钙钛矿锰氧化物的磁相变临界行为及磁热效应研究进展

张鹏; 朴红光; 张英德; 黄焦宏

doi:10.7498/aps.70.20210097

摘要

钙钛矿锰氧化物具备磁热效应高、性能稳定可控、成本低廉等显著优点, 是适用于室温磁制冷领域的优质候选工质材料之一. 但该体系内部电磁学性质复杂, 特别是关于铁磁相互作用机制和磁相变性质等关键科学问题仍然有待深入探索. 分析磁相变临界行为有利于揭示磁性材料内部的铁磁相互作用距离和机制等重要信息. 本文简要介绍了钙钛矿锰氧化物相关理论背景以及各种磁相变临界行为分析方法, 随后归纳了近年来多种钙钛矿锰氧化物的磁相变临界行为研究, 系统对比了不同带宽典型锰氧化物在单晶和多晶形态下的磁相变临界行为, 讨论了A/B位掺杂不同元素以及不同制备工艺条件对其临界参数的影响, 对其中渡越于一级和二级相变的La-Ca-Mn-O体系在不同磁场范围下的临界参数演化进行了讨论. 最后对处于磁相变三重临界点附近的部分锰氧化物材料的磁热效应研究进行了总结和展望.

关键词:

Abstract

Hole-doped perovskite-type manganites have received intensive attention due to their intriguing physical phenomena such as giant magnetocaloric effect and magnetic-phase transitions. However, the mechanism of internal ferromagnetic interaction still needs to be further explored due to the complex natures of competing double-exchange (DE) and super-exchange (SE) interaction, Jahn-Teller (JT) polaron localization, charge ordering, and phase separation scenarios. Critical exponent analysis near magnetic phase transition is a powerful tool to investigate the details of the ferromagnetic interactions and has been used frequently in various magnetocaloric materials. In this article, the critical behavior analyses of perovskite manganites in recent years are comprehensively reviewed. A large number of studies have shown that even in single-phase materials with uniform structure and composition, the critical behavior can be affected by multiple factors such as grain boundary density and the degree of disorder, making them difficult to fully describe the intrinsic ferromagnetism. In this review, firstly, the critical behaviors of typical manganites with different bandwidths in single crystal and polycrystalline are discussed. In a double-exchange dominated system such as La-Sr-Mn-O, short-range 3D-Heisenberg model is basically in good accordance with optimally-doped single crystal sample. However, it would be replaced by long-range mean-field critical behavior in polycrystalline sample when the correlation length exceeds the crystallite size. In a typical intermediate bandwidth system such as La-Ca-Mn-O exhibiting a complex phase diagram described by competing SE/DE interactions, JT polaron localization/delocalization, and Griffith phase disorder, the critical exponent can vary from 3D-Heisenberg model to tricritical mean-field model, for the crossover from first to second order phase transition. Secondly, the studies of elements doping and different fabrication methods indicate that the critical behavior of manganites can be effectively modulated, and vary between different theoretical models including even nonuniversal exponent for highly disordered magnetic system. In the following part, the influence of magnetic field on the critical behavior and field induced crossover phenomena of La-Ca-Mn-O system near tricritical point is analyzed and discussed in detail. Furthermore, the magnetocaloric effects of materials near the tricritical point collected in many studies are listed and compared with each other. Excellent magnetocaloric properties with high magnetic entropy change and relative cooling power in plenty of researches indicate that ideal magnetocaloric material would be very likely to be found in the materials near the tricritical point, which lay at the borderline between first-order and second-order phase transition. Consequently, it is suggested that perovskite manganites are still quite promising in the potential magnetic refrigeration applications, and need to be further developed.

