四方晶系下釹離子的基態(tài)分裂

王保松，劉紅艷，夏繼周

(1.菏澤學(xué)院物理系，山東菏澤 274015；2.淮北師范大學(xué)物理與電子信息學(xué)院，安徽淮北 235000；3.山東青年政治學(xué)院學(xué)生工作部，山東濟(jì)南 250014)

四方晶系下釹離子的基態(tài)分裂

王保松1，劉紅艷2，夏繼周3

(1.菏澤學(xué)院物理系，山東菏澤 274015；2.淮北師范大學(xué)物理與電子信息學(xué)院，安徽淮北 235000；3.山東青年政治學(xué)院學(xué)生工作部，山東濟(jì)南 250014)

采用點(diǎn)電荷晶場(chǎng)模型，通過(guò)模擬四方晶系化合物NdCuAs2和Nd2Ge2In的磁化率倒數(shù)-溫度曲線，得到了Nd3+的各級(jí)分裂能和相應(yīng)波函數(shù)，并分析了晶場(chǎng)效應(yīng)對(duì)化合物磁性質(zhì)的影響.結(jié)果表明，Kramers離子Nd3+的十重簡(jiǎn)并基態(tài)4I9/2在晶場(chǎng)效應(yīng)的作用下分裂為5個(gè)雙態(tài)，計(jì)算結(jié)果與實(shí)驗(yàn)吻合得較好.

NdCuAs2；Nd2Ge2In；磁化率；晶場(chǎng)效應(yīng)

稀土元素特殊的外電子層結(jié)構(gòu)使稀土化合物具有獨(dú)特的光、電、磁等性能，稀土化合物被譽(yù)為“新材料的寶庫(kù)”.稀土化合物中存在各種磁性效應(yīng)，這些磁性效應(yīng)各自都以不同的物理機(jī)制使稀土磁性材料起著轉(zhuǎn)換、傳遞和存儲(chǔ)能量、信息的作用，所以對(duì)稀土化合物進(jìn)行深入細(xì)致的研究具有非常重要的意義.稀土化合物中，局域4f電子受到周?chē)x子的晶場(chǎng)作用后，多重基態(tài)會(huì)發(fā)生分裂或激發(fā)，簡(jiǎn)并度會(huì)部分或完全消失，這會(huì)對(duì)系統(tǒng)的磁化率、比熱、電阻率和磁化強(qiáng)度等性質(zhì)產(chǎn)生極大的影響.文獻(xiàn)[1-4]分別對(duì)PrNi2Al5、NdNiAl4、Ce2Pd3Si5和Ce(Pd1-xMx)2Al3的磁化率倒數(shù)-溫度曲線進(jìn)行了模擬，得到了各化合物的晶場(chǎng)分裂能，結(jié)果與實(shí)驗(yàn)獲得了較好的吻合.本文根據(jù)Sengupta[5]和Zaremba[6]測(cè)量的NdCuAs2和Nd2Ge2In磁化率實(shí)驗(yàn)數(shù)據(jù)，對(duì)四方晶系化合物NdCuAs2和Nd2Ge2In中Nd3+的晶場(chǎng)分裂進(jìn)行研究，同時(shí)分析了晶場(chǎng)效應(yīng)對(duì)該系列化合物性質(zhì)的影響，這有助于進(jìn)一步了解稀土化合物的結(jié)構(gòu)和物理特性.

1 理論簡(jiǎn)介

是周?chē)x子的坐標(biāo)矢量，是金屬離子第i個(gè)價(jià)電子的坐標(biāo)矢量.

在晶體中，帶有未滿(mǎn)4f殼層的稀土離子的晶場(chǎng)作用項(xiàng)可以寫(xiě)為：

2 計(jì)算結(jié)果與討論

Sengupta[5]和Zaremba[6]用居里-外斯定律擬合磁化率曲線得到Nd3+有效磁矩的擬合值分別為3.86μB和3.60μB，與有效磁矩的理論值μtheo=相差很小，這表明Nd3+的有效磁矩具有很好的局域性.實(shí)驗(yàn)測(cè)得飽和磁化強(qiáng)度分別為1.5μB和0.92μB，遠(yuǎn)小于理論值.可以推測(cè)，晶場(chǎng)效應(yīng)的屏蔽引起了磁矩的部分猝滅[9].從文獻(xiàn)[5-6]中很容易看出，NdCuAs2和Nd2Ge2In兩化合物磁化率倒數(shù)-溫度曲線在50 K以下與居里-外斯擬合曲線產(chǎn)生了明顯的偏離，Zaremba[5]和Zaremba[6]預(yù)言這兩種化合物中可能存在強(qiáng)烈的晶場(chǎng)效應(yīng)，從而使稀土離子的基態(tài)發(fā)生分裂.本文選定表1的參數(shù)來(lái)計(jì)算NdCuAs2和Nd2Ge2In中Nd3+的基態(tài)分裂能和相應(yīng)波函數(shù).

