Chiral Spin Modes (CSM)

• Chiral Spin Modes (CSM) are collective spin excitations defined by handed, symmetry-constrained spin dynamics across various physical systems.
• They emerge in systems such as spin–orbit-coupled electron liquids, chiral magnets, topological magnonics, and even in QCD via chiralspin symmetry.
• Advanced theoretical models and experimental techniques, including Raman spectroscopy and micromagnetic simulations, probe their distinct dispersion and confinement properties.

Searching arXiv for papers on chiral spin modes across electronic, magnetic, and related contexts. Chiral spin modes (CSM) are collective spin excitations whose defining feature is a handed, symmetry-constrained spin dynamics. The term is used in several distinct literatures rather than for a single universal quasiparticle. In spin–orbit-coupled electron systems, it denotes exchange-stabilized collective spin-precession modes that split off from spin-flip particle–hole continua; in chiral magnets, it denotes Dzyaloshinskii–Moriya-interaction (DMI) governed spin-wave eigenmodes with fixed chirality, nonreciprocity, or confinement-induced helical profiles; in topological magnonics, it labels unidirectional boundary magnons; and in other settings it refers to collective excitations organized by chiralspin symmetry or chiral liquid order (Ashrafi et al., 2012, Kung et al., 2017, Savchenko et al., 2022, Glozman, 2018, Lu et al., 28 Jan 2026). The common thread is collective spin dynamics whose structure is fixed by an internal chiral field, a chiral texture, or a symmetry that mixes chirality-like degrees of freedom.

1. Terminology, scope, and defining mechanisms

The expression “chiral spin mode” is intrinsically context-dependent. In SOC-coupled electron liquids and topological-insulator surfaces, chirality refers to spin–momentum locking and to collective spin precession in an effective momentum-dependent internal field (Ashrafi et al., 2012, Kung et al., 2017). In chiral magnets, chirality is imposed by DMI and appears either as nonreciprocal propagation, as a helical spatial phase of the dynamic magnetization, or as fixed-handedness standing waves under confinement (Zingsem et al., 2016, Savchenko et al., 2022). In QCD, by contrast, “chiralspin” refers to an $SU(2)_{CS}$ symmetry that mixes right- and left-handed Dirac components and organizes collective excitations of quark bilinears (Glozman, 2018).

This terminological breadth creates a recurrent misconception: CSM are not a single experimentally uniform phenomenon. The label does not imply a magnon, a plasmon, or a spin exciton in every case. In the electronic SOC setting, CSM are collective poles in spin susceptibilities, often exchange-bound below a spin-flip continuum. In magnetic DMI systems, they are spin-wave eigenmodes whose dispersion satisfies $\omega(k)\neq\omega(-k)$ or whose standing-wave profiles acquire a helical phase. In topological magnonic crystals they are bulk-gap-crossing edge states classified by Chern numbers. In QCD they are diagnosed through multiplet structures in spatial correlators rather than through a conventional magnonic dispersion (Maiti et al., 2014, Shindou et al., 2013, Glozman, 2018).

A second misconception is to identify all chiral spin modes with charge-sector collective modes. The surface-state mode in Bi$_2$Se$_3$, for example, is explicitly distinguished from Dirac plasmons and surface plasmons: at $q\approx 0$ it is decoupled from charge, appears in the pseudovector $A_2$ Raman channel, and occurs at finite energy rather than with $\omega_p(q)\to0$ as $q\to0$ (Kung et al., 2017). More generally, several papers emphasize that the relevant response channel is spin or pseudovector, not scalar density (Kung et al., 2017, Shan et al., 20 Sep 2025).

2. Spin–orbit-coupled electron systems

In a two-dimensional Fermi liquid with Rashba or Dresselhaus SOC, chiral spin modes are collective oscillations of spin density driven by coherent precession in the internal SOC field and stabilized by electron–electron interactions (Ashrafi et al., 2012). In the long-wavelength limit, the magnetization dynamics is governed by Klein–Gordon-type equations,

$$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$

with $i\in\{x,z\}$ for the Rashba case, $\omega(k)\neq\omega(-k)$0, and $\omega(k)\neq\omega(-k)$1 (Ashrafi et al., 2012). The mode stiffnesses are interaction-sensitive; notably, $\omega(k)\neq\omega(-k)$2 throughout $\omega(k)\neq\omega(-k)$3, whereas $\omega(k)\neq\omega(-k)$4 changes sign at $\omega(k)\neq\omega(-k)$5, so the effective mass of a confined standing mode can switch sign (Ashrafi et al., 2012). The same line of work proposed observing standing CSM by microwave absorption in a gated 2DEG with a spatially modulated SOC splitting.

