Magnetic Order Parameter Research Articles

Temperature dependence ofEu 4fandEu 5dmagnetizations in the filled skutteruditeEuFe4Sb12

The element-specific and shell-specific magnetism of Eu in the filled skutterudite ferrimagnet Eu{sub 0.95}Fe{sub 4}Sb{sub 12} has been investigated using Eu M{sub 4,5}- and Eu L{sub 2,3}-edge x-ray magnetic circular dichroism (XMCD) spectroscopy as a function of temperature. Eu L{sub 3}-edge x-ray absorption spectroscopy shows that Eu is mostly in the divalent state. Eu M{sub 5}-edge x-ray absorption spectroscopy, measured by electron yield, shows nearly equal fractions of Eu{sup 2+} and Eu{sup 3+} states because it probes a significant portion of the surface volume which is dominated by the Eu{sup 3+} impurity state. Sum-rule analysis of the Eu M{sub 4,5}-edge XMCD spectrum measured at 4.9 K yielded the 4f spin moment of (7.15 {+-} 0.3){micro}{sub B} per Eu{sup 2+} ion. By comparing the Eu L{sub 2,3}-edge XMCD spectrum in the ferrimagnetic state of Eu{sub 0.95}Fe{sub 4}Sb{sub 12} to that of a divalent Eu reference compound, the clathrate Eu{sub 8}Ga{sub 16}Ge{sub 30}, we show that the 5d spin polarization of Eu in the skutterudite is strongly enhanced by the exchange coupling with the 3d band electrons of Fe, which were shown to have an ordered moment of ?0.21{micro}{sub B}/Fe in our earlier Fe L{sub 2,3} XMCD measurements. The temperature dependence ofmore » the magnetic order parameter, determined from the Eu L{sub 3}-edge XMCD intensity, yields a mean-field-like exponent ({approx} 0.52) in the skutterudite and a three-dimensional Heisenberg-type ({approx} 0.36) exponent in the clathrate.« less

Theory of spin magnetohydrodynamics

We develop a phenomenological hydrodynamic theory of coherent magnetic precession coupled to electric currents. Exchange interaction between electron spin and collective magnetic texture produces two reciprocal effects: spin-transfer torque on the magnetic order parameter and the Berry-phase gauge field experienced by the itinerant electrons. The dissipative processes are governed by three coefficients: the ohmic resistance, Gilbert damping of the magnetization, and the ``$\ensuremath{\beta}$ coefficient'' describing viscous coupling between magnetic dynamics and electric current, which stems from spin mistracking of the magnetic order. We develop general magnetohydrodynamic equations and discuss the net dissipation produced by the coupled dynamics. The latter in particular allows us to determine a lower bound on the magnetic-texture resistivity.

Antiferromagnetism in two-dimensional quasicrystals

Abstract Quasiperiodic structures possess long range positional order, but are freed of constraints imposed by translational invariance. For spins interacting via Heisenberg couplings, one may expect therefore to find novel magnetic configurations in such structures. We have studied magnetic properties for simple two dimensional models, as a first step towards understanding experimentally studied magnetic quasicrystals such as the Zn–Mg–R(rare earth) compounds. We analyse properties of the antiferromagnetic groundstate and magnon excitation modes for bipartite tilings such as the octagonal and Penrose tilings. In the absence of frustration, one has an inhomogeneous Neel-ordered ground state, with local quantum fluctuations of the local staggered magnetic order parameter. We study the spin wave spectrum and wavefunctions of such antiferromagnets within the linear spin wave approximation. Some results for spin-spin correlations in these systems are discussed.

Ground state phases of the spin-1/2J1–J2Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment

Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2 ${J}_{1}--{J}_{2}$ frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.

Strong coupling between magnetic and structural order parameters inSrFe2As2

X-ray and muon spin-relaxation experiments performed on ${\text{SrFe}}_{2}{\text{As}}_{2}$ polycrystals confirm a sharp first-order transition at ${T}_{0}=205\text{ }\text{K}$ corresponding to an orthorhombic phase distortion and to a commensurate antiferromagnetic Fe ordering with a larger distortion and larger size of the ordered moment than reported for ${\text{BaFe}}_{2}{\text{As}}_{2}$. The structural and the magnetic order parameters present a remarkable similarity in their temperature dependence from ${T}_{0}$ down to low temperatures, showing that both phenomena are intimately connected. Accordingly, the size of the ordered Fe moments scales with the lattice distortion when going from ${\text{SrFe}}_{2}{\text{As}}_{2}$ to ${\text{BaFe}}_{2}{\text{As}}_{2}$. Full-potential band-structure calculations confirm that the columnar magnetic order with propagation vector (1,0,1) and the orthorhombic lattice distortion are intrinsically tied to each other.

