Ising-like Anisotropy Research Articles

Ba6RE2Ti4O17 (RE = Nd, Sm, Gd, Dy-Yb): A Family of Rare-Earth-Based Layered Triangular Lattice Magnets.

The exploration of new rare-earth (RE)-based triangular-lattice materials plays a significant role in motivating the discovery of exotic magnetic states. Herein, we report a family of hexagonal perovskite compounds Ba6RE2Ti4O17 (RE = Nd, Sm, Gd, Dy-Yb) with a space group of P63/mmc, where magnetic RE3+ ions are distributed on the parallel triangular-lattice layers within the ab-plane and stacked in an 'AA'-type fashion along the c-axis. The low-temperature magnetic characterizations indicate that all synthesized Ba6RE2Ti4O17 compounds exhibit dominant antiferromagnetic (AFM) interactions and the absence of magnetic order down to 1.8 K. The isothermal magnetization and electron spin resonance results reveal the distinct magnetic anisotropy for the compounds with different RE ions. Moreover, the as-grown Ba6Nd2Ti4O17 single crystals exhibit Ising-like magnetic anisotropy with a magnetic easy-axis perpendicular to the triangle-lattice plane and no long-range magnetic order down to 80 mK, as the quantum spin liquid candidate with dominant Ising-type interactions.

Emergence of Spinons in Layered Trimer Iridate Ba_{4}Ir_{3}O_{10}.

Spinons are well known as the elementary excitations of one-dimensional antiferromagnetic chains, but means to realize spinons in higher dimensions is the subject of intense research. Here, we use resonant x-ray scattering to study the layered trimer iridate Ba_{4}Ir_{3}O_{10}, which shows no magnetic order down to 0.2K. An emergent one-dimensional spinon continuum is observed that can be well described by XXZ spin-1/2 chains with a magnetic exchange of ∼55 meV and a small Ising-like anisotropy. With 2% isovalent Sr doping, magnetic order appears below T_{N}=130 K along with sharper excitations in (Ba_{1-x}Sr_{x})_{4}Ir_{3}O_{10}. Combining our data with exact diagonalization calculations, we find that the frustrated intratrimer interactions effectively reduce the system into decoupled spin chains, the subtle balance of which can be easily tipped by perturbations such as chemical doping. Our results put Ba_{4}Ir_{3}O_{10} between the one-dimensional chain and two-dimensional quantum spin liquid scenarios, illustrating a new way to suppress magnetic order and realize fractional spinons.

Anisotropic magnetic property, magnetostriction, and giant magnetocaloric effect with plateau behavior in TbMn2Ge2 single crystal

The ternary RMn2Ge2 (R = rare earth) intermetallic compounds have attracted great attention due to their interesting magnetic behaviors and magnetotransport responses. Here, we reported our observation of anisotropic magnetic property, magnetostriction, and magnetocaloric effect (MCE) in TbMn2Ge2 single crystal. Below the transition temperature of Tb magnetic sublattices (T_{{text{C}}}^{{{text{Tb}}}} ~ 95 K), strong Ising-like magnetocrystalline anisotropy is observed with an out-of-plane ferromagnetic moments 5.98 μB/f.u. along the easy c axis, which is two orders of magnitude larger than that of field along a axis. Above T_{{text{C}}}^{{{text{Tb}}}}, a field-induced metamagnetic transition is observed from the spin-flip of Mn sublattices. During this transition, remarkable magnetostriction effect is observed, indicating of strong spin–lattice coupling. The responses of Tb and Mn sublattices to the magnetic field generate a giant magnetic entropy change (- Delta S_{M}) and large values of relative cooling power (RCP) and temperature-averaged entropy change (TEC). The calculated maximum magnetic entropy change (- Delta S_{M}^{max }), RCP, and TEC(10) with magnetic field change of 7 T along c axis reach 24.02 J kg−1 K−1, 378.4 J kg−1, and 21.39 J kg−1 K−1 near T_{{text{C}}}^{{{text{Tb}}}}, which is the largest among RMn2Ge2 families. More importantly, this giant MCE shows plateau behavior with wide window temperatures from 93 to 108 K, making it be an attractive candidate for magnetic refrigeration applications.

