Showing papers on "Spin-½ published in 1997"
TL;DR: In this paper, the spin response function for electrons confined in a quantum dot is studied within the time-dependent local spin density approximation (TDLSDA) of density functional theory.
Abstract: The spin response function for electrons confined in a quantum dot is studied within the time-dependent local spin density approximation (TDLSDA) of density functional theory. In the long-wavelength regime we predict the existence of a low-energy collective dipole (l = 1) spin mode. The evolution with electron number of the spin response is studied and compared with that of the density response. Predictions for the static dipole polarizability are given.
332 citations
TL;DR: In this article, the spin-orbit splitting in the dispersion relation for electrons in III-V semiconductor asymmetric quantum wells is studied within the standard envelope-function formalism starting from the eight-band Kane model for the bulk.
Abstract: The spin-orbit splitting in the dispersion relation for electrons in III-V semiconductor asymmetric quantum wells is studied within the standard envelope-function formalism starting from the eight-band Kane model for the bulk. The Rashba spin-orbit splitting in the different subbands is obtained for both triangular and square asymmetric quantum wells. It is shown, for example, that the Rashba splitting in AlAs/GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As square quantum wells is of the order of 1 meV and presents a maximum as a function of the well width. The splitting of the excited subband in square and triangular quantum wells is shown to be bigger and smaller than the splitting in the first subband, respectively. A simple single-band approach, employing spin-dependent boundary conditions and approximate coupling parameters, is also introduced and its range of validity assessed. The discussion presented clarifies the treatment of abrupt interfaces, the Ando argument against the splitting, and the use of common approximations such as neglecting the barrier penetration or the energy-dependent corrections to the parameters. Good agreement is found with available experimental data.
275 citations
TL;DR: In this article, it was shown that the conductivity of charge transport is characterized by inelastic collisions among thermally excited carriers at a rate of order kBT=h. This implies that the transport at frequencies! kBT = h is in the hydrodynamic, collision-dominated (or 'incoherent') regime, while! KBT =h is the collisionless regime.
Abstract: We describe the nature of charge transport at non-zero temperatures (T ) above the two-dimensional (d) superuid-insulator quantum critical point. We argue that the transport is characterized by inelastic collisions among thermally excited carriers at a rate of order kBT=h. This implies that the transport at frequencies ! kBT=h is in the hydrodynamic, collision-dominated (or ‘incoherent’) regime, while ! kBT=h is the collisionless (or ‘phasecoherent’) regime. The conductivity is argued to be e 2 =h times a non-trivial universal scaling function ofh!=kBT , and not independent of h!=kBT ,a s has been previously claimed, or implicitly assumed. The experimentally measured d.c. conductivity is the hydrodynamic h!=kBT ! 0 limit of this function, and is a universal number times e 2 =h, even though the transport is incoherent. Previous work determined the conductivity by incorrectly assuming it was also equal to the collisionless h!=kBT !1limit of the scaling function, which actually describes phase-coherent transport with a conductivity given by a dierent universal number times e 2 =h. We provide the rst computation of the universal d.c. conductivity in a disorder-free boson model, along with explicit crossover functions, using a quantum Boltzmann equation and an expansion in =3 d. The case of spin transport near quantum critical points in antiferromagnets is also discussed. Similar ideas should apply to the transitions in quantum Hall systems and to metal-insulator transitions. We suggest experimental tests of our picture and speculate on a new route to self-duality at two-dimensional quantum critical points.
250 citations
TL;DR: In this article, the presence of the fourth order term in the total spin justifies the irregularities in the spacing of the jumps, recently observed in the hysteresis loop of Mn12ac and attributed to acceleration of the relaxation of the magnetization due to Quantum Tunneling between degenerate M states of the ground S=10 multiplet of the cluster.
