J. Phys. Soc. Jpn. 83, 054713 (2014) [8 Pages]

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Magnetism in GdCo₂B₂ Studied on a Single Crystal

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Jiří Pospíšil¹, Hideaki Kitazawa², Ajeya Gupta², Saori Toyoizumi³, Akira Tamaki³, Martin Diviš¹, and Vladimír Sechovský¹

+ Affiliations

¹Faculty of Mathematics and Physics, Charles University, DCMP, Ke Karlovu 5, CZ-12116 Praha 2, Czech Republic²National Institute for Materials Science, Tsukuba, Ibaraki 305-0047, Japan³Tokyo Denki University, Adachi, Tokyo 120-8551, Japan

Received January 14, 2014; Accepted March 4, 2014; Published April 21, 2014

We have prepared a high quality single crystal of GdCo₂B₂ and studied complicated magnetism by measuring the magnetization, AC susceptibility and heat capacity. The results can be conceived in terms of low-temperature antiferromagnetism (below T_N = 22 K) undergoing three order to order magnetic phase transitions at T₁ = 18.5, T₂ = 13, and T₃ = 7 K, respectively. Measurements on the single crystal allowed us determining the weak magnetocrystalline anisotropy when the a-axis appears to be direction of the easy magnetization. In addition spin-flop transitions have been detected on magnetization loops. We have constructed complex H–T magnetic phase diagrams and calculated magnetocaloric effect (MCE). The large magnetic entropy change of \(\Delta S_{\text{mag}}^{(9\text{T})} = 24\) J kg⁻¹ K⁻¹ is attributed to the instability of antiferromagnetic ordering which can be easily changed to field-induced ferromagnetic state. The interpretation of experimental results is corroborated by ab initio electronic structure calculations.

https://doi.org/10.7566/JPSJ.83.054713

1. Introduction

GdCo₂B₂ crystallizes in the tetragonal ThCr₂Si₂-type structure type (space group \(I4/mmm\)) with lattice parameters \(a = 3.575\) Å and \(c = 9.561\) Å.¹⁾ The crystal unit cell contains two GdCo₂B₂ formula units. In literature very controversial reports can be found in all cases coming from experiments performed on polycrystalline samples. In early days ferromagnetism was reported below \(T_{\text{C}} = 26\) K¹⁾ but more recently antiferromagnetism below \(T_{\text{N}} = 15\) K²^,³⁾ has been proposed. The actual interest of scientific community about this compound comes from expected large reversible magnetocaloric effect.³⁾ The magnetic cooling is one of the potential new cooling mechanisms which are environment friendly when cooling gases and liquids in standard refrigerants are replaced by solid matter. The massive everyday using of the magnetic cooling is questioning of the observation of efficient and also cheap materials with high magnetocaloric effect. Although the primary target is using it in many standard refrigerant applications the magnetic cooling in low temperature scientific devices became important, as well. GdCo₂B₂, which is characterized by high magnetocaloric effect at low temperatures, would rather serve the latter purpose. The reversible magnetocaloric effect on GdCo₂B₂ is related to a field-induced first order metamagnetic transition from an antiferromagnetic to field-forced “ferromagnetic state”. The maximum isothermal magnetic entropy change \(-\Delta S_{\text{mag}}^{\text{max}}\) reaches 9.3 and 21.5 J kg⁻¹ K⁻¹ for the field change from 0 to 2 and 7 T, respectively, with no obvious hysteresis loss around 25 K.³⁾ The corresponding maximum magnetocaloric effect (MCE — adiabatic temperature change) \(T_{\text{ad}}^{\text{max}}\) has been evaluated to be 6.7 and 18.9 K, respectively.³⁾ These values are even larger than some of potential magnetic refrigerant materials reported in the same temperature range and also comparable to the room temperature giant magnetocaloric materials. Unfortunately, all available studies reporting on large MCE in GdCo₂B₂ were performed only on polycrystalline samples. Thus some effects could not be studied, mainly the magnetocrystalline anisotropy which plays an important role in physics of magnetic cooling.

