Influence of cobalt substitution on the magnetism of NiBr$_2$

TL;DR

This study investigates how cobalt substitution affects the structural and magnetic properties of NiBr$_2$, revealing a structural phase change and modifications in magnetic transitions across different cobalt concentrations.

Contribution

It provides new insights into the structural and magnetic evolution of NiBr$_2$ with cobalt substitution, including a phase transition and magnetic phase diagram.

Findings

Structural transition from CdCl$_2$ to CdI$_2$ type occurs between x=0.56 and 0.76.

Magnetic transitions are altered by cobalt content, with incommensurate phase persisting up to x=0.56.

Magnetic phase diagram summarizes the evolution of magnetic states with cobalt substitution.

Abstract

Co substituted Ni$_{1-x}$Co$_x$Br$_2$ (0 $\leq~x~\leq$ 1) single crystals were synthesized using vapor transport. The physical properties of the crystals were characterized by x-ray powder diffraction, magnetization, and specific heat measurements. Room temperature x-ray powder diffraction data indicate a change from the CdCl$_2$ structure type to the CdI$_2$ structure type occurs within 0.56 $<~x~<$ 0.76. NiBr$_2$ has a commensurate antiferromagnetic phase below $T_{\rm N} \approx$ 46 K and an incommensurate magnetic ground state below $T_{\rm IC} \approx$ 20 K. Both magnetic transitions are affected by cobalt substitution, and the incommensurate phase transition is present up to at least $x$ = 0.56. The evolution of magnetism has been studied as a function of cobalt content and is summarized in the temperature-composition phase diagram.

Tables

Table 1. Table 1: The nominal growth composition, the value obtained by EDS, and the corresponding standard deviations (STD) that provide the relative error for the EDS measurements.

Nominal	0.10	0.20	0.25	0.30	0.40	0.5	0.55	0.70	0.75	0.80
EDS$x$	0.11	0.18	0.25	0.31	0.39	0.5	0.56	0.67	0.76	0.85
STD ($\%$)	1.0	3.8	1.5	2.6	2.0	1.8	1.4	4.0	1.1	2.1

Full text

I Introduction

Binary transition metal dihalides $MX_{2}$ ($M$ = transition metal and $X$ = halogen) are of great interest to the low-dimensional magnetism community because of their novel physics and potential applicationsMushtaq et al. (2017); McGuire (2017); Chen et al. (2017). $MX_{2}$ compounds contain triangular nets of transition metal ions, and a helimagnetic ground state is observed in the few dihalides where long-range interactions are importantA.Adam et al. (1980); Kuindersma et al. (1981); Lio et al. (1990). The dihalides that host the helimagnetic structure have received attention in recent years due to the discovery of the coupling between helimagnetic order and ferroelectric polarizationKurumaji et al. (2011); Tokunaga et al. (2011); Wu et al. (2012); Kurumaji et al. (2013). NiBr2 has recently received renewed interest as a multiferroicTokunaga et al. (2011) and for its potential to host a magnetic vortex state upon chemical substitutionLin et al. (2016) or multiple-$q$ states under applied magnetic fieldOkubo et al. (2012); Babu et al. (2018), all of which are associated with its helimagnetic ground state.

