Spin-slip Structures Research Articles

Magnetic structures in ultra-thin Holmium films: Influence of external magnetic field

Abstract We address the magnetic phases in very thin Ho films at the temperature interval between 20 K and 132 K. We show that slab size, surface effects and magnetic field due to spin ordering impact significantly the magnetic phase diagram. Also we report that there is a relevant reduction of the external field strength required to saturate the magnetization and for ultra-thin films the helical state does not form. We explore the specific heat and the susceptibility as auxiliary tools to discuss the nature of the phase transitions, when in the presence of an external magnetic field and temperature effects. The presence of an external field gives rise to the magnetic phase Fan and the spin-slip structures.

On the ground-state magnetic structure in Er2Ni2Pb

We have studied the unusual low-temperature magnetic phase of Er2Ni2Pb using powder neutron diffraction measurements in zero field down to 460 mK. Our previous neutron diffraction experiments down to 1.5 K showed that magnetic Bragg reflections seen in Er2Ni2Pb can be indexed by several propagation vectors that partially coexist. All the incommensurate propagation vectors seemed to disappear in the low temperature limit. The present study, however, shows that reflections belonging to the propagation vector q’ = (0.47 0 1/2) do not disappear but remain present down to 460 mK. This highly unexpected result suggests that the magnetic structure described by this propagation vector might not be a simple sine-wave modulation. One interesting possibility here is a spin-slip structure as the ground state.

A [formula omitted] SR magnetic study of UNiGe

We have carried out μ SR spectroscopy on polycrystalline UNiGe between 2 K and 100 K. The existence of two magnetic transitions at T N = 51 K and T 1 = 41.5 K is confirmed. The μ SR spectra clearly reveal that the magnetic state between 51 K and 41.5 K is an incommensurate spin structure ruling out a spin–slip structure which had been considered an alternative. Below 41.5 K the spectra are compatible with simple antiferromagnetic order. The local field for T → 0 is B μ = 170 mT, a comparatively low value, indicating a rather small uranium ordered moment. When going from the commensurate to the incommensurate structures at T 1 a sudden reduction in local field by 23% occurs reflecting an equal change in ordered moment. The transition at T 1 is sharp, but T N extends over roughly 5 K. The antiferromagnetic spin structure exhibits persistent spin fluctuations in the limit T → 0 , implying the presence of some additional spin interactions which tries to suppress long-range magnetic order.

Spin-slip structure induced by the crystalline electric field in the incommensurate magnetic ordering of CePtSn

While neutron scattering shows incommensurate magnetic Bragg peaks in CePtSn and CePdSn, zero-field muon-spin relaxation (ZF-μSR) displays coherent oscillations indicating local commensurate ordering. To reconcile these, we had suggested spin-slip structure similar to that in holmium metal. Kadowaki has demonstrated some examples of this that are consistent with the neutron data. Numerical modeling shows that, given a simple incommensurate ordering mechanism, represented by a spiraling effective field at the cerium sites, the known Ce crystalline electric field (CEF) in CePtSn will generate that kind of spin-slip structure. Further numerical modeling shows that such CEF spin-slip structures generate field distributions at the muon sites with sharp peaks generally consistent with the coherent oscillations observed in μSR. CePdSn is likely to behave in a similar manner.

Magnetic fields acting on muons in textured and single crystalline holmium

The μSR method was used to measure the internal magnetic fields at interstitial sites of the crystal lattice in holmium, where muons are localized. In a simple helicoid structure all interstitial sites are magnetically equivalent, and thus in a μSR experiment only one muon-spin precession frequency should be observed at a given temperature. In the spin-slip structure, the interstitial fields in different sections of the helicoid are different and the frequency spectrum of the muon signal should be more complicated. Most of the ZF μSR measurements were performed on a holmium polycrystal with distinct texture. High-statistics ZF measurements below the Néel temperature were performed also on a holmium single crystal at several temperatures. The experimental spectrum was well described by a single frequency. This fact characterized the magnetic structure of holmium as a simple spiral. At the same time, the high values of the relaxation rate (up to 60 μs −1 at 10 K ), could be due to overlapping of several frequencies.

