晶场劈裂序参量导致稀土-硼十二化合物中磁性和比热反常的理论研究

doi:10.15541/jim20200623

无机材料学报 ›› 2021, Vol. 36 ›› Issue (8): 865-870.DOI: 10.15541/jim20200623

晶场劈裂序参量导致稀土-硼十二化合物中磁性和比热反常的理论研究

胡靖三¹(), 顾建飞¹, 章维益¹^,²()

1. 物理学院, 南京大学, 南京 210093
2.固体微结构国家重点实验室, 南京大学, 南京 210093

收稿日期:2020-11-03 修回日期:2021-01-18 出版日期:2021-08-20 网络出版日期:2021-03-01
通讯作者: 章维益, 教授. E-mail: wyzhang@nju.edu.cn
作者简介:胡靖三(1994-), 男, 博士研究生. E-mail: b111120046@smail.nju.edu.cn
基金资助:
国家重点研发计划(2017YFA0303202)

Mechanism of the Magnetic and Speciﬁc-heat Anomalies in Rare-earth Dodecaborides RB₁₂ (R=Tb-Tm): an Effect of Crystal-ﬁeld-splitting Order Parameter

HU Jingsan¹(), GU Jianfei¹, ZHANG Weiyi¹^,²()

1. School of Physics, Nanjing University, Nanjing 210093, China
2. National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China

Received:2020-11-03 Revised:2021-01-18 Published:2021-08-20 Online:2021-03-01
Contact: ZHANG Weiyi, professor. E-mail: wyzhang@nju.edu.cn
About author:HU Jingsan (1994-), male, PhD candidate. E-mail: b111120046@smail.nju.edu.cn
Supported by:
National Key Research and Development Program of China(2017YFA0303202)

摘要/Abstract

摘要：

在低温条件(T_C≈3~22 K)下, 除了4f电子满壳层的LuB₁₂之外, 其他稀土-硼十二化合物(简称RB₁₂, R为稀土元素Tb, Dy, Ho, Er, Tm)存在磁性和比热的反常现象, 该反常现象的机制至今仍存争议。尽管磁化率曲线上的隆起与R³⁺离子的反铁磁序类似, 但是中子衍射谱和莫斯堡尔谱的实验均没有明确给出稀土离子的磁结构。这些化合物磁化率、熵的反常行为和低温中子谱的结果都与RB₁₂具有幅度调制的磁结构一致。本课题组采用模型和数值计算相结合的方法来探究该反常行为的物理机制。研究表明: 由于稀土离子meV量级的晶场劈裂易受热涨落扰动, 晶场劈裂能不再是一个量子力学参量, 而是一个热力学序参量。物理图像中轨道角动量逐渐淬灭很好地解释了磁性和比热的反常现象。结合该类晶体低温下在(111)晶向的二聚化行为和非弹性散射谱的结果, 对中子散射谱中的双峰结构也给予了一个可能的解释。

关键词: 稀土化合物, 固体磁性, 晶场劈裂, 序参量

Abstract:

Rare-earth dodecaborides RB₁₂ (R=Tb, Dy, Ho, Er, Tm) are all characterized by a controversial and unresolved magnetic and speciﬁc-heat anomaly at low temperature (T_C≈3-22 K) except LuB₁₂ with closed f-shell. Although the bump feature in magnetic susceptibilities resembles that of antiferromagnetically ordered R³⁺ ions, no deﬁnite magnetic structure was identiﬁed by either neutron scattering or Mössbauer spectra. The anomalies in susceptibilities, entropy, and low temperature neutron diffraction pattern all pointed to the amplitude-modulated nature of complex magnetic structure. In view of the rather small crystal-field-splitting energies of the order of meV, we propose to treat crystal-field-splitting (CFS) energy as an order parameter rather than a quantum mechanical quantity. In this way, we found that not only the magnetic and speciﬁc-heat anomalies can be explained properly by a gradual quenching of R orbital moments, but also the low temperature satellite peaks of neutron scattering spectra can be understood in terms of the spontaneously (111) dimerised structure and inelastically absorbed rattling phonon modes.

Key words: rare-earth compound, magnetism in solid, crystal-electrical-splitting, order parameter

中图分类号:

TM28

胡靖三, 顾建飞, 章维益. 晶场劈裂序参量导致稀土-硼十二化合物中磁性和比热反常的理论研究[J]. 无机材料学报, 2021, 36(8): 865-870.

