Ruderman-Kittel Interaction Research Articles

Estimation of the magnitude of the Ruderman-Kittel interaction in 3d and 2d GaAs crystals

In this paper, estimates are made of the Ruderman-Kittel interaction in a gallium arsenide crystal and in GaAs quantum wells of varying widths. The calculation results indicate that this interaction may be weaker than the magnetic dipole-dipole interaction by an order of magnitude. Also discovered was a relatively strong dependence of this interaction on the level of doping.

Ruderman-Kittel interaction between Si in URu2Si2

29Si nuclear magnetic resonance (NMR) has been studied in a 29Si–enriched single crystal sample of URu2Si2. The spin-echo decay for applied field H || [110] and [001] directions has been measured at 50 K. A clear spin-echo decay oscillation is observed for both cases, reflecting the Ruderman-Kittel interaction between Si nuclei. Since the observed oscillation frequency depends on the direction of applied magnetic field, the Ruderman-Kittel and anisotropic pseudo-dipolar interactions may not be negligible in this compound. The origin of spin-echo decay oscillations is discussed.

29Si NMR spin-echo decay in YbRh2Si2

29Si nuclear magnetic resonance (NMR) has been measured in a 29Si-enriched single crystal sample of YbRh2Si2. The spin-echo decay for applied field H ∥, ⊥ the c-axes has been measured at 100 K. A clear spin-echo decay oscillation is observed for both cases, possibly reflecting the Ruderman-Kittel (RK) interaction. Since the observed oscillation frequency depends on the direction of applied magnetic field, anisotropic RK coupling and pseudo-dipolar (PD) interactions may not be negligible in this compound. The origin of spin-echo decay oscillations is discussed.

Sign memory of the Ruderman–Kittel interaction in disordered metals and magnetic coupling in mesoscopic metal/ferromagnet layered systems

Sign memory of the Ruderman–Kittel interaction in disordered metals and magnetic coupling in mesoscopic metal/ferromagnet layered systems

Superradiance by a system of highly polarized exchange-coupled nonequivalent spins

We propose a model of radiofrequency (rf) superradiance by a system of interacting nonequivalent spins in a point specimen. In contrast to the rf superradiance observed and described earlier, here spin-spin coupling acts as the interaction with the cavity. To be definite, we examine the spins of two isotopes of a metal that are coupled by the Ruderman-Kittel interaction. The analysis of such a system when the magnetization of one spin species is inverted shows that the system can have one resonance frequency and two different decay times, instead of two resonance frequencies and one decay time in the usual situation. When such “repulsion” of decay times occurs and the absolute values of the spin polarizations are large, transverse magnetization increases and exhibits features characteristic of superradiance. Finally, we calculate the parameters of this superradiance: the voltage across the terminals of an rf pickup coil, the pulse length, the delay time, and the superradiant intensity.

Ruderman-Kittel interaction in one dimension for arbitrary coupling constant.

The Ruderman-Kittel interaction in one dimension is presented for an arbitrary coupling constant, as a by-product of previous considerations for a problem with planar symmetry in three dimensions. For coupling constants which are smaller than or even comparable to the Fermi energy, the interaction oscillates as a function of distance like the perturbation result, however, with a reduced amplitude. The interaction between two parallel magnetic lines in two dimensions is also discussed. \textcopyright{} 1996 The American Physical Society.

Deviation from the Korringa law caused by the Ruderman-Kittel interaction

Near nuclear ordering, thermal relaxation rateT1−1 deviates from the Korringa law due to the growing short range correlation. For metallic nuclear magnets with the Ruderman-Kittel interaction,T1−1 is calculated by the high temperature expansion method up to the order of 1/T. It is shown in the first and second orders of expansion that the correction to the Korringa law acts to reduceT1−1.

Superradiance in highly-polarized spin-systems

The model of radio-frequency (RF) superradiance (SR) by the system of interacting non-equivalent spins in a point sample is suggested. Unlike RF SR observed and described before, here the role of interaction with a resonator is played by the spin-spin interaction. For the definity the spins of two isotopes of metal connected by Ruderman-Kittel interaction are considered. The analysis of such a system in the case when the magnetization of one sort of spins is inverted shows that this system can possess one resonance frequency and two different decay times instead of two frequencies and the same decay times in the usual situation. When such shift aside takes place and the absolute values of spins polarizations are sufficiently high, a pulse of transverse magnetization growth occurs which has typical features of SR.