It motivated us to grow single crystals of this compound as a well-defined material on which intrinsic properties including MCE can be studied in all aspects. In this work we focus on a detailed study of anisotropic magnetic properties and construction of the magnetic phase diagram. Interpretation of experimental results is also drawn in conjunction with our first principles electronic structure calculations. Therefore we present results of relativistic band structure calculations for GdCo₂B₂ in the simplified ferromagnetic structure in the framework of density functional theory (DFT). In the study of magnetic moments we moved beyond local spin density approximation (LSDA) when employing the static limit of dynamical mean field theory, the LSDA+U approximation in particular.

2. Experimental and Computational Details

The single crystal of the GdCo₂B₂ compound has been grown in a tetra-arc furnace by Czochralski pulling method from stoichiometric amounts of elements under the high-purity (6N) argon atmosphere. No significant evaporation has been observed during melting and growth process. The Ar atmosphere was purified during whole process by melting of piece of Ti on a separate spot of the furnace. The Ti getter remained silvery and intact by contaminants after the process.

The grown single crystal was a 30-mm-long cylinder with a diameter of 4–5 mm. The crystal quality was checked by Laue technique on natural cut plane. A small part of the crystal was pulverized in an agate grinding mortar and X-ray powder diffraction (XRPD) pattern was recorded at room temperature on a Bruker D8 Advance diffractometer equipped with a monochromator providing the Cu Kα radiation. The XRPD data were analyzed by means of the Rietveld profile procedure⁴⁾ using the program FullProf.⁵^,⁶⁾ The chemical composition of the crystal was checked by (SEM) Tescan Mira I LMH equipped by an energy dispersive X-ray detector (EDX) Bruker AXS. Only the expected phase GdCo₂B₂ of exact stoichiometry has been detected within the sensitivity of the experiment.

Laue technique was also used for fabrication of well-oriented and appropriately shaped samples needed for all expected types of measurements. The samples have been cut by fine wire saw (South Bay Technology 850). A prism-shaped (\(0.5\times 0.5\times 0.5\) mm³) sample with rectangular planes oriented perpendicular to the a- and c-axes was used for the magnetization measurements. Small plate samples of dimensions (\(1.5\times 1.5\times 0.2\) mm³) with the main plate plane perpendicular to the a- and c-axis, respectively were used for the specific-heat data measurement. The orientation of the each sample has been revised again by Laue technique.

The specific-heat, AC susceptibility and magnetization measurements were performed using a Quantum Design physical property measurement system (PPMS) and physical property measurement system (PPMS), respectively. The specific heat was measured at temperatures from 1.8 to 300 K in magnetic fields up to 9 T. The magnetization was measured in the temperature range from 1.8 to 400 K in magnetic fields 0–9 T.

To obtain direct information about the ground-state electronic structure and related properties we applied first principles theoretical methods. The ground-state electronic structure was calculated on the basis of the DFT within the LSDA.⁷⁾ For this purpose we used full-potential augmented-plane-wave plus local-orbitals method (APW-lo) as implemented in the latest version (WIEN2k) of the original WIEN code.⁸⁾ The calculations were performed with the following parameters. The non-overlapping atomic sphere (AS) radii of 2.8, 2.0, and 1.4 a.u. (1 a.u. = 52.9177 pm) were taken for Gd, Co, and B, respectively. The basis for expansion of the valence states (less than 8 Ry below the Fermi energy) consisted of more than 1400 basis function (more than 100 APW/atom) plus Gd (5s,5p) and Co (3p) local orbitals. The gadolinium 4f states were also treated as the valence Bloch states and thus gadolinium is characterized by a non-integer occupation number. The Brillouin-zone integrations were performed with tetrahedron method⁸⁾ on a 35–163 special k-points mesh. The unknown values of internal parameters for B were obtained by minimizing the forces at experimental values of \(a = 356.9\) pm and \(c = 952.7\) pm. We carefully tested the convergence of the results presented with respect to the parameters mentioned and found them to be fully sufficient for all presented characteristics of the GdCo₂B₂ compound. We also tried the self-interaction corrected (SIC) LDA+U method,⁸⁾ because by construction it is better suited for systems with a higher degree of localization, which should be the case of GdCo₂B₂ compound. The LDA+U potential is implemented in a rotationally invariant way. In these calculations we have chosen the parameters \(U = 7\) eV and \(J = 0.75\),⁹⁾ which were used to describe the onsite Coulomb (direct and exchange) interaction among highly correlated 4f electrons at the Gd-site.