HU Jingsan, GU Jianfei, ZHANG Weiyi. Mechanism of the Magnetic and Speciﬁc-heat Anomalies in Rare-earth Dodecaborides RB₁₂ (R=Tb-Tm): an Effect of Crystal-ﬁeld-splitting Order Parameter[J]. Journal of Inorganic Materials, 2021, 36(8): 865-870.

图/表 6

图1 稀土离子4f轨道能级示意图

Fig. 1 Schematic diagram of crystal-levels (a) Crystal-field-splitting energy reduction due to thermal expansion; (b) Crystal-levels broadening due to thermal lattice ?uctuation

表1 RB12的晶格常数、〈rn〉和晶场劈裂能

Table 1 Lattice constant,〈rn〉of rare-earth R and crystal-ﬁeld-splitting energy of RB12

RB₁₂	TbB₁₂	DyB₁₂	HoB₁₂	ErB₁₂	TmB₁₂
a/(0.1 nm)	7.503	7.500	7.491	7.483	7.475
$\langle {{r}^{4}}\rangle $/(×10^-4, nm⁴)	0.1295	0.1180	0.1081	0.09959	0.09206
$\langle {{r}^{6}}\rangle $/(×10^-6, nm⁶)	0.1505	0.1328	0.1181	0.1058	0.09530
$\text{ }\!\!\Delta\!\!\text{ }_{1}^{0}$/meV	7.53	6.36	6.36	5.90	5.49
$\text{ }\!\!\Delta\!\!\text{ }_{2}^{0}$/meV	14.22	12.99	11.97	11.09	10.31

图2 顺磁稀土离子中单空穴的能级劈裂示意图(a)和RB12系列的临界温度拟合图(b)

Fig. 2 Level scheme of 4f-orbitals of rare-earth ions in hole picture (a), and the measured and ﬁtted TC of RB12 (b)

表2 RB12的德拜温度、修正后的晶场劈裂能和相变温度

Table 2 Debye temperature, corrected crystal-field-splitting parameters, and transition temperature of RB12

RB₁₂	${{\theta }_{\text{D}}}$/K	$\text{ }\!\!\Delta\!\!\text{ }_{1}^{0}$/meV	$\text{ }\!\!\Delta\!\!\text{ }_{2}^{0}$/meV	${{T}_{\text{C}}}(\text{Cal}.)$/K	${{T}_{\text{C}}}(\text{Exp}.)$/K^[12]
TbB₁₂	377	10.66	20.21	22.69	22.05
DyB₁₂	375	9.42	17.81	16.61	16.35
HoB₁₂	374	7.63	14.38	10.69	7.38
ErB₁₂	372	6.24	11.74	6.52	6.65
TmB₁₂	371	5.07	9.51	3.51	3.28

图3 RB12的磁化率(a)和比热(b)随温度变化曲线

Fig. 3 Magnetic susceptibilities (a) and speciﬁc heat (b) of RB12 as functions of temperature

表3 磁性反常附近RB12的磁化率(×10-6, m3·mol-1)和比热跃变数据

Table 3 Magnetic susceptibility and speciﬁc heat jumps near the magnetic anomaly of RB12(×10-6, m3·mol-1)

RB₁₂	$\Delta \chi (\text{Exp}.)$	$\Delta \chi (\text{Cal}.)$	$\Delta C/R(\text{Exp}.)$	$\Delta C/R(\text{Cal}.)$
TbB₁₂	-	2.39	1.4	2.46
DyB₁₂	3.89	4.15	1.2	1.72
HoB₁₂	5.65	6.91	-	1.43
ErB₁₂	6.91	10.56	1.1	1.41
TmB₁₂	4.77	15.58	2.0	2.16

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晶场劈裂序参量导致稀土-硼十二化合物中磁性和比热反常的理论研究

Mechanism of the Magnetic and Speciﬁc-heat Anomalies in Rare-earth Dodecaborides RB₁₂ (R=Tb-Tm): an Effect of Crystal-ﬁeld-splitting Order Parameter

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晶场劈裂序参量导致稀土-硼十二化合物中磁性和比热反常的理论研究

Mechanism of the Magnetic and Speciﬁc-heat Anomalies in Rare-earth Dodecaborides RB12 (R=Tb-Tm): an Effect of Crystal-ﬁeld-splitting Order Parameter

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Mechanism of the Magnetic and Speciﬁc-heat Anomalies in Rare-earth Dodecaborides RB₁₂ (R=Tb-Tm): an Effect of Crystal-ﬁeld-splitting Order Parameter