Fermi Surface Model Research Articles

Spin dynamics, entanglement, and the nature of the spin liquid state in YbZnGaO4

Electron spin dynamics was studied down to 80 mK in the triangular-lattice quantum spin-liquid candidate ${\mathrm{YbZnGaO}}_{4}$ using muon spin relaxation, finding no evidence for freezing or ordering of the Yb spins. The muon spin relaxation rate can be represented by the sum of two contributions, one dependent on longitudinal magnetic field and the other independent of field. The field-dependent term follows the form expected for two-dimensional diffusion of mobile spin excitations. The spin-diffusion rate obtained for these excitations in the high temperature paramagnetic regime is comparable with the exchange coupling frequency $J/h$, reducing significantly in the low temperature quantum regime. This slowdown is assigned to the effect of quantum entanglement. The exchange coupling $J$ is estimated to be 2.0(2) K from the crossover between the two regimes. The field-independent term is only weakly dependent on temperature, and at 15 K its absolute value is consistent with dipolar coupling of the muon to the three Yb moments closest to the muon site, where the spin dynamics of these moments is determined by exchange fluctuations. The temperature-dependent properties in the quantum regime are compared against the three possible U(1) spin-liquid models that have been obtained for the strongly spin-orbit coupled triangular lattice by Y.-D. Li, Y.-M. Lu, and G. Chen [Phys. Rev. B 96, 054445 (2017)]. The comparison with theory takes published specific heat and thermal conductivity data into account, along with the spin-diffusion rate obtained from the muons. It is found that the nodal spin-liquid model U1A11 containing both linear and quadratic nodes provides better agreement with experiment than either the U1A00 spinon Fermi surface (FS) model or the U1A01 model that contains only linear nodes.

Magnetotransport studies of the Sb square-net compound LaAgSb2 under high pressure and rotating magnetic fields

Square-net-layered materials have attracted attention as an extended research platform of Dirac fermions and of exotic magnetotransport phenomena. In this study, we investigated the magnetotransport properties of $\mathrm{La}\mathrm{Ag}{\mathrm{Sb}}_{2}$, which has Sb-square-net layers and shows charge density wave (CDW) transitions at ambient pressure. The application of pressure suppresses the CDWs, and above a pressure of 3.2 GPa a normal metallic phase with no CDWs is realized. By utilizing a mechanical rotator combined with a high-pressure cell, we observed the angular dependence of the Shubnikov--de Haas (SdH) oscillation up to 3.5 GPa, and we confirmed the notable two-dimensional nature of the Fermi surface. In the normal metallic phase, we also observed a remarkable field-angular-dependent magnetoresistance (MR), which exhibited a ``butterflylike'' polar pattern. To understand these results, we theoretically calculated the Fermi surface and conductivity tensor at the normal metallic phase. We showed that the SdH frequency and Hall coefficient calculated based on the present Fermi surface model agree well with the experiment. The transport properties in the normal metallic phase are mostly dominated by the anisotropic Dirac band, which has the highest conductivity due to linear energy dispersions. We also proposed that momentum-dependent relaxation time plays an important role in the large transverse MR and negative longitudinal MR in the normal metallic phase, which is experimentally supported by the considerable violation of Kohler's scaling rule. Although quantitatively complete reproduction was not achieved, the calculation showed that the elemental features of the butterfly MR could be reasonably explained as the geometrical effect of the Fermi surface.

Reconstruction of the Fermi surface induced by high magnetic field in the quasi-two-dimensional charge density wave conductor η−Mo4O11