NiBr2 is a magnetic insulator that has a commensurate magnetic structure below an antiferromagnetic transition temperature of $T_{\rm N}\approx$ 48 KDay et al. (1981); Moore and Day (1985); Tokunaga et al. (2011). The magnetic structure changes from a commensurate one to an incommensurate one below $T_{\rm IC}\approx$ 20 K, and this magnetic ground state is a helical spin structureDay et al. (1981); A.Adam et al. (1980). In both magnetic phases, the moments are oriented within the basal plane of the rhombohedral structure (see Fig.1). The incommensurate structure is believed to result from a delicate balance between the first-neighbor ferromagnetic exchange constant $J_{1}$ and the longer-range antiferromagnetic exchange constants $J_{2}$ and $J_{3}$ (see Fig. 1 (c))Rastelli et al. (1979); Odisho and Al-Dorry (1989); Leonov and Mostovoy (2015). The competition between these exchange constants is affected by external control parameters including magnetic field, pressure, or chemical substitutionSugiyama et al. (1988); Yoshiyama et al. (1984, 1986); Day et al. (1981); Day and Vettier (1981); Adam et al. (1981); Régnault, L.P. et al. (1982); Moore and Day (1985), which destabilize the incommensurate spin structure. An applied magnetic field suppresses $T_{\rm IC}$, and the incommensurate phase changes to the commensurate one around 2.7 T at $T$ = 2 K for $H\perp c$Sugiyama et al. (1988). The helimagnetic structure of NiBr2 is also affected by hydrostatic pressure and it disappears with applied pressure above 10.6 kbar, while the antiferromagnetic phase remains unchangedDay and Vettier (1981); Adam et al. (1981).

Chemical substitution studies of NiBr2 have been reported and a complete Ni-site substitution by other transition metals (Ni${}_{1-x}TM_{x}$Br2, $TM$ = Mn, Fe, Zn) was hindered by solubility limitsMoore et al. (1981); Day and Vettier (1981); Moore and Day (1985). Fe-doping suppresses $T_{\rm N}$, and Fe content greater than $x\geq$ 0.112 is reported to eliminate the incommensurate phase and induce an easy-axis, collinear antiferromagnetic structureMoore and Day (1985). The highest reported Mn content is $x\approx$ 0.03, which slightly suppresses $T_{\rm IC}$ without changing $T_{\rm N}$Moore and Day (1985). In Ni1-xZnxBr2, the highest reported Zn content $x$ = 0.08 slightly suppresses $T_{\rm N}$ and $T_{\rm IC}$. Interestingly, the propagation vector of the incommensurate structure becomes disordered upon Zn substitutionMoore et al. (1981); Day and Vettier (1981), and it has been recently proposed that Ni0.92Zn0.08Br2 could contain an impurity-driven vortex lattice phaseLin et al. (2016). These results highlight the sensitivity of the incommensurate spin structure of NiBr2 to chemical perturbation.

To further explore the magnetism of NiBr2, we have investigated the impact of cobalt substitution in Ni1-xCoxBr2. CdCl2 and CdI2 are the prototypes for the two dominant structure types in the $MX_{2}$ family, shown in Fig. 1. In both structure types, triangular nets of transition metal ions are separated by two planes of halide ions that are weakly bonded by van der Waals forcesMcGuire (2017). The main difference between these structure types is the layer stacking, which is reflected in the lattice centering. NiBr2 crystallizes in the rhombohedral CdCl2 structure type with space group $R\bar{3}m$A.Adam et al. (1980) and has $ABC$ layer stacking yielding three NiBr2 layers per unit cell. CoBr2 crystallizes in the CdI2 structure type with space group $P\bar{3}m1$, and it has one CoBr2 layer per unit cellWilkinson et al. (1959); Katsumata et al. (1984); McGuire (2017). Thus, the $c$-axis lattice parameter of NiBr2 is approximately three times that of CoBr2. CoBr2 has a commensurate magnetic structure below $T_{\rm N}\approx$ 19 K and does not host a helimagnetic ground stateWilkinson et al. (1959); Katsumata et al. (1984).

In this study, single crystals of Ni1-xCoxBr2 (0 $\leq~{}x~{}\leq$ 1) have been synthesized and characterized using magnetization and specific heat measurements. A composition-induced transition from the CdCl2 structure type of NiBr2 to the CdI2 structure type of CoBr2 has been observed within 0.56 $<~{}x~{}<$ 0.76 by room temperature powder x-ray diffraction data. A magnetic phase diagram has been established based on magnetization and specific heat measurements. For samples with the CdCl2 structure type, $T_{\rm N}$ is continuously suppressed with increasing cobalt concentration. The stability of the incommensurate phase seems to be enhanced for $x\leq$ 0.26, and signatures of this phase are detected up to $x$ = 0.56.

