Spin-phonon Coupling Constant Research Articles

Spin-phonon coupling and giant dielectric constant in Bi0.5La0.5Fe0.4Al0.1Mn0.5O3

Spin-phonon coupling and giant dielectric constant in Bi0.5La0.5Fe0.4Al0.1Mn0.5O3

Spin–phonon dispersion in magnetic materials

Microscopic coupling between the electron spin and the lattice vibration is responsible for an array of exotic properties from morphic effects in simple non magnets to magnetodielectric coupling in multiferroic spinels and hematites. Traditionally, a single spin–phonon coupling constant is used to characterize how effectively the lattice can affect the spin, but it is hardly enough to capture novel electromagnetic behaviors to the full extent. Here, we introduce a concept of spin–phonon dispersion to project the spin moment change along the phonon crystal momentum direction, so the entire spin change can be mapped out. Different from the phonon dispersion, the spin–phonon dispersion has both positive and negative frequency branches even in the equilibrium ground state, which correspond to the spin enhancement and spin reduction, respectively. Our study of bcc Fe and hcp Co reveals that the spin force matrix, that is, the second-order spatial derivative of spin moment, is similar to the vibrational force matrix, but its diagonal elements are smaller than the off-diagonal ones. This leads to the distinctive spin–phonon dispersion. The concept of spin–phonon dispersion expands the traditional Elliott-Yafet theory in nonmagnetic materials to the entire Brillouin zone in magnetic materials, thus opening the door to excited states in systems such as CoF2 and NiO, where a strong spin-lattice coupling is detected in the THz regime.

Spin-Phonon Coupling in A2BMnO6 (A = La, Pr, Nd, Sm, Gd; B = Co, Ni) Double-Perovskite Thin Films: Impact of the A-Site Cation Radius

Two series of B-site ordered, double-perovskite A2CoMnO6 and A2NiMnO6 (A = La, Pr, Nd, Sm, Gd) epitaxial films with thickness d ~ 100 nm were grown on SrTiO3(111) substrates via metalorganic aerosol deposition. Polarization and temperature-dependent Raman spectroscopy were carried out in order to determine the spin-phonon coupling constant, λ, and the impact of the A-site cation radius on the phonon properties. The reduction of the A-site cation radius from La3+ down to Gd3+ systematically shifts the Raman modes to lower wavenumbers, and decreases the magnetization-induced softening of the Ag breathing mode, described by the spin-phonon coupling constant, λ, which changes from λ = 1.42 cm−1 (La2CoMnO6) and λ = 1.53 cm−1 (La2NiMnO6) down to λ = 0.58 cm−1 (Gd2CoMnO6) and λ = 0.44 cm−1 (Gd2NiMnO6). A similar effect of the A-cation radius was established for the c-lattice parameter and Curie temperature, TC, in this series of double-perovskite films. Our observations directly demonstrate a strong impact of the lattice structure on the ferromagnetic superexchange interaction in double perovskites. Moreover, the A2CoMnO6 and A2NiMnO6 series exhibit very similar behavior of spin-phonon coupling due to the only moderate difference of Co2+ and Ni2+ cation size.

Strong spin-phonon coupling and large dielectric constant observed in quasi-two-dimensional layered perovskite SrLaCo0.5Mn0.5O4

Recently from our group, we reported giant exchange bias value of 5.5 kOe at 5 K in a quasi-two-dimensional single layered polycrystalline Ruddlesden-Popper (RP) compound SrLaCo0.5Mn0.5O4. Here, a detailed temperature dependent Raman and dielectric spectroscopic studies are carried out on SrLaCo0.5Mn0.5O4 to understand the spin-phonon coupling and dielectric properties, respectively. A strong spin-phonon coupling constant of λ = 2.72 cm−1 is evident which is associated with Mn/Co‒O bonds. A large dielectric constant of ε' = 2904 at 1 kHz frequency at 297 K is found in this system. Data availabilityThe data that supports the findings of this study are available within the article [and its supplementary material]. Please see supplementary material for details of the impedance spectroscopy analysis.