3. Results and Discussion

3.1 Crystal structure analysis

The recorded Laue patterns on natural planes have shown sharp reflections signing a high quality single crystal. The EDX analysis confirmed a single phase sample of \(1:2:2\) stoichiometry within the resolution of the used method. Also XRPD analysis detected only the expected GdCo₂B₂ phase. All recorded reflections have been properly described by the structural model of the GdCo₂B₂ compound (see Fig. 1). XRPD data were evaluated using Reitveld method¹⁰⁾ implemented in FullProf software.⁵^,⁶⁾ The obtained crystallographic parameters and fractional coordinates (listed in Tables I and II) are in good agreement with previously published data.²⁾

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Figure 1. (Color online) XRPD patterns of the GdCo₂B₂ compound. The red points represent experimental data, the black line represents evaluated structural model and the blue line shows difference between the experimental data and evaluated model.

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Table I. Lattice parameters of GdCo₂B₂ obtained from PXRD pattern evaluation.

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Table II. Crystal structure parameters of GdCo₂B₂ obtained from PXRD pattern evaluation.

3.2 Magnetization and specific heat data analysis

The temperature dependence of heat capacity (see Fig. 2) exhibits three anomalies apparently reflecting magnetic phase transitions at temperatures \(T_{\text{N}} = 22\), \(T_{1} = 18.5\), and \(T_{2} = 13\) K, respectively, and a broad bump below 10 K.

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Figure 2. (Color online) Temperature dependence of specific heat data of the GdCo₂B₂ compound. The right panels show data which were measured with applied external magnetic field along the c-axis while left panels represent data with applied external magnetic field along the a-axis, respectively. The upper panels show data as a temperature dependence of \(C_{p}\) the lower panels as a temperature dependence of \(C_{p}/T\). The black lines point to critical temperatures of observed anomalies. The \(C_{p}/T\) vs T data also well shows the broad bump below 10 K.

The somewhat different response of the corresponding anomalies to the applied external magnetic field along the a- and c-axis, respectively, manifests a weak magneto-crystalline anisotropy. All three (\(T_{\text{N}}\), \(T_{1}\), and \(T_{2}\)) anomalies are wiped out already in 1 T applied in either directions leaving behind a broad maximum around 22 K. The existence of the last magnetic transition at \(T_{3}\) will be discussed latter in magnetization data. The magnetic transition is practically invisible in the specific heat data most likely due to very low magnetic entropy change connected with the transition and presence of strong bump of Schottky contribution. We have collected the values of critical temperatures for latter construction and discussion of the B–T magnetic phase diagram in conjunction with data from magnetization measurements.

In Fig. 3 temperature dependence of zero magnetic field specific heat data is shown at temperature up to 60 K. The specific heat was considered as a sum of four contributions: electron contribution \(C_{\text{e}}\), phonon contribution \(C_{\text{ph}}\), magnetic contribution \(C_{\text{mag}}\), and Schottky contribution \(C_{\text{Sch}}\).

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Figure 3. (Color online) Temperature dependence of zero magnetic field specific heat data of the GdCo₂B₂ compound. The colored lines represent various contributions to total specific heat. The Schottky contribution and magnetic part well explain origin of the observed transitions and also bump below 10 K, as well. The picture also shows temperature evolution of the magnetic entropy when the same scale is used both for specific heat and entropy axis.

