure 9b).

The beneficial effects of Cu²⁺ doping in RMn₇O₁₂ [13,14], RMn₃O₆ [11,12,15], and Y₂MnGaMn₄O₁₂ [20,21] originate from the fact that Cu²⁺ doping is aliovalent doping, which produces Mn⁴⁺ cations. A mixture of Mn³⁺ and Mn⁴⁺ at the B sites of perovskites significantly enhanced the exchange interactions and magnetic transition temperatures. On the other hand, Cu²⁺ doping in the parent Sm₂MnMn(MnTi₃)O₁₂ compound was isovalent doping. Such doping did not change the oxidation state of Mn, while the antisite disordering “degraded” the magnetic properties.

4. Conclusions

A new member of the A-site columnar-ordered quadruple perovskite family, Sm₂CuMn(MnTi₃)O₁₂, was prepared using a high-pressure, high-temperature method. Cu²⁺ doping significantly modified the properties of the parent Sm₂MnMn(MnTi₃)O₁₂ compound, as spin-glass magnetic properties at T_SG = 7 K were observed in Sm₂CuMn(MnTi₃)O₁₂ in comparison with the long-range ferrimagnetic order at T_C = 34–40 K in Sm₂MnMn(MnTi₃)O₁₂. In addition, relaxor-like dielectric properties of Sm₂MnMn(MnTi₃)O₁₂ disappeared in Sm₂CuMn(MnTi₃)O₁₂, which showed a nearly temperature and frequency-independent dielectric constant between 8 and 200 K with a value of about 50.

Author Contributions

A.A.B.: investigation, data analysis, conceptualization, supervision, writing—original draft, and writing—review and editing. R.L.: investigation. K.Y.: investigation, funding acquisition. All authors have read and agreed to the published version of the manuscript.

Funding

This study was partly supported by JSPS KAKENHI grant numbers JP20H05276 and JP22H04601.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are available from A.A.B. upon reasonable request.

Acknowledgments

This study was partly supported by JSPS KAKENHI grant numbers JP20H05276 and JP22H04601. The synchrotron radiation experiments were conducted at the former NIMS beamline (BL15XU) of SPring-8 with the approval of the former NIMS Synchrotron X-ray Station (proposal numbers: 2019A4501 and 2019B4500). We thank Y. Katsuya and M. Tanaka for their help at SPring-8.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Scanning electron microscopy (SEM) images of the fractured surface of the as-synthesized Sm₂CuMn(MnTi₃)O₁₂ sample. The scale bars are 100 µm (left) and 30 µm (right); magnification is 1000 (left) and 2000 (right). The surface is partially polished in the right panel. No polishing has been done in the left panel.

Figure 2. Laboratory powder X-ray diffraction pattern of Sm₂CuMn(MnTi₃)O₁₂ in a 2θ range from 14° to 60.5°. Possible Bragg reflection positions for Sm₂CuMn(MnTi₃)O₁₂ (the first row) and CuO impurities (the second row) are shown. The (hkl) indices of all of the observed reflections of Sm₂CuMn(MnTi₃)O₁₂ are given.

Figure 3. Full experimental (black crosses), calculated (red line), and difference (blue line at the bottom) room-temperature synchrotron powder X-ray diffraction patterns of Sm₂CuMn(MnTi₃)O₁₂ in a 2θ range of 6° and 60°. The brown tick marks show possible Bragg reflection positions for the main phase, the blue tick marks are for CuO impurity (2.0 wt.%), and the green ones are for Pt impurity (0.3 wt.%). The inset shows a tetragonal crystal structure of Sm₂CuMn(MnTi₃)O₁₂; TiO₆ octahedra (gray), MnO₄ tetrahedra (green), and ideal CuO₄ square-planar units (red) are plotted; Sm atoms are given by black circles; split Cu sites are shown by yellow circles.

