We investigate interacting spin susceptibilities in lattice models for $\mathcal{T}$-reversal symmetry-broken Weyl semimetals. We employ a random phase approximation method for the spin-SU(2)-symmetry-broken case that includes mixtures of ladder and bubble diagrams, beyond a SU(2)-symmetric case. Within this approach, the relations between the tendency towards magnetic order and the band structure tilt parameter $\gamma$ under different temperatures are explored. The critical interaction strength $U_c$ for magnetic ordering decreases as the tilt term changes from type-I Weyl semimetals to type II. The lower the temperature, the sharper is the drop in $U_c$ at the critical point between them. The variation of $U_c$ with a slight doping near half filling is also studied. It is generally found that these Weyl systems show a strongly anisotropic spin response with an enhanced doubly degenerate transverse susceptibility perpendicular to tilt direction, inherited from ${\mathcal{C}}_{4z}$ rational symmetry of a bare Hamiltonian, but with the longitudinal response suppressed with respect to that. For small tilts $\gamma$ and strong enough interaction, we find two degenerate ordering patterns with spin order orthogonal to the tilt direction but much shorter spin correlation length parallel to the spin direction. With increasing the tilt, the system develops instabilities with respect to in-plane magnetic orders with wave vector $(0,\pi ,q_z)$ and $(\pi ,0,q_z)$, with $q_z$ increasing from 0 to $\pi$ before the transition to a type-II Weyl semimetal is reached. These results indicate a greater richness of magnetic phases in correlated Weyl semimetals that also pose challenges for precise theoretical descriptions.

中文翻译：

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磁性 I 型和 II 型外尔半金属的自旋敏感性

我们研究了晶格模型中相互作用的自旋敏感性 $\mathcal{吨}$-反转对称性破坏的外尔半金属。我们对自旋 SU(2) 对称性破缺的情况采用随机相位近似方法，该方法包括阶梯图和气泡图的混合，超出了 SU(2) 对称情况。在这种方法中，磁序趋势与能带结构倾斜参数之间的关系$\gamma$在不同的温度下进行了探索。临界相互作用强度${你}_C$随着倾斜项从 I 型 Weyl 半金属变为 II 型，磁性有序性降低。温度越低，下降幅度越大${你}_C$在他们之间的临界点。的变化${你}_C$还研究了接近半填充的轻微掺杂。通常发现，这些 Weyl 系统显示出强烈的各向异性自旋响应，并具有增强的垂直于倾斜方向的双简并横向磁化率，继承自${\mathcal{C}}_{4z}$裸哈密顿量的有理对称性，但纵向响应被抑制。对于小倾斜$\gamma$和足够强的相互作用，我们发现了两个退化的排序模式，其自旋顺序与倾斜方向正交，但与自旋方向平行的自旋相关长度要短得多。随着倾斜度的增加，系统在具有波矢量的平面内磁阶数方面变得不稳定性$(0,\pi ,q_z)$ 和 $(\pi ,0,q_z)$， 和 $q_z$ 从 0 增加到 $\pi$在过渡到 II 型外尔半金属之前。这些结果表明相关的外尔半金属中磁性相更丰富，这也对精确的理论描述提出了挑战。