The most significant one mainly at high temperatures is the phonon contribution, which has been evaluated within the Debye and simplified Einstein model: \begin{equation} C_{\text{ph}} = R\left(\frac{1}{1 - \alpha_{\text{D}}T}C_{\text{D}} + \sum_{i = 1}^{3N - 3} \frac{1}{1 - \alpha_{\text{Ei}}T}C_{\text{Ei}}\right). \end{equation} (1) The estimated Debye (\(\theta_{\text{D}}\)) and Einstein (\(\theta_{\text{Ei}}\)) temperatures are listed in the Table III. In reality, the Einstein parts of phonon spectrum (acoustic branches) are anisotropic and their energy and degeneracy is a characteristic parameter for every unique point in reciprocal space. Nevertheless the used simplified model gives a reasonable result to subtract phonon part from the raw specific heat data.¹¹^,¹²⁾

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Table III. The phonon spectra of GdCo₂B₂ evaluated using Debye and Einstein model, anharmonic correction was included.

After that we were able to analyze, electron, magnetic and Schottky contributions to total specific heat as it is displayed in Fig. 3.

Before beginning the analysis we had to take into account the term of the Gd³⁺ which represents an exception among rare earth ions because of its zero angular momentum.¹³⁾ Due to this fact the multiplet \(J = {}^{8}S_{7/2}\) ground state remains fully degenerated in the crystal field. In the absence of external magnetic field, only an exchange magnetic field can lift the (\(2J + 1\))-fold degeneracy.¹³⁾

From the electronic contribution \begin{equation} C_{\text{e}} = \frac{2nk_{\text{B}}^{2}T}{E_{\text{F}}} = \gamma T \end{equation} (2) value of the Somerfield coefficient gamma \(\gamma\approx 5\) mJ mol⁻¹ K⁻² has been determined. The analysis of the magnetic part of specific heat allowed us to calculate the value of magnetic entropy using \begin{equation} S_{\text{mag}} = \int_{T_{1}}^{T_{2}} \frac{C_{\text{mag}}}{T}\,dT. \end{equation} (3)

The magnetic entropy shows tendencies toward saturation around 30 K — almost \(R\ln 8\) as is expected for Gd³⁺, but the \(R\ln 8\) value was reached around 80 K which reasonably agrees with occupation of states of split ground state multiplet \(J = {}^{8}S_{7/2}\). While the temperature evolution of the magnetic part of the specific heat data well explains the anomalies at \(T_{\text{N}}\), \(T_{1}\), and \(T_{2}\), the broad bump around 10 K can be explained by a Schottky contribution, which can be calculated according to formula: \begin{equation} C_{\text{Sch}} = \frac{R}{T^{2}}\left\{\cfrac{\displaystyle\sum_{i = 0}^{n} \Delta_{i}^{2}\exp\biggl(- \cfrac{\Delta_{i}}{T} \biggr)}{\displaystyle\sum_{i = 0}^{n} \exp\biggl(- \cfrac{\Delta_{i}}{T} \biggr)} - \left[\cfrac{\displaystyle\sum_{i = 0}^{n} \Delta_{i}\exp\biggl(- \cfrac{\Delta_{i}}{T}\biggr)}{\displaystyle\sum_{i = 0}^{n} \exp\biggl(- \cfrac{\Delta_{i}}{T} \biggr)} \right]^{2}\right\} \end{equation} (4) with \(\Delta_{i}\) values shown in in Table IV. As seen in Fig. 2 the bump is shifted to higher temperatures by applying magnetic field. This reflects the fact that the Schottky contribution is weakly affected by external magnetic field. We have evaluated the temperature dependence of heat capacity data measured in external magnetic field of 9 T by the same model and we have found broadening of the split multiplet when the energy of each level is also listed in Table IV.