Spin and valley ordering of fractional quantum Hall states in monolayer graphene

We study spin and valley ordering in the quantum Hall fractions in monolayer graphene at Landau level filling factors ${\ensuremath{\nu}}_{G}=\ensuremath{-}2+n/3\phantom{\rule{4pt}{0ex}}(n=2,4,5)$. We use exact diagonalizations on the spherical as well as toroidal geometry by taking into account the effect of realistic anisotropies that break the spin/valley symmetry of the pure Coulomb interaction. We also use a variational method based on eigenstates of the fully $\text{SU}(4)$ symmetric limit. For all the fractions we study, there are two-component states for which the competing phases are generalizations of those occurring at neutrality ${\ensuremath{\nu}}_{G}=0$. They are ferromagnetic, antiferromagnetic, charge-density wave, and K\'ekul\'e phases, depending on the values of Ising or $XY$ anisotropies in valley space. The varying spin-valley content of the states leads to ground-state quantum numbers that are different from the ${\ensuremath{\nu}}_{G}=0$ case. For filling factor ${\ensuremath{\nu}}_{G}=\ensuremath{-}2+5/3$, there is a parent state in the $\text{SU}(4)$ limit that has a flavor content $(1,1/3,1/3,0)$ where the two components that are one-third filled form a two-component singlet. The addition of anisotropies leads to the formation of new states that have no counterpart at ${\ensuremath{\nu}}_{G}=0$. While some of them are predicted by the variational approach, we find notably that negative Ising-like valley anisotropy leads to the formation of a state that is a singlet in both spin and valley space and lies beyond the reach of the variational method. Also fully spin polarized two-component states at $\ensuremath{\nu}=\ensuremath{-}2+4/3$ and $\ensuremath{-}2+5/3$ display an emergent $\text{SU}(2)$ valley symmetry because they do not feel point-contact anisotropies. We discuss implications for current experiments concerning possible spin transitions.

Paramagnetic Effects of j-electron Superconductivity and Application to UTe2

The putative spin-triplet superconductor UTe2 has an Ising-like magnetic anisotropy, indicating the Cooper pair spins parallel to the easy-axis. However, the upper critical field for the hard-axis direction is much larger than that for the easy-axis, implying the strong suppression of the Pauli depairing effect even for the hard-axis direction. This observation is consistent with the recent NMR measurements which show the tiny decrease of the Knight shift below the transition temperature Tc for hard-axis magnetic fields. We clarify that these behaviors are naturally understood as a result of multi-orbital f -electron bands with total angular momentum j=5/2. Taking into account spin-orbit couplings for an orthorhombic structure, we demonstrate that for hard-axis magnetic fields, the decrease of the spin susceptibility below Tc and the Pauli depairing effect are strongly suppressed.

Magnetic ground state of the one-dimensional ferromagnetic chain compoundsM(NCS)2(thiourea)2(M=Ni,Co)

The magnetic properties of the two isostructural molecule-based magnets, Ni(NCS)$_{2}$(thiourea)$_{2}$, $S$ = 1, [thiourea = SC(NH$_2$)$_2$] and Co(NCS)$_{2}$(thiourea)$_{2}$, $S$ = 3/2, are characterised using several techniques in order to rationalise their relationship with structural parameters and ascertain magnetic changes caused by substitution of the spin. Zero-field heat capacity and muon-spin relaxation measurements reveal low-temperature long-range ordering in both compounds, in addition to Ising-like ($D < 0$) single-ion anisotropy ($D_{\rm{Co}} \sim$ -100 K, $D_{\rm{Ni}} \sim$ -10 K). Crystal and electronic structure, combined with DC-field magnetometry, affirm highly quasi-one-dimensional behaviour, with ferromagnetic intrachain exchange interactions $J_{\rm{Co}}\approx+4$ K and $J_{\rm{Ni}}\sim+100$ K and weak antiferromagnetic interchain exchange, on the order of $J'$ $\sim-0.1$ K. Electron charge and spin-density mapping reveals through-space exchange as a mechanism to explain the large discrepancy in $J$-values despite, from a structural perspective, the highly similar exchange pathways in both materials. Both species can be compared to the similar compounds $M$Cl$_2$(thiourea)$_4$, $M$ = Ni(II) (DTN) and Co(II) (DTC), where DTN is know to harbour two magnetic field-induced quantum critical points. Direct comparison of DTN and DTC with the compounds studied here shows that substituting the halide Cl$^-$ ion, for the NCS$^-$ ion, results in a dramatic change in both the structural and magnetic properties.

