International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
We derive an exact expression for the orbital magnetization of electrons with short-range interactions (such as density-density interactions) in terms of exact zero-frequency response functions of the zero-field system. The result applies to weakly and strongly correlated electrons at zero and finite temperature, provided that the local grand potential density only depends on local thermodynamic parameters. We benchmark the formula for non-interacting and weakly-coupled electrons. To zeroth and first orders in the interaction strength, it agrees with the modern theory of orbital magnetization and its recent generalization to self-consistent Hartree-Fock bands. Our work provides an exact framework of interacting orbital magnetization beyond mean-field treatments, and paves the way for quantitative studies of strongly correlated electrons in external magnetic fields.
Recently, Berry phase in the semiclassical dynamical of Bloch electrons has been found to make a correction to the phase-space density of states and a general multi-band formula for finite-temperature orbital magnetization has been given [Phys. Rev. Lett. \textbf{97}, 026603 (2006)], where the orbital magnetization $\mathcal{M}$ consists of two parts, i.e., the conventional part $M_{c}$ and the Berry-phase correction part $M_Ω$. Using this general formula, we theoretically investigate the orbital magnetization and its effects on thermoelectric transport and magnetic susceptibility properties o…
The orbital magnetization and its effects on the two-dimensional kagomé lattice with spin anisotropies included in the general Hund's coupling region have been theoretically studied. The results show that the strength of the Hund's coupling, as well as the spin chirality, contributes to the orbital magnetization $\mathcal{M}$. Upon varying both these parameters, it is found that the two parts of $\mathcal{M}$, i.e., the conventional part $\mathbf{M}_{c}$ and the Berry-phase correction part $\mathbf{M}_Ω$, oppose each other. The anomalous Nernst conductivity is also calculated and a peak-valley…
We study the intrinsic orbital magnetization (OM) in antiferromagnets on the distorted face-centered-cubic lattice. The combined lattice distortion and spin frustration induce nontrivial $k$-space Chern invariant, which turns to result in profound effects on the OM properties. We derive a specific relation between the OM and the Hall conductivity, according to which it is found that the intrinsic OM vanishes when the electron chemical potential lies in the Mott gap. The distinct behavior of the intrinsic OM in the metallic and insulating regions is shown. The Berry phase effects on the thermoe…
Orbital Inverse Faraday and Cotton-Mouton Effects in Hall Fluids
Nordita（诺迪塔）；Stockholm University（斯德哥尔摩大学）；KTH Royal Institute of Technology（皇家理工学院）；Center for Quantum Spintronics, Department of Physics, Norwegian University of Science and Technology（挪威科技大学量子自旋电子学中心物理系）；Department of Physics, University of Connecticut（康涅狄格大学物理系）
Spin-orbit coupling introduces chirality into electronic structure. This can have profound effects on the magnetization induced by orbital motion of electrons. Here we derive a formula for the orbital magnetization of interacting electrons in terms of the full Green's function and vertex functions. The formula is applied within dynamical mean-field theory to the Kane-Mele-Hubbard model that allows both topological and trivial insulating phases. We study the insulating and metallic phases in the presence of an exchange magnetic field. In the presence of interactions, the orbital magnetization o…
Three symmetries prevent a twisted bilayer of graphene from developing an in-plane spontaneous magnetization in the absence of a magnetic field - time reversal symmetry, $C_2$ symmetry to $π$ rotation and $C_3$ symmetry to $2π/3$ rotation. In contrast, there are experimental and theoretical indications that, at certain electron densities, time reversal and $C_2$ symmetries are broken spontaneously, while the $C_3$ symmetry is often broken due to strain. We show that in-plane orbital magnetization is a very sensitive probe to the simultaneous breaking of these three symmetries, exhibiting surpr…
The effect of electronic correlations on the orbital magnetization in real materials has not been explored beyond a static mean-field level. Based on the dynamical mean-field theory, the effect of electronic correlations on the orbital magnetization in layered ferromagnet VI$_3$ has been studied. A comparison drawn with the results obtained from density functional theory calculations robustly establishes the crucial role of dynamical correlations in this case. In contrast to the density functional theory that leads to negligible orbital magnetization in VI$_3$, in dynamical mean-field approach…