Keywords:

作者及机构信息

1.
湖北工业大学理学院, 武汉　430068

2.
三峡大学理学院, 磁电子与纳磁探测研究所, 宜昌　443002

3.
包头稀土研究院, 包头　014030

通信作者: 朴红光, hgpiao@ctgu.edu.cn

基金项目: 湖北省自然科学基金(批准号: ZRMS2018001866)、湖北工业大学博士启动金(批准号: BSQD13030)和国家重点研发计划(批准号: 2017YFB0903702)资助的课题

Authors and contacts

1.
School of Science, Hubei University of Technology, Wuhan 430068, China

2.
Research Institute for Magnetoelectronics & Weak Magnetic-field Detection, College of Science, China Three Gorges University, Yichang 443002, China

3.
Baotou Research Institute of Rare Earths, Baotou 014030, China

Corresponding author: Piao Hong-Guang, hgpiao@ctgu.edu.cn

Funds: Project supported by the Natural Science Foundation of Hubei Province, China (Grant No. ZRMS2018001866), the Doctoral Research Startup Fund of Hubei University of Technology, China (Grant No. BSQD13030), and the National Key R&D Program of China (Grant No. 2017YFB0903702)

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施引文献

图 1 理想钙钛矿ABO₃立方结构示意图

Fig. 1. Ideal perovskite ABO₃ cubic structure.

下载: 全尺寸图片幻灯片

图 2 不同带宽钙钛矿锰氧化物的典型磁相图　(a)大带宽型La_1–_xSr_xMnO₃; (b)中等带宽型La_1–_xCa_xMnO₃; (c)小带宽型Pr_1–_xCa_xMnO₃^[15]

Fig. 2. Typical magnetic phase diagrams of different bandwidth manganites: (a) Large bandwidth La_1–_xSr_xMnO₃; (b) intermediate bandwidth La_1–_xCa_xMnO₃; (c) small bandwidth Pr_1–_xCa_xMnO₃^[15].

下载: 全尺寸图片幻灯片

图 3 三重临界点的示意图

Fig. 3. Schematic diagram of Tricritical point.

下载: 全尺寸图片幻灯片

表 1 典型理论模型的临界参数

Table 1. Critical parameters of theoretical models.

Model	β	γ	δ	Ref.
Mean-field	0.5	1.0	3.0	[23]
Tricritical-Mean-field	0.25	1.0	5.0	[23]
3D-Heisenberg	0.365	1.386	4.80	[24]
3D-Ising	0.325	1.241	4.82	[24]

下载: 导出CSV

表 2 典型锰氧化物材料在各种形态下的临界行为分析

Table 2. Critical behavior analysis of manganites in different morphologies (SC, single crystal; PC, polycrystalline).

