AI 中文总结
研究铁磁平面腔中两个自旋探针的有限频率磁性公共浴场，通过耦合腔的延迟磁性格林张量求解相关核，用横向对角极化率评估，给出了有限频率下的线宽分裂和集体兰姆位移等结果。
AI 中文摘要
我们构建了铁磁平面腔中两个自旋探针的有限频率磁性公共浴场。探针耦合到腔的延迟磁性格林张量，其虚部和实部分别决定集体衰变核\(\gamma_{12}\)和兰姆位移核\(\Omega_{12}\)。我们用横向对角极化率\(\mu_\perp(\omega,B)\)评估由非磁性导电衬底上的铁磁膜形成的有限厚度标量TE通道的这些核。在\(\omega\to0\)极限下，常数反射基准再现静态图像系列参考，有限平板保留相应静态TE反射幅度。对于微米级中间间隙腔中由代表性类镍参数集描述的\(t = 200\,\mathrm{nm}\)薄膜，GHz探针跃迁在毫开尔文温度下采样体辅助磁库的正频率响应。在共振时，非对角线宽分裂在\(\rho = 3\,\mu\mathrm m\)时达到单自旋散射线宽的约三分之二。由此产生的线宽分裂和集体兰姆位移提供了静态TE耦合频率偏移的有限频率对应物。
英文摘要
We formulate the finite-frequency magnetic common-bath problem of two spin probes in a ferromagnetic planar cavity. The probes couple to the retarded magnetic Green tensor of the cavity, whose imaginary and real parts determine the collective decay rate \(γ_{12}\) and the coherent exchange coupling \(Ω_{12}\), respectively. We evaluate these quantities for a finite-thickness scalar transverse-electric (TE) cavity channel formed by ferromagnetic films on nonmagnetic conducting substrates, using a Polder-type scalar permeability \(μ_\perp(ω,B)\) as the magnetic input. The normalization is fixed by the free-space magnetic-dipole decay rate. In the \(ω\to0\) limit, the Green-tensor kernel reduces to the magnetostatic response, and the finite slab retains its static TE reflection amplitude. For a \(t=200\,\mathrm{nm}\) film with a representative Ni-like parameter set, the GHz transition of a spin probe at the mid-gap of a micron-scale cavity samples the spectral density of the body-assisted magnetic reservoir at millikelvin temperature. At the resonant bias, the cavity-induced contribution \(2|δγ_{12}^{(zz)}|\) to the collective linewidth splitting in the \(zz\) transition-moment projection is about two thirds of the local single-spin linewidth correction \(δγ_{11}^{(zz)}\) at \(ρ=3\,μ\mathrm m\). Together, the linewidth splitting and collective Lamb shift probe the dissipative and dispersive finite-frequency response, respectively, while the shared Green-tensor normalization connects these observables to the static TE coupling-frequency shift.
Comments12 pages, 6 figures
