Fine tuning of magnetization relaxation parameters of the DyO⁺ single ion magnet in a hydroxy/fluoro-apatite solid solution

Abstract

DyO⁺ embedded in a hydroxy/fluoro-apatite matrix reveals robust and finely tunable single-ion-magnet properties. The energy barrier for magnetization reversal grows with the increase in the fluoride and Dy content. A high Dy concentration slows down the quantum tunneling of magnetization, contrary to a commonly observed trend for its acceleration.

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Introduction

Research on single molecule and single ion magnets (SMMs and SIMs, respectively) began a quarter of a century ago, as marked by the discovery of a polynuclear manganese acetate complex,¹ and has developed rapidly, showing prospects for applications in molecule-scale magnetic recording, molecular electronics, spintronics, and quantum computing.^2–6 The number of SIM compounds reported so far is nearly two hundred.⁷ In the recent past, new records have been reported for magnetic anisotropy with the energy barrier for magnetization reversal (U_eff) exceeding 1000 cm⁻¹ and magnetization blocking temperature (T_b) reaching 60 K for Dy³⁺-based SIMs.^8–10 The latter include rare cases of chemically and thermally stable purely inorganic extended solids as represented by Dy-doped calcium and strontium hydroxyapatites, showing a U_eff of up to 1043 cm⁻¹.¹¹ Dy³⁺ replaces Ca²⁺ at the Ca(2) site and forms an effective DyO⁺ ion with a very short Dy–O bond of 2.05 Å. In this diatomic group, Dy³⁺ is further weakly coordinated to six oxygen atoms of the phosphate groups, forming a distorted pentagonal bipyramid as the coordination polyhedron with the closest oxygen atom as the apex. This atom provides a strong axial crystal field, resulting in a high magnetic anisotropy of the Dy³⁺ ion.^11,12 The ground Kramers doublet represents a practically pure M_J = ±15/2 state and the excited doublets acquire consecutively decreasing M_J values from ±13/2 to ±1/2. U_eff is determined by magnetic moment tunneling through the fourth and third exited doublets for strontium and calcium compounds, respectively.

Notably, the apatite structure type allows for diverse cation and anion substitutions.^13–15 This offers opportunities to smoothly vary the crystal environment of the DyO⁺ as well as to modify the overall chemical properties of the compound. Since the fluoride for hydroxide substitution increases the chemical stability of the apatite¹⁵ and a substantial concentration of Dy³⁺ can be achieved only in the calcium compound,¹¹ in the present work, we studied the effect of both fluoride and Dy³⁺ concentrations on the SIM properties of DyO⁺ in the calcium apatite matrix.

Experimental

The samples were prepared by high temperature solid state synthesis and had the general nominal composition Ca_10−xDy_x(PO₄)₆(OH)_2−x−yO_xF_y, where x = 0.1 and y = 1 (1), x = 0.5 and y = 1 (2), x = 0.1 and y = 1.9 (3), x = 0.5 and y = 1.5 (4). Stoichiometric quantities of commercial reagents CaCO₃, SrCO₃, (NH₄)₂HPO₄, and Dy₂O₃ were ground and mixed in an agate mortar. All thermal treatment procedures were performed in air. The mixture was thermally treated in an electric furnace in air according to the following procedure: heating to 400 °C for 1 hour, annealing at 400 °C for 1 hour; heating to 600 °C for 1 hour, annealing at 600 °C for 1 hour; heating to 800 °C for 1 hour, annealing at 800 °C for 5 hours. The thoroughly ground product was annealed at 1150 °C for 8 h. The reground powder was pressed in pellets, and then annealed at 1300 °C for 6 h. The pellets were reground, pressed into pellets again, and annealed at 1300 °C for 12 h. The resulting pellets were reground, pressed into pellets once more, annealed at 1300 °C for 8 h, and air quenched.

X-ray powder diffraction was performed using a Rigaku D/MAX 2500 diffractometer with a rotating anode (CuKα radiation) in Bragg–Brentano geometry in the 2θ range of 10–80°, with a step size of 0.02°. Using the JANA 2006 computer program,¹⁶ the crystal structure of all the samples was refined, including unit cell dimensions and positional and isotropic atomic displacement parameters of all atoms except hydrogen (Fig. S1–S4 and Table S1–S4†). For samples with a high Dy content (2 and 4), the occupancy of Dy³⁺ at the Ca(2) site was refined. Since occupancies correlate with atomic displacement parameters, we performed the refinement with equal parameters for the Ca(1) and Ca(2) sites.

