Institut Néel, CNRS and UJF, BP 166, F-38042, Grenoble, France.
J Phys Condens Matter. 2010 Apr 28;22(16):164210. doi: 10.1088/0953-8984/22/16/164210. Epub 2010 Mar 30.
Bose-Einstein condensation (BEC) is a quantum phenomenon of formation of a collective quantum state in which a macroscopic number of particles occupy the lowest energy state and thus is governed by a single wavefunction. Here we highlight the BEC in a magnetic subsystem--the BEC of magnons, elementary magnetic excitations. The magnon BEC is manifested as the spontaneously emerging state of the precessing spins, in which all spins precess with the same frequency and phase even in an inhomogeneous magnetic field. The coherent spin precession was observed first in superfluid (3)He-B and this domain was called the homogeneously precessing domain (HPD). The main feature of the HPD is the induction decay signal, which ranges over many orders of magnitude longer than is prescribed by the inhomogeneity of magnetic field. This means that spins precess not with a local Larmor frequency, but coherently with a common frequency and phase. This BEC can also be created and stabilized by continuous NMR pumping. In this case the NMR frequency plays the role of a magnon chemical potential, which determines the density of the magnon condensate. The interference between two condensates has also been demonstrated. It was shown that HPD exhibits all the properties of spin superfluidity. The main property is the existence of a spin supercurrent. This spin supercurrent flows separately from the mass current. Transfer of magnetization by the spin supercurrent by a distance of more than 1 cm has been observed. Also related phenomena have been observed: the spin current Josephson effect; the phase-slip processes at the critical current; and the spin current vortex--a topological defect which is the analog of a quantized vortex in superfluids and of an Abrikosov vortex in superconductors; and so on. It is important to mention that the spin supercurrent is a magnetic phenomenon, which is not directly related to the mass superfluidity of (3)He: it is the consequence of a specific antiferromagnetic ordering in superfluid (3)He. Several different states of coherent precession have been observed in (3)He-B: the homogeneously precessing domain (HPD); a persistent signal formed by Q-balls at very low temperatures; coherent precession with fractional magnetization; and two new modes of coherent precession in compressed aerogel. In compressed aerogel the coherent precession has been also found in (3)He-A. We demonstrate that the coherent precession of magnetization is a true BEC of magnons, with the magnon interaction term in the Gross-Pitaevskii equation being provided by spin-orbit coupling which is different for different states of the magnon BEC.
玻色-爱因斯坦凝聚（Bose-Einstein condensation，BEC）是一种量子现象，表现为大量粒子占据最低能量状态，形成一个单一的波函数。在这里，我们强调的是磁子的 BEC，即基本磁激发的 BEC。磁子 BEC 表现为进动自旋的自发出现状态，其中所有自旋以相同的频率和相位进动，即使在不均匀磁场中也是如此。在超流（3）He-B 中首次观察到相干自旋进动，这个领域被称为均匀进动域（HPD）。HPD 的主要特征是感应衰减信号，其范围比磁场不均匀性规定的要长几个数量级。这意味着自旋不是以局部拉莫尔频率进动，而是以共同的频率和相位相干进动。这种 BEC 也可以通过连续的 NMR 泵送来创建和稳定。在这种情况下，NMR 频率起着磁子化学势的作用，决定了磁子凝聚体的密度。还证明了两个凝聚体之间的干涉。结果表明，HPD 表现出所有的自旋超流性质。主要性质是存在自旋超导电流。这种自旋超导电流与质量电流分开流动。已经观察到超过 1 厘米的距离上的磁化强度由自旋超导电流传递。还观察到了相关的现象：自旋超导电流约瑟夫森效应；临界电流处的位相滑移过程；以及自旋超导电流涡旋——一种拓扑缺陷，类似于超流体中的量子涡旋和超导中的 Abrikosov 涡旋；等等。值得一提的是，自旋超导电流是一种磁现象，与（3）He 的质量超流性没有直接关系：它是超流（3）He 中特定反铁磁序的结果。在（3）He-B 中观察到了几种不同的相干进动状态：均匀进动域（HPD）；在极低温度下由 Q 球形成的持续信号；具有分数磁化强度的相干进动；以及压缩气凝胶中的两种新的相干进动模式。在压缩气凝胶中，也在（3）He-A 中发现了磁化强度的相干进动。我们证明了磁化强度的相干进动是磁子的真正 BEC，其中 Gross-Pitaevskii 方程中的磁子相互作用项由自旋轨道耦合提供，而自旋轨道耦合在不同的磁子 BEC 状态下是不同的。
