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希土离子对铁磁共振的影响

霍裕平 孟宪振

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希土离子对铁磁共振的影响

霍裕平, 孟宪振

THE INFLUENCE OF RARE EARTH IONS ON FERRIMAGNETIC RESONANCE

HO YU-PING, MENG XIAN-ZHEN
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  • 本文利用关联函数的方法(久保理论),讨论了强交换耦合系统的亚铁磁共振,给出了系统总磁化率张量的一般表达式,由此可以定出铁磁支与交换支的共振场H0(或共振频率)和峯宽2△ω。所得结果表明,所谓快弛豫及慢弛豫机理不过是铁磁共振的两个分支(横分支与纵分支)。横分支相应于J及S的横向磁矩之间的耦合运动J,S分别为希土离子及铁离子的磁矩),而纵分支相应于J的纵向分量与S的横向分量之间的耦合运动。由于晶场及各向异性交换场的作用,J的量子化方向与S的量子化方向偏离一个角度φ。此外由于交换作用的各向异性,在交换作用哈密顿J·λ·S中,张量λ的非对角元可以相当大。结果表明,纵分支对峯宽的贡献近似地正比于φ2及λi3(i=1,2)。根据2△ω的一般表达式,在极低温下(4.2°K以下),峯宽主要是由横分支决定的。沿某些晶轴方向?a,当希土离子最低两个能级接近“交叉”时,共振场及峯宽应该出现反常峯值,这在实验上已经得到了证实。当温度升高时,纵分支将逐渐“压过”横分支。当纵向弛豫频率达到高频场的频率ω时,峯宽将出现极大值,一般实验中观察到的就是这个极大值。当温度继续升高时,横分支又将起主要作用。当横向弛豫频率接近相应于希土离子最低两个能级之间的间距ω21时(?=1),峯宽将出现第二个极大值。实验上只有沿希土离子最低两个能级接近交叉的方向进行测量时,才有可能观测到第二个峯值。当频率足够高,满足|ω21(?a)-ω|<<ω的条件时,在极低温下,将出现由横分支决定的尖锐的峯宽极大值。根据所得理论结果,除上述现象外,还可以统一地解释在希土石榴石铁氧体中观测到的下列实验事实:有效旋磁比随温度的显著变化;在抵消点附近峯宽的急剧上升;在镱铁氧体中观测到的在峯宽极大值出现的温度共振场显著上升等。指出了经典磁矩运动方程的局限性,在铁氧体中,晶场的作用与交换场其大小可以相比时,利用经典方程求解所得出的结果只能定性地解释某些与希土离子具体能级结构无关的现象。
    By utilizing the method of correlation function (theory of Kubo), the ferrimagnetic resonance behaviour of the tight exchange coupled system was discussed. The general formulae of the magnetic susceptibility tensor were given, from which the resonance field H0 (or resonance frequency) and the line width 2△ω of the ferromagnetic branch and that of the exchange branch were determined. The results obtained show that the so-called fast relaxation and slow relaxation mechanisms are nothing but two branches (the transverse branch and the longitudinal branch) of the ferromagnetic resonance. The transverse branch corresponds to the coupled motion between the transverse componentsof J and S (J and S are the magnetic moments of rare earth ion and iron ion respectively), while the longitudinal branch corresponds to the coupled motion between thelongitudinal component of J and the transverse component of S. Owing to the action of crystal field and anisotropic exchange field, the direction of quantization of J deviates from that of S by an angle φ. Besides, owing to the aniso-tropy of exchange interaction, the nondiagonal elements of the tensor λ in the Hamil-tonian of exchange interaction J·λ·S may be quite large. It was shown that the contribution of the longitudinal branch to 2 △ω is approximately proportional to φ2 and λi3=1, 2). According to the general formula for 2△ω, the latter is determined mainly by the transverse branch at very low temperatures (below 4.2°K). Along certain crystal directions θa, when the two lowest energy levels of rare earth ion nearly cross over, anomalous peaks of H0 and 2△ω should appear, as it was verified experimentally. As the temperature increases, the longitudinal branch shall gradually dominate over the transverse branch. When the longitudinal relaxation frequency reaches the value of the frequency ω of the high frequency field, the line width possesses a maximum, which is the one ordinarily observed in experiments. As the temperature is increased further, the transverse branch shall play the dominant rolc again. When the transverse relaxation frequency approaches the frequency ω21, corresponding to the energy difference of the two lowest energy levels of the rare earth ion, the line width possesses a second maximum. Experimentally it is possible to observe the second maximum only in those directions θa, along which the two lowest levels have a near cross-over. When ω is high enough so that the condition |ω21(θa)-ω|?ω is satisfied, at very low temperatures there shall be a very sharp maximum of line width determined by the transverse branch. With the theoretical results obtained, in addition to the phenomena mentioned above, the following experimental facts observed in rare earth garnets can also be satisfactorily explained: the strong dependence of effective gyromagnetic ratio on temperature; the abrupt increase of line width near the compensation point; the abrupt increase of H0 for YbIG at the temperature where the line width reaches its maximum; etc.The limitation of classical equations of motion of magnetic moment was pointed out. For ferrites, in which the crystal field is comparable with the exchange field, it was shown that the results obtained by solving the classical equations of motion can qualitatively explain only those experimental facts, which are not concerned with the concrete spectrum of the energy levels of rare earth ions.
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出版历程
  • 收稿日期:  1964-01-02
  • 刊出日期:  2005-08-05

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