A generalized-RPA treatment for arbitrarily strong Rashba SOC in both two and three dimensions sharpened this picture by showing that Rashba electron liquids support three spin-sector collective modes, conventionally labeled by the spin components $\omega(k)\neq\omega(-k)$6, $\omega(k)\neq\omega(-k)$7, and $\omega(k)\neq\omega(-k)$8 (Maiti et al., 2014). In two dimensions, the inter-subband continuum is gapped at $\omega(k)\neq\omega(-k)$9, so the spin modes can remain well defined below the continuum edge. In three dimensions, by contrast, the inter-subband continuum extends down to zero frequency, and the chiral-spin modes are strongly Landau damped and disappear for weak interaction (Maiti et al., 2014). That work also established a precise coupling structure: charge plasmons couple only to one of the three chiral-spin modes, and that coupling affects dispersions at finite but not zero wavenumber.

The first experimental observation of a transverse CSM on a three-dimensional topological-insulator surface was reported for Bi$_2$0Se$_2$1 using polarization-resolved resonant Raman spectroscopy (Kung et al., 2017). A sharp peak at $_2$2 meV appears only in the $_2$3 pseudovector channel and is identified as the transverse collective spin mode of the surface Dirac fermions. The surface states are modeled by

$_2$4

with hexagonal warping encoded in the $_2$5 component of $_2$6 (Kung et al., 2017). In this system, SOC supplies a momentum-dependent effective field, while exchange interactions “peel off” a bound spin-precession mode below the spin-flip continuum threshold $_2$7 meV. The Raman response in the $_2$8 channel probes the transverse spin susceptibility,

$_2$9

and the observed line is symmetry-pure, narrow, and robust up to room temperature (Kung et al., 2017).

An electronically distinct but conceptually related realization was reported in near-$_3$0 WSe$_3$1/WS$_3$2 moiré superlattices (Shan et al., 20 Sep 2025). There, the CSM is a gate-tunable inter-miniband spin-flip excitation between SOC-split conduction minibands, seen as a sharp resonance in the pseudovector-symmetry $_3$3 Raman channel. At filling $_3$4 and $_3$5 K, its frequency is $_3$6 cm$_3$7 with deconvoluted FWHM $_3$8 cm$_3$9, and away from $q\approx 0$0 it evolves from a chiral spin exciton into a chiral spin excitonic polaron (Shan et al., 20 Sep 2025). The spin-flip character is directly confirmed by an out-of-plane Zeeman shift with $q\approx 0$1. The same filling dependence is interpreted as evidence that the $q\approx 0$2 insulator is charge-transfer rather than Mott–Hubbard in character (Shan et al., 20 Sep 2025).

More recent work extended SOC-based CSM into high-frequency cross-response. In Rashba or Dresselhaus systems and in two-valley Dirac systems with Rashba and valley-Zeeman couplings, chiral-spin modes produce resonant Edelstein and inverse Edelstein responses at THz frequencies (Saleh et al., 27 Jan 2025). Near resonance,

$q\approx 0$3

and the electrically induced magnetization is resonantly enhanced, with predicted charge-to-spin conversion boosted by $q\approx 0$4–$q\approx 0$5 in graphene/TMD heterostructures (Saleh et al., 27 Jan 2025). A different transport-oriented realization appears in chiral tellurium, where the relevant collective objects are slow relaxons of the collision operator rather than propagating magnons. Those slow modes are described as CSM because they carry spin and orbital angular momentum, arise from spin–momentum entanglement, and resemble a persistent spin helix with a lifetime much longer than the mean momentum-scattering time (Barts et al., 2024).

3. DMI, nonreciprocity, and confined magnetic spin waves

In chiral magnets, the defining mechanism is DMI-induced nonreciprocity. A minimal description gives

$q\approx 0$6

so that $q\approx 0$7 (Zingsem et al., 2016). When such waves are confined between boundaries, counterpropagating components at the same frequency have different wavelengths. Their interference yields modes with fixed nodes but asymmetric, time-shifting envelopes rather than ordinary inversion-symmetric standing waves. In the weak-DMI limit,

$q\approx 0$8

and the confined profile becomes

$q\approx 0$9

which makes the envelope drift while the nodes remain fixed (Zingsem et al., 2016). This “generalized concept of mode confinement” predicts that DMI can render higher standing modes visible in ferromagnetic resonance and permits extraction of both the magnitude and sign of DMI (Zingsem et al., 2016).