II Experimental Methods

Single crystals of Ni1-xCoxBr2 (0 $\leq~{}x~{}\leq$ 1) were grown from anhydrous NiBr2 (99.99% purity) and CoBr2 (99.99% purity) using vapor transport. NiBr2 and CoBr2 were placed in a silica ampoule inside a helium-filled glovebox and sealed under vacuum without exposure to air. The ampoules were heated in a horizontal tube furnace at temperatures ranging from 900 ∘C (NiBr2) to 620 ∘C (CoBr2) for several days, and cooled to room temperature within 1 day. The growths resulted in crystals at the cold end of the ampoule, with crystalline facets that were the cleavage $ab$-plane. Despite optimizing the growth conditions for each composition, the size of the single crystals decreased with increasing $x$; a representative crystal ($x\approx$ 0.31) is shown in the inset of Fig. 2 (a). The Ni1-xCoxBr2 crystals are air sensitive and the sensitivity to air increases as Co content increases. We emphasize that care must be taken to avoid air exposure, especially for large $x$, or else anomalous physical properties may be observed below 10 K.

Room temperature powder x-ray diffraction data were collected in a PANalytical X’Pert Pro MPD diffractometer (Cu K$\alpha_{1}$ radiation). The crystals were mixed with glass powder, and the mixtures were ground into powders using a mortar and pestle inside a helium glovebox. The fine powders were sealed in an air-free sample holder. X-ray diffraction data were also collected from facets of freshly-cleaved single crystals, and these data contain the 00l reflections. The x-ray diffraction data were analyzed with the program FullProfRodríguez-Carvajal (1993) using the Le Bail technique. Energy dispersive x-ray spectroscopy (EDS) was employed to determine the $x$ values from relative Ni and Co concentrations assuming full transition metal occupancy; a Hitachi TM3000 with Bruker EDS detector was utilized. EDS was performed on both sides of at least two crystals for each $x$, and the EDS values were obtained by averaging the results of at least 20 spots per measurement with error bars being the standard deviation. The $x$ values provided in this work are the experimental ones obtained from EDS and are reported in the Table 1. The EDS measurements also provide important guidance on the growth optimization, as samples from growths that were not properly optimized exhibited a large variation in $x$. Anisotropic magnetization measurements were performed in a Quantum Design Magnetic Property Measurement System. To identify intrinsic magnetic behavior for the most air-sensitive samples, including CoBr2, the crystals were sealed inside a quartz tube containing helium exchange gas. Specific heat data were collected in a Quantum Design Physical Property Measurement System.

III Results and Discussion

III.1 Structure

Room temperature x-ray powder diffraction data are shown in Fig. 2. The NiBr2 (see Fig. 2 (a)) and CoBr2 (see Fig. 2 (b)) powder diffraction patterns are well described by the CdCl2 structure type and the CdI2 structure type, respectively, using Le Bail fitting. Figure 2 (c) shows the powder diffraction patterns of Ni1-xCoxBr2. The diffraction data show the change in structure type at room temperature occurs within 0.56 $<~{}x~{}<$ 0.76. This transition is best viewed by tracking the 104 and 102 reflections of NiBr2 and CoBr2, respectively.

The asymmetry and broadness of the Bragg reflections increase as $x$ approaches the change in the structure type. Indeed, the weakest h0l reflections are fully suppressed near the change in the structure type. The apparent asymmetric and broad Bragg reflections in such layered materials may result from a combination of stacking faults or disorder or strain Hendricks and Teller (1942); Ramesh et al. (2003). In our study, the 00l and hhl peaks obtained from diffraction data are not significantly broadened, even for $x$ = 0.67. The h0l reflections are broadened and this suggests stacking disorder contributes most to the broadeningRamesh et al. (2003). The compositions around the change in the structure type likely have a significant amount of disorder associated with layer stacking, and this makes defining a precise composition where the structure type changes inappropriate because layer stacking is what differentiates the structure types. For the $x$ = 0.67 sample where a large degree of stacking disorder and composition variation are evident, we obtained lattice parameters using the CdI2 model because it provided the best fitting of the diffraction data. However, near this composition it is probably not reasonable to ascribe a particular structure model.