Re-normalization of lattice vibrations below magnetic transition probed by Raman spectroscopy

Polycrystalline CuO thin film is grown using pulse laser deposition method. Magnetic measurement shows reduction in transition temperature from 213 K in bulk to 175 K in thin film which is attributed to the reduction in dimensionality. Temperature dependent Raman study showed existence of strong spin-phonon coupling below 175 K. The spin-phonon coupling constant is deduced by subtracting the variation in Ag mode position from the anharmonic behaviour and is found to be 9.08 cm−1. On the other hand the spin-phonon coupling constant deduced from the shift of the 230 cm−1 mode, which is supposed to be activated due to zone folding and is observed only below 175 K, is found to be ~30 cm−1 against ~50 cm−1 reported in bulk compound using this method.

Electronic structure and lattice dynamics of Li2Ni(WO4)2

We combined spectroscopic ellipsometry and Raman scattering measurements to explore the electronic structure and lattice dynamics in Li2Ni(WO4)2. The optical absorption spectrum of Li2Ni(WO4)2 measured at room temperature presents a direct optical band gap at 2.25 eV and two bands near 5.2 and 6.0 eV, which are attributed to charge-transfer transitions from oxygen 2p states to nickel 3d or tungsten 5p states. The Raman scattering spectrum of Li2Ni(WO4)2 measured at room temperature presents seventeen phonon modes at approximately 112, 143, 193, 222, 267, 283, 312, 352, 387, 418, 451, 476, 554, 617, 754, 792, and 914 cm−1. When the temperature is decreased to 20 K, the frequency, linewidth, and normalized intensity of all phonon modes exhibited almost no temperature dependence. Upon cooling across 13 K, which is the antiferromagnetic phase transition temperature, the oxygen octahedra stretching mode at 914 cm−1 exhibited a softening and an increase in intensity, thus suggesting a coupling between the magnetic and lattice degrees of freedom. The spin-phonon coupling constant was estimated to be 0.94 mRy/Å2, indicating a weak spin-phonon interaction in Li2Ni(WO4)2.

Spin-charge-lattice coupling in YBaCuFeO5: Optical properties and first-principles calculations

We combined spectroscopic ellipsometry, Raman scattering spectroscopy, and first-principles calculations to explore the optical properties of YBaCuFeO5 single crystals. Measuring the optical absorption spectrum of YBaCuFeO5 at room temperature revealed a direct optical band gap at approximately 1.41 eV and five bands near 1.69, 2.47, 3.16, 4.26, and 5.54 eV. Based on first-principles calculations, the observed optical excitations were appropriately assigned. Analysis of the temperature dependence of the band gap indicated anomalies in antiferromagnetic phase transition at 455 and 175 K. Additionally, a hardening in the frequency of the Eg phonon mode was observed at 175 K. The value of the spin–phonon coupling constant was 15.7 mRy/Å2. These results suggest a complex nature of spin–charge–lattice interactions in YBaCuFeO5.

Infrared probe of spin-phonon coupling in antiferromagnetic honeycomb lattice compound Li2MnO3

We investigated temperature-dependent infrared-active phonon modes of honeycomb Li2MnO3 which shows an antiferromagnetic transition at TN = 36 K. In the far-infrared frequency region, we observed fourteen phonon modes. We obtained the temperature dependence of each phonon mode from the analysis of optical conductivity spectra by using the Lorentz and the Fano-type oscillator models. We found that the resonance frequencies of nine phonon modes showed an anomalous behavior near TN that should be attributed to the spin-phonon coupling. We calculated the magnitude of the spin-phonon coupling constant from the shift in the resonance frequencies of the phonon modes below TN. Our results suggest that Li2MnO3 is weakly frustrated and that spin-phonon coupling plays a role in antiferromagnetic ordering.

