Crystal Electric Field Research Articles

μSRand inelastic neutron scattering investigations of the noncentrosymmetric antiferromagnetCeNiC2

The magnetic state of the noncentrosymmetric antiferromagnet ${\mathrm{CeNiC}}_{2}$ has been studied by magnetic susceptibility, heat capacity, muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$, and inelastic neutron scattering (INS) measurements. ${\mathrm{CeNiC}}_{2}$ exhibits three magnetic phase transitions at ${T}_{{N}_{1}}=19.5$ K, ${T}_{{N}_{2}}=10$ K, and ${T}_{{N}_{3}}=2.5$ K. The presence of long-range magnetic order below 20 K is confirmed by the observation of oscillations in the $\ensuremath{\mu}\mathrm{SR}$ spectra between 10 and 20 K and a sharp increase in the muon depolarization rate. INS studies reveal two well-defined crystal electric field (CEF) excitations around 8 and 30 meV. INS data have been analyzed using a CEF model and the wave functions were evaluated. We also calculated the direction and magnitude of the ground state moment using CEF wave functions and compare the results with that proposed from the neutron diffraction. Our CEF model correctly predicts that the moments order along the $b$ axis (or $y$ axis) and the estimated magnetic moment is $0.687(5){\ensuremath{\mu}}_{B}$, which is higher than the moment observed from the neutron diffraction $(0.25{\ensuremath{\mu}}_{B}/\mathrm{Ce})$. We attribute the observed reduced moment due to the Kondo screening effect.

Crossover regime of optical vortices generation via electro-optic nonlinearity: the problem of optical vortices with the fractional charge generated by crystals.

In this work, we analyze the behavior of topological defects of optical indicatrix orientation induced by a conically shaped electric field in crystals in a crossover regime that appears at intermediate fields separating the regimes of prevailing Pockels and Kerr electro-optic nonlinearities. We have found that increases in the electric voltage applied to a crystal induce neither topological defects, with the strengths being not multiples of ½, or the optical vortices with fractional charges. Instead, there appear some additional topological defects of the optical indicatrix orientation, the behavior of which we have studied in detail.

Lattice Strain Accompanying the Colossal Magnetoresistance Effect inEuB6

The coupling of magnetic and electronic degrees of freedom to the crystal lattice in the ferromagnetic semimetal EuB(6), which exhibits a complex ferromagnetic order and a colossal magnetoresistance effect, is studied by high-resolution thermal expansion and magnetostriction experiments. EuB(6) may be viewed as a model system, where pure magnetism-tuned transport and the response of the crystal lattice can be studied in a comparatively simple environment, i.e., not influenced by strong crystal-electric field effects and Jahn-Teller distortions. We find a very large lattice response, quantified by (i) the magnetic Grüneisen parameter, (ii) the spontaneous strain when entering the ferromagnetic region, and (iii) the magnetostriction in the paramagnetic temperature regime. Our analysis reveals that a significant part of the lattice effects originates in the magnetically driven delocalization of charge carriers, consistent with the scenario of percolating magnetic polarons. A strong effect of the formation and dynamics of local magnetic clusters on the lattice parameters is suggested to be a general feature of colossal magnetoresistance materials.

Anisotropic magnetic behavior of single crystalline CeTiGe3 and CeVGe3

We have grown the single crystals of iso-structural CeTiGe3 and CeVGe3 compounds by using Ce-Ge eutectic as flux. Using the techniques of magnetization, electrical resistivity and heat capacity, our data on single crystals reveal pronounced magnetic anisotropies in these compounds with hexagonal symmetry. The c-axis is the easy axis of magnetization in CeTiGe3 which orders ferromagnetically at 14 K, and a gap in the magnon excitation spectra of ∼28 K is inferred from both electrical resistivity and heat capacity. The electrical resistivity of CeTiGe3 shows anisotropic Kondo behavior and the heat capacity indicates the existence of the first excited crystal electric field split doublet lying at about ∼50 K. The nature of magnetic ordering changes to antiferromagnetic in CeVGe3, which undergoes a magnetic transition at TN ∼ 6 K with the a − b plane as the easy plane of magnetization. Below TN, the electrical resistivity of CeVGe3 along the c axis shows an upturn due to the opening of a gap. The 4f contribution to the resistivity ρ4f establishes that CeVGe3, like the Ti analog, is also a Kondo lattice compound. The present work on single crystals further advances our understanding of these materials based on polycrystalline samples which have been studied earlier in the literature.