Material	Technique	β	γ	δ	Model	Ref.
La_0.7Ba_0.3MnO₃^SC	MAP	0.35	1.41	5.5	3D-Heisenberg	[26]
La_0.7Ba_0.3MnO₃^PC	MAP	0.493	1.059	3.15	Mean-field	[27]
La_0.67Ba_0.33MnO₃^PC	MAP	0.464	1.29	3.78	Mean-field/3D-Heisenberg	[28]
La_0.7Sr_0.3MnO₃^SC	MAP	0.37	1.22	4.25	close to 3D-Heisenberg	[29]
La_0.75Sr_0.25MnO₃^SC	MAP	0.4	1.27	4.12	Mean-field/3D-Ising	[30]
La_0.8Sr_0.2MnO₃^PC	MAP	0.5	1.08	3.13	Mean-field	[31]
La_0.875Sr_0.125MnO₃^SC	MAP	0.37	1.38	4.72	3D-Heisenberg	[32]
La_0.6Ca_0.4MnO₃^PC	MAP	0.25	1.03	5	Tricritical-Mean-field	[33]
La_0.79Ca_0.21MnO₃^SC	MAP	0.09	1.71	20	nonuniversal	[34]
La_0.8Ca_0.2MnO₃^SC	MAP	0.374	1.382	4.779	3D-Heisenberg	[35]
La_0.82Ca_0.18MnO₃^SC	MAP	0.374	1.379	4.783	3D-Heisenberg	[35]
Nd_0.6Sr_0.4MnO₃^SC	KF	0.308	1.172	4.75	3D-Ising	[36]
Nd_0.6Sr_0.4MnO₃^PC	MAP	0.51	1.01	3.13	Mean-field	[37]
Nd_0.67Sr_0.33MnO₃^PC	MAP	0.23	1.05	5.13	Tricritical-Mean-field	[37]
Nd_0.7Sr_0.3MnO₃^PC	MAP	0.271	0.922	4.4	Tricritical-Mean-field	[38]
Pr_0.6Sr_0.4MnO₃^SC	KF	0.312	1.106	4.545	3D-Ising	[36]
Pr_0.6Sr_0.4MnO₃^SC	MAP	0.365	1.309	4.648	3D-Heisenberg	[39]
Pr_0.6Sr_0.4MnO₃^PC	MAP	0.276	0.918	4.325	Tricritical-Mean-field	[40]
Pr_0.6Sr_0.4MnO₃^PC	KF	0.273	1.001	4.325	Tricritical-Mean-field	[40]
Pr_0.71Ca_0.29MnO₃^SC	MAP	0.37	1.38	4.62	3D-Heisenberg	[41]
Pr_0.71Ca_0.29MnO₃^PC	MAP	0.521	0.912	2.71	Mean-field	[42]
Pr_0.73Ca_0.27MnO₃^SC	MAP	0.36	1.36	4.81	3D-Heisenberg	[41]
Pr_0.73Ca_0.27MnO₃^PC	MAP	0.362	1.132	4.09	3D-Heisenberg	[42]
注: SC表示单晶; PC表示多晶.

下载: 导出CSV

表 3 A位掺杂不同元素或空位的锰氧化物临界行为分析

Table 3. Critical behavior analysis of manganites doped with different elements (vacancy) at A site (□, Ion vacancy).

Material	Technique	β	γ	δ	Model	Ref.
La_0.67(Ca_0.5Ba_0.5)_0.33MnO₃	MAP	0.402	1.110	3.761	Mean-field/3D-Heisenberg	[28]
