SPIN-LATTICE RELAXATION IN RARE-EARTH SALTS
SPIN-LATTICE RELAXATION IN RARE-EARTH SALTS
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DOI：
10.1098/rspa.1961.0211
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发表时间：
1961-01-01
影响因子：
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通讯作者：
ORBACH, R
中科院分区：
文献类型：
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作者：
ORBACH, R
自旋晶格弛豫的一般方法给出了盐的结晶场理论是适当的。特别地，Elliott & Stevens关于稀土离子与静态离子环境的相互作用的理论被唯象地推广以表示稀土离子与晶格振动模式的相互作用。用几个常数来评价自旋-晶格相互作用是可能的。一个和两个声子的过程进行了调查和非Kramers和Kramers盐的弛豫时间计算。对于单声子（或直接）过程，非Kramers盐表现出典型的行为T1 H-2 T-1，Kramers盐表现出典型的行为T1 H-4 T-1。结果表明，对于一个给定的塞曼分裂的地面偶极子，后者可能会表现出巨大的各向异性相对于外场的方向，近似成比例的各向异性的温度无关的部分的磁化率。一般理论的应用是由两种盐，钬和镝乙基硫酸盐;前者是一个非克拉默斯，后者克拉默斯盐。结果表明，镝盐在直接过程区的弛豫时间为sin-2θcos-2θH-4 T-1，其中θ为外磁场与晶体对称轴的夹角。对于双声子过程，还必须区分德拜能（KθD）是否小于或大于基态和第一激发态之间的晶场分裂Δ。非Kramers盐的前一个条件适用（KθD< Δ），具有通常的拉曼型双声子弛豫过程。弛豫时间与T_（-7）成正比，与磁场无关。当K θD> Δ时，还存在一个由共振过程引起的项，类似于气体中的共振辐射效应。自旋系统优先吸收和发射能量为~ Δ的声子，这是因为声子与自旋态的晶场分裂共振。由于通常KT远小于Δ，这导致弛豫时间与exp（Δ/KT）成比例。除了在非常高和非常低的温度下，该过程将主导拉曼过程。它被证明是显着的权利下降到液氦范围内的比较，由于直接过程的弛豫速率。当K θD< Δ时，由于速率方程中的相互抵消，Kramers盐的拉曼弛豫时间与T-9成正比，与电场无关。这种“货车Vleck取消”被证明是时间反演对称性的后果。当K θD> Δ时，共振过程也存在，弛豫时间也与exp（Δ/KT）成正比。共振过程现在被证明是占主导地位的许多稀土盐低至1或2 °K。实验验证了稀土乙基硫酸盐的共振弛豫过程。一般认为，这一机制对K θD> Δ的磁性盐都是有意义的。
A general approach to spin-lattice relaxation is given for salts to which a crystalline field theory is appropriate. In particular, the theory of Elliott & Stevens for the interaction of a rare-earth ion with static ionic surroundings is generalized phenomenologically to represent the interaction of the rare-earth ion with the lattice vibrational modes. Evaluation of the spin-lattice interaction in terms of a few constants is possible. One- and two-phonon processes are investigated and the relaxation times for non-Kramers and Kramers salts computed. For the one-phonon (or direct) process the non-Kramers salts exhibit the typical behaviourT1∝H-2T-1, and the Kramers saltsT1∝H-4T-1. It is shown that, for a given Zeeman splitting of the ground doublet, the latter may exhibit an enormous anisotropy with respect to the direction of the external field, approximately proportional to the anisotropy of the temperature-independent part of the susceptibility. Application of the general theory is made to two salts, holmium and dysprosium ethyl sulphate; the former a non-Kramers, the latter a Kramers salt. It is shown that the dysprosium salt would be expected to show a relaxation time in the direct process region which will vary as sin-2θcos-2θH-4T-1, whereθis the angle the external magnetic field makes with the crystallographic symmetry axis. For two-phonon processes, the additional distinction of whether the Debye energy (KθD) is less than or greater than the crystalline field splitting Δ between the ground state and the first excited state must be made. Non-Kramers salts to which the former condition apply (KθD< Δ) are shown to possess two-phonon relaxation processes of the usual Raman type. The relaxation time is proportional toT-7and is independent of magnetic field. WhenKθD> Δ, there is present in addition a term arising from a resonance process, analogous to the resonance radiation effect in gases. Phonons of energy ~ Δ are absorbed and emitted by the spin system preferentially because of a phonon resonance with the crystalline field splitting of the spin states. As normallyKTis much less than Δ, this leads to a relaxation time proportional to exp (Δ/KT). This process will dominate the Raman process except at very high and low temperatures. It is shown to be significant right down to the liquid-helium range by comparison with the relaxation rate due to direct processes. Kramers salts, whenKθD< Δ, owing to a cancellation in the rate equation, exhibit a Raman relaxation time proportional toT-9and independent of field. This 'Van Vleck cancellation’ is shown to be a consequence of time reversal symmetry. WhenKθD> Δ, the resonance process is also present, the relaxation time again being proportional to exp (Δ/KT). The resonance process is now shown to be dominant down to 1 or 2 °K for many rare-earth salts. Experimental verification is found for the resonance relaxation process in the rare-earth ethyl sulphates. In general, it is expected that this mechanism will be significant for any magnetic salt in whichKθD> Δ.