Representation Analysis and Spin-Slip Model of the Incommensurate Structure of the Kondo Antiferromagnets CePdSn and CePtSn

Representation analysis of the neutron diffraction data of the Kondo antiferromagnets CePdSn and CePtSn shows that the incommensurate magnetic structures of the single- k type belong to the Γ 3 irreducible representation of the space group. The contradicting µSR observation supporting commensurate structures and the neutron data are shown to be explained semi-quantitatively by spin-slip structures which are derived by the Γ 3 incommensurate structures.

Neutron diffraction and ultrasonic studies of spin-slip structures in holmium

Spin-slip behaviour in high-purity holmium single crystals is characterized by neutron diffraction and ultrasonic velocity and attenuation measurements as a function of temperature and of magnetic field applied along b, c, and a axes. Neutron diffraction measurements of intensity and turn angle give information on wave vector lock-in effects for various spin-slip structures in applied fields. These findings are supplemented with ultrasonic studies of the elastic constants and and corresponding attenuation coefficients and . Various phase diagrams are presented and results compared with experiments by other groups and with some theoretical predictions.

Investigation of the magnetic structure of holmium by the muonic method

The possibility of investigating by the muonic method spin-incommensurate helicoidal structures of rare-earth magnets is examined for the example of holmium. It is shown that at temperatures 20 K <T<130 K only one precession frequency of the muon spin is observed in holmium; this is characteristic for a simple helicoidal structure. The broadening of the frequency spectrum increases sharply at temperatures T⩽20 K, possibly as a result of the appearance of spin-slip structure at these temperatures. The Fermi contact magnetic field of the conduction electrons of holmium at a muon is measured.

Magnetic transitions in single-crystal erbium

Commensurate spin slip structures were observed by Gibbs et al. in X-ray scattering studies. We have observed magnetic transitions in macroscopic measurements of magnetization, AC susceptibility, electrical resistivity, and thermal expansivity along the three crystal axes of single-crystal erbium that correspond to these spin slip structures. Our measurements show antiferromagnetic ordering of the c axis and basal plane components at TN//=89 K and TN perpendicular to =53 K, respectively, as well as ferromagnetic ordering along the c axis below 18 K. In addition, we observe anomalies at 27, 29, 34, 40 and 51 K. These anomalies correspond well with previous studies. The order of these transitions can be determined using thermal expansion data. We observe anomalies at 21.6 K and 23.3 K that we believe correspond to basal plane recording in the 2(44) magnetic phase. There are also anomalies above TN perpendicular to suggesting a short-range ordering of the basal plane moments. We have analysed the resistivity versus temperature plot in the ferromagnetic region to determine the temperature dependence and the spin wave activation energy along the b and c axes.

Trigonal interactions in holmium.

The low-temperature magnetic structure of Ho has been studied using a combination of neutron-scattering and mean-field calculations. Re-examination of the cone and one-spin-slip phases has shown that the structures are distorted by interactions of trigonal symmetry, similar to those recently hypothesized for Er. In the cone phase below 18.5 K the moments have two out-of-plane tilt angles with a difference in angle of approximately 1.0\ifmmode^\circ\else\textdegree\fi{} about a mean value of 9.0\ifmmode^\circ\else\textdegree\fi{}. The spin-slip phases are more complex. The moments are modulated with a period twice that of the basic spin-slip structure, giving rise to additional peaks in the scattering. Spin-slip structures found in a c-axis field are shown to be consistent with our model. In zero field, the phase transition to the cone phase occurs in two distinct steps, as suggested by anomalies found in several bulk measurements. The intermediate phase has the wave vector locked into (1/6)${\mathbf{c}}^{\mathrm{*}}$, where any group of four moments has two tilted in one sense along c, and the other two adopt an equal and opposite tilt, resulting in no net c-axis moment. Below 18.5 K this arrangement then tilts out of the basal plane, forming the distorted cone structure.