La_0.7Ca_0.15Ba_0.15MnO₃	MAP	0.438	1.032	3.360	Mean-field	[27]
La_0.7Ca_0.2Ba_0.1MnO₃	MAP	0.284	0.909	4.200	Tricritical-Mean-field/3D-Ising	[43]
La_0.7Ca_0.2Ba_0.1MnO₃	KF	0.297	0.925	4.110	Tricritical-Mean-field/3D-Ising	[43]
La_0.7Ca_0.15Sr_0.15MnO₃	MAP	0.491	1.054	3.150	Mean-field	[27]
La_0.7Ca_0.1Sr_0.2MnO₃	KF	0.360	1.220	4.400	3D-Heisenberg	[44]
La_0.7Ca_0.2Sr_0.1MnO₃	KF	0.260	1.060	5.100	Tricritical-Mean-field	[44]
La_0.69Dy_0.01Ca_0.3MnO₃	MAP	0.230	0.920	5.000	Tricritical-Mean-field	[45]
La_0.69Dy_0.01Ca_0.3MnO₃	KF	0.250	0.870	4.480	Tricritical-Mean-field	[45]
La_0.7Ca_0.28Sn_0.02MnO₃	KF	0.218	0.858	4.936	Tricritical-Mean-field	[46]
La_0.7Ca_0.26Sn_0.04MnO₃	KF	0.467	1.095	3.345	Mean-field	[46]
La_0.75Dy_0.05Sr_0.2MnO₃	MAP	0.266	0.920	4.460	Tricritical-Mean-field	[47]
La_0.75Dy_0.05Sr_0.2MnO₃	KF	0.272	0.931	4.420	Tricritical-Mean-field	[47]
La_0.1Nd_0.6Sr_0.3MnO₃	MAP	0.248	1.066	5.170	Tricritical-Mean-field	[48]
La_0.1Nd_0.6Sr_0.3MnO₃	KF	0.257	1.120	5.170	Tricritical-Mean-field	[48]
Pr_0.4Sm_0.15Sr_0.45MnO₃	KF	0.324	1.212	4.812	3D-Ising	[49]
Pr_0.3Sm_0.25Sr_0.45MnO₃	KF	0.255	0.957	5.105	Tricritical-Mean-field	[49]
La_0.57Nd_0.1Sr_0.33MnO₃	MAP	0.356	1.152	4.235	3D-Heisenberg	[50]
La_0.57Nd_0.1Sr_0.33MnO₃	KF	0.368	1.191	4.236	3D-Heisenberg	[50]
La_0.57Nd_0.1Sr_0.28□_0.05MnO₃	MAP	0.312	1.173	4.760	3D-Ising	[50]
La_0.57Nd_0.1Sr_0.28□_0.05MnO₃	KF	0.326	1.183	4.619	3D-Ising	[50]
Pr_0.6Sr_0.4MnO₃	MAP	0.276	0.918	4.325	Tricritical-Mean-field	[40]
Pr_0.6Sr_0.4MnO₃	KF	0.273	1.001	4.325	Tricritical-Mean-field	[40]
Pr_0.6Sr_0.3□_0.1MnO₃	MAP	0.253	0.987	4.890	Tricritical-Mean-field	[40]
Pr_0.6Sr_0.3□_0.1MnO₃	KF	0.242	0.945	4.890	Tricritical-Mean-field	[40]
Pr_0.5□_0.1Sr_0.4MnO₃	MAP	0.323	1.113	4.446	3D-Ising	[40]
Pr_0.5□_0.1Sr_0.4MnO₃	KF	0.325	1.092	4.446	3D-Ising	[40]
注: □表示离子空位.

