Quantum Altermagnetic Instability in Disordered Metals

TL;DR

The work addresses whether altermagnetic order can be stabilized in disordered two-dimensional metals in the diffusive regime, with and without Rashba spin-orbit coupling. It develops a replicated nonlinear sigma model to capture diffusive spin modes and derives an effective one-loop potential for competing ferromagnetic ($m_3$) and altermagnetic ($n_3$) order parameters, incorporating Dyakonov-Perel relaxation. The analysis shows that without spin-orbit coupling ferromagnetism dominates only at small anisotropy and coupling, while larger staggered anisotropy and interaction strength favor altermagnetism; with finite Rashba SOC a paramagnetic phase persists and a quantum critical point emerges, with the ferromagnet–altermagnet transition being first order. The results provide a controlled framework for predicting phase competition and the field robustness of altermagnetic order in realistic disordered 2D metals, with implications for spintronic devices and altermagnetic–superconductor hybrids.

Abstract

The possibility of a zero temperature, altermagnetic instability in anisotropic two dimensional electron systems in the diffusive regime is analyzed, in the presence and absence of spin-orbit coupling. Allowing for ferromagnetism, a phase diagram is built as a function of the parameter that controls anisotropy and the strength of the interactions. It is found that, at zero spin orbit coupling, ferromagnetism only dominates at small values of anisotropy and coupling constant. Larger values of these parameters favour the formation of altermagnetism. At finite spin-orbit coupling, a paramagnetic phase competes with the other two, and a quantum critical point appears. The phase transition from the paramagnetic to the magnetically ordered phases is of second order, while the phase transition between ferromagnet and altermagnet states is first order. The altermagnetic phase is robust under small magnetic fields, displaying a coexistence with a field-induced magnetization.

Figures (5)

• Figure 1: Illustration of the hopping structure of the anisotropic model considered in the text. The hopping amplitudes $r_1$ and $r_2$ break inversion symmetry. These amplitudes together with the indicated magnetic moments are invariant under $\{C_n\Vert C_2^{S}\}$. When spin-orbit coupling is included, the symmetry group stabilizing the altermagnetic phase is $\text{C}_4\cdot\text{T}$.
• Figure 2: Phase diagram corresponding the effective potential in Eq.(\ref{['integralaction']}) for three different values of the dimensionless Rashba coupling $\rho$. In the three panels, the lines separating the PM--FM and the PM--AM phases are the Eq. (\ref{['criticalferroU']}) and $r_n=0$. the FM--AM line is computed numerically. The different lines separating phases are labeled in Fig.(\ref{['fig:panelB']}).
• Figure 3: Character of the different phase transitions. In panels (a) and (b) the order parameters $m_3/\Lambda$ and $n_3/\Lambda$ are plotted for $\rho=0.4$ and zero magnetic field as a function of $\lambda$ and $g$, respectively. The transition PM--FM is of second order, while the transition FM--AM is first order type. panels (c) and (d) represent the same order parameters as before, but in presence of a finite (dimensionless) magnetic field $b=0.05$. The PM phase is heavily reduced, and the FM phase penetrates into the AM phase, generating phase coexistence.
• Figure 4: (a): Magnetic susceptibility $\chi(g,\lambda,b)$ (in arbitrary units) for $\rho=0.4$ and zero magnetic field. (b) $\chi(g,\lambda,b)$ for $\rho=0.4$ and dimensionless magnetic field $b=0.05$. The boundary lines between phases are depicted for clarity.
• Figure 5: Magnetization curve $m$ vs. $b$, for $\rho=0.4$, $g=1.5$, and $\lambda=1.8$. The transition AM--FM is first order. The inset figures represent eschematically the shape of the spin-polarized Fermi surfaces at each sides of the phase transition.