Intrinsic Magnetic Order of Chemically Exfoliated 2D Ruddlesden-Popper Organic-Inorganic Halide Perovskite Ultrathin Films.

Thin film fabrication of 2D layered organic-inorganic hybrid perovskites (2D-OIHPs) for spintronic applications has been attempted using solution-based process like Langmuir-Blodgett technique. However, monolayer or few-layered 2D magnets are not yet realized, even though a wide spectrum of 2D Ruddlesden-Popper (RP) OIHPs are known as quasi-2D Heisenberg magnets in bulk compounds. Here, chemical exfoliation by solvent engineering is applied to successfully synthesize large-sized, few unit-cell-thick 2D RP-OIHPs. Comprehensive structural characterization reveals that binary co-solvents with high relative polarity in spin coating technique are the most effective among nine kinds of solvents. Above all, this enables few-layered 2D RP-OIHP ultrathin films sustaining their intrinsic magnetic order. It is found that XY-like magnetic anisotropy driven by Jahn-Teller effect responsible for ferromagnetism in seven-layered (C6 H5 CH2 CH2 NH3 )2 CuCl4 ultrathin films remains very robust, whereas Ising-like dipolar anisotropy responsible for canted antiferromagnetism in ten-layered (C6 H5 CH2 CH2 NH3 )2 MnCl4 ultrathin films is greatly reduced. It is expected that ferromagnetism even at monolayer limit should be possible by means of further sophisticated solvent engineering as long as Jahn-Teller effect is active. The chemical exfoliation using solvent engineering unambiguously can bring about a new breakthrough in the development of 2D RP-OIHP van der Waals magnets for ultrahigh energy-efficient spintronic, opto-spintronic devices.

Field-free quantum-spin-1/2 XXZ model in three-dimensions:phases, phase transitions, and phase diagrams by renormalization group theory

The field-free quantum-spin-1/2 XXZ model is studied in three-dimensions using renormalization group theory. We obtain global phase diagrams and critical properties. We identify zero-temperature quantum phase transitions at isotropic points, as well as long-range order below critical temperatures at all anisotropies. We show that the excitation spectrum is gapless in XY-like, and gapped in Ising-like anisotropy regimes. Besides, internal energy density, specific heat, nearest-neighbor entanglement measures and spin-spin correlations are obtained globally at all temperatures. Our numerical results cover the global range of anisotropy parameter, for both ferromagnetic and antiferromagnetic cases.

Evidence for biquadratic exchange in the quasi-two-dimensional antiferromagnet FePS3

FePS3 is a van der Waals compound with a honeycomb lattice that is a good example of a two-dimensional antiferromagnet with Ising-like anisotropy. Neutron spectroscopy data from FePS3 were previously analyzed using a straightforward Heisenberg Hamiltonian with a single-ion anisotropy. The analysis captured most of the elements of the data; however, some significant discrepancies remained. The discrepancies were most obvious at the Brillouin zone boundaries. The data are subsequently reanalyzed, allowing for unequal exchange between nominally equivalent nearest-neighbors, which resolves the discrepancies. The source of the unequal exchange is attributed to a biquadratic exchange term in the Hamiltonian, which most probably arises from a strong magnetolattice coupling. The new parameters show that there are features consistent with Dirac magnon nodal lines along certain Brillouin zone boundaries.

Three-Magnon Bound State in the Quasi-One-Dimensional Antiferromagnet α-NaMnO_{2}.

