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Magnetic field and temperature dependence of the amplitude-modulated magnetic structure of PrNi2Si2 determined by single-crystal neutron diffraction
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The temperature and magnetic field dependence of the magnetic structure in the singlet crystal-field ground-state system PrNi2Si2 have been determined using single-crystal neutron diffraction. At the magnetic ordering temperature in zero field, TN=20.0±0.5K , an amplitude-modulated magnetic structure sets in with a propagation vector k=(0,0,0.87) and the magnetic moments of the Pr3+ ions parallel to the c axis of the body-centered tetragonal structure. The magnetic structure remains amplitude modulated down to low temperatures (T=1.6K) with only a small tendency to squaring up, as signaled by the weak intensity of the third harmonic that develops below 16 K. With applied field along the easy axis, the modulated structure goes smoothly over into a ferromagnetic state. At the critical field of Hc=58kOe , the first harmonic disappears and the field-induced ferromagnetic moment shows a kink, in agreement with magnetization measurements. Both the temperature and magnetic field dependence are well described by a periodic field Hamiltonian including magnetic exchange and the crystalline electric field.
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... It crystallizes in a body-centered tetragonal structure with space group I 4/mmm (No. 139) and lattice parameters a = 4.047 and c = 9.621Å. 27,28 The ordered magnetic moments are confined to be along the c axis (see Fig. 1) by the single-ion anisotropy, evidenced by the magnetic susceptibility ratio of χ c /χ a ≈ 4.5 above T N = 20 K. The magnetic structure at low temperature (4 K) is well described by a single propagation vector τ = (0,0,0.87) ...
... and an ordered moment of 2.35 μ B . 27 At even lower temperatures the observation of a third harmonic at 3τ reflects a weak tendency to "squaring up" of the AM moment, but the observed moment ratio of M 3τ /M τ ∼ 1/7 is far from the limit of complete squaring, M 3τ /M τ = 1/3. 17,27 Since studies of the magnetic excitations in PrNi 2 Si 2 below T N are scarce, [29][30][31] we have performed new inelastic neutron-scattering measurements of the dispersive low-energy excitations. ...
... 27 At even lower temperatures the observation of a third harmonic at 3τ reflects a weak tendency to "squaring up" of the AM moment, but the observed moment ratio of M 3τ /M τ ∼ 1/7 is far from the limit of complete squaring, M 3τ /M τ = 1/3. 17,27 Since studies of the magnetic excitations in PrNi 2 Si 2 below T N are scarce, [29][30][31] we have performed new inelastic neutron-scattering measurements of the dispersive low-energy excitations. The data obtained are analyzed using the random-phase approximation (RPA). ...
The magnetic excitations in the low-temperature amplitude-modulated magnetic structure of PrNi2Si2 have been investigated by inelastic neutron scattering. The dispersions and intensities of both longitudinal and transverse excitations are measured along the high-symmetry directions. The modulated magnitude of the ordered moments implies that the longitudinally polarized magnetic excitations are more intense and dispersive than the usual transverse spin waves. Several well-defined longitudinal amplitude modes are observed to coexist with the longitudinal phason mode. The experimental results are in good overall agreement with predictions from the random-phase approximation, using parameters already established from the macroscopic properties and the paramagnetic excitations. At low energies in the neighborhood of the magnetic zone center, the magnetic phason appears to hybridize with an unidentified dispersionless mode. © 2013 American Physical Society.
... ‡ bingli@imr.ac.cn has strong uniaxial anisotropy originating from crystalline electric field (CEF) effects, it is possible to obtain amplitudemodulated magnetic structures. Such a magnetic structure is unstable at low temperatures because the ordered magnetic moment is zero at some positions, the amplitude-modulated magnetic structure either squares up to evolve into a magnetic structure with an equal magnitude of magnetic moment in the form of appearing high-order harmonics or undergoes a lock-in magnetic transition to a commensurate magnetic structure [20,21]. ...