Low-dimensional charge density wave (CDW) systems, which undergo successive so-called Peierls phase transitions at characteristic temperatures associated with corresponding changes in electronic structure, are of great importance for exploring novel quantum physics. Here, we report systematic research of the magnetotransport properties for the quasi-two-dimensional CDW conductor $\ensuremath{\eta}\text{\ensuremath{-}}\mathrm{M}{\mathrm{o}}_{4}{\mathrm{O}}_{11}$ under high magnetic fields up to 59 T. Measurements of in-plane and out-of-plane magnetoresistance and Hall resistance have been carried out to determine the Fermi surface (FS) structure at low temperatures and high magnetic fields. Beyond the quantum limit (QL), fast quantum oscillations (QOs) with complex periods have been found in both MR and Hall resistance, representing a direct measurement of the area of the FS. In addition, we observe a conspicuous phase transition at 45 T. The QO frequency and carrier density successively increase above the QL and phase transition fields. Consequently, we propose that such remarkable feature of the magnetic field dependence of the fast QOs for $\ensuremath{\eta}\text{\ensuremath{-}}\mathrm{M}{\mathrm{o}}_{4}{\mathrm{O}}_{11}$ arises from the field-induced density wave transition and FS reconstruction. We have further discussed the mechanism and provided the evolution on the geometry of the FS with magnetic field in the second CDW state based on the field-dependent FS model.

Microscopic Eilenberger theory of Fulde-Ferrell-Larkin-Ovchinnikov states in the presence of vortices

We theoretically investigate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state by using the microscopic quasi-classical Eilenberger equation. The Pauli paramagnetic effects and the orbital depairing effects due to vortices are treated in an equal footing for three dimensional spherical Fermi surface model and $s$-wave pairing. The field evolution of the LO state is studied in detail, such as the $H$-$T$ phase diagram, spatial structures of the order parameter, the paramagnetic moment, and the internal filed. Field-dependences of various thermodynamic quantities: the paramagnetic moment, entropy, and the zero-energy density of states are calculated. Those quantities are shown to start quickly growing upon entering the LO state. We also evaluate the wave length of the LO modulation, the flux line lattice form factors for small angle neutron scattering, and the NMR spectra to facilitate the identification of the LO state. Two cases of strong and intermediate Pauli paramagnetic effect are studied comparatively. The possibility of the LO phase in Sr$_2$RuO$_4$, CeCoIn$_5$, CeCu$_2$Si$_2$, and the organic superconductors is critically examined and crucial experiments to identify it are proposed.

Strongly enhanced Gilbert damping anisotropy at low temperature in high quality single-crystalline Fe/MgO (0 0 1) thin film

The anisotropic behavior of Gilbert damping provides a new dimension for controlling and tuning magnetization relaxation within the same magnetic device. The single-crystalline ferromagnetic metals with a high symmetry have been predicted to possess significantly anisotropic damping for one decade. By decreasing temperature down to T = 4.5 K, we found that the anisotropic damping factor Q, defined as the fractional difference of damping between easy and hard axis, can be approached to 60%–90% in Fe (15 nm)/MgO (0 0 1) without applied fields dependent behavior. It is much larger than Q = 10%–20% obtained at room temperature. Furthermore, it is followed by explanations on the basis of the breathing Fermi surface model giving around Q = 30%–40% when electron-phonon scattering rate is small enough. This discovery will enrich the understanding of damping mechanism, and can provide clues for searching strongly anisotropic damping within 3d transition metals and alloys.

Unifying ultrafast demagnetization and intrinsic Gilbert damping in Co/Ni bilayers with electronic relaxation near the Fermi surface