Magnetic and transport properties of i- R -Cd icosahedral quasicrystals (R=Y,Gd-Tm)

We present a detailed characterization of the recently discovered i-$R$-Cd ($R$ = Y, Gd-Tm) binary quasicrystals by means of x-ray diffraction, temperature-dependent dc and ac magnetization, temperature-dependent resistance and temperature-dependent specific heat measurements. Structurally, the broadening of x-ray diffraction peaks found for i-$R$-Cd is dominated by frozen-in phason strain, which is essentially independent of $R$. i-Y-Cd is weakly diamagnetic and manifests a temperature-independent susceptibility. i-Gd-Cd can be characterized as a spin-glass below 4.6 K via dc magnetization cusp, a third order non-linear magnetic susceptibility peak, a frequency-dependent freezing temperature and a broad maximum in the specific heat. i-$R$-Cd ($R$ = Ho-Tm) is similar to i-Gd-Cd in terms of features observed in thermodynamic measurements. i-Tb-Cd and i-Dy-Cd do not show a clear cusp in their zero-field-cooled dc magnetization data, but instead show a more rounded, broad local maximum. The resistivity for i-$R$-Cd is of order 300 $\mu \Omega$ cm and weakly temperature-dependent. The characteristic freezing temperatures for i-$R$-Cd ($R$ = Gd-Tm) deviate from the de Gennes scaling, in a manner consistent with crystal electric field splitting induced local moment anisotropy.

Crystal electric field and the ground state properties of heavy fermion Ce3Ru4Sn13

We report on the electronic structure, electric transport and basic thermodynamic properties of the skutterudite-related Ce3Ru4Sn13 and La3Ru4Sn13. The calculated density of electronic states within the local spin density approximation (LSDA) method well fit the X-ray photoelectron spectroscopy (XPS) valence band spectra of Ce3Ru4Sn13. Magnetic susceptibility and specific heat measurements reveal that the sixfold degenerated multiplet of Ce3+ ions splits into three doublets, due to the tetragonal Ce point local symmetry in the cubic Ce3Ru4Sn13 system. Ce3Ru4Sn13 exhibits a large increase in the specific heat, C/T, data due to Kondo effect and strong electron and short-range magnetic correlations, we also suggest significant contribution of the crystal field effect. La3Ru4Sn13 is typical BCS superconductor, however, specific heat and electrical resistivity data show that La3Ru4Sn13 also exhibits a second superconducting phase at higher temperatures, which is characteristic of inhomogeneous superconductors.

Investigations of the singlet ground state system: PrIrSi3

We report our comprehensive study of physical properties of a ternary intermetallic compound PrIrSi3 investigated by dc magnetic susceptibility χ(T), isothermal magnetization M(H), thermo-remnant magnetization M(t), ac magnetic susceptibility χac(T), specific heat Cp(T), electrical resistivity ρ(T), muon spin relaxation (µSR) and inelastic neutron scattering (INS) measurements. A magnetic phase transition is marked by a sharp anomaly at Ttr = 12.2 K in χ(T) measured at low applied fields which is also reflected in the Cp(T) data through a weak anomaly at 12 K. An irreversibility between the zero field cooled and field cooled χ(T) data below 12.2 K and a very large relaxation time of M(t) indicates the presence of ferromagnetic correlation. The magnetic part of specific heat shows a broad Schottky-type anomaly near 40 K due to the crystal electric field (CEF) effect. An extremely small value of magnetic entropy below 12 K suggests a CEF-split singlet ground state which is confirmed from our analysis of INS data. The INS spectra show two prominent inelastic excitations at 8.5 meV and 18.5 meV that could be well accounted by a CEF model. The CEF splitting energy between the ground state singlet and the first excited doublet is found to be 92 K. Our µSR data reveal a possible magnetic ordering below 30 K, which is much higher than that found from the specific heat and magnetic susceptibility measurements. This could be due to the presence of short range correlations well above the long range magnetic ordering or due to the electronic changes induced by muons. The induced moment magnetism in the singlet ground state system PrIrSi3 with such a large splitting energy of 92 K is quite surprising.