Magnetic properties were measured on a Quantum Design SQUID VSM in the temperature range of 1.8–300 K and magnetic field range of −30–+30 kOe. A piece of a ceramic sample (50–200 mg) was fixed with GE-varnish (<0.3 mg) on a quartz rod. DC magnetization and susceptibility were measured in dc-SQUID mode. AC susceptibility (χ_ac) was measured under an ac field of 2.5–3 Oe in the frequency range of 1–945 Hz in the temperature range of 2–70 K. The core diamagnetism was subtracted from the calculated magnetization value using Pascal's constants. Isothermal measurements of the field dependence of magnetization were performed at 1.8 K with the field sweeping rate of 200 Oe s⁻¹. The generalized Debye model was applied to simultaneously fit the χ′ and χ′′ components of χ_ac(ω) (ω = 2πf) using the following equations:¹⁷

The relaxation time τ, the low-frequency susceptibility χ₀ and the high-frequency susceptibility χ_s (as a contribution of fast-relaxing magnetization), their difference χ_SR (as a contribution of slow-relaxing magnetization), and the relaxation time distribution parameter α were estimated. All the parameters were refined simultaneously for the temperature interval of 20–50 K, for which a χ′′(ω) local maximum was well observed. Then, χ_SR(T) was fitted by the Curie–Weiss equation. In order to escape strong correlations, for higher temperatures, χ_SR was fixed to the value calculated using the Curie–Weiss parameters and α was fixed to a value estimated for lower temperatures, while all other parameters were refined.

Fourier transform infrared spectra (FT-IR) were recorded on a Perkin Elmer Spectrum One FT-IR in the range of 450–4000 cm⁻¹ in diffuse-reflectance mode.

Microstructure observations and energy dispersive X-ray analysis (EDS) were performed using a Supra 50 VP LEO scanning electron microscope.

Results and discussion

Composition and crystal structure

X-ray powder diffraction (XRPD) analysis reveals an apatite-type phase (space group P6₃/m) and the presence of trace cubic Dy₂O₃ (Fig. S1–S4†). The parameters of the unit cell decrease both with the increase in F⁻ for OH⁻ and Dy³⁺ for Ca²⁺ substitutions, testifying the formation of a solid solution (Table S1†). Ceramic samples exhibit ensembles of sintered rounded grains of typically 1–5 μm in size (Fig. S5†). The content of Dy was reliably estimated by EDS in Dy-rich samples. The atomic ratio of Dy to Ca in the grains corresponds to x = 0.37(3) and 0.38(4) for 2 and 4, respectively, i.e., it is somewhat lower than the nominal ratio of x = 0.5, which we may expect taking into consideration the presence of the Dy₂O₃ admixture phase. Moreover, the refined occupancy of Dy³⁺ at the Ca(2) site corresponds to x = 0.42(2) and 0.43(2) for 2 and 4, respectively. The values overlap within a standard deviation of those obtained by EDS. This evidences that Dy substitutes Ca mostly at the Ca(2) site. In addition, the quantity of the Dy₂O₃ admixture estimated by the XRPD refinement corresponds to x = 0.04 and 0.03, implying that the total Dy³⁺ content may approach the nominal content. For samples with low Dy content, the initial structure refinements were performed for the undoped composition (x = 0). This resulted in substantially reduced atomic displacement parameters of Ca(2) in comparison with those of Ca(1), suggesting that Dy shares the Ca(2) site. In the next step, the occupancy of Dy was fixed to the nominal occupancy and refinement of the structure with Dy at the Ca(2) site resulted in lower R factors than those with Dy at the Ca(1) site. This indicates that Dy preferably enters the Ca(2) site even in the Dy-poor samples.

A fragment of the crystal structure is shown in Fig. 1. Ca(2)₃ triangles oriented normal to the c-axis form the walls of a trigonal channel running along the c-axis. Inside the channel, in case of a Dy-free hydroxy/fluoro-apatite, small anions, namely, OH⁻ and F⁻ are located. Under the conditions of preparation, we also expect a certain fraction of O₂²⁻ (ref. 18 and 19) and possibly O²⁻ (ref. 20) to be found in the channel. The heterovalent Dy³⁺ for Ca²⁺ substitution at the Ca(2) site corresponds to the charge-balance process Ca²⁺ + OH⁻ → Dy³⁺ + O²⁻; thus, the presence of O²⁻ ions is required.