The same logic acquires a fully three-dimensional form in finite-thickness skyrmion lattices (Savchenko et al., 2022). There, chiral standing spin waves are thickness-quantized modes whose dynamic magnetization winds helically along the film normal with chirality fixed by the bulk DMI. In the field-polarized state the analytic profiles are

$A_2$0

$A_2$1

with eigenfrequencies

$A_2$2

Because a uniform rf drive couples to the thickness-integrated moment, the overlap oscillates with thickness and vanishes when

$A_2$3

producing the paper’s “periodical fading” of absorption intensity (Savchenko et al., 2022). This is a chirality-driven selection rule rather than a conventional standing-wave effect.

A further confined chiral magnetic realization was reported for a hopfion-like state in Co/Pt nanodiscs (Arora et al., 2023). Micromagnetic simulations identified nonreciprocal spin-wave modes unique to that state, with resonances at $A_2$4, $A_2$5, and $A_2$6 GHz for a representative $A_2$7 nm disc. These modes combine breathing and quantized radial character, show continuous radial phase gradients, and can drive a hopfion-like to skyrmion transition after five oscillations of the $A_2$8 GHz mode, corresponding to $A_2$9 ns (Arora et al., 2023). A plausible implication is that chiral texture engineering can be used not only to shape spectra but also to trigger texture-to-texture switching through mode-selective excitation.

4. Edge localization, finite-size effects, and topological magnonics

Finite chiral spin chains provide a complementary setting in which the ground state itself is noncollinear. For bi-atomic Fe chains on Ir(001), a Heisenberg model with Dzyaloshinskii–Moriya coupling, uniaxial anisotropy, and Zeeman field yields a chiral spin spiral (Roldán-Molina et al., 2013). Quantization in the local rotating frame produces a bosonic Bogoliubov Hamiltonian with anomalous terms, so magnon number is not conserved in the spiral phase. Three principal consequences were emphasized: a significant zero-point reduction of the ground-state magnetization, two lowest-energy spin waves localized near the edges in the spiral phase, and an oscillatory dependence of the spin-wave spectrum on chain length with the same period as the spin helix (Roldán-Molina et al., 2013). Above a critical field the spiral collapses into a collinear ferromagnetic state, and those low-energy edge modes become confined bulk standing waves.

A topologically distinct edge realization occurs in dipolar magnetic thin films patterned into two-dimensional periodic arrays (Shindou et al., 2013). Linearized Landau–Lifshitz theory leads to a bosonic BdG band problem whose particle bands can carry nonzero Chern numbers. The corresponding boundary excitations are chiral spin-wave edge modes that cross bulk band gaps unidirectionally, with their chirality fixed by the sum of the Chern numbers of the bands below the gap (Shindou et al., 2013). This makes them the magnonic analogue of integer-quantum-Hall edge states rather than merely DMI-shifted standing waves. Their direction can reverse as the applied perpendicular field is tuned, because field-driven band inversions transfer Chern number between bulk bands. This field-magnitude-controlled chirality reversal sharply distinguishes them from Damon–Eshbach surface modes, whose handedness is not reversed simply by changing the field magnitude (Shindou et al., 2013).

The contrast between these two boundary settings is instructive. In finite chiral chains, low-energy localization is tied to the noncollinear spiral background and to open boundaries (Roldán-Molina et al., 2013). In dipolar magnonic crystals, edge propagation is fixed by bulk topology and survives as a band-gap phenomenon (Shindou et al., 2013). Both are legitimately described as CSM, but the protecting mechanisms are different: one is local noncollinearity plus confinement, the other is bulk–edge correspondence.