We present a formalism to calculate the orbital magnetization of interacting Dirac fermions under a magnetic field. In this approach, the divergence difficulty is overcome with a special limit of the derivative of the thermodynamic potential with respect to the magnetic field. The formalism satisfies the particle-hole symmetry of the Dirac fermions system. We apply the formalism to the interacting Dirac fermions in graphene. The charge and spin orderings and the exchange interactions between all the Landau levels are taken into account by the mean-field theory. The results for the orbital magn…
We report on a study of various RVO3 single-crystal samples (R = La, Nd, Sm, Gd, Er and Y) which show temperature-induced magnetization reversal. For compounds with lighter rare-earths (R = La, Nd and Sm), magnetization reversal can be observed for magnetic field applied in the ab plane and along the c axis, whereas for the heavy rare-earths (R = Gd, Er) magnetization reversal is only observed when the field is applied along the a axis. YVO3 has a magnetization reversal along all the main crystallographic axes in a modest applied field. We have found that some compounds are very sensitive to s…
We study the orbital magnetic quadrupole moment (MQM) in three dimensional higher-order topological phases. Much like electric quadrupole moment, which is associated with a charge response on the boundaries of a finite sample, the diagonal components of the MQM manifest as surface-localized magnetization and hinge currents. The hinge current is generally not equal to the difference of surface magnetizations that intersect at the hinge, and we show this mismatch is precisely quantified by the bulk MQM. We derive a quantum mechanical formula for the layer-resolved magnetization in slab geometrie…
Towards understanding the multi-orbital quantum antiferromagnetism in iron pnictides, effective spin couplings and spin fluctuation induced quantum corrections to sublattice magnetization are obtained in the $(π,0)$ AF state of a realistic three band interacting electron model involving $xz$, $yz$, and $xy$ Fe 3d orbitals. The $xy$ orbital is found to be mainly responsible for the generation of strong ferromagnetic spin coupling in the $b$ direction, which is critically important to fully account for the spin wave dispersion as measured in inelastic neutron scattering experiments. The ferromag…
A spin-orbital chain with different Landé $g$ factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Landé $g$ factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of t…
We report thermodynamic magnetization measurements of a 2-dimensional electron gas for several high mobility Si-MOSFETs. The low-temperature magnetization is shown to be strongly sub-linear function of the magnetic field. The susceptibility determined from the zero-field slope diverges as 1/T^α, with α=2.2-2.6 even at high electron densities, in apparent contradiction with the Fermi-liquid picture.
Contribution of remote bands to orbital magnetization in twisted bilayer graphene
ShanghaiTech University（上海科技大学）；State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（量子功能材料国家重点实验室，上海科技大学物理科学与技术学院）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（凝聚态物理北京国家实验室和中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Physics, Boston College（波士顿学院物理系）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Department of Physics and Institute for Quantum Science and Technology, Shanghai University（上海大学物理系和量子科学技术研究院）；Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University（上海高温超导重点实验室，上海大学）
We compute the orbital magnetization in real materials by evaluating a recently discovered formula for periodic systems, within density functional theory. We obtain improved values of the orbital magnetization in the ferromagnetic metals Fe, Co, and Ni, by taking into account the contribution of the interstitial regions neglected so far in literature. We also use the orbital magnetization to compute the EPR $g$-tensor in molecules and solids. The present approach reproduces the $g$-tensor obtained by linear response (LR), when the spin-orbit can be treated as a perturbation. However, it can al…
Dichroism from Chiral Thermoelectric Probes: Generalized Sum Rules for Orbital and Heat Magnetizations
Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（卡斯勒布罗塞尔实验室，法兰西学院，法国国家科学研究中心，巴黎高等师范学院-巴黎文理研究大学，索邦大学）；International Solvay Institutes（国际索尔维研究所）；Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles（非线性现象与复杂系统中心，布鲁塞尔自由大学）
Electrons in moiré flat band systems can spontaneously break time reversal symmetry, giving rise to a quantized anomalous Hall effect. Here we use a superconducting quantum interference device to image stray magnetic fields in one such system composed of twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap consistent with …
The plateau at 1/3 of the saturation magnetization, $M_s$, in the metamagnet CeSb is accompanied by a state of ferromagnetic layers of spins in an up-up-down sequence. We measured $M$ and the specific heat, $C$, in the plateau, spin wave analyses of which reveal two distinct branches of excitations. Those with $ΔS_z = 1$ as measured by $M$, coexist with a much larger population of $ΔS_z = 0$ excitations measured by $C$ but invisible to $M$. The large density of $ΔS_z = 0$ excitations, their energy gap, and their seeming lack of interaction with $ΔS_z = 1$ excitations suggest an analogy with as…
We present a general formula of the orbital magnetization of disordered systems based on the Keldysh Green's function theory in the gauge-covariant Wigner space. In our approach, the gauge invariance of physical quantities is ensured from the very beginning, and the vertex corrections are easily included. Our formula applies not only for insulators but also for metallic systems where the quasiparicle behavior is usually strongly modified by the disorder scattering. In the absence of disorders, our formula recovers the previous results obtained from the semiclassical theory and the perturbation…
We measure the thermodynamic magnetization of a low-disordered, strongly correlated two-dimensional electron system in silicon in perpendicular magnetic fields. A new, parameter-free method is used to directly determine the spectrum characteristics (Lande g-factor and the cyclotron mass) when the Fermi level lies outside the spectral gaps and the inter-level interactions between quasiparticles are avoided. Intra-level interactions are found to strongly modify the magnetization, without affecting the determined g* and m*.
Orbital magnetization is known empirically to play an important role in several magnetic phenomena, such as permanent magnetism and ferromagnetic superconductivity. Within the recently developed ''modern theory of orbital magnetization'', theoretical insight has been gained into the nature of this often neglected contribution to magnetism, but is based on an underlying mean-field approximation. From this theory, a few treatments have emerged which also take into account correlations beyond the mean-field approximation. Here, we apply the scheme developed in a previous work [Phys. Rev. B ${\bf …
Ferromagnetic Weyl semi-metals exhibit an anomalous Hall effect, a consequence of their topological properties. In the non-interacting case, the derivative of the orbital magnetization with respect to chemical potential is proportional to this anomalous Hall effect, the Str$\check{\text{e}}$da formula. Motivated by compounds such as $\text{Mn}_3\text{Sn}$, here we investigate how interactions modeled by a Hubbard $U$ impact on both quantities when the Fermi energy is either aligned with the Weyl nodes or away from them. Within Dynamical Mean-Field Theory, we find, in the Weyl semimetal regime,…
Skyrmions are small magnetic quasiparticles, which are uniquely characterized by their topological charge and their helicity. In this Rapid Communication, we show via calculations how both properties can be determined without relying on real-space imaging. The orbital magnetization and topological Hall conductivity measure the arising magnetization due to the circulation of electrons in the bulk and the occurrence of topologically protected edge channels due to the emergent field of a skyrmion crystal. Both observables quantify the topological Hall effect and distinguish skyrmions from antisky…
The low temperature magnetization process of the ferromagnetic-antiferromagnetic Heisenberg chain is studied using the interacting boson approximation. In the low field regime and near the saturation field, the spin wave excitations are approximated by the $δ$ function boson gas for which the Bethe ansatz solution is available. The finite temperature properties are calculated by solving the integral equation numerically. The comparison is made with Monte Carlo calculation and the limit of the applicability of the present approximation is discussed.