Abstract: EPR spectra have been recorded in very high field, up to 25T, and at high frequency, up to 525 GHz, on a polycristalline sample of Mn12ac (see paper for detailed formula), the first example of molecular cluster behaving like a nanomagnet. The simulation of the spectra has provided an accurate determination of the parameters of the spin hamiltonian (see paper for formula and values of the various parameters). The presence of the fourth order term in the total spin justifies the irregularities in the spacing of the jumps, recently observed in the hysteresis loop of Mn12ac and attributed to acceleration of the relaxation of the magnetization due to Quantum Tunneling between degenerate M states of the ground S=10 multiplet of the cluster. The term in (S_+^4 + S_-^4) is responsible of the transverse magnetic anisotropy and plays a crucial role in the mechanism of Quantum Tunneling. The HF-EPR spectra have for the first time evidenced its presence and quantified it.
244 citations
TL;DR: In this article, the authors report variational calculations of symmetric nuclear matter and pure neutron matter, using the new Argonne v{sub 18} two-nucleon and Urbana IX three-nuclearon interactions, and show that both symmetric and pure nuclear matter undergo transitions to phases with pion condensation at densities of 0.32 and 0.2 fm{sup {minus}3, respectively.
Abstract: We report variational calculations of symmetric nuclear matter and pure neutron matter, using the new Argonne v{sub 18} two-nucleon and Urbana IX three-nucleon interactions. At the equilibrium density of 0.16 fm{sup {minus}3} the two-nucleon densities in symmetric nuclear matter exhibit a short-range spin-isospin structure similar to that found in light nuclei. We also find that both symmetric nuclear matter and pure neutron matter undergo transitions to phases with pion condensation at densities of 0.32 fm{sup {minus}3} and 0.2 fm{sup {minus}3}, respectively. Neither transtion occurs with the Urbana v{sub 14} two-nucleon interaction, while only the transition in neutron matter occurs with the Argonne v{sub 14} two-nucleon interaction. The three-nucleon interaction is required for the transition to occur in symmetric nuclear matter, whereas the transition in pure neutron matter occurs even in its absence. The behavior of the isovector spin-longitudinal response and the pion excess in the vicinity of the transition, and the model dependence of the transition are discussed. {copyright} {ital 1997} {ital The American Physical Society}
235 citations
TL;DR: In this paper, the relativistic version of the EPRB experiment with massive particles is discussed, and the degree of violation of the Bell inequality is shown to depend on the velocity of the pair of spin- particles with respect to the laboratory.
Abstract: Two aspects of the relativistic version of the Einstein-Podolsky-Rosen-Bohm (EPRB) experiment with massive particles are discussed: (a) a possibility of using the experiment as an implicit test of a relativistic center-of-mass concept, and (b) influence of the relativistic effects on degree of violation of the Bell inequality. The nonrelativistic singlet state average 〈\ensuremath{\psi}|a\ensuremath{\cdot}\ensuremath{\sigma}\ensuremath{\bigotimes}b\ensuremath{\cdot}\ensuremath{\sigma}|\ensuremath{\psi}〉=-a\ensuremath{\cdot}b is relativistically generalized by defining spin via the relativistic center-of-mass operator. The corresponding EPRB average contains relativistic corrections which are stronger in magnitude than standard relativistic phenomena such as the time delay, and can be measured in Einstein-Podolsky-Rosen-Bohm-type experiments with relativistic massive spin- particles. The degree of violation of the Bell inequality is shown to depend on the velocity of the pair of spin- particles with respect to the laboratory. Experimental confirmation of the relativistic formula would indicate that for relativistic nonzero-spin particles centers of mass and charge do not coincide. The result may have implications for quantum cryptography based on massive particles.
191 citations
TL;DR: In this article, the authors performed plane-wave pseudopotential density functional theory calculations on the stoichiometric and reduced TiO2 ~110! surface, the 231 and 132 reconstructions of the surface formed by the removal of bridging-oxygen atoms, and on the oxygen vacancy in the bulk.