Thermal conductivity and Lorenz number of the Ce1−xLaxNiAl4 Kondo alloys

The temperature dependence of the thermal conductivity (κ) for Ce1−xLaxNiAl4 alloys has been studied. In comparison to LaNiAl4, the substitution of La by Ce reduces the κ values. The behaviour of the Lorenz number L in the Kondo alloys Ce1−xLaxNiAl4 differs considerably both in magnitude and in temperature dependence from L characteristic of pure metals. The Lorenz number of Ce1−xLaxNiAl4 exhibits positive values and peaks at low temperatures. The obtained values of L at low temperatures are higher than the theoretical value of L0. The reason for the increased Lorenz number may be the contribution of phonons, Kondo and crystal electric field (CEF) effects. The values of L/L0 are close to 1 at high temperatures, which is in agreement with the conclusion that the electronic part κe(T) dominates at high temperatures. Such a temperature dependence of L/L0 is commonly observed in Kondo compounds. Applying an external magnetic field has no significant effect on the thermal conductivity below 30K. Above this temperature a gentle changes of κ can be observed.

Crystalline field effect and magnetic ordering in the heavy fermion Kondo lattice Ce6Pd12In5

Results of magnetic, specific heat, electric and thermal transport studies carried out on the novel hexagonal-type structure Ce6Pd12In5 compound, with a unique site for Ce, two sites for In and four sites for Pd are reported. The compound exhibits long-range order, probably of antiferromagnetic type, below TN=1.6K in spite of a moment reducing Kondo effect acting on the magnetic Ce3+ ions. A strong influence of magnetic field on the low temperature dependencies of susceptibility, specific heat and electrical resistivity is observed. The crystal-electric field effect, CEF, plays an influential role in the ground state of this compound. The CEF parameters have been estimated. Based upon the low-temperature specific heat we observe heavy fermion behavior with the electronic specific heat coefficient that is enhanced to the value of γ=132mJ/Ce-molK2. In the electrical resistivity, a logarithmic character ρ4f(T)∼-lnT is observed that arises from incoherent Kondo scattering. Towards low temperature this behavior evolves into Kondo lattice formation with a coherence temperature Tcoh≃5.3K, before long-range order takes place. We propose that Ce6Pd12In5 presents a new case study for competing Kondo and magnetic ordering in a high-symmetry lattice, with CEF and magnetocrystalline anisotropy further impacting upon the cooperative magnetic behavior.

Sign of canted ferromagnetism in the quasicrystal approximants Au-SM-R (SM = Si, Ge and Sn / R = Tb, Dy and Ho)

Magnetic susceptibility and magnetization of the quasicrystal approximants Au-SM-R (SM = Si, Ge or Sn / R = Gd, Tb, Dy or Ho) are investigated. Ferromagnetic transitions are observed in all of these compounds, in contrast to the spin-glass behavior reported in similar compounds, Ag-In-R (R = Eu, Gd, Tb or Dy). Au-SM-Gd (SM = Si, Ge or Sn) exhibit a simple ferromagnetic transition at 22.5, 13 and 9 K, respectively, whereas Au-Si-(Tb, Dy or Ho) show indications of a canted ferromagnetic transition at 8.3, 5.9 and 3.8 K, respectively. The latter are attributed to a crystal electric field effect that is absent in the Gd-bearing compounds. The ferromagnetic behavior in Au-SM-R may be understood to be a consequence of the short R-R distances compared to those for Cd-R and Ag-In-R.