Figure 4. The left-hand axis shows the ZFC (filled symbols) and FCC (empty symbols) dc magnetic susceptibility curves (χ = M/H) of Sm₂CuMn(MnTi₃)O₁₂ at 100 Oe (black) and 10 kOe (red). The right-hand axis gives the 10 kOe FCC χ⁻¹ versus T curve with the Curie–Weiss fit between 250 K and 345 K (black line). Parameters of the fits are shown on the figure. The inset shows details below 30 K.

Figure 5. M versus H curves of Sm₂CuMn(MnTi₃)O₁₂ at T = 2 K (black) and T = 5 K (red) (f.u.: formula unit). The inset shows details near the origin. Parameters of the M versus H curve at T = 2 K are given: M_S is the magnetization value at H = 70 kOe, M_R is the remnant magnetization, and H_C is the coercive field.

Figure 6. (a) Real (χ′) and (b) imaginary (χ″) parts of the ac magnetic susceptibility curves of Sm₂CuMn(MnTi₃)O₁₂ at different frequencies. The insets in (a,b) show the χ′ versus T and χ″ versus T curves at different H_ac = 0.05, 0.5, and 5 Oe and one frequency (f = 300 Hz) (the χ″ data at H_ac = 0.05 Oe are not shown because they were too noisy).

Figure 7. (a–d) χ′ versus T curves of Sm₂CuMn(MnTi₃)O₁₂ at f = 2 Hz and 500 Hz and different bias dc fields: (a) H_dc = 0 Oe, (b) 100 Oe, (c) 1 kOe, and (d) 10 kOe. Insets show χ″ versus T curves (the χ″ data at f = 2 Hz and H_dc = 10 kOe were too noisy and not shown). (e) All χ′ versus T curves at f = 500 Hz are shown in one figure. (f) All χ″ versus T curves at f = 500 Hz are shown in one figure.

Figure 8. Relaxation curves defined as 100 × [M(t) − M(0)]/M(0) versus time (t) for Sm₂CuMn(MnTi₃)O₁₂ at temperatures of 2, 3, 4, 5, 6, 7, and 10 K. Experimental points are given by symbols, and the red line shows the fit at 3 K as an example. The equation used for fitting and the resultant parameters are listed in Table 3.

Figure 9. (a) C_p/T versus T curves of Sm₂CuMn(MnTi₃)O₁₂ at H = 0 Oe (red triangles) and 90 kOe (blue triangles) in comparison with the parent compound Sm₂MnMn(MnTi₃)O₁₂ at H = 0 Oe (black circles) and 90 kOe (brown circles). C_p is the total specific heat. The arrows show the positions of the magnetic anomalies. The inset shows the C_p/T versus T curve at H = 0 Oe below 30 K, and the C_p versus T curve at H = 0 Oe (green circles). For the C_p versus T curve, the C_p values were divided by 20, and the C_p unit is J K⁻¹ mol⁻¹. (b) Comparison of C_p/T versus T data for Sm₂CuMn(MnTi₃)O₁₂ (red triangles) and Sm₂MnZn(MnTi₃)O₁₂ (black circles) [34] at H = 0 Oe.

Figure 10. Temperature dependence of the dielectric constant at different frequencies in Sm₂CuMn(MnTi₃)O₁₂. The inset shows temperature dependence of dielectric loss in the logarithmic scale.

Table 1. Structure parameters of Sm₂CuMn(MnTi₃)O₁₂ from synchrotron powder diffraction data (λ = 0.65298 Å) at room temperature.

Crystal system	Tetragonal
Space group	P4₂/nmc (No. 137, cell choice 2)
Z	2
Caclulated density (g/cm³)	6.15
Formula weight (g/cm³)	809.737
Used d range (Å)	0.6507–6.238
a (Å)	7.53477(1)
c (Å)	7.69788(1)
V (Å³)	437.0301(8)
g(Sm)	0.9413(9)Sm + 0.0587Mn
z(Sm)	0.22194(4)
B(Sm) (Å²)	0.796(7)
g(Cu)	0.4597MC + 0.0403Sm
z(Cu)	0.7804(3)
B(Cu) (Å²)	1.25(7)
g(Mn)	0.963(3)Mn + 0.037Sm
B(Mn) (Å²)	0.38(6)
g(Ti)	0.25MC + 0.75Ti
B(Ti) (Å²)	0.400(9)
y(O1)	0.0571(3)
z(O1)	−0.0379(3)
B(O1) (Å²)	0.33(5)
y(O2)	0.5363(3)
z(O2)	0.5745(3)
B(O2) (Å²)	0.36(5)
x(O3)	0.44161(23)
B(O3) (Å²)	1.48(7)
R_wp (%)	3.16
R_p (%)	2.17
R_I (%)	2.63
R_F (%)	1.69

