Ferromagnetic Liquid Research Articles

Bosonic field theory of tunable edge magnetism in graphene

A bosonic field theory is derived for the tunable edge magnetism at graphene zigzag edges. The derivation starts from an effective fermionic theory for the interacting graphene edge states, derived previously from a two-dimensional interacting tight-binding model for graphene. The essential feature of this effective model, which gives rise to the weak edge magnetism, is the momentum-dependent non-local electron-electron interaction. It is shown that this momentum-dependence may be treated by an extension of the bosonization technique, and leads to interactions of the bosonic fields. These interactions are reminiscent of a \phi^4 field theory. Focussing onto the regime close to the quantum phase transition between the ferromagnetic and the paramagnetic Luttinger liquid, a semiclassical interpretation of the interacting bosonic theory is given. Furthermore, it is argued that the universal critical behavior at the quantum phase transition between the paramagnetic and the ferromagnetic Luttinger liquid is governed by a small number of terms in this theory, which are accessible by quantum Monte-Carlo methods.

Phases of the InfiniteUHubbard Model on Square Lattices

We apply the density matrix renormalization group (DMRG) to study the phase diagram of the infinite U Hubbard model on 2-, 4-, and 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice model. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n>n_F ~ 4/5. For n=3/4 we find an unexpected commensurate insulating "checkerboard" phase with coexisting bond density order with 4 sites per unit cell and block spin antiferromagnetic order with 8 sites per unit cell. For 3/4 > n, the wider ladders have unpolarized groundstates, which is suggestive that the same is true in 2D.

Stable dispersions of ferromagnetic carbon-coated metal nanoparticles: preparation via surface initiated atom transfer radical polymerization

Magnetic nanoparticle dispersions are traditionally made from superparamagnetic materials since the absence of magnetic particle–particle attraction under normal conditions (no external field) easily allows preparation of stable dispersions. For inductive heating in medicinal chemistry or material science, however, the much higher magnetization of ferromagnetic metals over the currently used oxides is attractive. Traditional attempts to prepare stable dispersions of ferromagnetic particles, however, failed since the strong magnetic particle–particle attraction usually overcomes repulsive effects from surfactants or steric stabilizers (typically polymers). In the present work, we demonstrate how the direct, covalent attachment of highly charged polymers can circumvent stabilizer detachment and loss, and permits preparation of stable dispersions of ferromagnetic particles. More specifically, carbon-coated metal nanoparticles were covalently functionalized with positively charged polymer brushes via surface initiated atom transfer radical polymerization (SI-ATRP). Particle size distributions with an average diameter of 24 nm provided a ferromagnetic liquid with unprecedented stability in water over several months. The stability was discussed by comparison of the potentials of non-functionalized and modified nanomagnets within a modified Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. Measurements for inductive heating at different frequencies and various field strengths showed an average specific absorption rate of 360 W g−1. Altogether, this suggests that efficiently stabilized dispersions of ferromagnetic nanoparticles could be an alternative to superparamagnetic iron oxide particles in a number of applications.

Electron scattering from domain walls in ferromagnetic Luttinger liquids

We study the properties of interacting electrons in a one-dimensional conduction band coupled to bulk noncollinear ferromagnetic order. The specific form of noncollinearity we consider is that of an extended domain wall. The presence of ferromagnetic order breaks spin-charge separation and the domain wall introduces a spin-dependent scatterer active over the length of the wall $\ensuremath{\lambda}$. Both forward and backward scattering off the domain wall can be relevant perturbations of the Luttinger liquid and we discuss the possible low-temperature phases. Our main finding is that backward scattering, while determining the ultimate low-temperature physics, only becomes important at temperatures $T/J<\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}/{\ensuremath{\lambda}}_{+})$, with $J$ being the magnetic exchange and ${\ensuremath{\lambda}}_{+}$ the backward scattering length scale. In physical realizations, $\ensuremath{\lambda}\ensuremath{\gg}{\ensuremath{\lambda}}_{+}$ and the physics will be dominated by forward scattering, which can lead to a charge-conducting but spin-insulating phase. In a perturbative regime at higher temperatures we furthermore calculate the spin and charge densities around the domain wall and quantitatively discuss the interaction-induced changes.