Anisotropic magnetic properties and giant magnetocaloric effect of single-crystal PrSi

A single crystal of PrSi was grown by the Czochralski method in a tetra-arc furnace. Powder x-ray diffraction of the as-grown crystal revealed that PrSi crystallizes in an FeB-type structure with space group Pnma (No. 62). The anisotropic magnetic properties were investigated by means of magnetic susceptibility, isothermal magnetization, electrical transport, and heat capacity measurements. Magnetic susceptibility data clearly indicate the ferromagnetic transition in PrSi with a ${T}_{C}$ of 52 K. The relative easy axis of magnetization was found to be the [010] direction. Heat capacity data confirm the bulk nature of the transition at 52 K and exhibit a huge anomaly at the transition. A sharp rise in the low-temperature heat capacity has been observed (below 5 K) which is attributed to the ${}^{141}$Pr nuclear Schottky heat capacity arising from the hyperfine field of the Pr moment. The estimated Pr magnetic moment 2.88 ${\ensuremath{\mu}}_{\mathrm{B}}$/Pr from the hyperfine splitting is in agreement with the saturation magnetization value obtained from the magnetization data measured at 2 K. From the crystal electric field analysis of the magnetic susceptibility, magnetization, and heat capacity data it is found that the degenerate $J=4$ Hund's rule derived state of the Pr${}^{3+}$ ion splits into nine singlets with an overall splitting of 284 K, the first excited singlet state separated by just 9 K from the ground state. The magnetic ordering in PrGe appears to be due to the exchange-generated admixture of low-lying crystal field levels. The magnetocaloric effect (MCE) has been investigated from magnetization data along all three principal crystallographic directions. The large magnetic entropy change, $\ensuremath{-}\ensuremath{\Delta}{S}_{M}=$22.2 J/kg K, and the relative cooling power, RCP = 460 J/kg, characteristic of the giant magnetocaloric effect are achieved near the transition temperature (${T}_{C}$ = 52 K) for $H=$ 70 kOe along $[010]$. Furthermore, the PrSi single crystal exhibits a giant MCE anisotropy.

Anomalous Elastic Softening due to the Crystal Electric Field Effect and Successive Phase Transitions in the Yb-Based Heavy-Fermion Antiferromagnet YbIrGe

To investigate the crystal electric field effect and antiferromagnetic transitions at 2.4 and 1.4 K, we carried out ultrasonic measurements on the Yb-based heavy-fermion antiferromagnet YbIrGe. We found characteristic softening of the elastic moduli originating from a quadrupole interaction. By theoretical analyses of the transverse elastic moduli, the magnetic susceptibility, and the Schottky specific heat between 10 and 300 K, we determined the crystal electric field: the ground doublet and an excited doublet separated by 138 K. The moduli exhibit elastic hardening below both 2.4 and 1.4 K, suggesting a strong coupling between a strain and magnetic order parameters. We estimated the strain dependence of the transition temperature at 2.4 K along the a- and c-axes from the Ehrenfest relation for the first time.

Magneto-Elastic Effects in Tb3Ga5O12

We report new results for the elastic constants studied in Faraday and Cotton–Mouton geometry in Tb3Ga5O12 (TGG), a frustrated magnetic substance with strong spin–phonon interaction and remarkable crystal-electric-field (CEF) effects. We analyze the data in the framework of CEF theory taking into account the individual surroundings of the six inequivalent Tb3+-ion positions. This theory describes both, elastic constants in the magnetic field and as a function of temperature. Moreover we present sound-attenuation data for the acoustic Cotton–Mouton effect in TGG.