Here we report on the formation of a three-magnon bound state in the quasi-one-dimensional antiferromagnet α-NaMnO_{2}, where the single-ion, uniaxial anisotropy inherent to the Mn^{3+} ions in this material provides a binding mechanism capable of stabilizing higher order magnon bound states. While such states have long remained elusive in studies of antiferromagnetic chains, neutron scattering data presented here demonstrate that higher order n>2 composite magnons exist, and, specifically, that a weak three-magnon bound state is detected below the antiferromagnetic ordering transition of NaMnO_{2}. Wecorroborate our findings with exact numerical simulations of a one-dimensional Heisenberg chain with easy-axis anisotropy using matrix-product state techniques, finding a good quantitative agreement with the experiment. These results establish α-NaMnO_{2} as a unique platform for exploring the dynamics of composite magnon states inherent to a classical antiferromagnetic spin chain with Ising-like single ion anisotropy.

Spin, charge and lattice dynamics of magnetization processes in frustrated Shastry-Sutherland system TmB4

TmB4 - the metallic tetraboride with a geometrically frustrated Shastry-Sutherland lattice (SSL) has attracted recently a lot of attention. It exhibits a strong Ising-like anisotropy along the c-axis and a rather complex phase diagram of the ordered magnetic phase below TN ≈ 11.7 K in which besides the main magnetization (M) plateau also small fractional plateaus can be observed. To learn more about the properties of fractional plateaus we have investigated the dynamics of magnetization processes in TmB4 by M vs. H (applied magnetic field) measurements at different temperatures and different field sweep rates (swr) 1.8 K. In addition, experiments of the charge carrier mobility and magnetostriction as a function of temperature and magnetic field were carried out to specify the interplay between magnetic structure and the charge dynamics, and the role of the magneto-elastic interaction in this compound, respectively. It was shown that the magnetization values of fractional plateaus become elevated with the increase of temperature at which magnetization takes place and with the decrease of magnetic field sweep rate, which points to inconsistency with theoretical predictions based on Glauber dynamics. Moreover, it turned out that the transitions between magnetic phases during magnetization processes are accompanied by an anomalous behavior of charge mobility and distinctive variations of magnetostriction.

Kondo-lattice ferromagnets and their peculiar order along the magnetically hard axis determined by the crystalline electric field

We show that Ce- and Yb-based Kondo-lattice ferromagnets order mainly along the magnetically hard direction of the ground state Kramers doublet determined by crystalline electric field (CEF). Here we argue that this peculiar phenomenon, that was believed to be rare, is instead the standard case. Moreover, it seems to be independent on the Curie temperature $T_\mathrm{C}$, crystalline structure, size of the ordered moment and type of ground state wave function. On the other hand, all these systems show the Kondo coherence maximum in the temperature dependence of the resistivity just above $T_\mathrm{C}$ which indicates a Kondo temperature of a few Kelvin. An important role of fluctuations is indicated by the non-mean-field like transition in specific heat measurements as well as by the suppression of this effect by a strong Ising-like anisotropy. We discuss possible theoretical scenarios.

Large easy-plane anisotropy induced spin reorientation in magnetoelectric materials (Co4−xMnx)Nb2O9

Neutron powder diffraction experiments were carried out on the magnetoelectric compound series (Co4−xMnx)Nb2O9 (x = 0, 1, 2, 3, 3.5, 3.9, 3.95 and 4) from base temperature to above their Néel temperatures. Their magnetic structures were analysed by using the irreducible representation analysis and Rietveld refinement method. Similar to Co4Nb2O9, the compounds with x ⩽ 3.9 have noncollinear in-plane magnetic structures (Γ6) with magnetic moments lying purely in the ab plane with certain canting angles. Mn4Nb2O9 has a collinear antiferromagnetic structure (Γ2) with magnetic moments aligning along the c axis. The compound of x = 3.95 shows two magnetic phases in the magnetization, which was confirmed to have the Γ2 magnetic structure above 60 K and develop a second Γ6 local phase in addition to the main Γ2 phase due to doping. This study indicates 2.5 at% Co2+ doping is sufficient to alter the collinear easy-axis magnetic structure of Mn4Nb2O9 into the noncollinear easy-plane magnetic structure, which is attributed to the large easy-plane anisotropy of Co2+ and relative small Ising-like anisotropy of Mn2+. The doping effects on the Néel temperature and occupancy are also discussed.