We uncover high-order harmonics and the reverse of the squaring-up process, in terms of analyzing the evolution of magnetic orders in a centrosymmetric layered triangular-lattice magnet HoPdAl 4 Ge 2 , based on a detailed study of the crystal structure, magnetic susceptibility, magnetization, heat capacity, and magnetic structure. Temperature dependencies of magnetic susceptibility and heat capacity show two magnetic transitions at T N = 10.5 K and T t = 5.5 K. Below T N , Ho 3+ spins order antiferromagnetically as a transverse spin-density wave with the propagation vector k 1 = (0 0 1.5 − δ) with δ ≈0.18. Upon further cooling through T t , the high-order harmonics with k n = (0 0 1.5 − nδ), n = 3, 5, 7 develop, suggesting a squaring-up process. It is surprising that the squaring-up process does not continue down to 0 K but reverses the trend below 3 K. Magnetic-field-induced metastable transitions were observed in M(H) curves with the fields applied both parallel and perpendicular to the triangular-lattice plane. Neutron-diffraction results suggest that the magnetization process in HoPdAl 4 Ge 2 involves the conversion of k n = (0 0 1.5 − nδ) with n = 1, 3, 5, 7, to a ferromagnetic k F = (0 0 0) component. It is worth noting that the already weak seventh harmonic magnetic peak is enhanced by applying a small magnetic field in the ab plane at 1.5 K or warming up to 3 K, accompanied by a slight decrease of δ.
... Similar to the paradigmatic case of PrNi 2 Si 2 [67][68][69][70], we have used a numerical procedure to calculate the magnetic excitations in the ordered phase within the random phase approximation (RPA), where we treat Eq. (4) in the mean-field approximation [71,72]. As commented above in Sec. ...
An ensemble of superantiferromagnetic NdCu2 nanoparticles has been produced to perform a detailed analysis of magnetic excitations using inelastic neutron scattering. Neutron diffraction measurements indicate a mean nanoparticle size of 〈D〉≈13 nm, where the bulk commensurate antiferromagnetic structure is retained at the nanoparticle core. Magnetic measurements evidence the interaction among the magnetic moments located at the nanoparticle surface to be strong enough to establish a spin glass behavior. Specific heat analyses show a broad Schottky contribution, revealing the existence of a crystalline electric field. Inelastic neutron scattering analyses disclose that the splitting of the crystalline electric field levels associated with the Nd3+ ions, as well as the spin-wave excitations that emerged below the Néel transition (TN≈6 K) in polycrystalline NdCu2 are maintained in the nanoparticle state. We have been able to isolate the scattering contribution arising from the nanoparticle surface where both crystalline electric field splitting and the collective magnetic excitations are well-defined despite the symmetry breaking. Quantitative analyses of this surface scattering reveal that finite-size effects and microstrain lead to a partial inhibition of the transitions from the ground state to the first excited level, as well as a positive shift (∼15%) of the energy associated to collective magnon excitations.
... Competing exchange interactions in such geometrically frustrated triangular lattice antiferromagnets lead to a helically modulated incommensurate structure for a weak single-ion anisotropy [4] or an incommensurate spin density wave (SDW) structure if the single-ion anisotropy is strong [5]. In general, the incommensurate magnetic structure is not very stable, and a small perturbation (such as a magnetic field) can lead to a transition from the incommensurate structure to a commensurate magnetic structure or to a magnetic structure in which all magnetic sites carry equal moments (ferrimagnet/ferromagnet) [6,7]. An incommensurate-commensurate magnetic phase transition has been observed in the triangular lattice antiferromagnet RbMnBr 3 [8], which has been explained in terms of the Landau theory using the row model [9]. ...
Neutron powder diffraction experiments have been performed to investigate the nature of magnetic ordering, as a function of temperature (1.5-100 K) and magnetic field (0, 2 and 4 T), in the compound CaCoFeO. In zero applied field, the compound orders magnetically in the incommensurate spin density wave (SDW) structure (T ∼ 20 K). Under an applied field of ∼2 T, an incommensurate-to-commensurate magnetic phase transition has been observed. With a further increase in the magnetic field (∼4 T), the commensurate magnetic structure transforms into a ferrimagnetic structure. In zero applied field, magnetic short-range ordering (SRO) coexists with the SDW long-range ordering (LRO) at all temperatures below T. In an applied magnetic field (2 and 4 T), SRO is converted into LRO only over the temperature range 12-20 K; however, below ∼12 K, an increase in the volume fraction of the SRO has been observed. The correlation length for the SRO (below ∼12 K) also gets affected by the application of a field.