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Table IV. Suggested spectra of the Gd³⁺ multiplet \(J = {}^{8}S_{7/2}\) split due to exchange field and external magnetic field of 9 T. The values of the upper levels can vary \(\pm 5\) K.

The model which was used for evaluation of the zero field and 9 T data was also used to calculate the value of MCE when the magnetic entropy change was calculated using: \begin{equation} \Delta S(T,\Delta \mu_{0}H) = \int_{0}^{T} \frac{C_{p}(T,\mu_{0}H) - C_{p}(T,0)}{T}\,dT. \end{equation} (5)

The results of our calculation are summarized in Fig. 4. It is evident that the maximum of and the magnetic entropy change is observed around 24 K that corresponds to the temperature of magnetic phase transition \(T_{\text{N}}\). We have not detected any significant difference of calculated quantities measured with magnetic field applied along the a- and c-axis, respectively, larger than 1 T. The maximum entropy change of \(\Delta S_{\text{mag}}^{\text{max}} = 5.2\) or 7.2 J mol⁻¹ K⁻¹ were found at \(T = 24\) K in the magnetic field 5 or 9 T, respectively. Considering molar mass of GdCo₂B₂ being 296 g/mol the corresponding maximum entropy change of \(\Delta S_{\text{mag}}^{\text{max}} = 17.5\) or 24 J kg⁻¹ K⁻¹ for 5 or 9 T, respectively, which is in good agreement with previously published work of Li.³⁾

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Figure 4. (Color online) Temperature dependence of magnetic entropy (upper panel) and magnetic entropy change (lower panel) calculated from specific heat data measured in applied external magnetic field along the c-axis. The results are identical with data collected in the field applied along the a-axis.

3.3 Magnetization measurements

The heat capacity measurements revealed three magnetic phase transitions and a weak magnetocrystalline anisotropy. The temperature dependence of magnetization and AC susceptibility displayed in Fig. 5 show anomalies at \(T_{\text{N}}\), \(T_{1}\), \(T_{2}\), and \(T_{3}\), respectively, in agreement with heat capacity data.

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Figure 5. (Color online) Temperature dependence of the magnetization (top) and real part of the AC susceptibility (bottom) measured in the field applied along the a- and c-axis, respectively and heat capacity in zero field as a \(C_{p}/T\) (middle). The vertical lines mark the critical temperatures \(T_{\text{N}}\), \(T_{1}\), \(T_{2}\), and \(T_{3}\).

Evolution of temperature dependence of the magnetization in various external magnetic fields is seen in Fig. 6. Magnetization data measured in fields higher than 1 T are practically identical and tend to saturate at 7 \(\mu_{\text{B}}\)/f.u. which well corresponds with value expected for the free Gd³⁺ ion. On the other hand, the corresponding low-field (\({<} 1\) T) μ vs T curves shows distinctly different character depending on the direction of applied field (a- and c-axis respectively) revealing weak magnetocrystalline anisotropy.

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Figure 6. (Color online) Temperature dependence of the magnetization measured in fields applied along the a- (left) and c-axis (right). The lower panels are focused on the critical temperatures region in low magnetic field. The vertical lines guide eyes the follow the evolution of critical temperature \(T_{\text{N}}\), \(T_{1}\), \(T_{2}\), and \(T_{3}\) in low magnetic fields.

The saturation tendency of the magnetic moment in field applied along the a-axis appears already at ≈0.4 T which manifests that the a-axis can be considered as the easy magnetization axis. The magnetization curves displayed in Fig. 7 for fields applied both along the a- and c-axis show increasing saturation tendency with decreasing temperature towards the terminal low-temperature saturated magnetic moment of \(\mu_{\text{sat}} = 7\) \(\mu_{\text{B}}\)/f.u. which is characteristic for a free Gd³⁺ ordered moment.

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Figure 7. (Color online) Temperature evolution of magnetization curves of GdCo₂B₂ measured in fields applied along the a- (left) and c-axis (right).