Intensity of the 2ω L NMR line in gold at nanokelvin temperatures

The nuclear spin Hamiltonian in gold consists of the dipolar and Ruderman-Kittel interactions. From double spin-flip NMR, one can obtain the relative strengths of these two interactions. Using the spherical model, we calculate the intensity of the double spin-flip NMR line for the gold nuclear spin system in order to determine whether this harmonic mode can be detected.

Nuclear ferromagnetic ordering in silver at negative nanokelvin temperatures

Nuclear ferromagnetic ordering in silver, caused by the antiferromagnetic Ruderman-Kittel interactions, has been observed at negative absolute temperatures T>−1.9 nK. The ordered states, reached by adiabatic demagnetization after population inversion at initial entropies S<Sc=0.82 ℜ ln2, are described by a saturation of susceptibility to −1 and by nonhysteretic response to an external field. These observations are consistent with the domain configurations calculated by Viertio and Oja in the mean field theory. The experimental critical entropy, however, does not agree with theoretical calculations. In addition to our NMR measurements leading to these findings, we also discuss basic thermodynamics at T<0 and the theoretically calculated domain configurations in simple terms.

Calculation of the Ruderman-Kittel interaction and the nuclear magnetic ordering in silver

Using first-principles energy bands and wave functions we have calculated the Ruderman-Kittel interaction between the nuclear spins of I = 1 2 in silver. We find, similar to copper, that the interaction is dominated by a nearest neighbor interaction and decreases more rapidly with distance than expected for the free electron model, further the dipolar interaction is relatively small. This makes the ideal fcc antiferromagnetic silver system particularly interesting. The uniform susceptibility and the Curie temperature is calculated using correlation theory and found in agreement with experimental observations. The calculated transition temperature. T N is somewhat higher than the quoted experimental value of 560 pK.

Vibrationally reduced magnetic interactions in Cu and the magnetic ordering in a magnetic field

The nuclear ordering temperatures in Cu is in the n-K range. Yet, the zero-point vibrational motion of the atoms is found to have the effect of reducing the calculated Ruderman-Kittel interaction significantly for all interactions J n beyond the nearest-neighbor interaction J 1. Using J 1 and J 2 = − J 1/10 and a spin wave calculation of the soft-mode transition from the ferromagnetically polarized state it is found that in Cu the antiferromagnetic state changes from a type-I (001) state for fields in the [100] and [110] direction to an incommensurate ( t + δ, t- δ, 0) state with t ≈ 2 3 and a small δ, for fields in a region around the [111] direction. In this region the ordering has not yet been solved experimentally. It is a result of the close competition between the dipole and Ruderman-Kittel forces in Cu.

Observation of nuclear ferromagnetic ordering in silver at negative nanokelvin temperatures.

The ferromagnetically ordered state in the nuclear spin system of silver has been reached at negative absolute temperatures by adiabatic nuclear demagnetization at entropies below 0.82 ln2. The ordering, caused by the antiferromagnetic Ruderman-Kittel interaction, was observed below -1.9 nK as a saturation of susceptibility close to -1 and as an increase of the NMR frequencies. Comparison with recent mean-field calculations by Vierti\o and Oja suggests a domain configuration. The phase diagram of silver nuclei at T0 is outlined in the magnetic field versus entropy plane.

Theory of a new type of antiferromagnetism in the ideal fcc system Cu

In Cu the competition between the dipolar and Ruderman-Kittel interaction results in a simple type-I-antiferromagnetic ordering with Q = (2 π/ a )(1, 0, 0), which is nearly degenerated with a ΓK ordering with Q = (2π/ a )(0, η, η) for 0.6

Cross relaxation by single spin flips in silver at nanokelvin temperatures.