The bulk magnetic measurements (dc magnetization, specific heat, ac-susceptibility) on Ho3Co suggest that its magnetic structure changes continuously below the Néel temperature TN=21 K until another antiferromagnetic (AFM) transition takes place at Tt=9 K. In the temperature range 3K≤T<TN, the magnetic structure is described by an incommensurate propagation vector k=(α,0,0) with 0.1605<α<0.1585 and a commensurate component k0=(0,0,0). For Tt<T≤TN, the spin arrangement consists of fanlike and cycloidal modulations for the Ho and Co sublattices, respectively. Below Tt, the presence of the 3k and 5k harmonics results in a highly complex anharmonic ground state associated with the squaring up of the modulation. The evolution of the magnetic modulations in Ho3Co within 3K≤T<TN is explained by two active irreducible representations under the Pnm′a(α00)000 magnetic superspace group, which allows the change of the structure without further symmetry breaking. A significant moment contribution is detected in Co. Experiments reveal the coexistence of glassy states, probably related to the complex noncollinear AFM structure at low temperature. In addition, externally applied pressure shifts both transitions at TN and Tt to higher temperatures. Eventually, high pressure strengthens the AFM interactions at low temperature while the weak glassy states persist up to 1.1 GPa.
We report the results of the ⁵⁷Fe Mössbauer study of iron-based compounds BaRFeO4 (R = Y, Dy), which undergo two magnetic phase transitions at TN1 ≈ 47 K (Y, Dy) and TN2 ≈ 35 K (Y), 23 K (Dy). The first transition (TN1) is related to a phase transformation from the paramagnetic state into a spin-density wave (SDW), and the second one (TN2) is associated with a phase transition to the cycloidal spin structure (CSS). Variable-temperature Mössbauer measurements were performed to clarify the magnetic behavior of these phases. In the intermediate temperature range TN2 < T < TN1, our investigations indicate an incommensurate SDW phase with inclusion of many high-order harmonics. For the both ferrites, the modulated incommensurate cycloid with the iron moments within the bc plane were supported at low temperature range of T < TN2. In contrast to BaDyFeO4, where the magnetic structure changes abruptly at ∼TN2, a region of coexistence between the SDW and CSS phases (ΔT ≈ 13 K) was observed for BaYFeO4. Magnetic measurements confirmed the phase transitions detected by Mössbauer spectroscopy and revealed an additional transition at TN3 ≈ 9 K in BaDyFeO4, which not manifests in the Mössbauer spectra below this transition point.
Mössbauer spectroscopy is used to study the FeVO4 multiferroic, which undergoes two magnetic phase transitions at TN1 ≈ 22 K and TN2 ≈ 15 K. The first transition (TN1) is related to transformation from a paramagnetic state into a magnetically ordered state of a spin density wave, and the second transition (TN2) is associated with a change in the type of the spatial magnetic structure of the vanadate. The electric field gradient tensor at ⁵⁷Fe nuclei is calculated to perform a crystal-chemical identification of the partial Mössbauer spectra corresponding to various crystallographic positions of Fe³⁺ cations. The spectra measured in the range TN2 < T < TN1 are analyzed on the assumption about amplitude modulation of the magnetic moments of iron atoms μFe. The results of model intersection of the spectra recorded at T < TN2 point to a high degree of anharmonicity of the helicoidal magnetic structure of the vanadate and to elliptic polarization of μFe. These features are characteristic of type-II multiferroics. The temperature dependences of the hyperfine interaction parameters of ⁵⁷Fe nuclei that were obtained in this work are analyzed in terms of the Weiss molecular field model on the assumption of orbital contribution to the magnetic moments of iron cations.