Abstract: We have performed plane-wave pseudopotential density-functional theory calculations on the stoichiometric and reduced TiO2 ~110! surface, the 231 and 132 reconstructions of the surface formed by the removal of bridging-oxygen atoms, and on the oxygen vacancy in the bulk. The effect of including spin polarization is investigated, and it is found to give a qualitatively different electronic structure compared with a spin-paired description. In the spin-polarized solutions, the excess electrons generated by oxygen reduction occupy localized band-gap states formed from Ti (3d) orbitals, in agreement with experimental findings. In addition, the inclusion of spin polarization substantially lowers the energy of all the systems studied, when compared with spin-paired solutions. However, spin-polarization does not change the relative stability of the two reconstructions, which remain energetically equivalent. @S0163-1829~97!02724-0#
184 citations
TL;DR: In this article, a Potts spin is assigned to each data point and an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors, is introduced.
Abstract: We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an interaction between neighboring points, whose strength is a decreasing function of the distance between the neighbors. This magnetic system exhibits three phases. At very low temperatures, it is completely ordered; all spins are aligned. At very high temperatures, the system does not exhibit any ordering, and in an intermediate regime, clusters of relatively strongly coupled spins become ordered, whereas different clusters remain uncorrelated. This intermediate phase is identified by a jump in the order parameters. The spin-spin correlation function is used to partition the spins and the corresponding data points into clusters. We demonstrate on three synthetic and three real data sets how the method works. Detailed comparison to the performance of other techniques clearly indicates the relative success of our method.
168 citations
TL;DR: In this article, a spin-boson model with a coupling parameter α ∈Racts in the tensor product H⊕Fbof a Hilbert space H and the boson (symmetric) Fock space FboverL2(Rν) is considered.
159 citations
TL;DR: In this article, the ground and low-lying excited states of uniform and dimerized alternating spin chains were analyzed using spin wave and density-matrix renormalization group (DMRG) studies.
Abstract: We report spin wave and density-matrix renormalization-group (DMRG) studies of the ground and low-lying excited states of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of the system. The ground state of a 2N spin system with spin-1 and spin- alternating from site to site and interacting via an antiferromagnetic exchange is found to be ferrimagnetic with total spin ${\mathrm{s}}_{\mathrm{G}}$=N/2 from both DMRG and spin wave analysis. Both the studies also show that there is a gapless excitation to a state with spin ${\mathrm{s}}_{\mathrm{G}}$-1 and a gapped excitation to a state with spin ${\mathrm{s}}_{\mathrm{G}}$+1. Surprisingly, the correlation length in the ground state is found to be very small from both the studies for this gapless system. For this very reason, we show that the ground state can be described by a variational ansatz of the product type. DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls' instability. The DMRG studies of magnetization, magnetic susceptibility (\ensuremath{\chi}), and specific heat show strong magnetic-field dependence. The product \ensuremath{\chi}T shows a minimum as a function of temperature (T) at low-magnetic fields and the minimum vanishes at high-magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature and the height of the maximum increases sharply at high-magnetic fields. It is hoped that these studies will motivate experimental studies at high-magnetic fields.
158 citations
TL;DR: In this paper, the degenerate frustration problem is defined in the case of discrete molecular species for which competing spin interactions lead to an orbitally degenerate ground state, with at least one magnetic component.
TL;DR: A comprehensive review of almost twenty years of research on nuclear magnetic ordering, first in copper and later in silver and rhodium metals, can be found in this article, where the authors discuss recent neutron-diffraction measurements that show that the antiferromagnetic structure at Tg0 is in a single-k type-I state.
Abstract: This paper is a comprehensive review of almost twenty years of research on nuclear magnetic ordering, first in copper and later in silver and rhodium metals. The basic principles of nuclear magnetism and the measurement of positive and negative spin temperatures are discussed first. Cascade nuclear refrigeration techniques, susceptibility and nuclear-magnetic-resonance (NMR) measurements, and arrangements for neutron-diffraction experiments at nanokelvin and picokelvin temperatures are described next. Comprehensive magnetic-susceptibility and neutron-diffraction measurements on copper, which led to the discovery of at least three antiferromagnetic phases, one displaying the novel (0 ) spin structure and the other two showing the type-I order of the fcc system, are then described in detail. NMR data on silver, at Tg0 and T0, are presented next leading to the observation that silver orders antiferromagnetically at positive spin temperatures and ferromagnetically at negative spin temperatures. The authors discuss recent neutron-diffraction measurements that show that the antiferromagnetic structure at Tg0 is in a single-k type-I state. NMR data on rhodium at Tg0 and T0 are also described. Results obtained on Tl, Sc, ${\mathrm{AuIn}}_{2}$, and metallic Pr compounds and on insulators like ${\mathrm{CaF}}_{2}$ are then discussed briefly. The paper is concluded by an extensive theoretical section. Calculations of conduction-electron mediated exchange interactions are described, and the mean-field theory of nuclear magnetic ordering is presented. The role of thermal and quantum fluctuations is then discussed, particularly in the selection of the antiferromagnetic ground state. Finally, theoretically calculated magnetic phase diagrams and ordered spin structures of copper and silver are presented in detail and compared with experimental results. The overall agreement is good, affirming the value of nuclear magnets in Cu and Ag as realizations of simple physical models.