Interplay of spin and lattice degrees of freedom in the frustrated antiferromagnetCdCr2O4: High-field and temperature-induced anomalies of the elastic constants

Temperature and magnetic field studies of the elastic constants of the chromium spinel CdCr_2O_4 show pronounced anomalies related to strong spin-phonon coupling in this frustrated antiferromagnet. A detailed comparison of the longitudinal acoustic mode propagating along the [111] direction with theory based on an exchange-striction mechanism leads to an estimate of the strength of the magneto-elastic interaction. The derived spin-phonon coupling constant is in good agreement with previous determinations based on infrared absorption. Further insight is gained from intermediate and high magnetic field experiments in the field regime of the magnetization plateau. The role of the antisymmetric Dzyaloshinskii-Moriya interaction discussed and we compare the spin-phonon coupling in CdCr_2O_4 in both the ordered and disordered states.

Spin-phonon coupling in multiferroic manganites RMnO3: comparison of pure (R = Eu, Gd, Tb) and substituted (R = Eu1- x Y x ) compounds

For rare-earth manganite RMnO3 compounds spin-phonon coupling manifests itself as a phonon softening in the temperature range of the magnetically ordered phases. Within this class of materials, a continuous tuning of the lattice and thus also of the magnetic properties of multiferroic manganites is achieved by Y doping in substituted Eu1- x Y x MnO3. We compare the impact on spin-phonon coupling within this partial-substitution approach in a series of Eu1- x Y x MnO3 samples 0 ≤ x ≤ 0.5) with the effect of a complete exchange of the rare earth ions R3+ in a series of pure RMnO3 compounds (R = Eu, Gd, Tb). For this purpose we employ polarized Raman scattering in the 10–300 K temperature range. The low-temperature results show phonon softening in all investigated compounds. For decreasing R3+ radius, i.e. an increasing orthorhombic distortion and magnetic frustration, we observe in both systems a weakening of the spin-phonon coupling. For known sublattice magnetization within the MnO2-plane, quantitative results for the spin-phonon coupling constant are derived for both cases within a molecular field approximation. Our results show, that the spin-phonon coupling strength in the magnetically ordered phases of the various investigated manganites does not correlate with the magnetization pattern. Instead, the pure RMnO3 compounds and the substituted Eu1- x Y x MnO3 fit excellently within a common scheme, in which the weakening of the spin-phonon coupling reflects the degree of tilting of the MnO6 octahedra due to the orthorhombic distortion of the crystal lattice.

Composition-dependent spin-phonon coupling in mixed crystals of the multiferroic manganiteEu1−xYxMnO3(0≤x≤0.5)studied by Raman spectroscopy

Yttrium substitution in ${\text{Eu}}_{1\ensuremath{-}x}{\text{Y}}_{x}{\text{MnO}}_{3}$ allows a quasicontinuous tuning of the lattice and magnetic properties of this multiferroic manganite without magnetic interference of rare-earth ions. In order to investigate the composition dependence of the spin-phonon coupling we employ polarized Raman scattering of orthorhombic mixed crystals of ${\text{Eu}}_{1\ensuremath{-}x}{\text{Y}}_{x}{\text{MnO}}_{3}$ $(0\ensuremath{\le}x\ensuremath{\le}0.5)$ in the 10--300 K temperature range. Phonon frequency shifts and mode-mixing effects occur, depending on the average rare-earth ion radius determined by the concentration of ${\text{Eu}}^{3+}$ and ${\text{Y}}^{3+}$. Moreover, we observe a strong spin-phonon coupling with systematic composition dependence. It manifests itself as a mode-specific softening of the phonon modes in the temperature range of the magnetic ordered phases. The spin-phonon coupling is weakened for increasing Y contents but remains nonzero also in the incommensurate spiral magnetic phase, which occurs for $0.3\ensuremath{\le}x\ensuremath{\le}0.5$. Thus for this class of manganites we report the observation of spin-phonon coupling in an ordered magnetic phase without ferromagnetic ordering within the ${\text{MnO}}_{2}$ plane. Additionally for known sublattice magnetization quantitative values of the spin-phonon coupling constant are derived. Our results prove the suitability of phonons as a sensitive probe for the spin-spin correlation.