The change in the lattice parameters as a function of $x$ is shown in Fig. 3. The $a$-axis lattice parameter increases continually from $x$ = 0 to 1 as shown in Fig. 3 (a). The layer spacing and the average volume per atom increase with increasing $x$ similar to the change in the $a$-axis lattice parameter (see Fig. 3 (b,c). The layer spacing is equal to $c$ for samples with the CdI2 structure type and is equal to $c$/3 for those with the CdCl2 structrure type. Le Bail fitting (2$\theta$ = 10∘ - 100∘) was performed to obtain the lattice parameters of Ni1-xCoxBr2, and the reported lattice parameters for $x$ = 0.56 and 0.67 were calculated excluding (h0l) Bragg reflections from the fitting.

X-ray diffraction data collected from the facets of single crystals are characterized by sharp 00l reflections for all samples examined, including $x$ = 0.56 (shown in Fig. 2 (d)). This suggests the crystals do not have significant macroscopic chemical inhomogeneity or immiscibility. The expansion of the layer spacing obtained by fitting these data is in agreement with that obtained from the powder diffraction data. We note, however, that the $x$ = 0.67 sample has much higher standard deviations in the EDS measurements and the symmetry is not well-defined. Thus, it is possible that near $x$ = 0.67 some immiscibility exists that is beyond our resolution.

III.2 Magnetic Properties

The temperature-dependent anisotropic magnetization $M$ of NiBr2 and CoBr2 was measured in an applied magnetic field $\mu_{0}H$ = 1 T, and the results are shown in Fig. 4. A broad cusp in the temperature-dependent magnetization $M/H$ is observed upon cooling, which corresponds to a transition from a paramagnetic phase to a commensurate antiferromagnetic phase. The transition temperatures $T_{\rm N}$ = 46(1) K for NiBr2 and 18(1) K for CoBr2 are determined from peaks in d($MT$)/d$T$Fisher (1962). In addition to $T_{\rm N}$ in NiBr2, when $H\perp c$, a small decrease in $M/H$ below $T\approx$ 20 K is observed and corresponds to the onset of the helimagnetic structure. The transition temperature $T_{\rm IC}$ = 20(1) K is also determined from a peak in d($MT$)/d$T$. $T_{\rm N}$ and $T_{\rm IC}$ determined from our study are in agreement with previous reportsWilkinson et al. (1959); Day and Vettier (1981). $T_{\rm IC}$ is not observed when $H\parallel c$ for NiBr2, and it is absent in CoBr2. We note that $T_{\rm IC}$ of NiBr2 is suppressed with applied magnetic field $H\perp c$Tokunaga et al. (2011).

Neutron diffraction studies on NiBr2 and CoBr2 reported that the moments align ferromagnetically within a layer and stack antiferromagnetically along the $c$ axis, and furthermore the studies suggest that the ordered moments orient in the $ab$ planeWilkinson et al. (1959); Day et al. (1976); Day (1988). Despite this similarity from the perspective of neutron diffraction, the measured anisotropy of the induced magnetization is opposite between NiBr2 and CoBr2 (see Fig. 4(a)). The temperature-dependent $M/H$ of both compounds shows Curie-Weiss behavior at high temperature. The effective moments and Weiss temperature $\theta_{W}$ are extracted from a linear fit (red line) of the inverse magnetic susceptibility $H/M$ at 150 K $\leq~{}T~{}\leq$ 350 K, as shown in Fig.4(b,c). For NiBr2, the experimental effective moment is 3.25 $\mu_{B}$/Ni, which is larger than the calculated spin-only ($S$ = 1) effective moment of 2.83 $\mu_{B}$/Ni*+2*. The experimental effective moment suggests some orbital contribution to the moment, which is consistent with the reported $g~{}\approx$ 2.2 of NiBr2Tuchendler and Katsumata (1985). For NiBr2, we obtained $\theta_{W}$ of 48 K and 51 K for $H\perp c$ and $H\parallel c$, respectively, indicating ferromagnetic correlations in the paramagnetic state that are consistent with a previous reportRégnault, L.P. et al. (1982). For CoBr2, the experimental effective moment of 5.53 $\mu_{B}$/Co is larger than the calculated spin-only value (3.87 $\mu_{B}$/Co*+2*), and a similar effective moment of 5.29 $\mu_{B}$/Co has been reported in isostructural CoCl2Starr et al. (1940). The $\theta_{W}$ are 7 K and -81 K for $H\perp c$ and $H\parallel c$, respectively, and this behavior may be driven by single ion anisotropy and/or anisotropic exchange interactionsJohnston (2017).