TL;DR: In this article, a relativistic formulation of the pion-nucleon-delta system is proposed and the most general structure of 1 M corrections for a heavy baryon chiral lagrangian including spin 3 2 resonances is given.
TL;DR: In this paper, Stein and Weiss introduced the notion of generalized gradients and proved ellipticity for certain systems, analogous to the Cauchy Riemann equations and to the (Riemannian signature) Maxwell and Dirac equations.
TL;DR: In this paper, the quantum mechanics of two identical particles with spin S in three dimensions is reformulated by employing not the usual fixed spin basis but a transported spin basis that exchanges the spins al...
Abstract: The quantum mechanics of two identical particles with spin S in three dimensions is reformulated by employing not the usual fixed spin basis but a transported spin basis that exchanges the spins al...
TL;DR: In this paper, a quark model calculation of the contribution of s{anti s} pairs arising from a complete set of OZI-allowed strong Y{sup *}K{sup*} hadronic loops to the net spin of the proton, to its charge radius, and to its magnetic moment is presented.
Abstract: Nontrivial q{anti q} sea effects have their origin in the low-Q{sup 2} dynamics of strong QCD. The authors present here a quark model calculation of the contribution of s{anti s} pairs arising from a complete set of OZI-allowed strong Y{sup *}K{sup *} hadronic loops to the net spin of the proton, to its charge radius, and to its magnetic moment. The calculation is performed in an ``unquenched quark model'' which has been shown to preserve the spectroscopic successes of the naive quark model and to respect the OZI rule. They speculate that an extension of the calculation to the nonstrange sea will show that most of the ``missing spin'' of the proton is in orbital angular momenta.
TL;DR: In this paper, a general method for finding algebraic expressions for matrix elements of any one and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors.
Abstract: A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to graphically calculate the irreducible tensorial products of the second-quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to graphically find the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second-quantization operators. As a result, it allows us to use standard quantities uniformly for both diagonal and off-diagonal matrix elements.
TL;DR: In this paper, the spin quantum beats of excitonic kind in the time-resolved photoluminescence of quantum wells in a magnetic field were reported, leading to a direct measurement of the electron-hole exchange energy of the 2D exciton and give important insights into the exciton properties.
Abstract: We report on spin quantum beats of excitonic kind in the time-resolved photoluminescence of quantum wells in a magnetic field. When this field is perpendicular to the growth direction, conditions for the manifestation of the electron or exciton spin precession in the circularly polarized components of the excitonic luminescence are obtained. These results lead to a direct measurement of the electron-hole exchange energy of the 2D exciton and give important insights into the exciton properties.
TL;DR: In this paper, the ground state of the Heisenberg spin chain with alternating spins 1 and and antiferromagnetic exchange interactions between nearest neighbors is constructed in a way that ensures given transformational properties under rotations, which allows one to fix the total spin, and its z projection, of the entire MP wave function.
Abstract: We present a method of constructing matrix-product (MP) states and apply it to the ground state of the Heisenberg spin chain with alternating spins 1 and and antiferromagnetic exchange interactions between nearest neighbors (the simplest example of a quantum ferrimagnet). The elementary matrix state is constructed in a way that ensures given transformational properties under rotations, which allows one to fix the total spin, and its z projection, of the entire MP wave function. We compare the variational MP results with the numerical results obtained through a quantum Monte Carlo method; the agreement is found to be within 0.4% for the ground-state energy and 5% for the correlation functions.