A free web page under the name MAGNDATA , which provides detailed quantitative information on more than 400 published magnetic structures, has been made available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. In the first article in this series, the information available on commensurate magnetic structures was presented [Gallego, Perez-Mato, Elcoro, Tasci, Hanson, Momma, Aroyo & Madariaga (2016). J. Appl. Cryst.49 , 1750–1776]. In this second article, the subset of the database devoted to incommensurate magnetic structures is discussed. These structures are described using magnetic superspace groups, i.e. a direct extension of the non-magnetic superspace groups, which is the standard approach in the description of aperiodic crystals. The use of magnetic superspace symmetry ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. The point-group symmetry of each structure is derived from its magnetic superspace group, and any macroscopic tensor property of interest governed by this point-group symmetry can be retrieved through direct links to other programs of the Bilbao Crystallographic Server. The fact that incommensurate magnetic structures are often reported with ambiguous or incomplete information has made it impossible to include in this collection a good number of the published structures which were initially considered. However, as a proof of concept, the published data of about 30 structures have been re-interpreted and transformed, and together with ten structures where the superspace formalism was directly employed, they form this section of MAGNDATA . The relevant symmetry of most of the structures could be identified with an epikernel or isotropy subgroup of one irreducible representation of the space group of the parent phase, but in some cases several irreducible representations are active. Any entry of the collection can be visualized using the online tools available on the Bilbao server or can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. These CIF-like files are supported by visualization programs like Jmol and by analysis programs like JANA and ISODISTORT .
Electron distributions in the main compounds of rare-earths and actinides are described in relation with the valence of these elements. Their changes as a function of the physical conditions, temperature, pressure and some potential applications of these materials are discussed. Cerium
compounds are particularly considered.
Inelastic neutron scattering (INS) experiments and random phase approximation calculations have been used to investigate the low-energy spin-wave excitations in PrNi2Si2. The modulated magnitude of the ordered magnetic moments of Pr3+ ions implies that the associate, longitudinally polarized magnetic excitations are more intense and dispersive than the usual transverse spin waves. Within the random phase approximation the results are in good overall agreement with the predictions made by the model determined previously from the paramagnetic excitations. The most unusual observation is the well-defined amplitude mode detected close to the magnetic Bragg point existing simultaneously with the phason mode. At low energies, an extra mode is observed to hybridize with the magnetic phasons in the neighborhood of the magnetic Brillouin zone center. A magnetoelastic interaction between the magnetic excitations and the longitudinal phonons is able to explain part of the disturbances, but it is concluded that the extra mode must be of some other, unknown origin.
The magnetic properties of PrRu2Si2 have been investigated experimentally by specific heat, single-crystal magnetization, 141Pr Mössbauer and muon spectroscopies, neutron powder diffraction, and inelastic neutron scattering, leading to the determination of its zero-field phase diagram and its crystal electric-field energy levels below 40 meV. PrRu2Si2 undergoes a magnetic phase transition at TN ≃ 16 K to an axial incommensurate sine-wave magnetic structure characterized by a wave vector τ = (0.133, 0.133, 0), followed by a first-order phase transition at TC ≃ 14.0 K to an axial ferromagnetic structure. The lowest crystal electric-field states are the two singlets |Γt1(1)〉 and |Γt2〉 separated by 2.25 meV. The low-temperature properties are described by a Hamiltonian identical to that of an Ising system with a transverse magnetic field. Since the ratio of the exchange energy to the energy splitting between the singlets is sufficiently large, it exhibits spontaneous magnetization. The nature of the two singlet states explains the giant magnetic anisotropy. The random-phase approximation predicts the value of the high-field magnetization but yields a low-field magnetization too small by ∼ 15%. Possible application of our results to uranium intermetallic compounds is pointed out.
The program package McPhase has been developed in order to calculate
static and dynamic magnetic properties of rare earth compounds. Crystal
field (CF) and exchange parameters are required as an input for the
calculation. The two ion interaction may be chosen anisotropic and also
terms of higher order (e.g. quadrupolar interactions) can be taken into
account. A mean-field calculation is repeated with randomly chosen
initial moment configurations in order to determine the most stable
magnetic structure at a given temperature and magnetic field. By
subsequent calculations at several temperatures and magnetic fields a
magnetic phase diagram can be mapped. Using a special module of the
program package the input parameters may be varied in order to find a
model description, which corresponds to experimental data.
Research performed within the program of the Sonderforschungsbereich 463
(funded by the Deutsche Forschungsgemeinschaft).