The low-field part of the magnetization curves (see Fig. 8) demonstrates the weak magnetocrystalline anisotropy of GdCo₂B₂. The a-axis magnetization loop measured at 1.8 K shows no hysteresis. In fields lower than 1 T one can trace three anomalies which can be better localized by inspecting the \(\partial\mu/\partial H\) vs \(\mu_{0}H\) curves. The corresponding c-axis shows nonlinear hysteretic behavior in field below 0.5 T most likely due to a kind of non-collinear antiferromagnetic order in ground state. The value of the hysteresis and of the other anomalies on the magnetization loops are strongly temperature dependent as it is seen in Figs. 8–10 .

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Figure 8. (Color online) Comparison of the evolution of the a- and c-axis magnetization loops measured at 1.8 K (upper panel) and 20 K; i.e., between \(T_{\text{N}}\) and \(T_{1}\) (lower panel). To visualize the anomalies also the corresponding \(\partial\mu/\partial H\) vs \(\mu_{0}H\) curves are plotted in the upper panel and the characteristic fields are marked by arrows.

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Figure 10. (Color online) The low magnetic field detail of the a-axis magnetization loops measured at various temperatures. The red arrows mark the anomalies on magnetization loops. Each curve is moved up of about 2 \(\mu_{\text{B}}\)/f.u. for better clarity of the picture.

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Figure 9. (Color online) The low magnetic field detail of the magnetization loops measured at various temperatures with external magnetic field applied along the c-axis. The red arrows mark the anomalies on magnetization loops. Each curve is moved up of about 1 \(\mu_{\text{B}}\)/f.u. for better clarity of the picture.

The detail measurements of the loops with external magnetic field applied along the c-axis show that the hysteresis is gradually suppressed with increasing temperature and vanishes at \(T\approx 12\) K which is very close to \(T_{2}\) (\(= 13\) K). Increasing temperature leads to vanishing of the first step anomaly located at ≈0.3 T in the low-temperature limit (1.8 K) around \(T\approx 18\) K, i.e., close to \(T_{1}\) (\(=18.5\) K). The second anomaly is (0.8 T at 1.8 K) detectable up to 22 K which corresponds to \(T_{\text{N}}\). Further increase of temperature leads to magnetization response typical for paramagnets.

The magnetization loops measured with external magnetic field applied along the a-axis shows also three anomalies but negligible or no hysteresis. At 1.8 K the first anomaly appears in ≈0.1 T, the second one in ≈0.2 T and the last one in ≈0.35 T. The first anomaly survives up to ∼8 K. The other two seem to survive up to at least 14 K whereas only one knee is presented in the magnetic field of 0.15 T at 20 K (Fig. 10).

Observation of the hysteresis of the c-axis magnetization curves at temperatures lower than \(T_{2}\) is consistent with the found thermal history irreversibility demonstrated by the diverging field cooled (FC) and zero field cooled (ZFC) curves of c-axis magnetization below this temperature (see Fig. 11).

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Figure 11. (Color online) Temperature dependence of magnetization which was measured with external magnetic field applied along the c-axis in FC and ZFC regime. The color numbers sign the value of the applied magnetic field in mT.

When we analyzed high temperature part of the magnetic susceptibility data we have found a weak jump at 57 K in low magnetic field (\({<}0.1\) T) signing presence of a magnetic impurity (we speculate presence GdCo₃B₂ compound). We estimate content of the impurity in the single crystal below 0.5% which can be also in agreement with X-ray data, because such low content is below detection limit of the method and at certain circumstance also EDX. It motivated us to perform correction of the temperature dependence of magnetization data on ferromagnetic impurities using \begin{equation} \chi = \frac{\chi_{\text{5T}}H_{\text{5T}} - \chi_{\text{1T}}H_{\text{1T}}}{H_{2} - H_{1}}. \end{equation} (6) The temperature dependence of the inverse paramagnetic susceptibility (for \(T > 100\) K) perfectly follows Curie–Weiss law as it is presented in Fig. 12. For both, the a- and c-axis the same value of effective moment of \(\mu_{\text{eff}} = 8.05\) \(\mu_{\text{B}}\)/Gd was found which perfectly fit to the effective magnetic moment of the free Gd³⁺ ion (7.94 \(\mu_{\text{B}}\)).