We have so far examined the temperature-dependent magnetization for NiBr2 and CoBr2. We now examine the impact of cobalt content on the magnetic properties. As shown in Fig.5(a,b), the commensurate phase transition at $T_{\rm N}$ of Ni1-xCoxBr2 is continually suppressed up to $x$ = 0.56, while a partial Ni substitution leads to an enhancement of $T_{\rm N}$ for CoBr2. For $H\perp c$, the incommensurate phase transition ($T_{\rm IC}$ = 20(1) K) of NiBr2 is first slightly enhanced with Co substitution and is last detected for $x$ = 0.56 (see in Fig. 5(a)).

The isothermal magnetization $M(H)$ at $T$ = 2 K is shown in Fig. 6. For a given magnetic field, $M$ of NiBr2 (left axis in Fig. 6(a)) is smaller than $M$ of CoBr2 (right axis in Fig. 6(a)). The induced magnetic moments are not saturated for $\mu_{0}H$ = 6 T, and the maximum moment $M(\mu_{0}H$ = 6 T, 2 K) increases continually from $x$ = 0 to 1. For NiBr2, a magnetic anomaly around $\mu_{0}H_{c}$ = 2.7 T is observed for $H\perp c$ (closed symbols), but it is absent for $H\parallel c$ (open symbols). The anomaly is related to a transition from the helimagnetic structure to the commensurate antiferromagnetic structureDay et al. (1981); Tokunaga et al. (2011). The observed magnetic hysteresis on increasing and decreasing magnetic fields (see in Fig. 6(b)) is consistent with previous reportsAdam et al. (1981); Tokunaga et al. (2011), and suggests a first-order transition. Recently, Tokunaga et al. investigated multiferroic properties in NiBr2 and reported a spontaneous polarization below $T_{\rm IC}$Tokunaga et al. (2011). The ferroelectric transition disappeared above $H_{c}$, and the hysteresis may be related to magnetostructural domain movement.

Specific heat $C_{p}(T)$ of Ni1-xCoxBr2 at $\mu_{0}H$ = 1 T are shown in Fig. 7. Strong anomalies are observed at $T$ = 44.6(2) K and $T$ = 18.4(2) K for NiBr2 and CoBr2, respectively, which are consistent with $T_{\rm N}$ observed from temperature-dependent $M/H$. The commensurate-incommensurate phase transition observed in the magnetization for NiBr2 is also observed in $C_{p}(T)$ as a weak anomaly around $T\approx$ 20 K (see in the inset of Fig. 7). We note that similar behavior was observed at $T_{\rm N}$ for specific heat in $H$ = 0, though the transition at $T_{\rm IC}$ was only observed in $C_{p}(T)$ with an applied magnetic field $H\perp c$ and thus results for $\mu_{0}H$ = 1 T are shown. $C_{p}(T)$ measurements were used to verify $T_{\rm N}$ of a few Ni1-xCoxBr2 compositions.