Exact diagonalization study of the tunable edge magnetism in graphene

The tunable magnetism at graphene edges with lengths of up to 48 unit cells is analyzed by an exact diagonalization technique. For this we use a generalized interacting one-dimensional model which can be tuned continuously from a limit describing graphene zigzag edge states with a ferromagnetic phase, to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism. This analysis sheds light onto the question why the edge states have a ferromagnetic ground state, while a usual one-dimensional metal does not. Essentially, we find that there are two important features of edge states: (a) Umklapp processes are completely forbidden for edge states, which allows a spin-polarized ground state; (b) the strong momentum dependence of the effective interaction vertex for edge states gives rise to a regime of partial spin-polarization and a second-order phase transition between a standard paramagnetic Luttinger liquid and ferromagnetic Luttinger liquid.

Physical properties of GdFe2(AlxZn1−x)20

The high ferromagnetic ordering temperature of the dilute, rare-earth-bearing, intermetallic compound ${\mathrm{GdFe}}_{2}{\mathrm{Zn}}_{20}$ has been understood as being the consequence of the Gd${}^{3+}$ moment being embedded in a nearly ferromagnetic Fermi liquid. To test this understanding in detail, single crystals of the pseudoternary series ${\mathrm{GdFe}}_{2}({\mathrm{Al}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{)}_{20}$ ($x\ensuremath{\leqslant}0.122$) and ${\mathrm{YFe}}_{2}({\mathrm{Al}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{)}_{20}$ ($x\ensuremath{\leqslant}0.121$) were grown out of Zn-rich solution. Magnetization, heat capacity, and resistivity measurements show that, with Al doping, the ferromagnetic phase transition temperatures of the ${\mathrm{GdFe}}_{2}({\mathrm{Al}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{)}_{20}$ compounds decrease from 86 K ($x=$ 0) to 10 K ($x=$ 0.122); for the nonmagnetic analog, the ${\mathrm{YFe}}_{2}({\mathrm{Al}}_{x}{\mathrm{Zn}}_{1\ensuremath{-}x}{)}_{20}$ series, the Stoner enhancement factor $Z$ decreases from 0.88 ($x=$ 0) to 0.35 ($x=$ 0.121) in a similar manner. Tight-binding linear-muffin-tin orbital atomic-sphere approximation band structure calculations are used to rationalize this trend. These results, together with the earlier studies of the $R({\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}{)}_{2}{\mathrm{Zn}}_{20}$ ($R=$ Gd and Y) series, clearly highlight the importance of band filling and the applicability of even a simple, rigid-band model to these compounds.

Ground state of interacting quantum magnetic dipoles: Transition from a ferromagnetic Fermi liquid to an antiferromagnetic solid

We show that the ground state of a system of magnetic dipoles, with no electric charge, is a ferromagnetic quantum Fermi liquid at high densities, driven by the dipolar exchange energy. As in the system of classical point dipoles, the direct dipole energy is zero in this case. With decreasing density, there is a transition to an antiferromagnetic lattice state. An addition of short range hard core repulsive potential will arrest the infinite density collapse of the ferromagnetic state, and possible melting of the low density antiferromagnetic lattice state.

Tunable edge magnetism at graphene/graphane interfaces

We study the magnetic properties of graphene edges and graphene/graphane interfaces under the influence of electrostatic gates. For this an effective one-dimensional low-energy theory for the edge states, which is derived from the Hubbard model of the honeycomb lattice, is used. We first study the edge-state model in a mean-field approximation for the Hubbard Hamiltonian and show that it reproduces the results of the two-dimensional lattice theory. Quantum fluctuations around the mean-field theory of the effective one-dimensional model are treated by means of the bosonization technique in order to check the stability of the mean-field solution. We find that edge magnetism at graphene/graphane interfaces can be switched on and off by means of electrostatic gates. We describe a quantum phase transition between an ordinary and a ferromagnetic Luttinger liquid---a realization of itinerant one-dimensional ferromagnetism. This effect may provide means to experimentally discriminate between edge magnetism or disorder as the reason for a transport gap in very clean graphene nanoribbons.

Lattice collapse and the magnetic phase diagram ofSr1−xCaxCo2P2

We report that the 122 type Sr$_{1-x}$Ca$_x$Co$_2$P$_2$ solid solution undergoes an anomalous structural transition from the uncollapsed to the collapsed ThCr$_2$Si$_2$ structure at a distinct onset composition near $x=0.5$. Correlated with the structural changes, the electronic system evolves from a nearly ferromagnetic Fermi liquid to an antiferromagnetic metal, through a complex crossover regime. The structural collapse, driven by P-P bonding across the (Sr,Ca) layers, is much more pronounced in this system than it is in the analogous Fe-based system, indicating a strong sensitivity of structure to total electron count in the transition metal pnictide 122 family.

