Spin Ice Compound Research Articles

Quantum Excitations in Quantum Spin Ice

A form of quantum electrodynamics emerges from interacting spins at low temperatures in the spin ice $Y\phantom{\rule{0}{0ex}}{b}_{2}\phantom{\rule{0}{0ex}}T\phantom{\rule{0}{0ex}}{i}_{2}\phantom{\rule{0}{0ex}}{O}_{7}$.

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy 2 Ti 2 O 7

Sources of magnetic fields-magnetic monopoles-have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes-classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

Magnetic Coulomb Phase in the Spin Ice Ho 2 Ti 2 O 7

Spin-ice materials are magnetic substances in which the spin directions map onto hydrogen positions in water ice. Their low-temperature magnetic state has been predicted to be a phase that obeys a Gauss' law and supports magnetic monopole excitations: in short, a Coulomb phase. We used polarized neutron scattering to show that the spin-ice material Ho2Ti2O7 exhibits an almost perfect Coulomb phase. Our result proves the existence of such phases in magnetic materials and strongly supports the magnetic monopole theory of spin ice.

A lattice dynamical investigation of the Raman and the infrared frequencies of the Dy 2Ti 2O 7 pyrochlore spin ice compound

A short range force constant model has been applied for the first time to investigate the Raman and the infrared frequencies in Dy 2Ti 2O 7 pyrochlore spin ice compound in its cubic phase of space group Fd3 m. The calculations of zone center phonons have been made with four stretching and two bending force constants. The calculated values of Raman and infrared frequencies are in good agreement with the observed ones. The contribution of the nearest atomic interaction between Dy and O has been found to be negligible and is quite likely to play an important role in spin ice compound.

Monopoles on the move

Magnetic materials provide a new context for observing magnetic monopoles. Numerical simulations now establish an experimentally measurable signature of their dynamics — one that has in fact already been seen in a spin-ice compound.

Direct Observation of a Nuclear Spin Excitation inHo2Ti2O7

A single nondispersive excitation is observed by means of neutron backscattering, at E_{0}=26.3 microeV in the spin ice Ho2Ti2O7 but not in the isotopically enriched 162Dy2Ti2O7 analogue. The intensity of this excitation is rather small, less, similar0.2% of the elastic intensity. It is clearly observed below 80 K but resolution limited only below approximately 65 K. The application of a magnetic field up to micro_{0}H=4.5 T, at 1.6 K, has no measurable effect on the energy or intensity. This nuclear excitation is believed to perturb the electronic, Ising spin system resulting in the persistent spin dynamics observed in spin ice compounds.

Temperature-dependent Raman and x-ray studies of the spin-ice pyrochloreDy2Ti2O7and nonmagnetic pyrochloreLu2Ti2O7

We present here temperature-dependent Raman, x-ray diffraction, and specific heat studies between room temperature and 12 K on single crystals of spin-ice pyrochlore compound ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ and its nonmagnetic analog ${\text{Lu}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$. Raman data show a ``new'' band not predicted by factor group analysis of Raman-active modes for the pyrochlore structure in ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$, appearing below a temperature of ${T}_{c}=110\text{ }\text{K}$ with a concomitant contraction of the cubic unit cell volume as determined from the powder x-ray diffraction analysis. Low-temperature Raman experiments on ${\text{O}}^{18}$-isotope substituted ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ confirm the phonon origin of the new mode. These findings, absent in ${\text{Lu}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$, suggest that the room-temperature cubic lattice of the pyrochlore ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ undergoes a ``subtle'' structural transformation near ${T}_{c}$. We find anomalous redshift of some of the phonon modes in both the ${\text{Dy}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ and the ${\text{Lu}}_{2}{\text{Ti}}_{2}{\text{O}}_{7}$ as the temperature decreases, which is attributed to strong phonon-phonon anharmonic interactions.

Observation of a novel phase transition induced by a magnetic field in the pyrochlore spinice compound

We present a novel field-induced phase transition in the spin ice compoundDy2Ti2O7 that is investigated by means of angle-resolved DC magnetization measurements. In thenear [112] field, the magnetization component perpendicular to the Kagomé plane shows afirst-order phase transition below 0.27 K. This transition is driven by a ferromagneticordering in the field-decoupled spins on the triangular lattice. Furthermore, we revealedanother first-order phase transition below 0.52 K in a magnetic field between the [110] and[111] directions. This phase transition is related to a breakdown of ferromagnetic Ising spinchains along or .