Spin dynamics in the neutral rare-earth single-molecule magnets[TbPc2]0and[DyPc2]0fromμSRand NMR spectroscopies

The spin dynamics in [TbPc$_{2}$]$^{0}$ and [DyPc$_{2}$]$^{0}$ single molecule magnets have been investigated by means of muon and nuclear spin-lattice relaxation rate measurements. The correlation time for the spin fluctuations was found to be close to 0.1 ms already at 50 K, about two orders of magnitude larger than the one previously found in other lanthanide based single molecule magnets. In [TbPc$_{2}$]$^{0}$ two different regimes for the spin fluctuations have been evidenced: a high temperature activated one involving spin fluctuations across a barrier $\Delta\simeq 880 K$ separating the ground and first excited states and a low temperature regime involving quantum fluctuations within the twofold degenerate ground-state. In [DyPc$_{2}$]$^{0}$ a high temperature activated spin dynamics is also evidenced which, however, cannot be explained in terms of a single spin-phonon coupling constant.

Quantum magnetostriction oscillations in a two-dimensional antiferromagnet with spin-phonon interaction in a magnetic field

The ground state of a two-dimensional antiferromagnet with S=1/2 interacting with acoustic phonons in a magnetic field was studied by the quantum Monte Carlo method in the nonadiabatic approximation. Oscillations of the amplitude of the root-mean-square displacement of ions and the average phonon occupation number in a magnetic field were found. Local maxima were revealed in the distribution functions of site magnetic moments and ion displacements. The saturation magnetization was calculated as a function of the spin-phonon coupling constant.

Isotope substitution effects on spin dynamics of the molecular nanomagnet Fe8 cluster studied by NMR

We have carried out 1H NMR at T=1.5 K in both 57Fe-enriched Fe8 cluster and non-enriched Fe8 cluster to investigate isotope substitution effects on magnetic properties. The field dependence of 1/T1 can be fitted well by using a simple model in terms of the thermal fluctuations of the total spin S=10 of the cluster originating from the spin–phonon interactions. The absence of a difference of the magnetic field dependence of 1/T1 between the two systems indicates that the spin–phonon coupling constant is not affected by the change of mass of the isotopes in the Fe8 cluster.

Quantum solitons in CuGeO3: a density matrixrenormalization group study

The one-dimensional spin-Peierls model with quantum phonons isstudied with an optimal phonon method combined with the densitymatrix renormalization group. By calculating the ground statein the sector Sz = 1 I obtain a soliton-antisoliton pair.The soliton is compared to nuclear magnetic resonanceexperiments which image the soliton lattice present inCuGeO3 under a high magnetic field. Reasonable agreementwith experiment can be achieved by choosing a large value of thephonon frequency and the spin phonon coupling constant. Thisindicates that CuGeO3 is in a non-adiabatic stronglycoupled parameter regime. A robust feature of the calculationsis an attraction between solitons even without interchain coupling.

Spin Dynamics of the Molecular Nanomagnet Fe8 Studied by 1 H-NMR

The proton nuclear spin-lattice relaxation rate 1/ T 1 has been measured as a function of temperature (T=1.4-4.2K) and magnetic field (H=0.6-5T) in the Fe8 cluster in its high spin S=10 ground state. The strong temperature and field dependence of 1/ T 1 can be fitted well by using a simple model in terms of the thermal fluctuations of the total spin S=10 of the cluster originating from the spin-phonon interactions. 1/ T 1 data of protons in a partially deuterated Fe8 cluster is also reported. The results indicate that the spin phonon coupling constant is not affected by the change of mass of the isotopes in the Fe8 cluster. Nanomagnet Fe8 cluster nuclear magnetic resonance

NMR study of the molecular nanomagnet[Fe8(N3C6H15)6O2(OH)12]⋅[Br8⋅9H2O]in the high-spin magnetic ground state