Spin-Orbit Origin of Anomalous Temperature Dependence of the Magnetic Susceptibility of PbVO3

We have shown that the V4+ ion, realized in PbVO3, with one d electron can have almost non-magnetic ground state under the action of the crystal field in the presence of the spin-orbit coupling. This weakly-magnetic ground state, with low lying crystal-electric-field (CEF) states at 0, 24 and 110 meV, causes anomalous temperature dependence of the magnetic susceptibility at low temperatures violating the magnetic Curie law. The formation of the weakly magnetic ground state is caused by the substantial orbital moment that almost cancels the spin moment.

Magnetic properties and specific heat data of R11Ni4In9 (R = Pr, Nd, Sm, Gd and Tb) compounds

Magnetic and thermal properties of R11Ni4In9 compounds (R=Pr, Nd, Sm, Gd and Tb) were investigated by means of magnetic and specific heat measurements. These compounds crystallize in orthorhombic Nd11Pd4In9-type crystal structure in which the rare earth atoms occupy five nonequivalent sublattices. For all these compounds except Gd11Ni4In9, the ground state at low temperature is antiferromagnetic. Except Pr11Ni4In9, in temperature dependence of the specific heat a two phase transitions are observed. For compounds with R=Nd and Tb with increasing of the external magnetic field and/or temperature the change to the ferrimagnetic state is observed. Sm11Ni4In9 is an antiferromagnet with small ferromagnetic component. The critical temperature of magnetic ordering does not fulfill the de Gennes scaling which indicates the influence of the crystal electric field in stabilizing the magnetic ordering.

X-ray photoemission, calorimetric, and electrical transport properties of CeCu4MnyAl1−y

We report the X-ray photoemission spectra (XPS) and the electrical resistivity measurements for the transition Kondo lattice – spin-glass (SG) in the series CeCu4MnyAl1−y. The study includes additionally the low temperature (down to T=400mK) heat capacity results. The XPS measurements revealed that the Ce 4f states are well localized. Electrical resistivity studies illustrate a smooth evolution from the ∼ −lnT relation to the metallic behaviour with the increase of the Mn content. Moreover, the specific heat has been analysed considering the electronic, phonon, Schottky (Crystal Electric Field – CEF), Kondo, and SG contributions. The assumption that the CEF splitting of the energy levels is similar for all the compositions allowed us to estimate the SG and Kondo contribution to the heat capacity. Additionally, the neutron diffraction experiment on the parent CeCu4Mn compound has confirmed that it does not show a long-range magnetic order.

Thermodynamic and transport properties of single crystalline RCo2Ge2 (R=Y, La–Nd, Sm–Tm)

Single crystals of RCo2Ge2 (R=Y, La–Nd, Sm–Tm) were grown using a self-flux method and were characterized by room-temperature powder X-ray diffraction; anisotropic, temperature and field dependent magnetization; temperature and field dependent, in-plane resistivity; and specific heat measurements. In this series, the majority of the moment-bearing members order antiferromagnetically; YCo2Ge2 and LaCo2Ge2 are non-moment-bearing. Ce is trivalent in CeCo2Ge2 at high temperatures, and exhibits an enhanced electronic specific heat coefficient due to the Kondo effect at low temperatures. In addition, CeCo2Ge2 shows two low-temperature anomalies in temperature-dependent magnetization and specific heat measurements. Three members (R=Tb–Ho) have multiple phase transitions above 1.8K. Eu appears to be divalent with total angular momentum L=0. Both EuCo2Ge2 and GdCo2Ge2 manifest essentially isotropic paramagnetic properties consistent with J=S=7/2. Clear magnetic anisotropy for rare-earth members with finite L was observed, with ErCo2Ge2 and TmCo2Ge2 manifesting planar anisotropy and the rest members manifesting axial anisotropy. The experimentally estimated crystal electric field (CEF) parameters B20 were calculated from the anisotropic paramagnetic θab and θc values and follow a trend that agrees well with theoretical predictions. The ordering temperatures, TN, as well as the polycrystalline averaged paramagnetic Curie–Weiss temperature, Θavg, for the heavy rare-earth members deviate from the de Gennes scaling, as the magnitude of both is the highest for Tb, which is sometimes seen for extremely axial systems. Except for SmCo2Ge2, metamagnetic transitions were observed at 1.8K for all members that ordered antiferromagnetically.

