External-field-induced transition from altermagnetic metal to fully-compensated ferrimagnetic metal in monolayer $\mathrm{Cr_2O}$

Abstract

Altermagnets and fully-compensated ferrimagnets are two canonical classes of zero-net-moment magnets. An altermagnetic (AM) half-metal cannot exist due to its AM spin splitting, while a fully-compensated ferrimagnetic (FC-FIM) metal seems impossible to realize because both spin channels remain gapless. Here, we propose that an FC-FIM metal can be realized by breaking the rotational or mirror symmetry that links two spin-opposite magnetic atoms in an AM metal. We further demonstrate that charge-carrier doping is fundamentally unable to generate a net magnetic moment in an altermagnet, whereas such a net moment can be readily induced in a fully-compensated ferrimagnet. We use the AM monolayer $\mathrm{Cr_2O}$ as a concrete example to validate our proposal. Either electric field or uniaxial strain can break the $S_{4z}$ symmetry of $\mathrm{Cr_2O}$, thereby inducing a transition from an AM metal to an FC-FIM metal. Uniaxial strain plus carrier doping creates a net moment in an altermagnet, and the so-called piezomagnetism is essentially a strain-driven switch from altermagnetism to fully-compensated ferrimagnetism. By analogy, we advance the concept of electromagnetism: an electric field drives the transition from altermagnetism to fully-compensated ferrimagnetism, and subsequent charge-carrier doping stabilizes a net magnetization. Our work provides a roadmap for further exploring the connection and distinction between altermagnet and fully-compensated ferrimagnet, and confirms the feasibility of FC-FIM metal.

Figures (6)

• Figure 1: (Color online) (a): the A-type AFM AM tetragonal monolayer, and the magnetic atoms with opposite spins are connected through [$C_2$$\parallel$$S_{4z}$] symmetry; (b): an out-of-plane electric field or in-plane uniaxial strain is applied in (a) to break [$C_2$$\parallel$$S_{4z}$] symmetry; (c): the (a) possesses semi-metallic bands with AM spin splitting between $\Gamma$-$k_x$ and $\Gamma$-$k_y$ directions; (d): the (c) transitions into an FC-FIM metallic bands due to broken [$C_2$$\parallel$$S_{4z}$] symmetry caused by an out-of-plane electric field or in-plane uniaxial strain; (e, f): by tuning the charge-carrier density with an electrostatic gate voltage, the AM metal (c) remains free of any net magnetic moment, whereas the FC-FIM metal (d) possesses a net moment that varies with carrier concentration. In (a, b), the blue, red, green, and horizontal gray arrows denote spin-up, spin-down, electric field, and uniaxial strain, respectively. In (c, d), the blue and red curves represent the spin-up and spin-down characteristic bands, respectively.
• Figure 2: (Color online)For $\mathrm{Cr_2O}$, (a, b): the top and side views of the crystal structures; (c): the spin-polarized band structures; (d, e): the upper- and lower-layer Cr projected band structures. In (a, b), the large blue and small red spheres represent Cr and O atoms, respectively. In (c), the blue and red curves denote the spin-up and spin-down characteristic bands, respectively, while the purple indicates the spin-degenerate bands. In (d, e), the size of the circles is proportional to the atomic weight.
• Figure 3: (Color online)For $\mathrm{Cr_2O}$, (a): the energy difference between FM and AFM orderings as a function of electric field $E$; (b): the absolute value of the sum of the magnetic moments of the upper- and lower-layer Cr atoms ($|M_{Cr1}+M_{Cr2}|$), along with the total magnetic moment ($M_{tot}$), as a function of electric field $E$; (c, d, e): the spin-polarized band structures at representative $E$=+0.00, +0.20 and +0.40 $\mathrm{V/{\AA}}$. In (c, d ,e), the blue and red curves denote the spin-up and spin-down characteristic bands, respectively, while the purple indicates the spin-degenerate bands.
• Figure 4: (Color online)For $\mathrm{Mg(CoN)_2}$, (a): the spin-polarized band structures without electric field; (b, c): the upper- and lower-layer Co projected band structures without electric field; (d): the spin-polarized band structures at $E$=+0.25 $\mathrm{V/{\AA}}$. In (a, d), the blue and red curves denote the spin-up and spin-down characteristic bands, respectively, while the purple indicates the spin-degenerate bands. In (b, c), the size of the circles is proportional to the atomic weight.
• Figure 5: (Color online)(Color online)For $\mathrm{Cr_2O}$, (a): the energy difference between FM and AFM orderings as a function of uniaxial strain $a/a_0$; (b): the absolute value of the sum of the magnetic moments of the upper- and lower-layer Cr atoms ($|M_{Cr1}+M_{Cr2}|$), along with the total magnetic moment ($M_{tot}$), as a function of uniaxial strain $a/a_0$; (c, d, e): the spin-polarized band structures at representative $a/a_0$=0.96, 1.00 and 1.04. In (c, d ,e), the blue and red curves denote the spin-up and spin-down characteristic bands, respectively, while the purple indicates the spin-degenerate bands.