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表 4 B位掺杂不同元素的锰氧化物临界行为分析

Table 4. Critical behavior analysis of manganites doped with different elements at B site.

Material	Technique	β	γ	δ	Model	Ref.
La_0.67Ba_0.33Mn_0.98Ti_0.02O₃	MAP	0.537	1.015	2.890	Mean-field	[51]
La_0.67Ba_0.33Mn_0.98Ti_0.02O₃	KF	0.551	1.020	2.851	Mean-field	[51]
La_0.67Ba_0.33Mn_0.95Fe_0.05O₃	KF	0.504	1.013	3.040	Mean-field	[52]
La_0.7Ba_0.3Mn_0.95Ti_0.05O₃	MAP	0.374	1.228	4.260	3D-Heisenberg	[53]
La_0.7Ba_0.3Mn_0.9Ti_0.1O₃	MAP	0.339	1.307	4.780	3D-Ising	[53]
La_0.8Ba_0.2Mn_0.8Fe_0.2O₃	MAP	0.365	1.227	4.362	3D-Heisenberg	[54]
La_0.8Ba_0.2Mn_0.8Fe_0.2O₃	KF	0.318	1.159	4.645	3D-Heisenberg	[54]
La_0.67Sr_0.33Mn_0.9Fe_0.1O₃	MAP	0.450	1.240	3.740	Mean-field/3D-Heisenberg	[55]
La_0.67Sr_0.33Mn_0.9Fe_0.1O₃	KF	0.538	1.330	3.470	Mean-field/3D-Heisenberg	[55]
La_0.7Sr_0.3Mn_0.95Al_0.05O₃	KF	0.458	1.001	3.185	Mean-field	[56]
La_0.7Sr_0.3Mn_0.95Ti_0.05O₃	KF	0.344	1.149	4.340	Mean-field/3D-Heisenberg	[56]
La_0.7Sr_0.3Mn_0.9Co_0.1O₃	KF	0.457	1.114	3.440	Mean-field/3D-Heisenberg	[57]
La_0.7Sr_0.3Mn_0.99Ni_0.01O₃	MAP	0.394	1.092	3.990	Mean-field/3D-Heisenberg	[58]
La_0.7Sr_0.3Mn_0.98Ni_0.02O₃	MAP	0.400	1.082	3.790	Mean-field/3D-Heisenberg	[58]
La_0.7Sr_0.3Mn_0.97Ni_0.03O₃	MAP	0.468	1.010	2.670	Mean-field	[58]
La_0.7Sr_0.3Mn_0.98Cu_0.02O₃	KF	0.464	1.162	3.546	close to Mean-field	[59]
La_0.7Sr_0.3Mn_0.96Cu_0.04O₃	KF	0.449	1.202	3.681	close to Mean-field	[59]
La_0.67Ca_0.33Mn_0.9Cr_0.1O₃	MAP	0.555	1.170	2.710	Mean-field	[60]
La_0.67Ca_0.33Mn_0.75Cr_0.25O₃	MAP	0.680	1.090	2.936	close to Mean-field	[60]
La_0.67Ca_0.33Mn_0.9Ga_0.1O₃	MAP	0.380	1.365	4.590	3D-Heisenberg	[61]
La_0.67Ca_0.33Mn_0.9Ga_0.1O₃	KF	0.387	1.362	4.520	3D-Heisenberg	[61]
La_0.7Ca_0.3Mn_0.95Ti_0.05O₃	KF	0.601	1.171	2.950	Mean-field	[62]
La_0.7Ca_0.3Mn_0.9Ti_0.1O₃	KF	0.389	1.403	4.400	3D-Heisenberg	[62]
La_0.7Ca_0.3Mn_0.91Ni_0.09O₃	MAP	0.171	0.976	6.700	Tricritical-Mean-field	[63]
La_0.7Ca_0.3Mn_0.88Ni_0.12O₃	MAP	0.262	0.978	4.700	Tricritical-Mean-field	[63]
La_0.7Ca_0.3Mn_0.85Ni_0.15O₃	MAP	0.320	0.990	4.100	3D-Ising	[63]
La_0.7Ca_0.3Mn_0.95Cu_0.05O₃	MAP	0.490	1.040	3.120	Mean-field	[64]
La_0.7Ca_0.3Mn_0.9Zn_0.1O₃	MAP	0.474	1.152	3.430	Mean-field	[65]
La_0.8Ca_0.2Mn_0.9Co_0.1O₃	MAP	0.204	1.969	11.983	nonuniversal	[66]
La_0.8Ca_0.2Mn_0.9Co_0.1O₃	KF	0.123	1.351	11.983	nonuniversal	[66]
La_0.8Ca_0.2Mn_0.8Co_0.2O₃	MAP	0.401	1.332	4.321	3D-Heisenberg	[66]
La_0.8Ca_0.2Mn_0.8Co_0.2O₃	KF	0.418	1.303	4.321	3D-Heisenberg	[66]
Nd_0.67Sr_0.33Mn_0.9Cr_0.1O₃	MAP	0.337	0.784	3.326	nonuniversal	[67]
Nd_0.67Sr_0.33Mn_0.9Fe_0.1O₃	MAP	0.436	0.94	3.156	Mean-field	[67]
Nd_0.67Sr_0.33Mn_0.9Co_0.1O₃	MAP	0.431	0.929	3.155	Mean-field	[67]
Pr_0.67Sr_0.33Mn_0.95Al_0.05O₃	MAP	0.381	1.323	4.635	3D-Heisenberg	[68]
Pr_0.67Sr_0.33Mn_0.95Al_0.05O₃	KF	0.381	1.320	4.635	3D-Heisenberg	[68]
Pr_0.67Sr_0.33Mn_0.9Al_0.1O₃	MAP	0.374	1.333	4.667	3D-Heisenberg	[68]
Pr_0.67Sr_0.33Mn_0.9Al_0.1O₃	KF	0.377	1.331	4.667	3D-Heisenberg	[68]

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表 5 不同制备方法锰氧化物的临界行为对比分析

Table 5. Critical behavior analysis of manganites from different preparation methods (SS, solid state reaction; SG, sol-gel; WM, wet mixing; BM, ball milling).