Fig. 1 A fragment of the crystal structure of Dy-doped hydroxy/fluoro-apatite (sample 2) showing a c-directed trigonal channel formed by Ca²⁺ and filled randomly with small anions, OH⁻, F⁻, and O²⁻ coupled to Dy³⁺. Only one adjacent phosphate group is shown for clarity.

In the FT-IR spectra of all the samples, a new band arises at a wavenumber of ca. 550 cm⁻¹, which is most pronounced in the Dy-rich samples (Fig. S6†). We attribute this band to the DyO⁺ stretching vibration. The band wavenumber practically coincides with that of the DyO⁺ band (552 cm⁻¹) found in the Dy-doped hydroxyapatite,¹¹ suggesting that a strong Dy–O bond persists in the fluoro/hydroxyapatite analogs.

Magnetic properties

Temperature dependence of magnetic susceptibility for all the samples, expressed as χT(T) (Fig. S7†), is very similar to that of Dy-doped hydroxyapatite.¹¹ As expected, χT values at room temperature are nearly equal for all the samples and are slightly lower than that for a free Dy³⁺ ion. This confirms that the total content of Dy in each sample is close to the nominal content. On lowering the temperature, χT decreases due to depopulation of the Stark levels, and at the lowest temperatures, χT characterizes the magnetism of the ground state with M_J = ±15/2. However, the low-temperature values differ for different samples and show a general trend to be smaller in comparison with the expected χT values for Dy-doped apatite with a strong axial magnetic anisotropy¹¹ (see Fig. S7†). This finding is connected to the presence of the Dy₂O₃ admixture phase that exhibits much lower χT at these conditions. The deviation from the expected χT(T) is qualitatively related to the amount of trace Dy₂O₃ determined by XRPD analysis. It should be mentioned that while Dy₂O₃ contributes to the samples' magnetization, its effect on the magnetic properties (including magnetization relaxation parameters) of the main apatite phase approaches zero as this phase occupies a very small space (a part percent) and may affect only a few atomic layers of the adjacent matrix phase, so that the fraction of the disturbed apatite phase is vanishingly small.

According to the ac susceptibility measurements, all the samples show slow relaxation of magnetization under zero magnetic field at temperatures up to 70 K (Fig. S8–S11†). The parameter of the relaxation time distribution (α) is relatively large at a temperature of 20 K (∼0.3) and reduces to values in the range of 0.05–0.12 at higher temperatures. These values are quite low to clearly distinguish SIMs. The Arrhenius plots for the relaxation time τ are shown in Fig. 2. The ln τ (1/T) curves fall close to each other and show the same trend—a slow decrease with the increase in temperature at low temperatures and faster decrease and approaching linear behavior at higher temperatures where the Orbach process dominates. The curves were fitted using eqn (3), which includes terms from the Raman and Orbach processes as the major parameters in the considered temperature interval.

τ⁻¹ = CTⁿ + τ₀⁻¹ exp(−U_eff/k_BT) (3)

Fig. 2 Arrhenius plots for the magnetization relaxation time τ (s) of the samples prepared. Symbols–experimental points, lines–fitting (for sake of clarity, only shown for 1, 3, and 4).

The fitted parameters are presented in Table 1 along with the crystal cell volumes. The U_eff values are quite close to our earlier reported values for the Dy-doped calcium apatite species (up to 792 cm⁻¹),¹¹ demonstrating the particular robustness of this SIM. At the same time, U_eff varies with the composition of the material. The uncertainties arising due to U_eff correlation with τ₀ hinder the direct comparison of U_eff. The values of τ₀ scatter at around 1 × 10⁻¹² s. Assuming the same τ₀ for all the samples and fixing it to this value, the fitting provides the U_eff values with much smaller error bars (see Table 1), allowing for qualitative analysis. There are two distinct tendencies. First, at constant Dy content, U_eff grows with the F content: from 1 to 3 and from 2 to 4. Second, U_eff grows with the Dy content: from 1 to 2 at constant F⁻ content and from 3 to 4 even at decreasing F⁻ content. Both types of substitution lead to contraction of the unit cell, and U_eff monotonously grows with the decrease in unit cell volume.