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Figure 12. (Color online) Temperature dependence of the inverse magnetic susceptibility of GdCo₂B₂ for magnetic field applied along both crystallographic directions.

The magnetization data were also used for calculation of adiabatic entropy change using formula: \begin{equation} \Delta S_{\text{mag}} = \int_{B_{1}}^{B_{2}} \left(\frac{\partial M}{\partial T}\right)_{B}dB. \end{equation} (7) For the upper field \({\geq}1\) T the broad maximum of \(\Delta S_{\text{mag}}\) is always found around 24 K which is close to \(T_{\text{N}}\) (Fig. 13). The maximum value of \(\Delta S_{\text{mag}}^{\text{(a)}} = 18.6\) J kg⁻¹ K⁻¹ has obviously been found for the change from 0 T to the maximum magnetic field of 5 T in direction of the magnetic field along the a-axis. The value exceeds \(\Delta S_{\text{mag}}^{\text{max}} = 17.5\) J kg⁻¹ K⁻¹ found for polycrystalline data.³⁾ The magnetization data also reveal anisotropy of the MCE effect when the reduced value of the \(\Delta S_{\text{mag}}^{\text{(c)}} = 11.5\) J kg⁻¹ K⁻¹ was found along the c-axis. The value of adiabatic entropy change and the temperature of the maximum along the a-axis are in agreement with results of previous calculations from heat capacity data (see Fig. 4).

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Figure 13. (Color online) Temperature dependence of magnetic entropy change of the GdCo₂B₂ compound calculated from magnetization data.

3.4 Magnetic phase diagrams

The characteristic temperatures and fields of corresponding anomalies in heat capacity and magnetization data were used for construction of the B–T magnetic phase diagrams for magnetic field applied along the a- and c-axis, respectively (Fig. 14). The two phase diagrams are very similar owing to weak magnetocrystalline anisotropy, which is manifested by differences seen only in magnetic fields lower than 1 T.

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Figure 14. (Color online) Magnetic phase diagrams of GdCo₂B₂ for magnetic field applied along the a- and c-axis, respectively.

The main difference between the two phase diagrams is that for the a-axis all values of critical fields are significantly lower than the corresponding values for the fields applied along the c-axis mainly in the high field phase I. While the phase I survives up to \(\mu_{0}H_{\text{crit}}^{c}\approx 0.8\) T at the lowest temperature a much lower field \(\mu_{0}H_{\text{crit}}^{a}\approx 0.4\) T is necessary in the a-axis field. Because of lack of any microscopic study one can only speculate about magnetic structures of the individual phases. Most likely the GdCo₂B₂ in zero field orders first antiferromagnetically at \(T_{\text{N}}\) and with further cooling it undergoes two consecutive magnetic phase transitions to other antiferromagnetic structures. Application of the magnetic field leads a transition to the field induced phase I. All phases I, III, and IV survive to lowest temperatures only the phase II exists as a bounded dome between the phases I and III. The low temperature antiferromagnetic phases III and IV transform by spin flop transitions up to field induced ferromagnetic phase I.

3.5 Electronic structure calculations

The total spin polarized density of electronic states (DOS) from LSDA calculations at experimental equilibrium are shown in Fig. 15. The lowest band that is at about −10.5 to −6.2 eV originates from B 2s states. There is a gap from −6.5 to −5.9 eV. The Co 3d states form the main contribution to the occupied energy range in the energy range −5.9 to −0.8 eV (“3d band”) but they show an admixture of the gadolinium 6s,5d states, cobalt 4s states, and boron 2s,2p states. The highest occupied bands (between −0.8 eV and Fermi level) originate mainly from the hybridized gadolinium 5d states and cobalt 3d states but all remaining (Gd 6s; B 2s,2p states) are also present. Finally we see that the sharp narrow 4f states are situated 4 eV below Fermi level (spin-up states) and just above the Fermi level (spin-down states). In the LSDA+U calculations the 4f states are more localized (−6.2 eV for spin-up states and 4.2 eV for spin-down states). Otherwise the LSDA+U spectrum is very similar to LSDA one (see Fig. 16).

