Third-order Magnetic Susceptibility Research Articles

Nonlinear optical response of strain-mediated gallium arsenide microwire in the near-infrared region

Abstract Gallium arsenide (GaAs) semiconductor wires have emerged as potent candidates for nonlinear optical devices, necessitating bandgap engineering for an expanded operational wavelength range. We report the successful growth of strain-mediated GaAs microwires (MWs) with an average diameter of 1.1 μm. The axial tensile strain in these wires, as measured by X-ray diffraction and Raman scattering, ranges from 1.61 % to 1.95 % and from 1.44 % to 2.03 %, respectively. This strain condition significantly reduces the bandgap of GaAs MWs compared to bulk GaAs, enabling a response wavelength extension up to 1.1 μm. Open aperture Z-scan measurements reveal a nonlinear absorption coefficient of −15.9 cm/MW and a third-order magnetic susceptibility of −2.8 × 10−8 esu at 800 nm for these MWs. I-scan measurements further show that the GaAs saturable absorber has a modulation depth of 7.9 % and a nonsaturation loss of 3.3 % at 1050 nm. In laser applications, GaAs MWs have been effectively used as saturable absorbers for achieving Q-switched and dual-wavelength synchronous mode-locking operations in Yb-bulk lasers. These results not only offer new insights into the use of large diameter semiconductor wires but also expand the potential for applications requiring bandgap tuning.

Third-Order Magnetic Susceptibility of an Ideal Fermi Gas**Supported by National Natural Science Foundation of China under Grant No. 11675051

At low temperature and under weak magnetic field, non-interacting Fermi gases reveal both Pauli paramagnetism and Landau diamagnetism, and the magnitude of the diamagnetic susceptibility is 1/3 of that of the paramagnetic one. When the temperature is finite and the magnetic field is also finite, we demonstrate that the paramagnetism and diamagnetism start to deviate from the ratio 1/3. For understanding the magnetic properties of an ideal Fermi gas at quite low temperature and under quite weak magnetic field, we work out explicitly the third-order magnetic susceptibility in three cases, from intrinsic spin, orbital motion and in total. An interesting property is in third-order magnetic susceptibilities: when viewing individually, they are both diamagnetic, but in total it is paramagnetic.

Third-order magnetic susceptibility of the frustrated square-lattice antiferromagnet

We present results from our analysis of the finite-temperature properties of the spin 1 2 J 1 – J 2 Heisenberg model on a square lattice. The analysis is based on the exact diagonalisation of small clusters with 16 and 20 sites utilising the finite-temperature Lanczos method. In particular, we focus on the temperature dependence of the third-order magnetic susceptibility as a method to resolve the ambiguity of exchange constants. We discuss the entire range of the frustration angle φ = tan - 1 ( J 2 / J 1 ) parameterising the different possible phases of the model, including the large region in the phase diagram with at least one ferromagnetic exchange constant.

Possibility of third-order magnetic susceptibility investigations in magnetic materials

Three-coordinate vector magnetometer for investigations of the magnetic field dependencies of the three separate magnetic moment components, along and perpendicular to the applied magnetic field, is described. Additionally to investigations of the sample magnetic moments orientations with respect to sample axis in magnetically ordered materials, possibilities in investigations of non-linear magnetic field dependencies of sample magnetic moments components of some paramagnetic materials are discussed.

Spin freezing in the decagonal phase of the Al-Mn-Pd alloy system

We report the results of measurements of the low-temperature specific heat ${C}_{p}(T)$ of annealed samples of decagonal ${\mathrm{Al}}_{69.8}{\mathrm{Mn}}_{18.1}{\mathrm{Pd}}_{12.1}.$ A comparison with similar data, previously obtained for decagonal Al-Cu-Co quasicrystals, indicate a substantial excess specific heat ${C}_{\mathrm{ex}}(T)$ in the Al-Mn-Pd material, most likely due to magnetic degrees of freedom. The temperature dependence of ${C}_{\mathrm{ex}}(T)$ suggests a spin freezing phenomenon at ${T}_{\mathrm{f}}=12\mathrm{K},$ which is confirmed by the temperature dependence of the third-order magnetic susceptibility ${\ensuremath{\chi}}_{3}(T)$ and the time dependence of the remanent magnetization well below ${T}_{\mathrm{f}}.$

Magnetic properties in the antiferroquadrupolar order compound DyB2C2 studied by the magnetic susceptibility

Temperature dependence of the third-order magnetic susceptibility χM(3) along the a,[110] and c-axis were measured on a single-crystalline sample of an antiferroquadrupolar (AFQ) ordering compound DyB2C2. The χM(3) values are negative below 80K in all directions. For H||c,χM(3) has a minimum around 28K and shows divergent behavior at TQ=24.7K with decreasing temperature, while χM(3) for H||a and H||[110] decrease monotonically as temperature decreases, but these decreasing rates increase slightly at TQ.