Table 1 Parameters obtained by fitting of temperature dependencies of τ using eqn (3) along with crystal cell volumes for Ca_10−xDy_x(PO₄)₆(OH)_2−x−yO_xF_y

Sample	1	2	3	4
x	0.1	0.5	0.1	0.5
y	1	1	1.9	1.5
C × 10^4 (s^−1 K^−n)	0.39 ± 0.16	1.2 ± 0.3	0.53 ± 0.16	1.0 ± 0.2
n	4.51 ± 0.12	4.25 ± 0.08	4.40 ± 0.09	4.27 ± 0.06
U eff (cm^−1)	766 ± 32	788 ± 37	794 ± 35	815 ± 33
τ 0 × 10^12 (s)	0.9 ± 0.6	1.3 ± 1.0	1.0 ± 0.8	0.9 ± 0.6
U eff at τ0 = 10^−12 s (cm^−1)	761 ± 2	800 ± 2	796 ± 2	808 ± 2
V (Å^3)	525.42(2)	524.00(2)	524.26(2)	523.92(2)

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One of the possible reasons for these correlations might be the following. Shrinking of the crystal lattice will lead to a decrease in the interatomic distances, including that in the DyO⁺ ion. This provides a stronger axial crystal field at Dy³⁺ and thus elevated energy separations between the ground and excited doublets within the ground term ⁶H_15/2. Unfortunately, XRPD does not allow for precisely determining the Dy–O interatomic distance, particularly due to disorder in the position of the intra-channel oxygen atoms.¹¹ The wavenumber of the DyO⁺ stretching vibration observed in the FT-IR spectra is the same for all the samples. This implies that the expected variation in the DyO⁺ bond strength is too small to be probed in this manner. However, the spectra differ in intensity of the stretching vibration of OH (see Fig. S6†). An undisturbed OH⁻ vibration (as in pure hydroxyapatite²¹) is observed at 3571 ± 1 cm⁻¹. Its intensity decreases in the sample in the sequence 1, 3, 2, 4, i.e., with the increase in U_eff. A vibrational peak of OH⁻ hydrogen-bonded to F⁻ (commonly observed in hydroxy/fluoro-apatite²²) appears at 3539 ± 1 cm⁻¹ and has higher oscillator strength. Its intensity is lower for 2 and 4 than for 1 and 3. Therefore, some effect of the OH⁻ ions on DyO⁺ might be another possible reason for the variation of U_eff with doping. The respective O–O separation allows for the formation of a hydrogen bond between OH⁻ and DyO⁺ (see Fig. 1). Such an interaction would weaken the DyO⁺ bond and hence the axial crystal field strength at Dy³⁺, leading to a decrease in U_eff. Fluoride replacing the hydroxide groups will reduce the number of hydrogen bonds formed, which would make the average U_eff value increase. Replacement of Ca²⁺ by Dy³⁺ is coupled with substitution of OH⁻ by O²⁻, which similarly lowers the probability of hydrogen bonding. Till now, we could not discriminate the respective contribution of the two factors of influence, namely, the unit cell contraction and the hydrogen bonding. Nevertheless, the obtained data clearly demonstrate that with a slight change in the crystal environment of DyO⁺, it is possible to directionally regulate its magnetic anisotropy and corresponding energy barrier for magnetization reversal.

At low temperatures, relaxation becomes very slow and at a temperature of 1.8 K, all the samples exhibit a hysteresis loop in isothermal magnetization M(H) (Fig. 3a). The difference ΔM between the decreasing M_down and increasing M_up branches of magnetization at a certain magnetic field reflects the relaxation time: the larger the ΔM the higher the τ. ΔM is relatively low under a zero field due to the quantum tunneling of magnetization (QTM) between nearly degenerate energy levels. As expected, at first, ΔM increases with the increase in magnetic field, which splits the levels to remove the degeneracy, and then decreases as the direct process of spin-phonon relaxation becomes pronounced.²³ The somewhat narrow hysteresis for 1 may be related to the higher admixture of Dy₂O₃, the magnetization of which is reversible.¹¹

Fig. 3 Magnetization at T = 1.8 K. a). Magnetization curves at a field sweeping rate of 200 Oe s⁻¹. Coercive fields are of 134, 283, 126, and 326 Oe for 1, 2, 3, and 4 respectively. b). Low field dependence of ΔM = M_down − M_up, the color designation of the samples is the same as in a).