Resistivity and magnetic measurements as well as neutron diffraction studies have been performed on the tetragonal PrNi2Si2 compound. Below TN = 18 K a colinear modulated antiferromagnetic structure with Qm = (0, 0, 0.87) is observed down to the lowest temperature investigated. Mi is non-magnetic and Pr moments are along the c-axis with a maximum value of 2.6 ± 0.1μB at 5.5 K. Magnetic measurements performed on a single crystal reveal a large uniaxial magnetocrystalline anisotropy. From the anisotropy of the paramagnetic susceptibility, the second-order crystal field parameter V20=+190K. is deduced. The stability of the modulated structure at low temperature should be associated with a crystal field splitting of the Pr3+ multiplet which gives rise to a non magnetic singlet ground state.
The calculation of energy levels of magnetic ions in crystalline electric fields is often the cause of considerable confusion. This confusion largely arises, not through the fundamental theoretical principles which are now well established, but from the large number of different and often not fully defined notations used, occasional errors, and the fact that one author seldom gives an example of calculation from start to finish. This chapter contains no original contribution to the problem, but it is hoped that by illustrating how the energy levels may be calculated on the basis of a simple Point-charge ionic model of the crystal lattice, the connection between the various forms of crystal-field Hamiltonians will be clarified. Particular reference is made to fields of cubic symmetry. If the crystalline electric field effects are taken as a perturbation on the appropriate free-ion wave functions and energy levels, the problem becomes that of finding the perturbing Hamiltonian and its matrix elements. The energy levels in the crystal field can then be found from standard perturbation theory. The simple point-charge model used to calculate the Hamiltonian is known to possess several weaknesses. It neglects the finite extent of charges on the ions, the overlap of the magnetic ions' wave functions with those of neighboring ions, and the complex effects of “screening” of the magnetic electrons by the outer electron shells of the magnetic ion. However, it serves as a first approximation to illustrate the principles involved, and may be used to calculate ratios of terms of the same degree in the Hamiltonian for lattice sites of high symmetry, since these ratios are independent of the model used and are determined solely by the symmetry.
The solid solutions (1- x )FeTiO 3 - x Fe 2 O 3 exhibit strong ferromagnetic moments in the composition range 0.1< x <0.6. In this region cation ordering is thought to occur such that the Fe 2+ and Ti 4+ ions occupy alternate (111) layers, thus forming sublattices A[ x Fe 3+ , (1- x )Fe 2+ ] and B[ x Fe 3+ , (1- x )Ti 4+ ]. A neutron diffraction study shows that at least 95% of the Ti ions are located on the B layer but that they are not ordered within the layer. The temperature dependence of the magnetic intensities of a number of ferrimagnetic phases reveals that both sublattice moments, at zero magnetic field, fall considerably short of the theoretical values. In addition, Mossbauer patterns indicate that paramagnetic behavior persists over a rather wide temperature range below the Neel temperatures of solid solutions in which x =0.21 and x =0.33. These results are interpreted as a consequence of inhomogeneity in the magnetic structure, due to competing interactions as a result of the Ti ions being dis...
Neutron diffraction experiments on phosphorus-rich Eu(As1-xPx)3 have established that the ordered magnetic phase just below TN (8.5 K) is a sine-wave phase which undergoes a first-order phase transition at about 7.5 K to a helimagnetic phase. This is the first observation of such a sine-wave-to-helical phase transition in real magnetic system.
The dispersion curves for magnetic excitations along the principal directions of the Brillouin zone of the singlet ground state compound PrNi2Si2 have been measured at 30 K by inelastic neutron-scattering experiments in the paramagnetic phase. From these data we have extracted information about the main exchange interaction coupling parameters Jij that are responsible for the appearance of an amplitude modulated magnetic order in this compound below TN=20K. The results are consistent with the long-range character of Ruderman-Kittel-Kasuya-Yosida interactions because in order to describe the dispersion curves observed at 30 K it is necessary to consider the influence of the interaction to the eighth nearest-neighbor Pr3+ ion along the c direction. In addition, we have studied the thermal dependence of the excitations at several representative points in the Brillouin zone that show an important softening as the temperature is lowered to TN.