The magnetic molecular cluster $[{\mathrm{Fe}}_{8}({\mathrm{N}}_{3}{\mathrm{C}}_{6}{\mathrm{H}}_{15}{)}_{6}{\mathrm{O}}_{2}(\mathrm{OH}{)}_{12}{]}^{8+}[{\mathrm{Br}}_{8}\ensuremath{\cdot}9{\mathrm{H}}_{2}\mathrm{O}{]}^{8\ensuremath{-}},$ in short Fe8, has been investigated at low temperature by ${}^{1}\mathrm{H}$-NMR and relaxation measurements. Some measurements of ${}^{2}\mathrm{D}$-NMR in partially deuterated Fe8 clusters will also be reported. Upon decreasing temperature the NMR spectra display a very broad and structured signal which is the result of the internal local fields at the proton sites due to the local moments of the Fe(III) ions in the total $S=10$ magnetic ground state. The proton and deuteron NMR spectra have been analyzed and the different resonance peaks have been attributed to the different proton groups in the molecule. The simulation of the spectra by using a dipolar hyperfine field and the accepted model for the orientation of the Fe(III) local moments do not agree with the experiments even when the magnitude of the local Fe(III) moments is allowed to vary. It is concluded that a positive contact hyperfine interaction of the same order of magnitude as the dipolar interaction is present for all proton sites except the water molecules. The temperature and magnetic field dependence of the nuclear spin-lattice relaxation rate is ascribed to the fluctuations of the local Fe(III) moments, which follow rigidly the fluctuations of the total ground state magnetization of the nanomagnet. By using a simple model already utilized for the Mn12 cluster, we derive the value of the spin phonon coupling constant which determines the lifetime broadening of the different magnetic quantum number m substates of the $S=10$ ground state. It is shown that the lifetime broadening decreases rapidly on lowering the temperature. When the lifetime becomes longer than the reciprocal of the frequency shift of the proton lines a structure emerges in the NMR spectrum reflecting the ``frozen'' local moment configuration.

Pulsed field ultrasonic and ESR experiments in low-dimensional spin systems

We present the ultrasonic and ESR results for several low-dimensional spin systems in high magnetic fields up to 50 T. With these experiments, we obtain information on the spin state in high fields, their magnetic excitations and on the interaction of these magnetic excitations with phonons. The deduced spin–phonon coupling constant gives information on the structural properties and their connection to low-dimensional magnetism of the systems.

Dimerised second-neighbour Heisenberg chain and the spin-Peierls transition

A recent study of second-neighbour effects in uniform magnetic chains is extended to dimerised antiferromagnetic chains. This is the first time that the Jordan-Wigner transformation has been applied to the NNN dimerised chain. The resulting Hamiltonian is then treated in the thermal Hartree-Fock approximation, yielding a distortion of the mirror symmetric bands found in the NN case. While the formalism is developed for the XY-Ising model, a detailed application is made for the Heisenberg case with weak NNN exchange interactions. Elastic (phonon) contributions to the free energy of the dimerised system are made by following the Beni-Pincus approach in order to study the spin-Peierls transition. The authors find a limiting value of the spin-phonon coupling constant ( lambda ) such that for lambda 0.611, it increases with -G. A comparison is made with the results of an alternate approach using the NNN XY uniform chain and XY spin-phonon interactions according to Pytte (1974).

Antiferromagnetic vs Spin-Peierls State in 1-D Heisenberg Antiferromagnets

We have treated the 1-D Heisenberg antiferromagnet in a mean-field theory, and determined a phase diagram showing the regions for the antiferromagnetic state, the spin-Peierls state and the paramagnetic state. When a spin-phonon coupling constant is greater than 1.08, the antiferromagnetic state is stable below a Neel temperature T N =0.568 J / k B . When it is less than 1.08, the spin-Peierls state is stable below a transition temperature T P , which is higher than T N and increases as the coupling constant decreases.