Dynamical Properties of the One-Dimensional Spin-1/2Bose-Hubbard Model near a Mott-Insulator to Ferromagnetic-Liquid Transition

We investigate the dynamics of the one-dimensional strongly repulsive spin-1/2 Bose-Hubbard model for filling nu <or= 1. While at nu=1 the system is a Hubbard-Mott insulator exhibiting dynamical properties of the Heisenberg ferromagnet, at nu<1 it is a ferromagnetic liquid with complex spin dynamics. We find that close to the insulator-liquid transition the system admits for a complete separation of spin and density degrees of freedom valid at all energy and momentum scales within the t-J approximation. This allows us to derive the propagator of transverse spin waves and the shape of the magnon peak in the dynamic spin structure factor.

Magnetic properties ofRFe2Zn20andRCo2Zn20(R=Y,Nd,Sm,Gd–Lu)

Magnetization, resistivity, and specific heat measurements were performed on solution-grown single crystals of $R{\text{Fe}}_{2}{\text{Zn}}_{20}$ and $R{\text{Co}}_{2}{\text{Zn}}_{20}$ $(R=\text{Y},\text{Nd},\text{Sm},\text{Gd-Lu})$. Whereas ${\text{LuCo}}_{2}{\text{Zn}}_{20}$ and ${\text{YCo}}_{2}{\text{Zn}}_{20}$ manifest unremarkable metallic behavior, ${\text{LuFe}}_{2}{\text{Zn}}_{20}$ and ${\text{YFe}}_{2}{\text{Zn}}_{20}$ display behaviors such as characteristic of nearly ferromagnetic Fermi liquids. When the well-defined $4f$ local moments $({\text{Gd}}^{3+}{\text{-Tm}}^{3+})$ are embedded into this strongly polarizable host, they manifest enhanced ferromagnetic ordering and the values of ${T}_{\text{C}}$ for $R{\text{Fe}}_{2}{\text{Zn}}_{20}$ $(R=\text{Gd-Tm})$ scale with the de Gennes factor. In addition, data on the $R{\text{Fe}}_{2}{\text{Zn}}_{20}$ compounds indicate a small crystal electric field (CEF) effect compared with the interaction energy scale. On the other hand, the local moment bearing members of $R{\text{Co}}_{2}{\text{Zn}}_{20}$ $(R=\text{Nd},\text{Sm},\text{Gd-Tm})$ manifest weak magnetic interactions and the magnetic properties for $R=\text{Dy-Tm}$ members are strongly influenced by the CEF effect on the $R$ ions. The magnetic anisotropy and specific heat data for the Co series were used to determine the CEF coefficient of $R$ ion with its cubic point symmetry. These CEF coefficients, determined for the Co series, are consistent with the magnetic anisotropy and specific heat data for the Fe series, which indicates similar CEF effects for the Fe and Co series. Such analysis, combined with specific heat and resistivity data, indicates that for $R=\text{Tb-Ho}$, the CEF splitting scale is smaller than their ${T}_{\text{C}}$ values, whereas for ${\text{ErFe}}_{2}{\text{Zn}}_{20}$ and ${\text{TmFe}}_{2}{\text{Zn}}_{20}$ the $4f$ electrons lose part of their full Hund's rule ground state degeneracy above ${T}_{\text{C}}$. ${\text{YbFe}}_{2}{\text{Zn}}_{20}$ and ${\text{YbCo}}_{2}{\text{Zn}}_{20}$ manifest typical but distinct heavy fermion behaviors associated with different Kondo temperatures.

Phase transitions and ordering of confined dipolar fluids

We apply a modified mean-field density functional theory to determine the phase behavior of Stockmayer fluids in slit-like pores formed by two walls with identical substrate potentials. Based on the Carnahan-Starling equation of state, a fundamental-measure theory is employed to incorporate the effects of short-ranged hard-sphere-like correlations while the long-ranged contributions to the fluid interaction potential are treated perturbatively. The liquid-vapor, ferromagnetic-liquid-vapor, and ferromagnetic-liquid-isotropic-liquid first-order phase separations are investigated. The local orientational structure of the anisotropic and inhomogeneous ferromagnetic liquid phase is also studied. We discuss how the phase diagrams are shifted and distorted upon varying the pore width.