While the overall hysteresis loops look similar for all the samples, the behavior under low fields differs substantially (Fig. 3b). Samples with high Dy content exhibit more than a two-fold higher coercive field and 30–40% larger ΔM in a zero field than samples with a low Dy content. However, in intermediate fields, ΔM is comparable for all the samples. Hence, a high Dy concentration suppresses QTM. Absence of such a difference between 2 and 4 as well as between 1 and 3 implies that the fluoride for hydroxide replacement does not appreciably affect the ΔM(H) dependencies and QTM.

In order to verify this unusual trend, we checked our previous data on Dy-doped calcium hydroxyapatites (Fig. S12†). Indeed, ΔM under zero field increased with the change in the Dy content x from 0.5 to 1.0. Direct quantitative comparison with the current samples is not possible because the samples were measured at different field sweep rates. We may take relative values r₁ = ΔM(H = 0)/ΔM(H = 2 kOe) and calculate their ratio r₂ for pairs of samples with higher and lower Dy content. For the pairs 2–1 and 4–3, we obtain equal r₂ values of 1.40, and for the pair of hydroxyapatites, we obtained an r₂ value of 1.38. Therefore, the trend distinctly persists in the whole x range of 0.1–1.0.

As a rule, an increase in the paramagnetic ion concentration in the compound accelerates QTM, which is commonly related to the enhanced inter-ion interactions of the dipole–dipole or exchange types, causing tunnel splitting of the ground state Kramers doublet.²³ The apatite samples under discussion behave in the opposite manner. Recent studies on single-chains of SIMs in a crystal lattice show that the parameters of Dy- and Tb-based SIMs may be substantially modified due to inter-ion interactions.^24–26 In particular, dipolar interactions can significantly slow down the relaxation process under a zero field, as reported for a structurally ordered one-dimensional array of magnetically correlated Tb³⁺ ions.²⁴ Such QTM suppression is explained in the following way. The probability of QTM for a pair of ferromagnetically coupled ions is equal to a product of probabilities of QTM for each ion. Therefore, the two-ion QTM probability is always lower. In this study, we observed a similar effect in the Dy³⁺-based SIM. Moreover, it is a disordered system in which the Dy³⁺ ions are randomly distributed over the Ca(2) sites. The average inter-ion distance between the Dy³⁺ ions in 2 and 4 is 10.2 Å and the closest individually possible separations are 4.1 and 5.6 Å when a second Dy³⁺ ion is located in the neighboring Ca(2)₃ triangle. The latter distances provide a magnetic dipole interaction of an order of 1 cm⁻¹. This may be sufficient to correlate spins of the neighboring ions at a measurement temperature of 1.8 K. Such a ferromagnetic interaction may manifest itself in the increase in χT at low enough temperatures.²⁴ However, we do not observe such an increase (or a substantial decrease in the case of antiferromagnetic interaction) in the measured χT(T) values (see Fig. S7†). At temperatures of 10–20 K, ferromagnetic interaction may be masked by a general decrease of χT with lowering temperature (see discussion above), while at the lowest temperatures of a few K, the magnetization becomes irreversible, which hinders the precise measurement of an equilibrium magnetization. It is worth mentioning that the expected directions of the magnetic moments of two neighboring DyO⁺ units can lie under an angle of ca. 120°. Hence, the expected increase in susceptibility may be smaller or even change its sign. Therefore, without experimental evidence, the discussed reason for the observed effect of the QTM suppression remains a hypothesis. Indeed, more detailed studies are necessary to clear up this issue.

In summary, by varying the atomic environment of the single ion magnet DyO⁺ embedded in an apatite crystal lattice, high SIM properties are retained and thus, as demonstrated, appropriate substitutions allow for their fine tuning. Fluoride for hydroxide substitution as well as increasing the DyO⁺ concentration results in enhancement of the energy barrier for magnetization reversal. The observed U_eff relations with the crystal lattice parameters and the hydrogen bonding suggest probable mechanisms for tuning. An inter-ion interaction in the Dy-rich compounds elongates relaxation time at low temperatures under a zero field, implying that QTM is suppressed. To the best of our knowledge, such an effect is reported for the first time for a Dy³⁺-containing SIM as well as in a disordered system. Notably, the compounds studied are chemically and thermally stable. Hence, these findings may promote the development of robust SIM-containing materials for high-density magnetic recording and spintronics applications.

The study was supported by Russian Science Foundation under Grant No. 16-13-10031.

Conflicts of interest

There are no conflicts to declare.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Powder X-ray diffraction patterns, crystal structure data, magnetisation relaxation data plots, FT-IR plots, and hysteresis magnetization data plots. See DOI: 10.1039/c8ce01706a

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