Amplitude mode in the planar triangular antiferromagnet Na0.9MnO2

Amplitude modes arising from symmetry breaking in materials are of broad interest in condensed matter physics. These modes reflect an oscillation in the amplitude of a complex order parameter, yet are typically unstable and decay into oscillations of the order parameter’s phase. This renders stable amplitude modes rare, and exotic effects in quantum antiferromagnets have historically provided a realm for their detection. Here we report an alternate route to realizing amplitude modes in magnetic materials by demonstrating that an antiferromagnet on a two-dimensional anisotropic triangular lattice (α-Na0.9MnO2) exhibits a long-lived, coherent oscillation of its staggered magnetization field. Our results show that geometric frustration of Heisenberg spins with uniaxial single-ion anisotropy can renormalize the interactions of a dense two-dimensional network of moments into largely decoupled, one-dimensional chains that manifest a longitudinally polarized-bound state. This bound state is driven by the Ising-like anisotropy inherent to the Mn3+ ions of this compound.

Enforcing Ising-like magnetic anisotropy via trigonal distortion in the design of a W(v)-Co(ii) cyanide single-chain magnet.

A new octacyanotungstate(v) based single chain magnet {[(Tpm)Co(DMF)W(CN)8]2[Co(DMF)4]·2DMF} n (1, Tpm = 1,1,1-trispyrazoylmethane), with an effective barrier of 39.7(3) cm-1 is reported. The Ising-like magnetic anisotropy of the chain originates from the nearly parallel local orientations of the Co(ii) ions with the source of the uniaxial magnetic anisotropy being a trigonal distortion of the octahedral environment with the fac-tridentate capping Tpm ligand.

Thermal conductivity of Ca3Co2O6 single crystals

Ca3Co2O6 is a rare example of one-dimensional Ising spin-chain material with the moments preferentially aligned along the c axis. In this work, we study the c-axis thermal conductivity (κc) of Ca3Co2O6 single crystal at low temperatures down to 0.3 K and in magnetic fields up to 14 T. The zero-field κc(T) shows a large phonon peak and can be well fitted by using the classical Debye model, which indicates that the heat transport is purely phononic. Moreover, the low-T κc(H) isotherms with H || c display a field-independent behavior. These results indicate that there is no contribution of magnetic excitations to the thermal conductivity in Ca3Co2O6, neither carrying heat nor scattering phonons, which can be attributed to the Ising-like spin anisotropy.

Time-of-Flight Elastic and Inelastic Neutron Scattering Studies on the Localized 4d Electron Layered Perovskite La5Mo4O16

The magnetic structure and spin-wave excitations in the quasi-square-lattice layered perovskite compound La$_5$Mo$_4$O$_{16}$ were studied by a combination of neutron diffraction and inelastic neutron scattering techniques using polycrystalline sample. Neutron powder diffraction refinement revealed that the magnetic structure is ferrimagnetic in the $ab$ plane with antiferromagnetic stacking along the $c$ axis where the magnetic propagation vector is $\mathbf{k}=\left(0,0,\frac{1}{2}\right)$. The ordered magnetic moments are estimated to be $0.54(2)\mu_\text{B}$ for Mo$^{5+}$ ($4d^1$) ions and $1.07(3)\mu_\text{B}$ for Mo$^{4+}$ ($4d^2$) ions at 4 K, which are about half of the expected values. The inelastic neutron scattering results display strong easy-axis magnetic anisotropy along the $c$ axis due to the spin-orbit interaction in Mo ions evidenced by the spin gap at the magnetic zone center. The model Hamiltonian consisting of in-plane anisotropic exchange interactions, the interlayer exchange interaction, and easy-axis single-ion anisotropy can explain our inelastic neutron scattering data well. Strong Ising-like anisotropy and weak interlayer coupling compared with the intralayer exchange interaction can explain both the high-temperature magnetoresistance and long-time magnetization decay recently observed in La$_5$Mo$_4$O$_{16}$.