表1 NdCuAs2和Nd2Ge2In中Nd3+的晶場(chǎng)系數(shù)Table 1 Coefficient of Crystal Field of Nd3+ in NdCuAs2 and Nd2Ge2In

圖1給出了NdCuAs2和Nd2Ge2In的磁化率倒數(shù)晶場(chǎng)模擬曲線和實(shí)測(cè)曲線.

表2 NdCuAs2中Nd3+晶場(chǎng)分裂的各級(jí)能量值和相應(yīng)波函數(shù)Table 2 Energy Values and Corresponding Wave Functions of Different Energy Levels of Nd3+ in Cristal Field Splitting of NdCuAs2

由圖 1可看出，通過(guò)計(jì)算得到的模擬曲線較好地再現(xiàn)了實(shí)驗(yàn)曲線.通過(guò)模擬磁化率倒數(shù)-溫度曲線可得到NdCuAs2和Nd2Ge2In中Nd3+的各能級(jí)能量值和相應(yīng)波函數(shù)，見(jiàn)表2和表3.從表2和表3中可以看到，由于晶場(chǎng)效應(yīng)的影響，新的本征函數(shù)是相同總角動(dòng)量J、不同磁量子數(shù)M的波函數(shù)的線性組合.Kramers離子Nd3+分裂得到的是雙基態(tài)，但不再是純的雙基態(tài)，而是混合的雙基態(tài)，這與Kramers定理當(dāng)稀土元素具有奇數(shù)個(gè)f電子時(shí)，必定擁有雙重基態(tài)是一致的.兩種四方晶系化合物NdCuAs2和Nd2Ge2In中，Nd3+的十重簡(jiǎn)并基態(tài)4I9/2都分裂為5個(gè)雙態(tài)，所不同的是NdCuAs2中4f電子和過(guò)渡金屬Cu中的傳導(dǎo)電子之間存在強(qiáng)烈的雜化，這使其各級(jí)晶場(chǎng)分裂能都高于Nd2Ge2In.

表3 Nd2Ge2In中Nd3+晶場(chǎng)分裂的各級(jí)能量值和相應(yīng)波函數(shù)Table 3 Energy Values and Corresponding Wave Functions of Different Energy Levels of Nd3+in Cristal Field Splitting of Nd2Ge2In

3 結(jié) 論

本文基于晶場(chǎng)理論，通過(guò)對(duì)磁化率倒數(shù)-溫度曲線的模擬，得到了稀土化合物 NdCuAs2和Nd2Ge2In中Nd3+的各級(jí)分裂能和相應(yīng)波函數(shù)，并從理論上進(jìn)行了分析.由于低溫下磁化率隨溫度的變化比較復(fù)雜，且化合物也不僅僅是只受到晶場(chǎng)效應(yīng)一種作用的影響，所以很難對(duì)曲線的低溫部分進(jìn)行準(zhǔn)確模擬，更準(zhǔn)確的計(jì)算還要借助于中子散射等能精確檢測(cè)磁結(jié)構(gòu)的實(shí)驗(yàn)手段.

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Ground States’ Splittings of Nd3+in Tetragonal Crystal System

WANG Baosong1, LIU Hongyan2, XIA Jizhou3
(1. Department of Physics, Heze University, Heze, China 274015; 2. School of Physics and Electronic Information, Huaibei Normal University, Huaibei, China 235000; 3. Department of Student Affairs, Shandong Youth University of Political Science, Ji’nan, China 250014)

The splitting energy at different levels and their corresponding wave functions for Nd3+in NdCuAs2and Nd2Ge2In (compounds of tetragonal crystal system) had been obtained by means of adopting simple point-charge crystal field model and simulating the curve of temperature dependence of the magnetic susceptibility’s reciprocal. Then the influence of crystalline electric field (CEF) effect on compound’s magnetic properties had been analyzed. Results showed that the ten-fold degenerate ground state4I9/2of Nd3+(Kramers ion) had been transformed into five doublet states with the influence of CEF. The CEF analysis suggests that the calculated results were in good agreement with the experimental data.

NdCuAs2; Nd2Ge2In; Magnetic Susceptibility; Crystalline Electric Field Effect

(編輯：王一芳)

O482.54

A

1674-3563(2011)02-0036-05

10.3875/j.issn.1674-3563.2011.02.007 本文的PDF文件可以從xuebao.wzu.edu.cn獲得

2010-06-25

菏澤學(xué)院自然科學(xué)基金(XY08WL02)

王保松(1979- )，男，山東曹縣人，講師，碩士，研究方向：凝聚態(tài)物理