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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...
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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
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Paramagnets are materials with unpaired electrons that possess a finite magnetic moment. In the absence of a magnetic field, these moments are randomly oriented, and thus the net moment is zero. Under an external field, a torque acting on the moments tends to align them along the field's direction. However, the random thermal motion of electrons produces a torque opposite to the external field and tries to disorient the moments. These two competing effects align only a few moments along the...
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Relativistic Spin-Momentum Locking in Altermagnets.

Carmine Autieri1,2, Amar Fakhredine3

  • 1International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02668 Warsaw, Poland.

The Journal of Physical Chemistry Letters
|December 30, 2025
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Relativistic spin-momentum locking in altermagnets, like YVO3 and MnTe, arises from spin-orbit coupling and antisymmetric exchange, influencing spin canting and k-space properties. This study reveals distinct relativistic spin-momentum locking characteristics in these materials.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Spintronics

Background:

  • Spin-momentum locking, crucial for spintronics, has been studied in the nonrelativistic limit.
  • Altermagnets exhibit unique magnetic and electronic properties due to their crystal structure and magnetic ordering.
  • Spin-orbit coupling introduces antisymmetric exchange interactions, leading to spin canting in magnetic materials.

Purpose of the Study:

  • To investigate relativistic spin-momentum locking in altermagnets by including spin-orbit coupling.
  • To analyze the impact of antisymmetric exchange interactions and spin canting on spin-momentum locking.
  • To explore the specific characteristics of relativistic spin-momentum locking in orthorhombic YVO3 and hexagonal MnTe.

Main Methods:

  • Theoretical investigation of spin-momentum locking in altermagnetic systems.
  • Analysis of spin-orbit coupling effects on electronic band structure and spin polarization.
  • Characterization of spin-momentum locking in terms of different angular momentum components (s-, d-waves).

Main Results:

  • Relativistic spin-momentum locking in YVO3 comprises s-, dxy-, and dxz-wave components.
  • In MnTe, the dominant Sy component retains nonrelativistic g-wave locking, but symmetry breaking lowers it to d-wave.
  • Relativistic spin-momentum locking in MnTe is composed of dxz-, dyz-, and s-wave components.
  • Canted spin components, though small in real space, significantly contribute to k-space properties.

Conclusions:

  • Spin-orbit coupling and antisymmetric exchange fundamentally alter spin-momentum locking in altermagnets, leading to relativistic effects.
  • The symmetry of the crystal structure and the orientation of the Néel vector dictate the specific form of relativistic spin-momentum locking.
  • Relativistic spin-momentum locking in altermagnets has significant implications for charge and spin transport phenomena, including spin-Hall conductivity and spin photocurrents.