Zero Field NMR of BiFeO3

The zero-field 209 Bi NMR of bismuth ferrite, BiFeO 3 is studied at 4.2 K. The complicated multicomponent spectrum is related to a combination of the Zeeman interaction of 209 Bi nuclei with the local magnetic field, and of the quadrupolar coupling with spatially modulated electric field gradients (EFG) in the antiferromagnetic/ferroelectric phase of BiFeO 3 . The sinusoidal-wave modulation of the EFG is characterized by the variation of the 209Bi quadrupole interaction from 300 to 350 MHz. The microscopic mechanism of coupling between the ferroelectric and magnetic order parameters is studied using the density functional theory (DFT) calculations.

Investigation of Magnetoelectric Coupling in Single-Phase Multiferroic Ceramics

In this work, electrical permittivity measurements in lead iron niobate ceramics (PFN) were performed in the frequency and temperature range from 10 kHz to 1.2 GHz and from 15 K to 450 K, respectively. The microwave dielectric results revealed unambiguously the magnetoelectric effect in the PFN and demonstrated that the nature of such coupling arises indirectly via ferroelastic contribution rather than a direct coupling between electrical and magnetic order parameters. Moreover, it was also verified that such coupling can be enhanced or suppressed depending on the relative orientation between the probing electric field and the macroscopic polarization.

Magnetically induced ferroelectricity in the buckled Kagome antiferromagnetNi3V2O8

Ni3V2O8 is one of several recently identified multiferroic materials in which ferroelectricity is producedby long-range magnetic order. This staircase Kagome compound adopts a sequence of distinctlow temperature magnetic phases, which exhibit different optical, dielectric, and transportproperties, most notably ferroelectric order arising from a polar incommensurate magneticstructure. We give an overview of the experimental results from the existing literature onNi3V2O8, and briefly discuss models that describe the coupling between magneticand ferroelectric properties. We show that the temperature dependenceof the dielectric constant provides evidence for spin–charge coupling inNi3V2O8 away from the ferroelectric phase. An anomaly in the thermal conductivity at theincommensurate–commensurate phase transition suggests that spin scattering may limitthermal transport in the incommensurate phase. We associate each of the twoincommensurate phase transitions with one magnetic order parameter, and we show thatthe temperature dependence of the ferroelectric polarization closely follows the product ofthese two magnetic order parameters—corroborating the validity of the phenomenologicaltrilinear coupling model. Finally, we present inelastic powder neutron scatteringmeasurements that provide evidence of several weakly dispersive magnetic modes thatare typical for strongly frustrated antiferromagnets with large spin anisotropies.

Magnetic ordering and negative thermal expansion in PrFeAsO

We report the structure and magnetism of PrFeAsO, one of the parent phases of the Fe-As family of superconductors, as measured by neutron powder diffraction. In common with other REFeAsO materials, a tetragonal-orthorhombic phase transition is found on cooling below 136 K and striped Fe magnetism with $k=(1,0,1)$ is detected below $\ensuremath{\sim}85\text{ }\text{K}$. Our magnetic order-parameter measurements show that the ordered Fe moment along the $a$ axis reaches a maximum at $\ensuremath{\sim}40\text{ }\text{K}$, below which an anomalous expansion of the $c$ axis sets in that results in a negative thermal volume expansion of 0.015% at 2 K. We propose that this effect, which is suppressed in superconducting samples, is driven by a delicate interplay between Fe and Pr ordered moments.

Inelastic neutron scattering study of the multipolar order parameter inNpO2

We have performed polarized inelastic neutron scattering experiments in the ordered phase of neptunium dioxide. The observation of magnetic scattering between 11 and 18 meV can be attributed to a transition between two states with the same expectation value of the electric quadrupole but opposite values of the magnetic triakontadipole. In contrast to resonant x-ray scattering, which detects the secondary order parameter (electric quadrupoles) associated with the 25 K phase transition, the results reported here are a manifestation of the primary (magnetic) order parameter. The experimental observations are discussed in relation to the current theoretical understanding of the low-energy magnetic dynamics of ${\text{NpO}}_{2}$.

Observation of magnetoelectric coupling in Bi0.7Dy0.3FeO3 thin films at room temperature

Spatial coexistence of ferroelectric and magnetic domains in micrometer scale is confirmed by multimode scanning probe microscopy of pulsed laser deposited Bi0.7Dy0.3FeO3 thin films. The observed change in ferroelectric polarization with applied magnetic field proves the coupling between magnetic and ferroelectric order parameters. Moreover, the alignment of magnetic domains with externally applied electric field further confirms the presence of coupling in this system. Remarkably, the effect persists even after the electric field is removed, thereby implying an electric field induced magnetic hysteresis phenomenon in the magnetic domain structure. The results suggest an in-principle usability of this system for multifunctional applications.