TL;DR: In this paper, angle-resolved photo-emission studies on one-dimensional Cu-O chain were conducted to reveal a behavior of a hole in the chain, which cannot be explained within conventional band theory, but require a picture in which the spin and charge degrees of freedom for a single electron are separated.
Abstract: In this paper we expand on our earlier results [Phys. Rev. Lett. 77, 4054 (1996)] on angle-resolved photoemission studies on one-dimensional ${\mathrm{SrCuO}}_{2}$ that reveal a behavior of a hole in Cu-O chain. The results cannot be explained within the conventional band theory, but require a picture in which the spin and charge degrees of freedom for a single electron are separated. Instead of a single branch as predicted in band theory, $E$ versus $k$ relationship can be explained by underlying spinon and holon excitations scaled by hopping energy $t$ and exchange energy $J,$ respectively, indicating separated spin and charge excitations. This is an experimental observation of direct consequence of the spin-charge separation driven by electron correlations that was first predicted thirty years ago. It also shows spinon and holons are real particles with definite energy-momentum dispersions.
TL;DR: In this article, the low-temperature properties of alternating spin chains with antiferromagnetic nearest-neighbour exchange couplings using analytical techniques as well as a quantum Monte Carlo method were investigated.
Abstract: We study the low-temperature properties of S = 1 and S = 1/2 alternating spin chains with antiferromagnetic nearest-neighbour exchange couplings using analytical techniques as well as a quantum Monte Carlo method. The spin-wave approach predicts two different low-lying excitations, which are gapped and gapless, respectively. The structure of low-lying levels is also discussed using perturbation theory in terms of the strength of the Ising anisotropy. These analytical findings are compared with the results of quantum Monte Carlo calculations, and it turns out that spin-wave theory describes the present system well. We conclude that the quantum ferrimagnetic chain exhibits both ferromagnetic and antiferromagnetic aspects.
TL;DR: In this article, the effect of free carriers on photoluminescence from modulation-doped self-assembled quantum dots was studied and exact diagonalization studies of up to N=8 electrons and a single exciton in InAs selfassembled dots, and a Hartree-Fock calculation for up to 20 electrons were carried out.
Abstract: We study the effect of free carriers on photoluminescence from modulation-doped self-assembled quantum dots. Exact diagonalization studies of up to N=8 electrons and a single exciton in InAs self-assembled dots, and a Hartree-Fock calculations for up to N=20 electrons, are carried out. The total spin and total angular momentum are found to oscillate with the number of electrons. The photoluminescence spectrum is calculated and the band-gap renormalization in zero-dimensional systems is discussed. The tendency of electrons in degenerate, partially filled electronic shells to maximize the total spin leads to a strong dependence of the spectrum on the number of electrons N, the magnetic field B, and the polarization of light.
TL;DR: In this article, the problem of a hole moving in an antiferromagnetic spin background was investigated and it was shown that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom.
Abstract: We reexamine the problem of a hole moving in an antiferromagnetic spin background and find that the injected hole will always pick up a sequence of nontrivial phases from the spin degrees of freedom. Previously unnoticed, such a stringlike phase originates from the hidden Marshall signs which are scrambled by the hopping of the hole. We can rigorously show that this phase string is nonrepairable at low energy and give a general proof that the spectral weight Z must vanish at the ground-state energy due to the phase-string effect. Thus, the quasiparticle description fails here and the quantum interference effect of the phase string dramatically affects the long-distance behavior of the injected hole. We introduce a so-called phase-string formulation of the t-J model for a general number of holes in which the phase-string effect can be explicitly tracked. As an example, by applying this new mathematical formulation in one dimension, we reproduce the well-known Luttinger-liquid behaviors of the asymptotic single-electron Green's function and the spin-spin correlation function. We can also use the present phase-string theory to justify previously developed spin-charge separation theory in two dimensions, which offers a systematic explanation for the transport and magnetic anomalies in the high-${\mathrm{T}}_{\mathrm{c}}$ cuprates.
