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International Symposium on Nuclear Structure Problems

Tensor Correlations on Spin-Orbit Splittings and Spin Dependent Excitations

Hiroyuki Sagawa, Li-Gang Cao, C. L. Bai, G. Colò

Published Nov 25, 2012• 0 citations
Publisher
DOI
10.1142/9789814417952_0011

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Altermagnetism has recently emerged as a distinct collinear magnetic phase exhibiting momentum-dependent spin-splitting despite vanishing net magnetization, as a consequence of inequivalent non-magnetic environments. Lately, it has been proposed that strong electronic correlations may yield spontaneous altermagnetism due to orbital ordering even for equivalent non-magnetic environments. While previous studies have largely focused on the electronic structure, a unified understanding of the collective excitations associated with these two different microscopic mechanisms stabilizing altermagnetism remains absent. Here, we develop an extended Kugel'-Khomskiĭ spin-orbital model on a decorated square lattice that simultaneously incorporates inequivalent non-magnetic environments and correlation-driven orbital ordering within a common theoretical framework. Employing a self-consistent mean-field spin-wave orbital-wave formalism, we demonstrate the emergence of mutually unhybridized but interdependent magnon and orbiton excitations exhibiting characteristic chiral-splitting. We show that the splitting originates from two distinct microscopic contributions: a lattice-dependent term arising from inequivalent non-magnetic environments and an orbital-order-induced exchange-anisotropy term that survives even for equivalent non-magnetic environments. The proposed framework therefore unifies the collective excitations associated with both types of altermagnetism. We further investigate the finite-temperature evolution of the coupled spin-orbital system, revealing the breakdown of spin-wave and orbital-wave approximations through spurious 1st-order transitions, while complementary classical Monte Carlo simulations recover the expected continuous 2nd-order behaviour. Our work establishes a unified microscopic framework for understanding collective magnon and orbiton excitations in altermagnets.
The full frequency dependence of electronic interactions is central to dynamical correlations, but its numerical cost restricts multiorbital calculations. We formulate the multiloop functional renormalization group directly in the quantics tensor train representation, retaining all three independent vertex frequencies over broad ranges without an explicit high-frequency parametrization. Analytical tensor operators perform frequency transformations and internal summations without dense vertex intermediates. Multiloop corrections improve agreement of vertices and responses with independent references and reproduce the low-energy numerical renormalization group self-energy. Lower-temperature calculations resolve a quadratic frequency contribution to the analytically continued scattering rate. A degenerate two-orbital impurity exhibits distinct spin, orbital, and charge responses at fixed Hund coupling. In a compensated altermagnetic environment, an orbital-level splitting induces a local spin response despite zero magnetization of the unperturbed impurity. Increasing Hund coupling suppresses the orbital response while increasing its spin polarization. Renormalized one-particle propagation alone does not reproduce this strong polarization dependence. These results extend compressed multiloop calculations to dynamical correlations in multiorbital environments.
The emission intensity of diamond samples containing negatively charged nitrogen-vacancy centres are measured as a function of magnetic field along the ⟨111⟩ direction for various temperatures. At low temperatures the responses are sample and stress dependent and can be modelled in terms of the previous understanding of the 3 E excited state fine structure which is strain dependent. At room temperature the responses are largely sample and stress independent, and modelling involves invoking a strain independent excited state with a single zero field spin-level splitting of 1.42 GHz. The change in behaviour is attributed to a temperature dependent averaging process over the components of the excited state orbital doublet. It decouples orbit and spin and at high temperature the spin levels become independent of any orbit splitting. One significant implication of this averaging is that it simplifies the development of room temperature applications.