The ability to controllably manipulate the laser-induced ultrafast magnetic dynamics is a prerequisite for future high-speed spintronic devices. The optimization of devices requires the controllability of the ultrafast demagnetization time ${\ensuremath{\tau}}_{M}$ and intrinsic Gilbert damping ${\ensuremath{\alpha}}_{\mathrm{intr}}$. In previous attempts to establish a relationship between ${\ensuremath{\tau}}_{M}$ and ${\ensuremath{\alpha}}_{\mathrm{intr}}$, the rare-earth doping of a permalloy film with two different demagnetization mechanisms was not a suitable candidate. Here, we choose Co/Ni bilayers to investigate the relations between ${\ensuremath{\tau}}_{M}$ and ${\ensuremath{\alpha}}_{\mathrm{intr}}$ by means of the time-resolved magneto-optical Kerr effect (TR-MOKE) via adjusting the thickness of the Ni layers, and obtain an approximately proportional relation between these two parameters. The remarkable agreement between the TR-MOKE experiment and the prediction of a breathing Fermi-surface model confirms that a large Elliott-Yafet spin-mixing parameter ${b}^{2}$ is relevant to the strong spin-orbital coupling at the Co/Ni interface. More importantly, a proportional relation between ${\ensuremath{\tau}}_{M}$ and ${\ensuremath{\alpha}}_{\mathrm{intr}}$ in such metallic films or heterostructures with electronic relaxation near the Fermi surface suggests the local spin-flip scattering dominates the mechanism of ultrafast demagnetization, otherwise the spin-current mechanism dominates. It is an effective method to distinguish the dominant contributions to ultrafast magnetic quenching in metallic heterostructures by simultaneously investigating both the ultrafast demagnetization time and Gilbert damping. Our work can open an avenue to manipulate the magnitude and efficiency of terahertz emission in metallic heterostructures such as perpendicular magnetic anisotropic Ta/Pt/Co/Ni/Pt/Ta multilayers, and then it has an immediate implication for the design of high-frequency spintronic devices.

Finite-energy spin fluctuations as a pairing glue in systems with coexisting electron and hole bands

We study, within the fluctuation-exchange approximation, the spin-fluctuation-mediated superconductivity in Hubbard-type models possessing electron and hole bands, and compare them with a model on a square lattice with a large Fermi surface. In the large Fermi surface model, superconductivity is more enhanced for better nesting for a fixed band filling. By contrast, in the models with electron and hole bands, superconductivity is optimized when the Fermi surface nesting is degraded to some extent, where finite-energy spin fluctuations around the nesting vector develop. The difference lies in the robustness of the nesting vector, namely, in models with electron and hole bands, the wave vector at which the spin susceptibility is maximized is fixed even when the nesting is degraded, whereas when the Fermi surface is large, the nesting vector varies with the deformation of the Fermi surface. We also discuss the possibility of realizing in actual materials the bilayer Hubbard model, which is a simple model with electron and hole bands, and is expected to have a very high ${T}_{c}$.

Ultra-low magnetic damping of perovskite La0.7Sr0.3MnO3 thin films

The perovskite La0.7Sr0.3MnO3 (LSMO) films grown on different substrates were investigated by an angle resolved broadband ferromagnetic resonance technique. All films exhibited a four-fold magnetocrystalline anisotropy, which is in accord with the crystal structure. Moreover, a perpendicular uniaxial anisotropy changed from the (001)pc easy plane to the [001]pc easy direction when the strain of LSMO films varies from tensile to compressive. The ultra-low magnetic damping constant of 5.2 × 10−4 was obtained for a 44.6 nm LSMO film on an NdGaO3 (110) substrate. The breathing Fermi surface model in which the damping constant is proportional to the density of states at Fermi energy is the dominant mechanism for the intrinsic magnetic relaxation.

Anisotropic Upper Critical Field of Iron-Based Superconductors

The upper critical field and its anisotropy are the easiest properties to examine in the research of iron-based superconductors. Based on warped cylindrical Fermi surface models, we investigate the temperature and angle dependence of the upper critical field in detail by employing the quasi-classical formalism of the Werthamer–Helfand–Hohenberg (WHH) theory. Our numerical results reveal the anisotropy of the upper critical field, which may be caused by an anisotropic gap function (e.g., d-wave pairing) or an anisotropic Fermi surface, respectively. Further, according to our analysis, this anisotropy can be modulated by the deformation of the Fermi surface and will be strongly suppressed by the Pauli paramagnetic effect.

