Spin Ice Ground State Research Articles

Local Excitation of Kagome Spin Ice Magnetism Seen by Scanning Tunneling Microscopy.

The kagome spin ice can host frustrated magnetic excitations by flipping its local spin. Under an inelastic tunneling condition, the tip in a scanning tunneling microscope can flip the local spin, and we apply this technique to kagome metal HoAgGe with a long-range ordered spin ice ground state. Away from defects, we discover a pair of pronounced dips in the local tunneling spectrum at symmetrical bias voltages with negative intensity values, serving as a striking inelastic tunneling signal. This signal disappears above the spin ice formation temperature and has a dependence on the magnetic fields, demonstrating its intimate relation with the spin ice magnetism. We provide a two-level spin-flip model to explain the tunneling dips considering the spin ice magnetism under spin-orbit coupling. Our results uncover a local emergent excitation of spin ice magnetism in a kagome metal, suggesting that local electrical field induced spin flip climbs over a barrier caused by spin-orbital locking.

Emergence of weak pyrochlore phase and signature of field induced spin ice ground state in Dy2−xLaxZr2O7; x = 0, 0.15, 0.3

The pyrochlore oxides Dy2Ti2O7 and Ho2Ti2O7 are well studied spin ice systems and have shown the evidences of magnetic monopole excitations. Unlike these, Dy2Zr2O7 is reported to crystallize in a distorted fluorite structure. We present here the magnetic and heat capacity studies of La substituted Dy2Zr2O7. Our findings suggest the absence of spin ice state in Dy2Zr2O7 but the emergence of the magnetic field induced spin freezing near T ≈ 10 K in ac susceptibility measurements which is similar to Dy2Ti2O7. The magnetic heat capacity of Dy2Zr2O7 shows a shift in the peak position from 1.2 K in zero field to higher temperatures in the magnetic field, with the corresponding decrease in the magnetic entropy. The low temperature magnetic entropy at 5 kOe field is R ln2 − (1/2)R ln(3/2) which is the same as for the spin ice state. Substitution of non-magnetic, isovalent La3+ for Dy3+ gradually induces the structural change from highly disordered fluorite to weakly ordered pyrochlore phase. The La3+ substituted compounds with less distorted pyrochlore phase show the spin freezing at lower field which strengthens further on the application of magnetic field. Our results suggest that the spin ice state can be stabilized in Dy2Zr2O7 either by slowing down of the spin dynamics or by strengthening the pyrochlore phase by suitable substitution in the system.

Long-wavelength correlations in ferromagnetic titanate pyrochlores as revealed by small-angle neutron scattering

We have carried out small angle neutron scattering measurements on single crystals of two members of the family of cubic rare-earth titanate pyrochlores that display ferromagnetic Curie-Weiss susceptibilities,Yb$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$. Ho$_2$Ti$_2$O$_7$ is established as displaying a prototypical classical dipolar spin ice ground state, while Yb$_2$Ti$_2$O$_7$ has been purported as a candidate for a quantum spin ice ground state. While both materials have been well studied with neutron scattering techniques, neither has been previously explored in single crystal form with small angle neutron scattering (SANS). Our results for Yb$_2$Ti$_2$O$_7$ show distinct SANS features below its $\Theta_{CW}$$\sim$ 0.50 K, with rods of diffuse scattering extending along $\langle 111 \rangle$ directions in reciprocal space, off-rod scattering which peaks in temperature near $\Theta_{CW}$, and quasi-Bragg scattering at very small angles which correlates well with T$_C$ $\sim$ 0.26 K. The quasi-Bragg scattering corresponds to finite extent ferromagnetic domains $\sim$ 140 \AA$~$ across, at the lowest temperatures. We interpret the $\langle 111\rangle$ rods of diffuse scattering as arising from domain boundaries between the finite-extent ferromagnetic domains. In contrast the SANS signal in Ho$_2$Ti$_2$O$_7$ is isotropic within the (HHL) plane around $\textbf{Q}$=0. However the strength of this overall SANS signal has a temperature dependence resembling that of the magnetic heat capacity, with a peak near 3 K. Below the break between the field-cooled and the zero-field cooled susceptibility in Ho$_2$Ti$_2$O$_7$ at $\sim$ 0.60 K, the SANS signal is very low, approaching zero.

Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7

In a quantum spin liquid, the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic length scales1,2. Such phases offer promising perspectives for device applications in quantum information technologies, and their study can reveal new physics in quantum matter. Quantum spin ice is an appealing proposal of one such state, in which the fundamental ground state properties and excitations are described by an emergent U(1) lattice gauge theory3–7. This quantum-coherent regime has quasiparticles that are predicted to behave like magnetic and electric monopoles, along with a gauge boson playing the role of an artificial photon. However, this emergent lattice quantum electrodynamics has proved elusive in experiments. Here we report neutron scattering measurements of the rare-earth pyrochlore magnet Pr2Hf2O7 that provide evidence for a quantum spin ice ground state. We find a quasi-elastic structure factor with pinch points—a signature of a classical spin ice—that are partially suppressed, as expected in the quantum-coherent regime of the lattice field theory at finite temperature. Our result allows an estimate for the speed of light associated with magnetic photon excitations. We also reveal a continuum of inelastic spin excitations, which resemble predictions for the fractionalized, topological excitations of a quantum spin ice. Taken together, these two signatures suggest that the low-energy physics of Pr2Hf2O7 can be described by emergent quantum electrodynamics. If confirmed, the observation of a quantum spin ice ground state would constitute a concrete example of a three-dimensional quantum spin liquid—a topical state of matter that has so far mostly been explored in lower dimensionalities. A detailed and systematic neutron scattering study of rare-earth pyrochlore magnet Pr2Hf2O7 provides evidence for a quantum spin ice state, and emergent lattice quantum electrodynamics consistent with theoretical predictions.

Chain-based order and quantum spin liquids in dipolar spin ice

Recent experiments on the spin-ice material Dy2Ti2O7 suggest that the Pauling "ice entropy", characteristic of its classical Coulombic spin-liquid state, may be lost at low temperatures [D. Pomaranski et al., Nature Phys. 9, 353 (2013)]. However, despite nearly two decades of intensive study, the nature of the equilibrium ground state of spin ice remains uncertain. Here we explore how long-range dipolar interactions D, short-range exchange interactions, and quantum fluctuations combine to determine the ground state of dipolar spin ice. We identify a new organisational principle, namely that ordered ground states are selected from a set of "chain states" in which dipolar interactions are exponentially screened. Using both quantum and classical Monte Carlo simulation, we establish phase diagrams as a function of quantum tunneling g, and temperature T, and find that only a very small g_c << D is needed to stabilize a quantum spin-liquid ground state. We discuss the implications of these results for Dy2Ti2O7.

Monopole Holes in a Partially Ordered Spin Liquid

If spin liquids have been famously defined by what they are not, i.e., ordered, the past years have seen the frontier between order and spin liquid starting to fade, with a growing number of materials whose low-temperature physics cannot be explained without co-existence of (partial) magnetic order and spin fluctuations. Here, we study an example of such co-existence in the presence of magnetic dipolar interactions, related to spin ice, where the order is long range and the fluctuations support a Coulomb gauge field. Topological defects are effectively coupled via energetic and entropic Coulomb interactions, the latter one being stronger than for the spin-ice ground state. Depending on whether these defects break the divergence-free condition of the Coulomb gauge field or the long-range order, they are respectively categorized as monopoles — as in spin ice — or monopole holes, in analogy with electron holes in semiconductors. The long-range order plays the role of a fully-occupied valence band, while the Coulomb spin liquid can be seen as an empty conducting band. These results are discussed in the context of other lattices and models which support a similar co-existence of Coulomb gauge field and long-range order. We conclude this work by explaining how dipolar interactions lift the spin-liquid degeneracy at very low energy scale by maximizing the number of flippable plaquettes, in light of the equivalent quantum dimer model.