The Sm site is in the 4d site (0.25, 0.25, z); Cu is in the 4c site (0.75, 0.25, z); Mn is in the 2b site (0.75, 0.25, 0.25); Ti is in the 8e site (0, 0, 0); O1 and O2 are in the 8g site (0.25, y, z), and O3 is in the 8f site (x, −x, 0.25). g is the occupation factor. g(O1) = 1, g(O2) = 1, and g(O3) = 1. MC is a virtual atom: 0.5Mn + 0.5Cu.

Table 2. Bond lengths (in Å), bond angles (in deg), and distortion parameters of TiO₆ (Δ) in Sm₂CuMn(MnTi₃)O₁₂ at room temperature.

Sm–O1 × 2	2.352(3)
Sm–O1 × 2	2.472(2)
Sm–O2 × 2	2.437(2)
Sm–O3 × 4	2.744(1)
Cu–O3 × 4	2.055(2)
Mn–O2 × 4	2.102(3)
Ti–O1 × 2	1.954(1)
Ti–O2 × 2	1.988(1)
Ti–O3 × 2	2.023(1)
Δ(TiO₆)	2.0 × 10⁻⁴
Ti–O1–Ti × 2	149.17(9)
Ti–O2–Ti × 2	142.75(9)
Ti–O3–Ti × 2	144.17(9)

Table 3. Results of the fittings of the relaxation curves of Sm₂CuMn(MnTi₃)O₁₂ at different temperatures.

T (K)	M₀	M_SG	t_r (s)	β
2	22.80(13)	23.67(18)	1270(24)	0.4362(4)
3	26.01(12)	27.20(20)	979(16)	0.4461(4)
4	22.81(10)	23.94(18)	800(11)	0.4495(4)
5	17.74(6)	18.62(13)	671(8)	0.4558(4)
6	12.34(14)	13.01(9)	554(6)	0.4654(4)

The fitting equation is f(t) = M₀ − M_SG × exp[−(t/t_r)^β] [30] applied to the 100 × [M(t) − M(0)]/M(0) versus time (t) curves.

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Belik, A.A.; Liu, R.; Yamaura, K. Dielectric and Spin-Glass Magnetic Properties of the A-Site Columnar-Ordered Quadruple Perovskite Sm₂CuMn(MnTi₃)O₁₂. Materials 2022, 15, 8306. https://doi.org/10.3390/ma15238306

AMA Style

Belik AA, Liu R, Yamaura K. Dielectric and Spin-Glass Magnetic Properties of the A-Site Columnar-Ordered Quadruple Perovskite Sm₂CuMn(MnTi₃)O₁₂. Materials. 2022; 15(23):8306. https://doi.org/10.3390/ma15238306

Chicago/Turabian Style

Belik, Alexei A., Ran Liu, and Kazunari Yamaura. 2022. "Dielectric and Spin-Glass Magnetic Properties of the A-Site Columnar-Ordered Quadruple Perovskite Sm₂CuMn(MnTi₃)O₁₂" Materials 15, no. 23: 8306. https://doi.org/10.3390/ma15238306

APA Style

Belik, A. A., Liu, R., & Yamaura, K. (2022). Dielectric and Spin-Glass Magnetic Properties of the A-Site Columnar-Ordered Quadruple Perovskite Sm₂CuMn(MnTi₃)O₁₂. Materials, 15(23), 8306. https://doi.org/10.3390/ma15238306

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