Ising-like anisotropy stabilized 13 and 23 magnetization plateaus in the V3+ kagome lattice antiferromagnets Cs2KV3F12,Cs2NaV3F12 , and Rb2NaV3F12

We have investigated crystal structure and magnetic properties of three $S=1\phantom{\rule{4pt}{0ex}}{\mathrm{V}}^{3+}$ Ising-like anisotropic kagome lattice antiferromagnets, ${\mathrm{Cs}}_{2}\mathrm{K}{\mathrm{V}}_{3}{\mathrm{F}}_{12},{\mathrm{Cs}}_{2}\mathrm{Na}{\mathrm{V}}_{3}{\mathrm{F}}_{12}$, and ${\mathrm{Rb}}_{2}\mathrm{Na}{\mathrm{V}}_{3}{\mathrm{F}}_{12}$, using single crystals. Each compound crystallizes in a monoclinic system and has a slightly distorted kagome lattice. Although the magnetic properties are similar, the details depend on the magnitude of magnetic anisotropy. The magnetization and magnetic susceptibility are highly anisotropic owing to anisotropic $g$ factors and Ising-like single ion anisotropy originating from partially unquenched orbital moments of ${\mathrm{V}}^{3+}$, and the easy axis of Ising-like anisotropy is perpendicular to the kagome plane. In contrast to disordered ground states in the isostructural ${\mathrm{Ti}}^{3+}$ $(S=1/2)$ compounds, the ${\mathrm{V}}^{3+}$ $(S=1)$ compounds exhibit antiferromagnetic ordering with distorted ${120}^{\ensuremath{\circ}}$ structure or other nearly coplanar magnetic structure whose basal spin plane includes the easy axis, which is mainly due to large magnetic anisotropy and decrease of quantum fluctuation. Moreover, when magnetic fields are applied perpendicular to the kagome plane, magnetization curves of them show distinct 1/3 and 2/3 magnetization plateaus, which are stabilized by Ising-like single ion anisotropy. In particular, the 2/3 magnetization plateaus are notable magnetic phenomena in kagome lattice antiferromagnets and are due to the combination of spin frustration, Ising-like single ion anisotropy, and the small monoclinic distortion of kagome lattices.

Candidate quantum spin ice in the pyrochlorePr2Hf2O7

We report the low temperature magnetic properties of the pyrochlore Pr$_2$Hf$_2$O$_7$. Polycrystalline and single-crystal samples are investigated using time-of-flight neutron spectroscopy and macroscopic measurements, respectively. The crystal-field splitting produces a non-Kramers doublet ground state for Pr$^{3+}$, with Ising-like anisotropy. Below 0.5 K ferromagnetic correlations develop, which suggests that the system enters a spin ice-like state associated with the metamagnetic behavior observed at $\mu_0H_c\sim2.4$~T. In this regime, the development of a discrete inelastic excitation in the neutron spectra indicates the appearance of spin dynamics which are likely related to cooperative quantum fluctuations.

Anisotropic magnetic properties and magnetic structure of YbPdSi

YbPdSi with orthorhombic crystal structure (space group Pmmn) exhibits a magnetic transition at K, below which a ferromagnetic moment develops with an enhanced electronic specific-heat coefficient mJ K−2 mol−1. We have investigated the magnetization, electrical resistivity, and specific heat of YbPdSi using single crystalline samples as functions of temperature and magnetic field. It has been found that the ferromagnetic moment points to the c-direction, although the magnetic moments have an Ising-like anisotropy along the b-direction above the magnetic-transition temperature. Field dependence of the magnetization and electrical resistivity shows a metamagnetic-like transition at T when field is applied along the b-axis below T = 3 K, suggesting the existence of an antiferromagnetic component along this direction. The magnetic structure has been investigated by neutron diffraction using powder samples. The magnetic unit cell is identical to the crystal unit cell. The Rietveld fitting has revealed that Yb at the 2a and 2b positions exhibit a collinear ferromagnetic order along the c-axis, whereas Yb at the 4e position undergoes a non-collinear order, involving the ferromagnetic moment along the c-axis and an antiferromagnetic component along the b-axis. The ferromagnetic moments determined by the neutron diffraction are 0.26, 1.3, and 0.15 for Yb at the 4e, 2b, and 2a sites, respectively. The reduced moments for the 4e and the 2a sites suggest that the Kondo screening effect is important in YbPdSi.