Third-Order Magnetic Susceptibility and Quadrupolar Order Parameter of Kondo-Lattice Compound Ce3Pd20Ge6

We present a report on crystalline-electric-field effects observed in the electrical resistivity and the specific heat of Ce 3 Pd 20 Ge 6 , which are discussed within an energy level scheme of the Γ 8 ground state and the Γ 7 excited state at 50 K for both inequivalent crystallographic sites of Ce atom. The third-order magnetic susceptibility was deduced from the magnetization measurement in the paramagnetic phase of a single-crystalline sample in magnetic fields applied along [0 0 1] and [1 1 1]. In order to explain the temperature dependence of the third-order magnetic susceptibility along [0 0 1], a positive total quadrupolar pair interaction constant of 22 mK is required in addition to a small antiferromagnetic exchange interaction, thereby suggesting ferroquadrupolar ordering with the Γ 3 symmetry in this compound.

Magnetoelastic interactions in the series of rare-earth phosphates RPO4 (R = Tb-Tm)

The magnetic and magnetoelastic properties of RPO4 (R = Dy, Ho, Er), which have the zircon-type tetragonal structure, are investigated in the paramagnetic phase within the extended susceptibility formalism. The characteristic behaviour of the first-order magnetic susceptibility allows us to refine the values of the crystalline electric field parameters and to determine the strength of the magnetic interactions. The magnetoelastic coefficients and quadrupolar constants for all the symmetry-lowering modes are then determined from third-order magnetic susceptibility and parastriction measurements. Their coherency within the series of RPO4 is emphasized: all the magnetoelastic couplings keep the same sign and order of magnitude; the tetragonal magnetoelastic coefficients are sizeable in comparison with those determined in the rare-earth intermetallics. The variation of the crystalline electric field interactions and of the magnetoelastic couplings throughout the series of RPO4 (Tb-Tm) is discussed, which is an essential step towards a coherent understanding of the magnetic behaviour of the whole series.

Quadrupolar couplings and magnetic phase diagrams in tetragonal TmAu2

The occurrence of a quadrupolar ordering within the γ orthorhombic symmetry at 7 K in TmAu2 (MoSi2-type tetragonal structure) was recently discovered with properties closely reminiscent of the ones observed in isomorphous TmAg2. Both the magnetoelastic couplings and the quadrupolar pair interactions are here determined by means of third-order magnetic susceptibility and parastriction measurements. The existence of an antiferromagnetic ordering around 3 K in the quadrupolar phase leads to complex magnetic phase diagrams in the (H,T) plane, which have been established along the main crystallographic directions of the tetragonal cell and appear to result from the balance between magnetic and quadrupolar interactions.

Magnetic and magnetoelastic properties of

The rare-earth oxide compound (tetragonal zircon structure) is investigated using the extended susceptibility formalism, which considers at any temperature all of the features of the crystalline electric field within the ground-state multiplet in the joint analysis of the magnetic, magnetoelastic and elastic properties. The magnetoelastic coefficients are determined from third-order magnetic susceptibility, parastriction and elastic constant measurements for the different symmetry modes. The dominant magnetoelastic coupling is associated with the orthorhombic -symmetry; however, tetragonal and symmetry-lowering modes are also observed to give rise to noticeable effects, in particular in the thermal expansion. The close coherency between the magnetoelastic coefficients in and is then emphasized: the tetragonal magnetoelastic coefficients are sizeable and all of the magnetoelastic couplings keep the same sign and order of magnitude in the two phosphates. This coherency appears to be valid throughout the large family of rare-earth zircons. Through these two examples, the occurrence of a quadrupolar ordering is then discussed as being governed by the crystalline electric field, and the role of undercritical quadrupolar interactions is emphasized in .

Comparative study of the third-order magnetic susceptibility and the specific heat of antiferromagnetic MnBr2·4H2O

We report a comparative study of the third-order magnetic susceptibility χ3(T) and of the specific heatCp(T) of an antiferromagnetically ordering MnBr2·4H2O single crystal withTN=2.13 K. The dominant feature in χ3(T) is a positive singularity nearTN. The critical exponents of χ3 are negative both above and belowTN. On the contrary, the critical behaviour of the magnetic contributionCm(T) to the specific heatCp(T) is logarithmic belowTN and may be described by a large and positive critical exponent definitely exceeding the value of 0.3 aboveTN. These results suggest that the critical behaviour of χ3(T) of a moderately anisotropic antiferromagnet is qualitatively different from that ofCm(T).

