A. S. Oja

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 temperatureTc 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 fieldBc=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 ofTc from the mean field calculationTMF=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.

Spontaneous nuclear magnetic ordering in copper and silver at nano- and picokelvin temperatures

Owing to the weak mutual interactions, spontaneous nuclear magnetic ordering in metallic copper and silver occurs at 60 nK and 560 pK, respectively. These extremely low spin temperatures can be reached by two-stage adiabatic nuclear demagnetization. Spin ordering has been investigated by employing magnetic susceptibility measurements on copper and silver and by using neutron diffraction techniques on copper. Three antiferromagnetic phases in the field-entropy plane have been discovered in copper, caused by competition between the dipolar and Ruderman-Kittel exchange interactions; only one ordered state has been found in silver. Negative spin temperatures have been produced in silver as well, and a clear ferromagnetic tendency was observed when T < 0. The theoretically calculated spin-spin interactions, ordering temperatures, magnetic phase diagrams and ordered spin structures are in good overall agreement with experimental data for these two metals.

A Versatile Nuclear Demagnetization Cryostat for Ultralow Temperature Research

A new cascade nuclear demagnetization cryostat has been designed and constructed. Our aim was to build a versatile, modular cryostat, with a large experimental space providing an excellent platform for various types of ultralow temperature measurements. A powerful dilution refrigerator, combined with a massive copper nuclear cooling stage, enables us to reach lattice temperatures below 100μK continuously for more than two months. The cryostat is equipped with a second magnet for operating a double-stage nuclear demagnetization setup. Details of the design and performance are presented.

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 Bardeens 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.

Nuclear magnetic ordering in copper and silver at nanokelvin temperatures

Abstract Recent experiments and theoretical results on nuclear magnetic ordering in copper and silver are reviewed. Below the critical field Bc = 0.25 mT, early susceptibility measurements revealed three antiferromagnetic phases in copper at temperatures below Tc = 60 nK. Later, these spin structures have been characterized by neutron diffraction experiments. The low- and high-field phases show an antiferromagnetic type-I Bragg peak (1 0 0), while a novel ( 0 2 3 2 3 ) reflection was found at intermediate fields. The phase diagram and the ordered spin structures of copper have been calculated in recent theoretical work as well, in excellent agreement with the experiments. In silver, the spin-spin interactions are dominated by antiferromagnetic exchange forces, which make this metal an ideal model of a spin 1 2 Heisenberg antiferromagnet in an fcc lattice. Experimentally, antiferromagnetic ordering has been found in susceptibility measurements at the record-low Tc = 600 pK. At negative spin temperatures, a ferromagnetic tendency was observed.

Investigations of nuclear magnetism in silver down to Picokelvin temperatures. I

Nuclear magnetic ordering in silver has been investigated by the low-field NMR technique using an rf SQUID. Spin entropies down to 0.50 · R ln 2, corresponding to polarizations up to 78%, were obtained. An indication of antiferromagnetic ordering was observed in the static magnetic susceptibility, which showed clear saturation at the beginning of warmup after cooling to T<1 nK by adiabatic demagnetization to B=10±5 µT; the critical entropy of the transition was found to be Sc=(0.60±0.04) · R ln 2. The NMR absorption increased in the ordered state at frequencies around 75 Hz. Remnants of this increase were observed in the paramagnetic phase as well. The feasibility of experiments at negative spin temperatures was demonstrated by a quick reversal of the external magnetic field.

Mean-field calculation and Monte Carlo simulation of ferromagnetic ordering at negative temperatures

Abstract The ferromagnetically ordered state of nuclear spins in silver at negative absolute temperatures was investigated by the mean-field theory and by Monte Carlo simulations. The principal results, such as the obtained domain configurations, describe general features of ferromagnetic order at T

The phase diagram and the magnetic structure of nuclear spins in elemental copper below 60 nK

Abstract The phase diagram for nuclear magnetic order is elemental copper and the corresponding ordering vectors were investigated by neutron diffraction at nanokelvin temperatures. The intermediate phase is characterized by an ordering vector (O 2 3 2/3 . This is the first time that this type of order is observed in an fcc antiferromagnet.

Isotropic type I Fcc antiferromagnet in an external field

Abstract We report a Monte Carlo study of a classical Type I antiferromagnet in an fcc lattice with isotropic spin-spin interactions. In accord with recent predictions, the ordered spin structure is a single- → k state in low fields and a triple- → k configuration in high fields. Thermal fluctuations stabilize the up-up-up-down form of the triple- → k structure over a finite field interval.

Breaking of degeneracy in classical Heisenberg antiferromagnets

Abstract According to arguments given by Henley, thermal effects select collinear spin structures when the classical ground state exhibits continuous degeneracy in the mean-field theory and the spin-spin interactions are isotropic. We generalize this result and derive an approximate free energy describing ground-state selection for anisotropic spin-spin interactions using thermal perturbation theory. Reasonable agreement is found with Monte Carlo simulations for Type I fcc antiferromagnets.