Nature of the magnetoelectric coupling in multiferroicPb(Fe1/2Nb1/2)O3ceramics

In this work, electrical permittivity measurements in lead iron niobate (PFN) ceramics were performed in the frequency and temperature ranges from 10 kHz to 1.2 GHz and from 15 to 450 K, respectively. The microwave dielectric results characterized unambiguously the magnetoelectric effect in PFN and demonstrated that the nature of such coupling arises indirectly via ferroelastic contribution rather than a direct coupling between electrical and magnetic order parameters. Moreover, it was also verified that such coupling can be enhanced or suppressed depending on the relative orientation between the probing electric field and the macroscopic ferroelectric polarization.

Electric Field Switching of Antiferromagnetic Domains inYMn2O5: A Probe of the Multiferroic Mechanism

We employ neutron spherical polarimetry to determine the nature and population of the coexisting antiferromagnetic domains in multiferroic YMn2O5. By applying an electric field, we prove that reversing the electrical polarization results in the population inversion of two types of in-plane domains, related to each other by inversion. Our results are completely consistent with the exchange-striction mechanism of ferroelectricity, and support a unified model where cycloidal ordering is induced by coupling to the main magnetic order parameter.

Effect of inversion symmetry on the incommensurate order in multiferroicRMn2O5(R=rareearth)

Starting from the irreducible representations of the group of the wave vector, we construct the spin-wave functions consistent with inversion symmetry, neglected in the usual representation analysis. We obtain the relation between the basis functions of different members of the star of the wave vector. We introduce order parameters and determine their transformation properties under the operations of the space group of the paramagnetic crystal. The results are applied to construct terms in the magnetoelectric interaction, which are quadratic and quartic in the magnetic order parameters. The higher-order magnetoelectric interactions can in principle induce components of the spontaneous polarization, which are not allowed by the lowest-order magnetoelectric interaction. We also obtain the relation between the spin-wave functions of the incommensurate phase and those of the commensurate phase, which lead to analogous relations between the order parameters of these two phases.

Magnetic ordering of EuTe∕PbTe multilayers determined by x-ray resonant diffraction

In this work we use resonant x-ray diffraction combined with polarization analysis of the diffracted beam to study the magnetic ordering in EuTe∕PbTe multilayers. The presence of satellites at the (12 12 12) magnetic reflection of a 50 repetition EuTe∕PbTe superlattice demonstrated the existence of magnetic correlations among the alternated EuTe layers. The behavior of the satellites intensity as T increases toward the Nèel temperature TN indicates that these correlations persist nearly up to TN and suggests the preferential decrease of the magnetic order parameter of external monolayers of each EuTe layer within the superlattice.

A continuum thermodynamics formulation for micro-magneto-mechanics with applications to ferromagnetic shape memory alloys

A continuum thermodynamics formulation for micromagnetics coupled with mechanics is devised to model the evolution of magnetic domain and martensite twin structures in ferromagnetic shape memory alloys. The theory falls into the class of phase-field or diffuse-interface modeling approaches. In addition to the standard mechanical and magnetic balance laws, two sets of micro-forces and their associated balance laws are postulated; one set for the magnetization order parameter and one set for the martensite order parameter. Next, the second law of thermodynamics is analyzed to identify the appropriate material constitutive relationships. The proposed formulation does not constrain the magnitude of the magnetization to be constant, allowing for spontaneous magnetization changes associated with strain and temperature. The equations governing the evolution of the magnetization are shown to reduce to the commonly accepted Landau–Lifshitz–Gilbert equations for the case where the magnetization magnitude is constant. Furthermore, the analysis demonstrates that under certain limiting conditions, the equations governing the evolution of the martensite-free strain are shown to be equivalent to a hyperelastic strain gradient theory. Finally, numerical solutions are presented to investigate the fundamental interactions between the magnetic domain wall and the martensite twin boundary in ferromagnetic shape memory alloys. These calculations determine under what conditions the magnetic domain wall and the martensite twin boundary can be dissociated, resulting in a limit to the actuating strength of the material.

Competition of Magnetic and Quadrupolar Order Parameters in HoB4

The successive magnetic phase transitions of HoB 4 with T N1 =7.1 K and T N2 =5.7 K have been investigated in detail by neutron and X-ray diffraction. Since Ho ions in the c -plane form a Shastry–Sutherland lattice, geometrical frustration has been expected in this compound. Below T N1 , HoB 4 exhibits an incommensurate antiferromagnetic order with q =(δ, δ, δ') (δ=0.022, δ'=0.43), followed by a first-order transition at T N2 into a commensurate order with q =(0, 0, 0), where four magnetic moments are antiferromagnetically coupled in a unit cell. After determining the magnetic structures of the two phases by neutron powder diffraction, we pay particular attention to diffuse scatterings responsible for the critical behavior. Very broad diffuse scatterings, extending almost to the zone boundary, are observed already in the paramagnetic phase at around q =(0, 0, 0) and (0, 0, 1/2) with magnetic correlation lengths of ξ< 10 A. Below T N1 , a strong diffuse scattering develops in a more concentrated region at ...