The chemical and magnetic structures of holmium-yttrium and holmium-lutetium superlattices

We present the results of a study of the chemical and magnetic structures of Ho/Y and Ho/Lu superlattices, all grown by molecular beam epitaxy. By combining the results of high-resolution X-ray diffraction with detailed modelling we show that the superlattices have high crystallographic integrity: the average structural coherence length in the growth direction is ~2000 Å, while the interfaces between the two elements are well defined, extending over approximately four lattice planes. The magnetic structures were determined using neutron scattering techniques. In the case of the Ho/Y superlattices, the Ho 3+ moments form a basal-plane helix at all temperatures in the ordered phase, with an apparent suppression of the low-temperature cone phase. Instead spin-slip structures are formed, including some not observed in bulk Ho. For the Ho/Lu superlattices the magnetic structure was found to depend on n Ho, the number of atomic planes in the Ho block. If n Ho > 20, then the Ho 3+ moments form a basal-plane helix down to the lowest temperatures. For n Ho ≤20, the Ho 3+ moments undergo a phase transition at low temperatures from a helix to a state where they are ferromagnetically coupled within one block. In this phase, successive Ho blocks are antiferromagnetically coupled, and there is a small component of the moment along the c axis.

Magnetic structure of holmium-yttrium superlattices.

We present the results of a study of the chemical and magnetic structures of a series of holmium-yttrium superlattices and a 5000 \AA{} film of holmium, all grown by molecular-beam epitaxy. By combining the results of high-resolution x-ray diffraction with detailed modeling, we show that the superlattices have high crystallographic integrity: the structural coherence length parallel to the growth direction is typically \ensuremath{\approxeq}2000 \AA{}, while the interfaces between the two elements are well defined and extend over approximately four lattice planes. The magnetic structures were determined using neutron-scattering techniques. The moments on the ${\mathrm{Ho}}^{3+}$ ions in the superlattices form a basal-plane helix. From an analysis of the superlattice structure factors of the primary magnetic satellites, we are able to determine separately the contributions made by the holmium and yttrium to the total helical turn angle per bilayer. It is found that the effective turn angle per atomic plane in the yttrium, which has a value of approximately 50\ifmmode^\circ\else\textdegree\fi{}, is independent of both temperature and the number of yttrium or holmium planes. The turn angle in the holmium blocks changes with temperature, and always has a value that is greater than in bulk holmium. The variation in the turn angle with temperature depends on the length of the holmium block, but is largely independent of the thickness of the yttrium block. At low temperatures, the (1/6)${\mathbf{c}}^{\mathrm{*}}$ phase found in bulk holmium is suppressed. The observation of high-order magnetic satellites indicates that the moments instead form long-period, commensurate spin-slip structures. The results are discussed in terms of the strain present in these samples.

Magnetoelastic effects in single-crystal erbium

The authors have measured the ultrasonic elastic constants C33, C44, C11 and C66 and their associated attenuation coefficients ( alpha ij) for a single crystal of erbium as a function of temperature. They have observed anomalous behaviour in both Cij and alpha ij which they attribute to commensurate spin-slip structures as observed by Gibbs et al. and Lin et al. using synchrotron X-ray scattering and neutron diffraction techniques.

Neutron diffraction and ultrasonic measurements on holmium at the b=2 spin-slip structure

The magnetic (002-δ) and (10-δ) reflections associated with the spiral structure of Ho as observed by neutron diffraction show an anomaly near 98 K when fields are applied along either the c- or b-direction. This is compared with ananomaly displayed by the elastic constant C 44 near 98K. Lock-in behaviour, whereby an induced commensurate temperature plateau in spiral turn angle results from application of a magnetic field, is also investigated.