Material	Technique	β	γ	δ	Model	Ref.
La_0.6Sr_0.4MnO₃^{SG/800 ºC}	KF	0.560	1.140	3.035	close to Mean-field	[69]
La_0.6Sr_0.4MnO₃^{SG/1100 ºC}	KF	0.480	1.052	3.190	Mean-field	[69]
La_0.6Sr_0.4MnO₃^SS	KF	0.530	1.110	3.094	Mean-field	[69]
La_0.67Sr_0.33MnO₃^SS	MAP	0.333	1.325	4.978	3D-Heisenberg	[70]
La_0.67Sr_0.33MnO₃^SG	MAP	0.500	1.150	3.290	Mean-field	[55]
La_0.67Sr_0.33MnO₃^SG	KF	0.479	1.260	3.630	Mean-field	[55]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^WM	MAP	0.448	1.148	3.563	Mean-field	[71]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^WM	KF	0.476	1.029	3.096	Mean-field	[71]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^SG	MAP	0.235	1.153	5.906	Tricritical-Mean-field	[71]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^SG	KF	0.262	1.165	5.447	Tricritical-Mean-field	[71]
La_0.7Ca_0.2Ba_0.1MnO₃^BM	MAP	0.265	0.867	4.271	Tricritical-Mean-field	[72]
La_0.7Ca_0.2Ba_0.1MnO₃^BM	KF	0.261	0.988	4.386	Tricritical-Mean-field	[72]
La_0.7Ca_0.2Ba_0.1MnO₃^SS	MAP	0.284	0.909	4.200	Tricritical-Mean-field/3D-Ising	[43]
La_0.7Ca_0.2Ba_0.1MnO₃^SS	KF	0.297	0.925	4.110	Tricritical-Mean-field/3D-Ising	[43]
La_0.7Ca_0.2Sr_0.1MnO₃^BM	MAP	0.397	0.966	3.430	3D-Heisenberg	[73]
La_0.7Ca_0.2Sr_0.1MnO₃^SS	MAP	0.276	0.966	4.500	Tricritical-Mean-field	[74]
La_0.7Ca_0.2Sr_0.1MnO₃^SS	KF	0.315	0.954	4.028	Tricritical-Mean-field	[74]
La_0.7Ca_0.2Sr_0.1MnO₃^SG	MAP	0.484	1.037	3.143	Mean-field	[74]
La_0.7Ca_0.2Sr_0.1MnO₃^SG	KF	0.469	1.013	3.160	Mean-field	[74]
La_0.7Ca_0.3MnO₃^{BM/40 nm}	MAP	0.485	1.051	3.100	Mean-field	[75]
La_0.7Ca_0.3MnO₃^{BM/16 nm}	MAP	0.621	0.825	2.200	nonuniversal	[75]
La_0.7Ca_0.3MnO₃^SG	MAP	0.240	1.010	3.090	Tricritical-Mean-field	[76]
La_0.75Ca_0.25MnO₃^SG	MAP	0.521	0.94	2.804	Mean-field	[77]
La_0.75Ca_0.25MnO₃^SG	KF	0.529	0.939	2.775	Mean-field	[77]
La_0.8Ca_0.2MnO₃^SG	MAP	0.505	1.004	3.060	Mean-field	[78]
La_0.8Ca_0.2MnO₃^SG	KF	0.499	1.007	3.060	Mean-field	[78]
Nd_0.7Ca_0.15Sr_0.15MnO₃^{BM/4 h}	KF	0.243	0.907	4.540	Tricritical-Mean-field	[79]
Nd_0.7Ca_0.15Sr_0.15MnO₃^{BM/24 h}	KF	0.311	1.100	4.130	3D-Ising	[79]
Pr_0.6Ca_0.1Sr_0.3Mn_0.975Fe_0.025O₃^SS	MAP	0.644	1.075	2.763	Mean-field	[80]
Pr_0.6Ca_0.1Sr_0.3Mn_0.975Fe_0.025O₃^SS	KF	0.622	1.097	2.763	Mean-field	[80]
Pr_0.6Ca_0.1Sr_0.3Mn_0.975Fe_0.025O₃^SG	MAP	0.357	1.292	4.290	3D-Heisenberg	[80]
Pr_0.6Ca_0.1Sr_0.3Mn_0.975Fe_0.025O₃^SG	KF	0.370	1.220	4.290	3D-Heisenberg	[80]
Pr_0.8Sr_0.2MnO₃^SG	MAP	0.260	0.978	4.760	Tricritical-Mean-field	[81]
Pr_0.8Sr_0.2MnO₃^SG	KF	0.260	0.993	4.810	Tricritical-Mean-field	[81]
Pr_0.8Sr_0.2MnO₃^SS	MAP	0.318	1.260	4.960	3D-Ising	[82]
Pr_0.8Sr_0.2MnO₃^SS	KF	0.326	1.246	4.960	3D-Ising	[82]
注: SS表示固相反应法; SG表示溶胶凝胶法(附烧结温度工艺条件); WM表示湿混法; BM表示球磨法(附平均粒径尺寸或球磨时间等工艺条件).