The magnetic transitions of the Ni1-xCoxBr2 series derived from peaks in $C_{p}(T)$ and d($MT$)/d$T$Fisher (1962) are summarized in the temperature-composition phase diagram shown in Fig. 8. Both magnetic transitions of NiBr2 are affected by Co substitution. The commensurate phase transition is continually suppressed from $T_{\rm N}\approx$ 46 K for $x$ = 0 to $T_{\rm N}\approx$ 21 K for $x$ = 0.56. A slight enhancement of $T_{\rm N}$ for CoBr2 is observed with a partial Ni substitution, and a local maximum of $T_{\rm N}$ occurs near $x$ = 0.75. Interestingly, $T_{\rm IC}$ shows a slight enhancement for small $x$, reaching a maximum at $T_{\rm IC}$ = 22(1) K for $x$ = 0.26 and then finally $T_{\rm IC}$ is suppressed beyond detection for $x>$ 0.56 at $\mu_{0}H$ = 1 T. The evolution of $H_{c}$ as a function of cobalt content in $M(H)$ measurements follows a similar trend as $T_{\rm IC}$ in temperature-dependent $M/H$, indicating a strong correlation between $H_{c}$ and $T_{\rm IC}$.

The presence of $T_{\rm IC}$ up to at least $x$ = 0.56 is robust compared to the behavior observed for other transition metal substitutions in NiBr2. In contrast, the incommensurate magnetic structure of NiBr2 disappears by $x$ = 0.112 in Ni1-xFexBr2Moore and Day (1985), although the CdCl2 structure type is retained up to $x$ = 0.41. Interestingly, Ni1-xFexBr2 with the helimagnetic structure and a finite easy-axis anisotropy is predicted to host magnetic field induced skyrmionsHayami et al. (2016). Moreover, a neutron scattering study on Ni0.92Zn0.08Br2 observed a ring of magnetic scattering in the $a^{*}b^{*}$ plane around (00$\frac{3}{2}$) and (10$\frac{\bar{1}}{2}$) resulting from a disordered propagation vector of the helimagnetic structureDay et al. (1981). It has been proposed that the ground state associated with this magnetic scattering is an impurity-driven vortex lattice phaseLin et al. (2016); Batista et al. (2016). These experimental and theoretical results highlight the relevance of using chemical substitution in NiBr2 to tune the exotic ground statesLin et al. (2016); Hayami et al. (2016). As such, Ni1-xCoxBr2 with the CdCl2 structure type is a strong candidate to inspect for nontrivial spin textures like the magnetic vortex lattice phase or other multiple-$q$ spin textures. Examining the nature of the magnetic ground state of Ni1-xCoxBr2 and the correlation between $T_{\rm IC}$ and $H_{c}$ requires additional characterization like neutron scattering, which is underway.

IV Conclusions

We synthesized single crystals of Ni1-xCoxBr2 (0 $\leq~{}x~{}\leq$ 1) using vapor transport. A composition-induced transition from the CdCl2 structure type of NiBr2 to the CdI2 structure type of CoBr2 occurs within 0.56 $<x<$ 0.76 at 300 K. The in-plane lattice parameter, layer spacing, and the average volume per atom continually increase with $x$. For Ni1-xCoxBr2 with the CdCl2 structure type, increasing the cobalt content leads to a suppression of the commensurate antiferromagnetic phase transition of NiBr2. The transition temperature to the incommensurate phase is first slightly enhanced with cobalt substitution, then it is suppressed and last detected for $x$ = 0.56. The presence of $T_{\rm IC}$ up to at least $x$ = 0.56 indicates the delicate balance between ferromagnetic and antiferromagnetic exchange constants is perhaps still satisfied. Given that Ni1-xCoxBr2 with the CdCl2 structure type has both $T_{\rm N}$ and $T_{\rm IC}$ transitions in common with NiBr2, which hosts the helimagnetic spin structure, these compositions appear as promising candidates in the ongoing search for topologically-nontrivial spin textures.

V Acknowledgements

This research was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Science and Engineering Division. We thank D. Parker and C. D. Batista for helpful discussions.