Effect of spin slip structures on the resistivity of erbium and holmium

Single-crystal erbium and holmium each have a series of magnetic phases which have become known as ‘spin slip’ structures. These structures were first observed using X-ray and neutron diffraction by Gibbs et al. Recently the present authors reported anomalies in the temperature dependence of the magnetization of single crystals of holmium and erbium. These anomalies correspond well with the results of Gibbs et al. In this paper the results of resistivity as a function of temperature for pure single crystals of erbium and holmium are reported. In single-crystal erbium, transitions in resistivity are seen at T = 19, 25, 30, 33, 40, 50, 53 and 86 K. Resistivity data for holmium clearly show transitions at T c = 13, 20, 24 and 42 K and T N = 132 K. In addition, a large increase in the electrical noise for holmium in the temperature range 80–105 K is observed. These electrical measurements are the first reported for erbium and holmium to show the effects of spin slip structures on resistivity.

Magnetization and thermal expansion of single-crystal Er and Tm

The magnetization and ac susceptibility data of single-crystal Er show the antiferromagnetic ordering of the c axis and basal plane moment components at TN∥ = 87 K and TN⊥ = 53 K, respectively. In addition, we observe anomalies at 51, 40, 34, 29, and 27 K. These anomalies correspond to the commensurate spin-slip structures observed by Gibbs et al. [Phys. Rev. B 34, 8182 (1986)] in x-ray synchrotron scattering studies. From the thermal expansion study of single-crystal Er, we find that the phase transitions at TN∥ and 51 K are second order, whereas the transitions at TN⊥, 27, and 18 K are first order. The order of these transitions are in poor agreement with earlier studies of single-crystal Er. The magnetization measurements of single-crystal Tm show anomalies at TN = 57 K, Tc = 30 K, and an anomaly at 41.5 K.

Evidence for a devil's staircase in holmium produced by an applied magnetic field.

The magnetic structure of holmium has been studied using neutron diffraction when a magnetic field is applied along the {ital c} axis. The field has the effect of suppressing the onset of the commensurate cone phase found at low temperatures in zero field, and instead produces a series of spin-slip structures. In contrast to the zero-field diffraction experiments, where a continuous variation of the magnetic wave vector {bold q} was observed, we find that below {approx}15 K the wave vector {bold q} is always commensurate and forms a devil's staircase with increasing field.

Magnetization of single-crystal erbium.

We present the results of magnetization and ac-susceptibility measurements on single-crystal erbium along all three crystal axes. We observe antiferromagnetic ordering of the {ital c} axis and the basal-plane-moment components at 89 and 53 K, respectively. In addition, we observe anomalies at 51, 40, 34, 29, and 27 K. These anomalies in magnetization and ac-susceptibility data correspond to the commensurate spin-slip structures observed by Gibbs {ital et} {ital al}. in x-ray synchrotron scattering studies. In addition, we find that the basal-plane ordering at {ital T}{sub {ital N}{perpendicular}}=53 K takes place before any spin-slip transition appears as the temperature is lowered.

Observation of transitions to spin-slip structures in single-crystal holmium.

We present the results of magnetization measurements on single-crystal holmium using a SQUID magnetometer in the temperature range from 4.2 to 140 K in magnetic fields from 0.01 to 3 T applied along the {ital b} axis. Our magnetization data shows the Neel temperature to be {ital T}{sub {ital N}}=132 K. In addition, we observe anomalies in the temperature dependence of the magnetization at 21, 42, and 98 K. These anomalies can be accounted for within the spin-slip model; Bohr {ital et} {ital al}. (Physica (Amsterdam) 140{ital A}, 349 (1986)) have pointed out the existences of ferrimagnetic structures spin slip and Cowley and Bates (J. Phys. C 21, 4113 (1988)) additional structures that breaks the hexagonal symmetry.