GdI2: A New Ferromagnetic Excitonic Solid?

The two-dimensional, colossal magnetoresistive system GdI2 develops an unusual metallic state below its ferromagnetic transition and becomes insulating at low temperatures. We argue that this geometrically frustrated, correlated poor metal is a possible candidate for a ferromagnetic excitonic liquid. The renormalized Fermi surface supports a further breaking of symmetry to a charge-ordered, excitonic solid ground state at lower temperatures via order by disorder mechanism. Several experimental predictions are made to investigate this unique orbitally correlated ground state.

Reflection and refraction of acoustic waves at the boundary between the ferromagnetic Heusler alloy and liquid

Reflection and refraction of quasi-longitudinal and quasi-transverse acoustic waves at a flat interface between a liquid and a ferromagnetic crystal of the Heusler alloy Ni2 + x + y Mn1 − x Ga1 − y (in the region of its premartensitic and martensitic phase transitions) is considered. The directions of propagation and polarization and the amplitude of reflected quasi-longitudinal and quasi-transverse and of transmitted longitudinal waves in the (110) plane of the crystal are determined. In a wide region of phase transformations of this alloy, the possibility is shown of using temperature to efficiently control the angles of reflection and refraction of wave modes and the coefficients of their conversion due to a colossal acoustic anisotropy of the crystal. Beginning from a certain critical angle of the quasi-transverse wave, the quasi-longitudinal wave arising upon reflection acquires the nature of the accompanying surface vibration and at a large proximity to phase transition can be emitted into the bulk of the crystal. On the basis of the available experimental data for Ni2MnGa crystals, numerical estimations of the above acoustic effects have been carried out.

Variation of the magnetic ordering inGdT2Zn20(T=Fe, Ru, Os, Co, Rh and Ir) and its correlation with the electronic structure of isostructuralYT2Zn20

Magnetization, resistivity, and specific heat measurements were performed on solution-grown single crystals of six $\text{Gd}{T}_{2}{\text{Zn}}_{20}$ ($T=\text{Fe}$, Ru, Os, Co, Rh, and Ir) compounds, as well as on their Y analogs. For the Gd compounds, the Fe column members manifest a ferromagnetic (FM) ground state (with an enhanced Curie temperature ${T}_{C}$ for $T=\text{Fe}$ and Ru), whereas the Co column members manifest an antiferromagnetic (AFM) ground state. Thermodynamic measurements on $\text{Y}{T}_{2}{\text{Zn}}_{20}$ revealed that the enhanced ${T}_{C}$ for ${\text{GdFe}}_{2}{\text{Zn}}_{20}$ and ${\text{GdRu}}_{2}{\text{Zn}}_{20}$ can be understood within the framework of Heisenberg moments embedded in a nearly ferromagnetic Fermi liquid. Furthermore, electronic structure calculations indicate that this significant enhancement is due to a large transition metal partial density of states at the Fermi level that places these compounds close to the Stoner FM criterion. The change from FM to AFM ordering (between the Fe and Co column materials) is associated with the filling of electronic states with two additional electrons/f.u. The degree of this sensitivity is addressed by the studies of the pseudoternary compounds $\text{Gd}{({\text{Fe}}_{x}{\text{Co}}_{1\ensuremath{-}x})}_{2}{\text{Zn}}_{20}$ and $\text{Y}{({\text{Fe}}_{x}{\text{Co}}_{1\ensuremath{-}x})}_{2}{\text{Zn}}_{20}$, which clearly reveal the effect of $3d$-band filling on their magnetic properties.

Voltage self-sustained oscillation and phase separation dynamics in a thin layer of a weakly conducting ferromagnetic liquid with periodically emerging electrohydrodynamic flows

It is shown that voltage self-sustained oscillations, which are determined by the properties of the near-electrode layer and electrohydrodynamic flows that are periodically formed in the colloid layer, emerge for a preset direct current at the electrodes of a plane-parallel cell filled with a colloid system consisting of stabilized magnetic nanoparticles dispersed in a weakly conducting liquid. The effect of self-sustained oscillations and periodic electrohydrodynamic flows in phase separation in the colloid system is analyzed. It is found that new dynamic formations are generated, which are regions of elevated concentration of magnetite particles having the shape of labyrinths of millimeter size. The emergence of a negative real part of the permittivity of the colloid layer is detected and attributed to the fact that the normal component of the internal electric field produced by volume charges becomes codirectional with the applied field when steady-state electrohydrodynamic flows appear in the system.