Polarization dependent asymmetric magneto-resistance features in nanocrystalline diamond films

Polar angle-dependence of magneto-resistance (AMR) in heavily nitrogen-incorporated ultra-nanocrystalline diamond (UNCD) films is recorded by applying high magnetic fields, which shows strong anisotropic features at low temperatures. The temperature-dependence of MR and AMR can reveal transport in the weak-localization regime, which is explained by using a superlattice model for arbitrary values of disorder and angles. While a propagative Fermi surface model explains the negative MR features for low degree of disorder the azimuthal angle-dependent MR shows field dependent anisotropy due to the aligned conducting channels on the layers normal to film growth direction. The analysis of MR and AMR can extract the temperature dependence of dephasing time with respect to the elastic scattering time which not only establishes quasi-two dimensional features in this system but also suggests a potential application in monitoring the performance of UNCD based quantum devices.

Gilbert damping tensor within the breathing Fermi surface model: anisotropy and non-locality

In magnetization dynamics, the Gilbert damping α is often taken as a parameter. We report on a theoretical investigation of α, taking into account crystal symmetries, spin–orbit coupling and thermal reservoirs. The tensor is calculated within the Kamberský breathing Fermi-surface model. The computations are performed within a tight-binding electronic structure approach for the bulk and semi-infinite systems. Slater–Koster parameters are obtained by fitting the electronic structure to first-principles results obtained within the multiple-scattering theory. We address the damping tensor for the bulk and surfaces of the transition metals Fe and Co. The role of various contributions are investigated: intra- and interband transitions, electron and magnetic temperature as well as surface orientation. Our results reveal a complicated non-local, anisotropic damping that depends on all three thermal reservoirs.

Erratum: Generalized Gilbert equation including inertial damping: Derivation from an extended breathing Fermi surface model [Phys. Rev. B84, 172403 (2011)

Erratum: Generalized Gilbert equation including inertial damping: Derivation from an extended breathing Fermi surface model [Phys. Rev. B<b>84</b>, 172403 (2011)

Evolution of the multiband Ruderman–Kittel–Kasuya–Yosida interaction: application to iron pnictides and chalcogenides

The indirect Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in iron pnictide and chalcogenide metals is calculated for a simplified four-band Fermi surface model. We investigate the specific multi-band features and show that distinct length scales of the RKKY oscillations appear. For the regular lattice of local moments, the generalized RKKY interaction is defined in momentum space. We consider its momentum dependence in paramagnetic and spin density wave phases, discuss its implications for the possible type of magnetic order and compare it with the results obtained from a more realistic tight-binding-type Fermi surface model. Our finding can give important clues to the magnetic ordering of 4f-iron-based superconductors.

Tuneable anisotropic transport in nitrogen-doped nanocrystalline diamond films: Evidence of a graphite-diamond hybrid superlattice

We show strong evidence of superlattice-like carbon layered structures in heavily nitrogen-doped ultrananocrystalline diamond (UNCD) films through the experimental demonstration of temperature-dependent anisotropic diffusive transport. The superlattice periodicity, in the range of several nanometers, is derived from the analysis of both magneto-resistance and the temperature-dependent conductivity based on the generalized diffusive Fermi surface model. The effect of quasi–two-dimensionality on the magneto-transport of these films yields a weak temperature dependence of the electron dephasing length. These results explain a reasonably strong coupling between the conducting carbon layers separated by the insulating nanodiamond grains producing the anisotropic transport in UNCD films controlled by the level of nitrogen incorporation.

Origin of Spontaneous Broken Mirror Symmetry of Vortex Lattices in Nb

Combining the microscopic Eilenberger theory with the first-principles band calculation, we investigate the stable flux line lattice (FLL) for a field applied to the fourfold axis, i.e., H ∥[001] in cubic Nb. The observed FLL transformation along H c2 is almost perfectly explained without using adjustable parameter, including the tilted square, scalene triangle with broken mirror symmetry, and isosceles triangle lattices upon increasing T . We construct a minimum Fermi surface model to understand such morphologies, particularly the stability of the scalene triangle lattice attributed to the lack of mirror symmetry about the Fermi velocity maximum direction in k-space.