The magnetism in the ferromagnetic superconductor UCoGe has been studied using a combination of magnetic Compton scattering, bulk magnetization, X-ray magnetic circular dichroism and electronic structure calculations, in order to determine the spin and orbital moments. The experimentally observed total spin moment, $M_s$, was found to be -0.24 $\pm$ 0.05~$μ_B$ at 5~T. By comparison with the total moment of 0.16 $\pm$ 0.01~$μ_B$, the orbital moment, $M_l$, was determined to be 0.40 $\pm$ 0.05~$μ_B$. The U and Co spin moments were determined to be antiparallel. We find that the U 5\textit{f} ele…
We have determined the temperature evolution of the spin and orbital moments in the zero magnetization ferromagnet Sm$_{1-x}$Gd$_x$Al$_2$ (x = 0.024) by combining polarized and unpolarized single crystal neutron diffraction data. The sensitivity of the polarized neutron technique has allowed the moment values to be determined with a precision of $\approx 0.1$~\mub. Our results clearly demonstrate that, when magnetised by a field of 8T, the spin and orbital moments in Sm$_{1-x}$Gd$_x$Al$_2$ are oppositely directed so that the net magnetization is very small. Below 60 K the contributions from sp…
We report the results of magnetization, heat capacity and neutron scattering studies of LaVO3 single crystals. From the neutron diffraction studies, it was found that the compound is magnetically ordered with a C-type antiferromagnetic spin structure at about 136 K. In the vicinity of the ordering temperature, we also observed hysteresis in the neutron diffraction data measured on cooling and heating which indicates the first order nature of the phase transition. In the antiferromagnetically ordered phase, the inelastic neutron scattering studies reveal the presence of a temperature independen…
Single Crystals of Nd$_{1-x}$Ca$_{1+x}$MnO$_{4}$ have been prepared by the traveling floating-zone method, and possible evidence of a charge -orbital density wave in this material presented earlier [PRB68,092405 (2003)] using High Resolution Electron Microscopy [HRTEM] and Electron Diffraction [ED]. In the current note we present direct evidence of charge-orbital ordering in this material using heat capacity measurements. Our heat capacity measurements indicate a clear transition consistent with prior observation. We find two main transitions, one at temperature $T_{_H}^{HC}=310-314$ K, and ot…
We examine the magnetic phase diagram of iron pnictides using a five band model. For the intermediate values of the interaction expected to hold in the iron pnictides, we find a metallic low moment state characterized by antiparallel orbital magnetic moments. The anisotropy of the interorbital hopping amplitudes is the key to understanding this low moment state. This state accounts for the small magnetization measured in undoped iron pnictides and leads to the strong exchange anisotropy found in neutron experiments. Orbital ordering is concomitant with magnetism and produces the large zx orbit…
We study the behavior of magnetization curve as a function of magnetic field in the immediate vicinity of the magnetization plateaus of 1D electron systems within the bosonization formalism. First we discuss the plateau that is formed at the saturation magnetization of 1D electron system. Interactions between electrons we treat in the lowest order of perturbation. We show that for isolated systems, where total number of electrons is not allowed to vary, magnetic susceptibility stays always finite away of half filling. Similar statement holds for many other magnetization plateaus supporting non…
The weakly interacting S=1/2 dimers system Sr3Cr2O8 has been investigated by powder neutron diffraction and inelastic neutron scattering. Our data reveal a structural phase transition below room temperature corresponding to an antiferro-orbital ordering with nearly 90 degrees arrangement of the occupied 3z^2-r^2 d-orbital. This configuration leads to a drastic reduction of the inter-dimer exchange energies with respect to the high temperature orbital-disorder state, as shown by a spin-dimer analysis of the super-superexchange interactions performed using the Extended Huckel Tight Binding metho…
In experiments and applications usually the spin magnetic moment of magnons is considered. In this Paper we identify an additional degree of freedom of magnons: an \emph{orbital} magnetic moment brought about by spin-orbit coupling.Our microscopic theory uncovers that spin magnetization $\vec{M}^\mathrm{S}$ and orbital magnetization $\vec{M}^\mathrm{O}$ are independent quantities. They are not necessarily collinear; thus, even when the total spin moment is compensated due to antiferromagnetism ($\vec{M}^\mathrm{S} = \vec{0}$), $\vec{M}^\mathrm{O}$ may be nonzero. This scenario of orbital weak …
We investigated the Ru 4d and O 2p electronic structure and magnetic properties of an ultra-high-quality SrRuO3 film on SrTiO3 grown by machine-learning-assisted molecular beam epitaxy. The high itinerancy and long quantum lifetimes of the quasiparticles in the Ru 4d t2g-O 2p hybridized valence band are confirmed by observing the prominent well-screened peak in the Ru 3d core-level photoemission spectrum, the coherent peak near the Fermi energy in the valence band spectrum, and quantum oscillations in the resistivity. The element-specific magnetic properties and the hybridization between the R…
Phase transition and critical properties of Ising-like spin-orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin-orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin-orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin-orbital order-disorder transition is far from the second-order, rather, it is more close to the first-order, implying that the widely obs…