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表 6 关于不同磁场强度范围所得磁相变临界参数的对比分析

Table 6. Comparative analysis of critical parameters in different magnetic field ranges.

Material	Field range	Technique	β	γ	δ	Model	Ref.
La_0.6Ca_0.4MnO₃	1—2 T	KF	0.249	1.008	5.043	Tricritical-Mean-field	[83]
	2—3 T	KF	0.255	0.857	4.359	crossover
	3—4 T	KF	0.262	0.833	4.18	crossover
	4—5 T	KF	0.267	0.797	3.983	crossover
	5—6 T	KF	0.263	0.776	3.954	close to Tricritical-Mean-field
La_0.8Ca_0.2MnO₃	1—2 T	KF	0.349	1.231	4.524	3D-Heisenberg/Ising	[83]
	2—3 T	KF	0.316	1.081	4.421	crossover
	3—4 T	KF	0.281	0.992	4.534	crossover
	4—5 T	KF	0.272	0.91	4.341	crossover
	5—6 T	KF	0.259	0.918	4.552	Tricritical-Mean-field
La_0.7Ca_0.275Ba_0.025MnO₃	2—3 T	MAP	0.209	—	—	Tricritical-Mean-field	[84]
	3—4 T	MAP	0.218	1.098	6.04
	4—5 T	MAP	0.227	1.06	5.67
La_0.7Ca_0.25Ba_0.05MnO₃	1—2 T	MAP	0.221	—	—	Tricritical-Mean-field	[84]
	2—3 T	MAP	0.225	1.052	5.68
	3—4 T	MAP	0.235	1.012	5.31
	4—5 T	MAP	0.249	1.022	5.1
La_0.7Ca_0.225Ba_0.075MnO₃	1—2 T	MAP	0.216	0.973	5.5	Tricritical-Mean-field	[84]
	2—3 T	MAP	0.224	0.982	5.38
	3—4 T	MAP	0.238	1.016	5.27
	4—5 T	MAP	0.253	0.992	4.92
La_0.7Ca_0.2Ba_0.1MnO₃	1—2 T	MAP	0.301	1.382	5.59	Tricritical-Mean-field/3D-Ising	[84]
	2—3 T	MAP	0.312	1.38	5.42	3D-Ising
	3—4 T	MAP	0.322	1.381	5.29	3D-Ising
	4—5 T	MAP	0.326	1.342	5.12	3D-Ising
La_0.7Ca_0.3MnO₃	10—14 T	MAP	0.252	1.005	—	Tricritical-Mean-field	[85]

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表 7 接近三重临界点的部分近室温钙钛矿锰氧化物的最大磁熵变和相对制冷能力

Table 7. Maximum magnetic entropy change and RCP values of perovskite manganites near tricritical point.