5. Chiral spin liquids and neutral collective modes

In the $\omega_p(q)\to0$0-symmetric chiral spin liquid phase of the spin-$\omega_p(q)\to0$1 square-lattice $\omega_p(q)\to0$2–$\omega_p(q)\to0$3–$\omega_p(q)\to0$4 model, the label CSM is applied to neutral bulk collective excitations in the spin-singlet sector rather than to propagating magnons (Lu et al., 28 Jan 2026). Two such modes were identified by exact diagonalization and time-dependent variational principle calculations. The first is a low-energy chiral $\omega_p(q)\to0$5-wave roton at momentum $\omega_p(q)\to0$6, created most strongly by the chiral bond operator

$\omega_p(q)\to0$7

with the mode residing in the $\omega_p(q)\to0$8 channel for $\omega_p(q)\to0$9 and flipping chirality when the sign of $q\to0$0 is reversed (Lu et al., 28 Jan 2026). Deep in the chiral spin liquid, the roton appears at $q\to0$1 in units of $q\to0$2 and carries strong spectral weight in the singlet bond structure factors.

The second mode is a higher-energy long-wavelength $q\to0$3-wave nematic excitation at $q\to0$4, probed by

$q\to0$5

Unlike the long-wavelength graviton mode in fractional quantum Hall liquids, this nematic mode shows no evident chirality: the chiral combinations $q\to0$6 do not produce a clear splitting or strong dichroism (Lu et al., 28 Jan 2026). As $q\to0$7 is increased, the nematic mode softens strongly and becomes the lowest singlet excitation at $q\to0$8, while low-lying spin-triplet two-spinon bound states also approach zero energy near $q\to0$9 or $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$0. This was interpreted as evidence for proximity to nematic and stripe instabilities (Lu et al., 28 Jan 2026).

This usage broadens the scope of CSM beyond semiclassical spin dynamics. Here the chirality resides in the orbital character of neutral singlet excitations and in the parity- and time-reversal-breaking ground state. A plausible implication is that “chiral spin mode” can denote an internal symmetry channel of a neutral collective excitation even when neither a classical spin texture nor an SOC-induced effective field is present.

6. Chiralspin symmetry and QCD

In QCD, the relevant concept is not a magnetic spin wave but chiralspin symmetry, $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$1, acting in Dirac space and mixing right- and left-handed components (Glozman, 2018). The generators are

$$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$2

which satisfy the $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$3 algebra and embed into $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$4 together with flavor (Glozman, 2018). The key structural point is that the fermion charge

$$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$5

is invariant under this larger group, whereas the free Dirac Lagrangian is not. Consequently, the chromo-electric interaction is $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$6- and $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$7-symmetric, while chromo-magnetic and kinetic terms break those symmetries (Glozman, 2018).

Within that framework, CSM are collective excitations of quark bilinears that transform under $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$8 and $$(\partial_t^2+\Omega_{i0}^2-D_i\nabla^2)M_i(\mathbf r,t)=0,$$9 in regimes where chromo-magnetic effects are suppressed (Glozman, 2018). Two diagnostic settings were discussed. At $i\in\{x,z\}$0, artificial low-mode truncation of the Dirac operator reveals degeneracies larger than those implied by ordinary chiral symmetry, organizing $i\in\{x,z\}$1 meson operators into $i\in\{x,z\}$2 and $i\in\{x,z\}$3 multiplets. At high temperature, above the chiral restoration crossover, lattice correlators of isovector bilinears form approximate $i\in\{x,z\}$4 and $i\in\{x,z\}$5 multiplets; at $i\in\{x,z\}$6 MeV the symmetry breaking is at the $i\in\{x,z\}$7 level, while $i\in\{x,z\}$8 and $i\in\{x,z\}$9 are essentially restored (Glozman, 2018). The resulting matter is described as a “stringy fluid,” meaning quarks with definite chirality bound by chromo-electric fields with suppressed chromo-magnetic interactions (Glozman, 2018).

This use of the term is the furthest from condensed-matter practice and is a common source of confusion. The phrase “chiral spin mode” here does not refer to SOC, DMI, plasmons, or magnons. It refers to collective dynamics organized by an emergent approximate symmetry of quark bilinears. The shared vocabulary reflects a symmetry between chirality and spinor structure, not a shared microscopic Hamiltonian.

Taken together, these bodies of work show that chiral spin modes are best understood as a family resemblance concept. In every case, a spinful collective excitation is constrained by a handed internal structure—spin–orbit locking, DMI, band topology, chiral liquid order, or chiralspin symmetry—but the observables, equations of motion, and experimental diagnostics are domain-specific. The most reliable way to interpret the term is therefore not by the name alone, but by the underlying mechanism and response channel specified in each context (Kung et al., 2017, Savchenko et al., 2022, Glozman, 2018, Lu et al., 28 Jan 2026).