The cross-relaxation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{x}}$ between the Zeeman temperatures of the $^{107}\mathrm{Ag}$ and $^{109}\mathrm{Ag}$ spin species in silver metal has been measured over five decades at low nanokelvin temperatures as a function of the external magnetic field B. Besides increasing with B, ${\mathrm{\ensuremath{\tau}}}_{\mathit{x}}$ decreases with spin polarization. From the data, the strength of the Ruderman-Kittel interaction between the nuclei is determined. These experiments demonstrate that thermal equilibrium is not reached via mutual flips of unlike spins, but in much slower processes involving single spin flips, caused by the dipolar interaction.

Spin glasses and other lattice systems with long range interactions

We study classical lattice systems, in particular real spin glasses with Ruderman-Kittel interactions and dipole gases, with interactions of very long (non-summable) range but variable sign. Using the Kac-Siegert representation of such systems and Brascamp-Lieb inequalities we are able to establish detailed properties of the high-temperature phase, such as decay of connected correlations, for these systems.

Indirect nuclear spin interactions and nuclear ordering in metals

All conduction electron-mediated nuclear spin interactions that arise from the electron-nuclear hyperfine Hamiltonian are calculated using Bardeen's spherical approximation for electronic wave functions. The results are applied to nuclear magnetic ordering in copper, where non-s-electron-mediated interactions are found to be important for the understanding of the ordered state properties. The ordered structure of silver nuclei is predicted to be a generalized form of a type I antiferromagnet due to the dominating Ruderman-Kittel interaction.

Investigations of nuclear antiferromagnetic ordering in copper at nanokelvin temperatures

Nuclear magnetism in metallic copper has been studied by demagnetizing highly polarized spins to low fields where spin-spin interactions dominate. In earlier experiments anomalous spin-lattice relaxation caused by impurities warmed up nuclear spins too fast; this adverse effect was overcome by selective oxidation of impurities. In zero field the critical temperatureT c of the antiferromagnetic transition is 58±10 nK, and during the first-order phase change the entropy increases from (0.48±0.03)ℛ ln 4 to (0.61±0.03)ℛ ln 4. The critical fieldB c =0.27±0.01 mT. The entropy and the static susceptibility of the nuclear spins were measured as a function of temperature whenB=0. These curves agree with theory in the paramagnetic state. In a polycrystalline sample two anomalies were observed at the lowest entropies in the NMR line shapes of the dynamic susceptibility and in the behavior of the static susceptibility. However, when measuring the static susceptibility of a single-crystal specimen in the three Cartesian directions, three different ordered phases were found. These antiferromagnetic states are described and theB-S phase diagram is presented. Metastability and nonadiabaticity are discussed. The observed large reduction ofT c from the mean field calculationT MF=230 nK is caused by fluctuations. The free electron model of the Ruderman-Kittel (RK) interaction seems to be able to explain only one ordered phase. However, relatively small changes to the RK range function or inclusion of non-s-electron-mediated interactions to the Hamiltonian may increase the number of ordered phases to three. Long-living metastable states are another possible explanation for the observations.

Calculation of the Ruderman-Kittel interaction and magnetic ordering in copper

Using first principles energy bands and wave functions we find the Ruderman-Kittel interaction having a more predominant nearest neighbor coupling than expected for free electrons. Using the correlation theory and including dipolar interactions we find the most probable structure to be a simple type I antiferromagnet. For smaller values of the interaction strength the structure should be incommensurate with Q along ΓK.

Investigation of the magnitude and range of the Ruderman-Kittel interaction in SmRh4B4 and ErRh4B4.

The superconductive and magnetic transition temperatures taken together are shown to provide a unique probe which separately determines both the magnitude and range of the Ruderman-Kittel interaction in the $R{\mathrm{Rh}}_{4}{\mathrm{B}}_{4}$ magnetic superconductors ($R=\mathrm{E}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{S}\mathrm{m}$). Experimentally, an unexpected peak is found in the antiferromagnetic-ordering temperature of Sm${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$ versus electron mean free path, while for Er${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$ the ferromagnetic-ordering temperature decreases monotonically. These qualitative features, as well as the quantitative differences between Sm${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$ and Er${\mathrm{Rh}}_{4}$${\mathrm{B}}_{4}$, are in excellent agreement with calculations using a mean-free-path-dependent Ruderman-Kittel interaction.