TL;DR: In this paper, the motion of a relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin, is considered.
Abstract: We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The correct account for the spin influence on the particle trajectory is obtained with the noncovariant description of spin. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is demonstrated that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals to unity (as well as for the charged Kerr hole the gyromagnetic ratio equals to two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.
TL;DR: In this article, an effective low temperature, classical model for spin transport in the one-dimensional, gapped, quantum nonlinear model is developed, and its correlators are obtained by a mapping to a model solved earlier by Jepsen.
Abstract: An effective, low temperature, classical model for spin transport in the one-dimensional, gapped, quantum $\mathrm{O}(3)$ nonlinear $\ensuremath{\sigma}$ model is developed. Its correlators are obtained by a mapping to a model solved earlier by Jepsen. We obtain universal functions for the ballistic-to-diffusive crossover and the value of the spin diffusion constant, and these are claimed to be exact at low temperatures. Implications for experiments on one-dimensional insulators with a spin gap are noted.
TL;DR: In this article, an expression for the EPR line shape of a nitroxide free radical undergoing spin exchange in the slow exchange limit is derived and tested experimentally and against a rigorous theory.
Abstract: An expression for the EPR line shape of a nitroxide free radical undergoing spin exchange in the slow exchange limit is derived and tested experimentally and against a rigorous theory. The line shape is the sum of the absorption and dispersion of Lorentzian lines, in which the dispersion component is of opposite signs for the outer lines and zero for the inner. The relative amplitude of the absorption and the dispersion is shown to be a linear function of the spin exchange frequency. Nonlinear least-squares fitting of the spectra allows the separation of the absorption and dispersion components determining their relative amplitudes to high precision yielding values of the spin exchange frequency that are of precision comparable to those derived from the more traditional line broadening. This new way to measure spin exchange frequencies is attractive because there are no complications from dipolar interactions and no measurements at low concentrations are required. The resonance fields of the absorption co...
TL;DR: In this paper, a set of ground states for a five-dimensional manifold of S = 3/2 Hamiltonians is constructed in two dimensions by using so called vertex state models, which are graphical generalizations of the well-known matrix product ground state for spin chains.
Abstract: Optimum ground states are constructed in two dimensions by using so called vertex state models. These models are graphical generalizations of the well-known matrix product ground states for spin chains. On the hexagonal lattice we obtain a one-parametric set of ground states for a five-dimensional manifold of S = 3/2 Hamiltonians. Correlation functions within these ground states are calculated using Monte-Carlo simulations. In contrast to the one-dimensional situation, these states exhibit a parameter-induced second order phase transition. In the disordered phase, two-spin correlations decay exponentially, but in the Neel ordered phase alternating long-range correlations are dominant. We also show that ground state properties can be obtained from the exact solution of a corresponding free-fermion model for most values of the parameter.
TL;DR: In this article, the effects of carrier doping on spin dynamics in NMR and NQR were investigated in the context of a ladder configuration and showed that the spin gap for the ladder increases with the Y and La substitutions for Sr.
Abstract: Carrier doping effects on spin dynamics in ${\mathrm{Sr}}_{14\ensuremath{-}x}{A}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ ( $A\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathrm{Ca}$, Y, and La) are investigated by Cu NMR and NQR. The energy gaps in the spin excitation spectra (spin gap) are confirmed to be $\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}140\mathrm{K}$ for the Cu${\mathrm{O}}_{2}$ chain and $\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}470\mathrm{K}$ for the C${\mathrm{u}}_{2}$${\mathrm{O}}_{3}$ ladder in S${\mathrm{r}}_{14}$C${\mathrm{u}}_{24}$${\mathrm{O}}_{41}$. The spin gap for the ladder increases with the Y and La substitutions for Sr (up to $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$), while it decreases with increasing x in ${\mathrm{Sr}}_{14\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ and seems to collapse around $x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}13$ of the Ca substitution. Hole-doping effects on the spin gaps for the ladder configuration are interpreted in terms of magnon and hole-depairing excitations for the spin $S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{2}$ ladder.