Magnetic properties ofGdxY1−xFe2Zn20: Dilute, large-Smoments in a nearly ferromagnetic Fermi liquid

Single crystals of the dilute, rare earth bearing, pseudo-ternary series, Gd_xY_{1-x}Fe_2Zn_{20} were grown out of Zn-rich solution. Measurements of magnetization, resistivity and heat capacity on Gd_xY_{1-x}Fe_2Zn_{20} samples reveal ferromagnetic order of Gd^{3+} local moments across virtually the whole series ($x \geq 0.02$). The magnetic properties of this series, including the ferromagnetic ordering, the reduced saturated moments at base temperature, the deviation of the susceptibilities from Curie-Weiss law and the anomalies in the resistivity, are understood within the frame work of dilute, $\textbf {S}$ moments (Gd^{3+}) embedded in a nearly ferromagnetic Fermi liquid (YFe_2Zn_{20}). The s-d model is employed to further explain the variation of $T_{\mathrm{C}}$ with x as well as the temperature dependences of of the susceptibilities.

Myriad of correlated electron effects found in the [formula omitted] family

The dilute, rare earth bearing family of RT 2 Zn 20 (R = rare earth, T = transition metal) intermetallic compounds can be tuned to a nearly ferromagnetic Fermi liquid that is closer to the Stoner limit than Pd (for R = Y, Lu and T = Fe). The submersion of moment bearing rare earths (Gd–Tm) into this highly polarizable matrix gives rise to exceptionally high temperature ferromagnetism (e.g. T C = 86 K for GdFe 2 Zn 20 ) for a compound with only one moment bearing ion out of 23 in the formula unit. In addition to this d-shell correlated electron behavior, 4f hybridization gives rise to six, new, Yb-based heavy fermion compounds: YbT 2 Zn 20 (T = Fe, Ru, Os, Co, Rh, Ir). These half dozen compounds manifest a range of Yb ion degeneracy values ( N ) for T ∼ T K , ranging from N = 4 – 8 . Not only do these compounds offer a clear testing ground for the effects of low temperature degeneracy on the correlated electron state, they also present an exceptionally clear experimental confirmation of the generalized Kadowaki–Woods formalism.

Nearly ferromagnetic Fermi-liquid behaviour in YFe2Zn20 and high-temperature ferromagnetism of GdFe2Zn20

One of the historic goals of alchemy was to turn base elements into precious ones. Although the practice of alchemy has been superseded by chemistry and solid-state physics, the desire to dramatically change or tune the properties of a compound, preferably through small changes in stoichiometry or composition, remains. This desire becomes even more compelling for compounds that can be tuned to extremes in behaviour. Here, we report that the RT2Zn20 (R=rare earth and T=transition metal) family of compounds manifests exactly this type of versatility, even though they are more than 85% Zn. By tuning T, we find that YFe2Zn20 is closer to ferromagnetism than elemental Pd, the classic example of a nearly ferromagnetic Fermi liquid. By submerging Gd in this highly polarizable Fermi liquid, we tune the system to a remarkably high-temperature ferromagnetic (TC=86 K) state for a compound with less than 5% Gd. Although this is not quite turning lead into gold, it is essentially tuning Zn to become a variety of model compounds.

Global phase diagrams of binary dipolar fluid mixtures

We apply a modified mean-field density functional theory to determine the phase behaviour of binary mixtures of Stockmayer fluids whose spherical constituents interact according to Lennard-Jones (LJ) pair potentials with embedded pointlike dipole moments. On the basis of systematic numerical calculations we construct the global phase diagrams of these systems in the three-dimensional thermodynamic space of temperature, pressure and chemical potential difference of the two components. The vapour–liquid, isotropic liquid–isotropic liquid, isotropic liquid–ferromagnetic liquid and ferromagnetic liquid–ferromagnetic liquid first-order phase separations are investigated. The loci of the second-order isotropic fluid–ferromagnetic fluid transition are calculated from Landau theory. Liquid–vapour and liquid–liquid critical lines, tricritical lines, triple lines and lines of critical end points of the binary Stockmayer mixtures are also determined. We discuss how the topology of the phase diagrams changes upon varying the strengths of the two dipole moments of the two species as well as their sizes.