Kagomé Ice State in the Dipolar Spin IceDy2Ti2O7

We have investigated the kagomé ice behavior of the dipolar spin-ice compound Dy2Ti2O7 in a magnetic field along a [111] direction using neutron scattering and Monte Carlo simulations. The spin correlations show that the kagomé ice behavior predicted for the nearest-neighbor interacting model, where the field induces dimensional reduction and spins are frustrated in each two-dimensional kagomé lattice, occurs in the dipole interacting system. The spins freeze at low temperatures within the macroscopically degenerate ground states of the nearest-neighbor model.

Uniaxial pressure effects on spin-ice compound Dy 2Ti 2O 7

We measured the magnetization curve of Dy 2Ti 2O 7 at T = 1.7 K under uniaxial pressure up to 13.0 kbar. The magnetic field ( H ) was applied along three crystal directions [0 0 1], [1 1 0] and [1 1 1]. Then the direction of applying pressure ( P ) was parallel to the field direction. For all directions, the magnetization almost saturates at around H = 3 T , and the saturation moment was suppressed with increasing pressure. This pressure-induced suppression of saturation moment can be quantitatively understood by assuming that the lattice distortion is as much as 1%. For P , H // [0 0 1], the pressure-induced enhancement of initial magnetic susceptibility was observed, while for other direction, it was suppressed by shrinkage. This enhancement of initial susceptibility for P , H // [0 0 1] should originate in some change of the degeneracy in the ground state.

Field-Induced Transition on a Triangular Plane in the Spin-Ice CompoundDy2Ti2O7

The origin of the lowest-temperature anomaly reported several years ago using a polycrystalline sample of the spin-ice compound Dy2Ti2O7 has remained unresolved. Here we finally clarify its origin by susceptibility measurements down to 65 mK using single crystals under accurate control of the magnetic fields in two independent directions. We demonstrate that the transition is induced under a subtle field combination that precisely cancels the nearest-neighbor spin interactions acting on the spins on the triangular lattice within the pyrochlore structure. Contrary to the other two field-induced transitions, this transition is driven only by the interactions beyond the nearest neighbors. Our observation thus provides the first qualitative evidence for the essential importance of the dipolar interaction beyond the nearest neighbors in the spin ice.

Why Spin Ice Obeys the Ice Rules

The low-temperature entropy of the spin ice compounds, such as and , is well described by the nearest-neighbor antiferromagnetic Ising model on the pyrochlore lattice, i.e., by the "ice rules." This is surprising since the dominant coupling between the spins is their long ranged dipole interaction. We show that this phenomenon can be understood rather elegantly: one can construct a model dipole interaction, by adding terms of shorter range, which yields precisely the same ground states, and hence entropy, as the nearest-neighbor interaction. A treatment of the small difference between the model and true dipole interactions reproduces the numerical work by Gingras et al. in detail. We are also led to a more general concept of projective equivalence between interactions.

Magnetodielectric response of the spin-iceDy2Ti2O7

We report the magneto-dielectric response of single crystals of the spin-ice compound Dy2Ti2O7 down to 0.26 K. The dielectric constant under zero magnetic field exhibits a clear decrease reflecting the development of the local two-spins-in, two-spins-out structure below about 1.2 K. Both the real and imaginary parts of the dielectric constant under magnetic fields sensitively respond to various changes in the spin structures. We found that the real part can be described in terms of local spin correlations among the moments of tetrahedra, rather than among individual Dy3+ moments. Using the peaks in the imaginary part, we have constructed a precise field-temperature phase diagram in the [111] field direction. We thus demonstrate that the magneto-dielectric response can be a high-sensitivity local probe of the spin state of geometrically frustrated systems.

Spin dynamics in Ho2Ru2O7

The spin relaxation processes within the pyrochloreHo2Ru2O7 have been investigated by neutron scattering and bulk property techniques. Asingle-ion process, that is thermally activated, dominates the spin–spin relaxationspectrum above 2 K. Assuming Arrhenius behaviour, we found an activation energyΔ = (329 ± 6) K and characteristicrelaxation time τ0 = (5.2 ± 0.3) × 10−12 s in the paramagnetic state, akin to those found in the spin ice,Ho2Ti2O7. Atlowtemperature (T<95 K) the activation energy lowers and below 20 K the entropy and ac susceptibilityare similar to that observed in other spin ice compounds within a 10 kOe field.