Magnetic phase transitions and monopole excitations in spin ice under uniaxial pressure: A Monte Carlo simulation.

In this work, we explore the spin ice model under uniaxial pressure using the Monte Carlo simulation method. For the known spin ices, the interaction correction (δ) introduced by the uniaxial pressure varies in quite a wide range from positive to negative. When δ is positive, the ground state characterized by the ferromagnetic spin chains is quite unstable, and in real materials it serves as intermediate state connecting the ice state and the long range ordered dipolar spin ice ground state. In the case of negative δ, the system relaxes from highly degenerate ice state to ordered ferromagnetic state via a first order phase transition. Furthermore, the domain walls in such ferromagnetic state are the hotbed of the excitations of magnetic monopoles, thus indicating that the uniaxial pressure can greatly increase the monopole density.

Evidence of impurity and boundary effects on magnetic monopole dynamics in spin ice

In the highly degenerate spin-ice ground state, flipped spins give rise to magnetic charges, or monopoles, which form a measurable current in a magnetic field. The low-temperature relaxation dynamics of spin-ice materials now reveal that defects can impede monopole flow—creating a magnetic analogue of electrical resistance. Electrical resistance is a crucial and well-understood property of systems ranging from computer microchips to nerve impulse propagation in the human body. Here we study the motion of magnetic charges in spin ice and find that extra spins inserted in Dy2Ti2O7 trap magnetic monopole excitations and provide the first example of how defects in a spin-ice material obstruct the flow of monopoles—a magnetic version of residual resistance. We measure the time-dependent magnetic relaxation in Dy2Ti2O7 and show that it decays with a stretched exponential followed by a very slow long-time tail. In a Monte Carlo simulation governed by Metropolis dynamics we show that surface effects and a very low level of stuffed spins (0.30%)—magnetic Dy ions substituted for non-magnetic Ti ions—cause these signatures in the relaxation. In addition, we find evidence that the rapidly diverging experimental timescale is due to a temperature-dependent attempt rate proportional to the monopole density.

Spin ice and soft spin ice ground state under high pressure: comparative study by neutron scattering

We performed high pressure neutron diffraction experiments in two geometrically frustrated pyrochlore magnets. The soft spin ice Tb2Sn2O7 was studied up to 4.6 GPa and down to 60 mK. Its ordered spin ice structure with k 0=0 propagation vector partly transforms under pressure into a magnetic structure with k 1=(0 0 1). The reduction of the total ordered Tb moment with respect to ambient pressure suggests that spin liquid fluctuations are also enhanced by pressure. The pressure-induced state is discussed by considering the influence of both isotropic pressure and stress. In contrast, in the true spin ice Ho2Ti2O7, no effect of pressure is observed up to 6 GPa and down to 1.4 K.

Revisiting static and dynamic spin-ice correlations inHo2Ti2O7with neutron scattering

Elastic and inelastic neutron-scattering studies have been carried out on the pyrochlore magnet ${\text{Ho}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$. Measurements in zero applied magnetic field show that the disordered spin-ice ground state of ${\text{Ho}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ is characterized by a pattern of rectangular diffuse elastic scattering within the [HHL] plane of reciprocal space, which closely resembles the zone-boundary scattering seen in its sister compound ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$. Well-defined peaks in the zone-boundary scattering develop only within the spin-ice ground state below $\ensuremath{\sim}2\text{ }\text{K}$. In contrast, the overall diffuse-scattering pattern evolves on a much higher-temperature scale of $\ensuremath{\sim}17\text{ }\text{K}$. The diffuse scattering at small wave vectors below [001] is found to vanish on going to $\mathbf{Q}=0$, an explicit signature of expectations for dipolar spin ice. Very high energy-resolution inelastic measurements reveal that the spin-ice ground state below $\ensuremath{\sim}2\text{ }\text{K}$ is also characterized by a transition from dynamic to static spin correlations on the time scale of ${10}^{\ensuremath{-}9}\text{ }\text{s}$. Measurements in a magnetic field applied along the $[1\overline{1}0]$ direction in zero-field-cooled conditions show that the system can be broken up into orthogonal sets of polarized $\ensuremath{\alpha}$ chains along $[1\overline{1}0]$ and quasi-one-dimensional $\ensuremath{\beta}$ chains along [110]. Three-dimensional correlations between $\ensuremath{\beta}$ chains are shown to be very sensitive to the precise alignment of the $[1\overline{1}0]$ externally applied magnetic field.