Field induced strain response of lead-free BaZrO3-modified Bi0.5Na0.5TiO3–BaTiO3 ceramics

Lead-free (0.935−x)[Bi0.5Na0.5TiO3–0.065BaTiO3]–xBaZrO3 (BNBT–xBZ, with x=0−0.07) ceramics were prepared by a conventional solid-state reaction method. The effect of BZ addition on the crystal structure, microstructure, dielectric, ferroelectric and electric field induced strain behavior of BNBT ceramic was investigated. X-ray diffraction patterns of BNBT–xBZ ceramics revealed the formation of single phase perovskite structure in the studied composition range. Addition of BZ in BNBT transform the crystal structure from tetragonal to pseudocubic symmetry. However, with increasing BZ content, the maximum dielectric constant decreased and the dielectric maximum temperature (Tm) shifted towards lower temperature. The field induced strain response of BNBT–xBZ increases from 0.16% for x=0 to 0.38% for x=0.03, at an applied field of 7kV/mm. The corresponding dynamic piezoelectric coefficient for these composition were (Smax/Emax=231pm/V) and (Smax/Emax=542pm/V), respectively. These results suggest that the BNBT–0.03BZ ceramic can be considered as a promising candidate material for piezoelectric application.

Pressure-induced ferromagnetism with strong Ising-type anisotropy in YbCu2Si2

We report dc magnetic measurements on YbCu$_2$Si$_2$ at pressures above 10 GPa using a miniature ceramic anvil cell. YbCu$_2$Si$_2$ shows a pressure-induced transition from the non-magnetic to a magnetic phase at 8 GPa. We find a spontaneous dc magnetization in the pressure-induced phase above 9.4 GPa. The pressure dependence of the ferromagnetic transition temperature T_C and the spontaneous magnetic moment m_0 at 2.0 K have been determined. The value of m_0 in the present macroscopic measurement is less than half of that determined via Mossbauer experiment. The difference may be attributed to spatial phase separation between the ferromagnetic and paramagnetic phases. This separation suggests that the pressure-induced phase boundary between the paramagnetic and ferromagnetic states is of first order. Further, we have studied the magnetic anisotropy in the pressure-induced ferromagnetic state. The effect of pressure on the magnetization with magnetic field along the magnetic easy $c$-axis is much larger than for field along the hard $a$-axis in the tetragonal structure. The pressure-induced phase has strong Ising-type uniaxial anisotropy, consistent with the two crystal electric field (CEF) models proposed for YbCu$_2$Si$_2$.

Complex and strongly anisotropic magnetism in the pure spin system EuRh2Si2

In divalent Eu systems, the 4f local moment has a pure spin state J = S = 7/2. Although the absence of orbital moment precludes crystal electric field effects, we report a sizable magnetic anisotropy in single crystals of EuRh2Si2. We observed a surprisingly complex magnetic behavior with three successive phase transitions. The Eu2+ moments order in a probably amplitude-modulated structure below 24.5 K, undergoing a further transition to a structure that is possibly of the equal-moment type, and a first order transition at lower temperatures, presumably into a spin spiral structure. The sharp metamagnetic transition observed at low fields applied perpendicular to the hard axis is consistent with a change from a spiral to a fan structure. These magnetic structures are presumably formed by ferromagnetic planes perpendicular to the c axis, stacked antiferromagnetically along c but not of type I, at least just below the ordering temperature. Since EuRh2Si2 is isoelectronic and isostructural to EuFe2As2 at room temperature, our results are also relevant for the complex Eu-magnetism observed there, especially for the transition from an antiferromagnetic to a ferromagnetic state observed in EuFe2P2 upon substituting As by P.