Quantum and thermal spin relaxation in the diluted spin iceDy2−xMxTi2O7(M=Lu,Y)

We have studied the low temperature a.c. magnetic susceptibility of the diluted spin ice compound Dy(2-x)MxTi2O7, where the magnetic Dy ions on the frustrated pyrochlore lattice have been replaced with non-magnetic ions, M = Y or Lu. We examine a broad range of dilutions, 0 <= x <= 1.98, and we find that the T ~ 16 K freezing is suppressed for low levels of dilution but re-emerges for x > 0.4 and persists to x = 1.98. This behavior can be understood as a non-monotonic dependence of the quantum spin relaxation time with dilution. The results suggest that the observed spin freezing is fundamentally a single spin process which is affected by the local environment, rather than the development of spin-spin correlations as earlier data suggested.

Magnetocaloric Effect Study on the Pyrochlore Spin Ice Compound Dy2Ti2O7in a [111] Magnetic Field

Field variation of the entropy S ( H ) of the spin ice compound Dy 2 Ti 2 O 7 has been examined by means of magnetocaloric effect measurements in a magnetic field H ∥[111], with attention focused o...

Low Temperature Specific Heat of Dy2Ti2O7in the Kagome Ice State

We report the specific heat of single crystals of the spin ice compound Dy$_2$Ti$_2$O$_7$ at temperatures down to 100 mK in the so-called Kagome ice state. In our previous paper, we showed the anisotropic release of residual entropy in different magnetic field directions and reported new residual entropy associated with spin frustration in the Kagome slab for field in the [111] direction. In this paper, we confirm the first-order phase transition line in the field-temperature phase diagram and the presence of a critical point at (0.98 T, 400 mK), previously reported from the magnetization and specific-heat data. We newly found another peak in the specific heat at 1.25 T below 0.3 K. One possible explanation for the state between 1 T and 1.25 T is the coexistence of states with different spin configurations including the 2-in 2-out one (Kagome ice state), the 1-in 3-out state (ordered state) and paramagnetic one (free-spin state).

Low-temperature spin freezing in theDy2Ti2O7spin ice

We report a study of the low temperature bulk magnetic properties of the spin ice compound Dy2Ti2O7 with particular attention to the (T < 4 K) spin freezing transition. While this transition is superficially similar to that in a spin glass, there are important qualitative differences from spin glass behavior: the freezing temperature increases slightly with applied magnetic field, and the distribution of spin relaxation times remains extremely narrow down to the lowest temperatures. Furthermore, the characteristic spin relaxation time increases faster than exponentially down to the lowest temperatures studied. These results indicate that spin-freezing in spin ice materials represents a novel form of magnetic glassiness associated with the unusual nature of geometrical frustration in these materials.

Low-temperature magnetic properties of the geometrically frustrated pyrochlore Pr2Sn2O7

We have measured the temperature dependence of AC magnetic susceptibility at various frequencies and the magnetization process of the pyrochlore oxide Pr 2 Sn 2 O 7 down to 90 mK. Pr 2 Sn 2 O 7 shows the slow dynamics of thermal activated type below 0.5 K. Finally, the magnetic moment freezes below 0.1 K. The spin freezing behavior of Pr 2 Sn 2 O 7 is very similar to the one of spin ice compounds.

Ferromagnetic Ising Spin Chains Emerging from the Spin Ice under Magnetic Field

A spin-ice compound dysprosium titanate, Dy2Ti2O7, is studied by specific heat measurements in magnetic fields applied along the [110] direction of the cubic unit cell. Above a magnetic field of 0.4 T a relatively sharp peak at T = 1.1 K in the specific heat appears from a broad peak associated with spin-ice freezing at low fields. This new peak is almost independent of field up to 1.5 T, while another broad, field-dependent peak is detected at higher temperature. Under magnetic field along [110] Ising spins on the pyrochlore lattice can be considered to form two orthogonal sets of chains; parallel and perpendicular to the field direction. It is suggested that these perpendicular chains behave as unique ferromagnetic Ising spin chains without long-range order.