Material	T_C/K	ΔH/ T	–ΔS_M/(J·kg^–1·K^–1)	RCP/(J·kg^–1)	Ref.
La_0.7Ba_0.2Ca_0.1MnO₃^SG	350	2	2.35	70	[87]
La_0.7Ba_0.2Ca_0.1MnO₃^SG	350	5	5.80	167	[87]
La_0.7Ba_0.2Ca_0.1Mn_0.95Al_0.05O₃^SG	321	2	2.12	85	[87]
La_0.7Ba_0.2Ca_0.1Mn_0.95Al_0.05O₃^SG	321	5	5.30	180	[87]
La_0.7Ba_0.2Ca_0.1Mn_0.9Al_0.1O₃^SG	300	2	1.86	96	[87]
La_0.7Ba_0.2Ca_0.1Mn_0.9Al_0.1O₃^SG	300	5	4.60	193	[87]
La_0.7Ca_0.3MnO₃^SS	255	1	4.52	45.2	[46]
La_0.7Ca_0.28Sn_0.02MnO₃^SS	200	1	2.79	55.8	[46]
La_0.7Ca_0.26Sn_0.04MnO₃^SS	167	1	1.58	69.5	[46]
La_0.69Dy_0.01Ca_0.3MnO₃^SS	246	5	14.94	100.24	[45]
La_0.6Ca_0.3Ag_0.1MnO₃^SS	256	2	3.89	55.51	[88]
La_0.6Ca_0.3Ag_0.1MnO₃^SS	256	5	6.95	179.78	[88]
La_0.6Ca_0.3Ag_0.1MnO₃^SG	270	2	5.55	84.46	[88]
La_0.6Ca_0.3Ag_0.1MnO₃^SG	270	5	8.67	230.35	[88]
La_0.6Ca_0.3Sr_0.1MnO₃^SG	304	2	2.89	98.17	[89]
La_0.6Ca_0.3Sr_0.1MnO₃^SG	304	5	5.26	262.53	[89]
La_0.7Ca_0.2Sr_0.1MnO₃^SS	284	3	4.30	150	[90]
La_0.7Ca_0.2Sr_0.1MnO₃^BM	297	1	1.47	54.4	[73]
La_0.7Ca_0.19Sr_0.11MnO₃^BM	301	1	1.42	52.5	[73]
La_0.7Ca_0.18Sr_0.12MnO₃^BM	309	1	1.38	44.2	[73]
La_0.7Ca_0.27Na_0.03MnO₃^SS	260	4	8.10	232	[91]
La_0.7Ca_0.24Na_0.06MnO₃^SS	263	4	7.00	234	[91]
La_0.7Ca_0.21Na_0.09MnO₃^SS	271	4	6.90	236	[91]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^WM	315	2	1.34	102.51	[71]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^WM	315	5	3.16	284.53	[71]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^SG	330	2	2.58	74.92	[71]
La_0.7Ba_0.1Ca_0.1Sr_0.1MnO₃^SG	330	5	4.89	229.29	[71]
La_0.8Na_0.2Mn_0.97Bi_0.03O₃^SS	320	5	4.77	218	[92]
La_0.8Na_0.2Mn_0.97Bi_0.03O₃^SG	257	5	5.88	252	[92]
La_0.4Pr_0.3Ca_0.1Sr_0.2MnO₃^SS	289	2	3.08	83.3	[86]
La_0.6Gd_0.1Sr_0.3Mn_0.8Si_0.2O₃^SG	271	5	5.35	180	[93]
La_0.7Bi_0.05Sr_0.15Ca_0.1Mn_0.95In_0.05O₃^SG	310	5	6.00	258	[94]
注: 1) 表中符号含义如下: T_C为居里温度; ΔH为磁场变化范围; –ΔS_M为最大磁熵变值; RCP为相对制冷能力, 由磁熵变曲线的峰值与半峰宽数值相乘而得; 2) SS表示固相反应法; SG表示溶胶凝胶法; WM表示湿混法; BM表示球磨法.

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