Magnetoelastic properties and level crossing in HoVO4.

The rare-earth oxide compound ${\mathrm{HoVO}}_{4}$ (tetragonal zircon structure) is investigated in the extended susceptibility formalism, which includes all the features of the crystalline electric field in the analysis of the magnetic, magnetoelastic, and elastic properties as a function of temperature. The characteristic behavior of the first-order magnetic susceptibility allows us to refine the values of the crystalline electric-field parameters and to determine the strength of the magnetic interactions. The magnetoelastic coefficients are then found from third-order magnetic susceptibility, parastriction, and elastic-constants measurements for the different symmetry modes. Their coherency with values determined for ${\mathrm{TbPO}}_{4}$ is then emphasized: They have the same sign and order of magnitude; in particular the magnetoelastic coefficients for the tetragonal symmetry are sizable in these rare-earth oxides in contrast to the case of rare-earth intermetallics. The unusual temperature dependence of the third-order magnetic susceptibility along the tetragonal axis is a precursor of the level crossing in high magnetic fields associated with a magnetization jump of about 8${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ at 11.4 T, which we study as a function of temperature down to 0.1 K. The existence of a two-step jump of the magnetization at low temperatures, if not driven by mechanical stresses, remains an intriguing result.

Magnetic and magnetoelastic properties in tetragonal TbPO4.

The magnetic and magnetoelastic properties (third-order magnetic susceptibility and parastriction) of ${\mathrm{TbPO}}_{4}$, which has the zircon-type tetragonal structure, are analyzed in the paramagnetic phase. The susceptibility formalism is then used to describe all the symmetry-lowering modes in a rare-earth insulator. The dominant magnetoelastic coupling is associated with the \ensuremath{\delta} symmetry and is, at least partly, responsible for the transition occuring at 2.15 K in the antiferromagnetic phase and clearly dominates the \ensuremath{\gamma}-symmetry mode. However, none of the different symmetry-lowering modes can be completely neglected and we determine parameters for the \ensuremath{\alpha}1 and \ensuremath{\alpha}2 tetragonal modes and the \ensuremath{\varepsilon} monoclinic mode. Owing to the close vicinity of the first excited singlet to the ground-state doublet, the \ensuremath{\alpha} quadrupolar interactions play an important role in determining the temperature dependence of the level spacing at low temperature, in particular in the ordered phases. The determination of all the magnetoelastic modes of ${\mathrm{TbPO}}_{4}$ is an essential step towards the understanding of the complex magnetic properties in the ordered phases, where numerous interactions coexist.

Quadrupolar ordering in tetragonal TmAg2.

The occurrence of a nonmagnetic transition at 5 K in ${\mathrm{TmAg}}_{2}$ (${\mathrm{MoSi}}_{2}$-type tetragonal symmetry) is analyzed as a ferroquadrupolar ordering within the orthorhombic \ensuremath{\gamma}-symmetry-lowering mode. The crystalline-electric-field parameters are obtained by inelastic-neutron-scattering and magnetic-susceptibility measurements. Both the magnetoelastic couplings and the quadrupolar pair interactions are then determined by third-order magnetic-susceptibility, parastriction, and ultrasonic-velocity experiments. The great coherency between these determinations allows us to understand completely the magnetic properties in both the orthorhombic and tetragonal phases. ${\mathrm{TmAg}}_{2}$ is then an archetype for compounds ruled by quadrupolar interactions.

Paramagnetic torque in cubic rare-earth compounds.

Paramagnetic torque appears in cubic rare-earth intermetallics as an interesting experimental probe for studying the magnetic response to different couplings such as bilinear exchange, crystalline electric field, and quadrupolar interactions. Starting from the high-order magnetic susceptibility tensor for 432, 4\ifmmode\bar\else\textasciimacron\fi{}3m, m3m high-symmetry classes, its expression is given within the mean-field approximation and allows one to determine the anisotropy of the initial curvature of the isothermal magnetization in the presence of an applied magnetic field. It is shown that at the magnetic transition, the twofold axis is never the easy magnetization direction. Torque measurements in the paramagnetic phase of CsCl-type structure compounds, TmZn and TmCd, are then presented. They are in full agreement with the third-order magnetic susceptibility previously studied and allow a more precise determination of the quadrupolar interactions in these systems.