Generalized Gilbert equation including inertial damping: Derivation from an extended breathing Fermi surface model

In a recent paper [M.-C. Ciornei et al., Phys. Rev. B 83, 020410(R) (2011)], it has been shown by mesoscopic nonequilibrium thermodynamics that, for relatively fast magnetization dynamics, Gilbert's equation of motion for the magnetization has to be supplemented by an ``inertial'' damping term that contains the second derivative of the magnetization with respect to time. In the present Brief Report, it is shown that such an additional damping term can be derived and evaluatedvery naturally also within a slightly extended breathing Fermi surface model for magnetization damping.

Near Doping-Independent Pocket Area from an Antinodal Fermi Surface Instability in Underdoped High Temperature Superconductors

Fermi surface models applied to the underdoped cuprates predict the small pocket area to be strongly dependent on doping whereas quantum oscillations in YBa(2)Cu(3)O(6+x) find precisely the opposite to be true--seemingly at odds with the Luttinger volume. We show that such behavior can be explained by an incommensurate antinodal Fermi surface nesting-type instability--further explaining the doping-dependent superstructures seen in cuprates using scanning tunneling microscopy. We develop a Fermi surface reconstruction scheme involving orthogonal density waves in two dimensions and show that their incommensurate behavior requires momentum-dependent coupling. A cooperative modulation of the charge and bond strength is therefore suggested.

Relating Gilbert damping and ultrafast laser-induced demagnetization

Based on the breathing Fermi-surface model of Gilbert damping and on the Elliott-Yafet relation for the spin-relaxation time, a relation is established between the conductivitylike contribution to the Gilbert damping $\ensuremath{\alpha}$ at low temperatures and the demagnetization time ${\ensuremath{\tau}}_{\text{M}}$ for ultrafast laser-induced demagnetization at low laser fluences. Thereby it is assumed that, respectively, the same types of spin-dependent electron-scattering processes are relevant for $\ensuremath{\alpha}$ and ${\ensuremath{\tau}}_{\text{M}}$. The relation contains information on the properties of single-electron states which are calculated by the ab initio electron theory. The predicted value for $\ensuremath{\alpha}/{\ensuremath{\tau}}_{\text{M}}$ is in good agreement with the experimental value.

Calculation of the Gilbert damping matrix at low scattering rates in Gd

In rare-earth metals the magnetization dynamics is determined by the interplay between the magnetization ${\mathbf{M}}_{4f}$ of localized $4f$ electrons and the magnetization $\mathbf{m}$ of delocalized $5d6sp$ valence electrons, whereby both subsystems can deliver angular momentum to the lattice, thus producing damping. It is shown within the framework of a phenomenological version of the $s\text{\ensuremath{-}}f$ model that the effective Gilbert damping parameter for ${\mathbf{M}}_{4f}(t)$ is given by ${\ensuremath{\alpha}}_{4f}^{eff}={\ensuremath{\alpha}}_{4f}+{\ensuremath{\alpha}}_{5d6sp}/(1+{M}_{4f}/m)$, where ${\ensuremath{\alpha}}_{4f}$ is a direct $4f$ contribution and ${\ensuremath{\alpha}}_{5d6sp}$ describes the Gilbert damping for the valence magnetization. By a combination of the ab initio density-functional electron theory with the breathing Fermi-surface model it is shown that for a [0001] orientation of the magnetization the indirect valence contribution to ${\ensuremath{\alpha}}_{4f}^{eff}$ is comparable to the damping parameter of Co (which is considerably smaller than the one of Ni). Measurements of the damping at low temperatures and for Gd samples with high purity are required to figure out whether there is a considerable larger direct contribution ${\ensuremath{\alpha}}_{4f}$.

Damping of near-adiabatic magnetization dynamics by excitations of electron-hole pairs

Excitation of electron hole pairs and subsequent relaxation is the most important mechanism of intrinsic damping in near-adiabatic magnetization dynamics in metallic ferromagnets. Intraband scattering dominates in the low temperature regime and is described by the breathing Fermi surface model. A Gilbert-like equation of motion is derived within this model where the constant damping scalar is replaced by a magnetization dependent and in general nonlocal damping matrix. In collinear systems the damping term shows two types of anisotropy, and in a general noncollinear situation nonlocal damping matrices enter the equation of motion.