Erratum: Landau analysis of the symmetry of the magnetic structure and magnetoelectric interaction in multiferroics [Phys. Rev. B76, 054447 (2007)

This paper presents a detailed instruction manual for constructing the Landau expansion for magnetoelectric coupling in incommensurate ferroelectric magnets, including ${\mathrm{Ni}}_{3}{\mathrm{V}}_{2}{\mathrm{O}}_{8}$, $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$, $\mathrm{Mn}\mathrm{W}{\mathrm{O}}_{4}$, $\mathrm{Tb}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Y}{\mathrm{Mn}}_{2}{\mathrm{O}}_{5}$, $\mathrm{Cu}\mathrm{Fe}{\mathrm{O}}_{2}$, and $\mathrm{Rb}\mathrm{Fe}{(\mathrm{M}{\mathrm{O}}_{4})}_{2}$. The first step is to describe the magnetic ordering in terms of symmetry adapted coordinates which serve as complex-valued magnetic order parameters whose transformation properties are displayed. In so doing, we use the previously proposed technique to exploit inversion symmetry, since this symmetry has seemingly been universally overlooked. Inversion symmetry severely reduces the number of fitting parameters needed to describe the spin structure, usually by fixing the relative phases of the complex fitting parameters. By introducing order parameters of known symmetry to describe the magnetic ordering, we are able to construct the trilinear magnetoelectric interaction which couples incommensurate magnetic order to the uniform polarization, and thereby we treat many of the multiferroic systems so far investigated. In most cases, the symmetry of the magnetoelectric interaction determines the direction of the magnetically induced spontaneous polarization. We use the Landau description of the magnetoelectric phase transition to discuss the qualitative behavior of various susceptibilities near the phase transition. The consequences of symmetry for optical properties such as polarization induced mixing of Raman and infrared phonons and electromagnons are analyzed. The implication of this theory for microscopic models is discussed.

Orientation dependence of the anomalous Hall resistivity in single crystals ofYb14MnSb11

The Hall resistivity, electrical resistivity and magnetization of single crystals of the tetragonal ferromagnet Yb14MnSb11 are reported as a function of the direction of the current, I, and magnetic field, H with respect to the principal crystallographic axes. With I along the unique c direction and H in the a-b plane, the anomalous Hall resistivity in the limit of zero applied field is negative for all temperatures T< Tc= 53 K. An intrinsic Hall conductivity , !xy 0, of -32 -1 cm-1 is found for T << Tc, which decreases linearly with the spontaneous magnetization (order parameter) as the temperature is increased to Tc . In this direction, the anomalous Hall effect behaves in a manner similar to that observed in other ferromagnets such as Fe, Co, Mn5Ge3, and EuFe4Sb12. However, with I in the a-b plane and H along the c direction, the anomalous Hall behavior is completely different. The anomalous Hall resistivity data are positive for all T < Tc and a similar analysis of these data fails. In this direction, the anomalous response is not a simple linear function of the magnetization order parameter, and for a fixed temperature (T < Tc) does not depend on themore » magnitude of the magnetization perpendicular to the current in the a-b plane. That is, when the magnetization and applied field are rotated away from the c direction, the anomalous Hall resistivity does not change. In all other soft ferromagnets that we have examined (including La doped crystals of Yb14MnSb11, i.e. 2 Yb13.3La0.7MnSb11) rotation of the magnetization and magnetic field by an angle # away from a direction perpendicular to I results in a decrease in both the anomalous and normal portions of the Hall resistivity that approximately scales as cos(#). We suggest that the unique response exhibited by Yb14MnSb11 is a direct reflection of the delicate balance between a ferromagnetic and a non-magnetic Kondo lattice ground state« less

Skutterudite Results Shed Light on Heavy Fermion Physics

Only few selected examples among the great diversity of anomalous rare earth skutterudite are reviewed. Focus is first given on PrFe4P12 in comparison with URu2Si2. For PrFe4P12, great progress has been made on determining the nature of the order parameter (OP). A non magnetic order parameter with a multipolar component emerges here while for URu2Si2 the nature of the so-called hidden order remains mysterious. The two systems have several similarities in their temperature--pressure (T, P) and magnetic field--temperature (H, T) phase diagrams, in their spin dynamics, in their nesting character and in their high sensitivity to impurities. Advances on one side must stimulate new views on the other. Besides general considerations on the choice of the OP, a simple basic problem is the treatment of the Kondo coupling in a system with low charge carrier number for the cases of uncompensated and compensated semi-metal. An interesting problem is also the possible decoupling between exciton modes and itinerant carriers.