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Figure 15. Total spin polarized density of states of GdCo₂B₂ using LSDA+U.

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Figure 16. Total spin polarized density of states of GdCo₂B₂ using LSDA+U.

4. Conclusions

We have successfully prepared a high quality GdCo₂B₂ single crystal. Magnetization measurements together with heat capacity data confirmed Gd³⁺ ion responsible for GdCo₂B₂ magnetism. Both the effective paramagnetic and ordered magnetic moment and also the magnetic entropy value agree with values expected for free Gd³⁺ ion. Consequently, we do not expect any magnetic component from the Co sublattice or this component is negligible compared to the Gd moment. These conclusions are in reasonable agreement with results of theoretical calculations. The calculated LSDA magnetic moment is 6.97 \(\mu_{\text{B}}\) per Gd AS. Magnetic moment of cobalt is small −0.02 \(\mu_{\text{B}}\) as well as magnetic moment of the interstitial region (0.07 \(\mu_{\text{B}}\)). Total magnetic moment of unit cell is almost equal to 7 \(\mu_{\text{B}}\) which compares reasonably well with our results of magnetization measurements. The results of LSDA+U calculations are little bit larger (total magnetic moment of unit cell equal 7.16 \(\mu_{\text{B}}\)) due to increasing localization of spin-up polarized 4f orbitals. Surprisingly our detail single crystal study reveals not only one but four magnetic transitions at temperatures \(T_{\text{N}} = 22\), \(T_{1} = 18.5\), \(T_{2} = 13\), and \(T_{3} = 7\) K. Also weak magnetocrystalline anisotropy was detected with the a-axis as the easy magnetization axis. These results point to that GdCo₂B₂ has quite complicated magnetic phase diagram. We have also inspected both magnetization and heat capacity data from point of view of expected huge magnetocaloric effect. We have found maximum entropy change of \(\Delta S_{\text{mag}}^{\text{max}} = 17.5\) J kg⁻¹ K⁻¹ (specific heat) or \(\Delta S_{\text{mag}}^{\text{max}} = 18.6\) J kg⁻¹ K⁻¹ (magnetization data) for 5 T, which is in good agreement with previously published work of Li.³⁾ We have also found that the MCE effect is almost isotropic with respect to crystallographic direction according to specific heat data. The proper analysis of the much sensitive magnetization data reveals anisotropy of the MCE effect, when higher value was found along the axis a. Although the value of entropy change is quite large in comparison to many magnetic materials the found value is far from the best known magnetic refrigerants like Gd₅Si₂Ge₂,¹⁴⁾ Fe–Rh,¹⁵^,¹⁶⁾ or Mn(As,Sb)¹⁷⁾ which exceed GdCo₂B₂ two or three times.¹⁸⁾ To understand mechanism of transformations between individual magnetic phases and their magnetic structures the microscopic studies are highly desirable. Unluckily the neutron diffraction as the most powerful tool is not negotiable due to the extremely strong neutron absorption both Gd and B. Therefore X-ray methods like XMCD or X-ray resonant magnetic scattering together with Mössbauer and μSR spectrometry should be applied in this case.

Acknowledgements

This work was supported by the Czech Science Foundation (GACR P204/12/0692). Experiments performed in MLTL (http://mltl.eu/) were supported within the program of Czech Research Infrastructures (project LM2011025).

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Magnetism in GdCo2B2 Studied on a Single Crystal

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Magnetism in GdCo₂B₂ Studied on a Single Crystal