Dilution effects in Ho2-xYxSn2O7: From the spin ice to the single-ion magnet

A study of the modifications of the magnetic properties of Ho2-YxSn2O7 upon varying the concentration of diamagnetic Y3+ ions is presented. Magnetization and specific heat measurements show that the Spin Ice ground-state is only weakly affected by doping for x ≤ 0.3, even if non-negligible changes in the crystal field at Ho3+ occur. In this low doping range μSR relaxation measurements evidence a modification in the low-temperature dynamics with respect to the one observed in the pure Spin Ice. For x → 2, or at high temperature, the dynamics involve fluctuations among Ho3+ crystal field levels which give rise to a characteristic peak in 119Sn nuclear spin-lattice relaxation rate. In this doping limit also the changes in Ho3+magnetic moment suggest a variation of the crystal field parameters.

Ordered spin-ice state in the geometrically frustrated metallic ferromagnetSm2Mo2O7

The recent discovery of spin ice is a spectacular example of the noncoplanar spin arrangements that can arise in the pyrochlore ${A}_{2}{B}_{2}{\mathrm{O}}_{7}$ structure. We present magnetic and thermodynamic studies on the metallic ferromagnet pyrochlore ${\mathrm{Sm}}_{2}{\mathrm{Mo}}_{2}{\mathrm{O}}_{7}$. Our studies, carried out on oriented crystals, suggest that the Sm spins have an ordered spin-ice ground state below about ${T}^{*}=15\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The temperature and field evolution of the ordered spin-ice state are governed by an antiferromagnetic coupling between the Sm and Mo spins. We propose that as a consequence of a robust feature of this coupling, the tetrahedra aligned with the external field adopt a one-in, three-out spin structure as opposed to the three-in, one-out structure in dipolar spin ices, as the field exceeds a critical value.

Single-crystal growth and magnetic properties of the metallic molybdate pyrochlore Sm 2Mo 2O 7

We have successfully grown cm 3-size single crystals of the metallic-ferromagnet Sm 2Mo 2O 7 by the floating-zone method using an infrared image furnace. The growth difficulties and the remedies found using a 2-mirror image furnace are discussed. Magnetization studies along the three crystalline axes of the compound are presented and discussed based on our recent proposal of an ordered spin-ice ground state for this compound.

How 'spin ice' freezes.

The large degeneracy of states resulting from the geometrical frustration of competing interactions is an essential ingredient of important problems in fields as diverse as magnetism, protein folding and neural networks. As first explained by Pauling, geometrical frustration of proton positions is also responsible for the unusual low-temperature thermodynamics of ice and its measured 'ground state' entropy. Recent work has shown that the geometrical frustration of ice is mimicked by Dy2Ti2O7, a site-ordered magnetic material in which the spins reside on a lattice of corner-sharing tetrahedra where they form an unusual magnetic ground state known as 'spin ice'. Here we identify a cooperative spin-freezing transition leading to the spin-ice ground state in Dy2Ti2O7. This transition is associated with a very narrow range of relaxation times, and represents a new form of spin-freezing. The dynamics are analogous to those associated with the freezing of protons in ice, and they provide a means through which to study glass-like behaviour and the consequences of frustration in the limit of low disorder.