Quadrupolar properties and magnetic phase diagrams in PrB 6 hexaboride compound

The magnetoelastic and quadrupolar properties of the hexaboride compound PrB 6 are determined by measurements of the elastic constants, the parastriction and the third-order magnetic susceptibility. The magnetoelastic effects are sizeable only for the trigonal symmetry lowering mode. The quadrupolar pair interactions are negative in the paramagnetic phase in agreement with the multiaxial spin structure stabilized at low temperature by antiferroquadrupolar interactions. The quadrupolar couplings seem to coexist with additional terms. Spin fluctuations are in particular present above the Néel temperature. The quadrupolar interactions do not appear to be responsible for the first-order magnetic transition. The magnetic phase diagrams have been build for the three main crystallographic directions of the cubic cell. They exhibit at low field a transition from the double- k structure to the simple- k one, which was previously observed along the twofold axis by neutron diffraction. Only weak field-dependences of the Néel temperature and of the commensurate-incommensurate phase transition temperature have been observed.

Magnetic and quadrupolar properties of TmAg

The quadrupolar interactions (one-ion magnetoelasticity and pair interactions) have been determined in the CsCl-type structure compound TmAg by means of parastriction, elastic constants and third-order magnetic susceptibility. They are then compared with previous determinations in other thulium isomorphous compounds. In particular a comparison is made with TmCu, which exhibits very similar crystalline electric field and bilinear interactions, but different quadrupolar couplings. This comparison allows us to explain the different magnetic properties (magnetic transition and magnetic structure) in these two compounds.

Parastriction and third-order paramagnetic susceptibility of DySb

Parastriction and third-order paramagnetic susceptibility results in DySb are presented here for both tetragonal and trigonal symmetries. They allow a temperature analysis of all the magnetic and magnetoelastic properties of this compound in its paramagnetic phase. Quadrupolar interactions originating from the magnetoelasticity and the pair coupling appear to be insufficient and additional interactions seem to exist in DySb: the presence of a two-ion magnetoelastic coupling is quite possible, strongly influencing in particular the third-order magnetic susceptibility for the tetragonal symmetry. In addition, fluctuations appear to be active in the neighbourhood of the Neel temperature. The first-order character of the antiferromagnetic ordering agrees with the positive third-order susceptibility as expected in a Landau expansion of the free energy, and results from a complex balance between various interactions.

Magnetic and quadrupolar properties of PrPb3

The cubic rare earth intermetallic compound PrPb3 (AuCu3-type structure) undergoes a transition at 0.35 K: as it is a Van Vleck paramagnet, the low temperature phase was assumed to be quadrupolarly ordered. In order to specify this possibility, we first discuss the cubic level scheme using specific heat and first-order magnetic susceptibility results; afterwards we present an extensive study of the two (tetragonal and trigonal) symmetry lowering modes, investigated in the cubic paramagnetic phase by means of parastriction and third-order magnetic susceptibility. For the tetragonal symmetry, the quadrupolar pair interactions appear as negative, dominating the magnetoelastic coupling; as a result, the low temperature ordering may be antiferroquadrupolar, a new situation among rare earth intermetallics, the TmZn and TmCd ordering being ferroquadrupolar.

Third-order magnetic susceptibility as a new method for studying quadrupolar interactions in rare-earth compounds

We present a new method based on the detailed analysis of the magnetization curve in the paramagnetic range for studying the quadrupolar interactions in cubic rare-earth intermetallic compounds; the third-order magnetic susceptibility characterizes the anisotropic curvature of the magnetization curve. It corresponds to the ${H}^{3}$ coefficient in the odd field development of the magnetization. This high-order coefficient receives a contribution from the induced quadrupolar moment which varies as ${H}^{2}$. Thus studied in the nonordered (cubic and paramagnetic) range with magnetic fields applied along the [001] and [111] directions, the third-order magnetic susceptibility provides information on the quadrupolar interactions associated with the two tetragonal and trigonal symmetry-lowering modes. Using perturbation theory and mean-field approximation, we give analytical expressions for the third-order magnetic susceptibility in the presence of a crystalline electric field, bilinear exchange, and quadrupolar (exchange and magnetoelastic) interactions. Application to ${\mathrm{Tm}}^{3+}$ cubic intermetallic compounds, for which large quadrupolar interactions have been shown to exist, is then given, illustrating the reliability of the method.