2 Dimers with Strong Anisotropy in MoCl5

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Ferromagnetic Spin-1/2 Dimers with Strong Anisotropy in MoCl5 Michael A. McGuire, Tribhuwan Pandey, Sai Mu, and David S. Parker Chem. Mater., Just Accepted Manuscript • Publication Date (Web): 25 Mar 2019 Downloaded from http://pubs.acs.org on March 26, 2019

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Chemistry of Materials

Ferromagnetic Spin-1/2 Dimers with Strong Anisotropy in MoCl5 † Michael A. McGuire,∗ Tribhuwan Pandey, Sai Mu, and David S. Parker Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 USA E-mail: [email protected]

Abstract

and anisotropy is predicted for isolated Mo2 Cl10 molecules, indicating the potential for true molecular magnetism. Together these results identify Mo1−x Wx Cl5 as novel molecular crystals that combine spin-1/2 with strong magnetic anisotropy and exhibit surprisingly high Curie temperatures considering their molecular nature.

The pentachloride MoCl5 adopts several molecular crystal structures, all comprising isolated Mo2 Cl10 units with well separated Mo-Mo magnetic dimers. Using magnetization measurements, single crystal x-ray diffraction, and firstprinciples calculations we confirm ferromagnetism with strong anisotropy below a Curie temperature of 22 K in α-MoCl5 , and report a fifth polymorph, -MoCl5 , that we find to be a ferromagnetic below 14 K. Magnetization measurements indicate unquenched orbital moments antialigned with the spins. This is confirmed by first-principles calculations, which also predict an unusually strong magnetocrystalline anisotropy in α-MoCl5 arising from spinorbit coupling. An anisotropy field near 80 T is calculated, while a smaller but still substantial anisotropy field exceeding 12 T is realized experimentally. Further increased anisotropy and Curie temperature are predicted when W is substituted for Mo. Similarly strong magnetism

Introduction There is currently a strong interest in the magnetism of 4d and 5d transition metal compounds arising primarily due to the more covalent interactions with coordinating anions and strong spin-orbit coupling. 1 Increased covalency can lead to stronger magnetic interactions and high transition temperatures, 2–5 and spin-orbit coupling is the origin of strong magnetocrystalline anisotropy. Strong anisotropy is key in producing hard ferromagnetic behavior in permanent magnets, 6,7 as well as stabilizing magnetic order in low dimensions 8 and enabling single molecule magnetism. 9–11 Transition metal halides are ideal systems in which to study low-dimensional magnetic phenomena due to their tendency to form molecular, 1D, and 2D structures. 12 Recent studies of magnetism in the layered compounds MoCl3 13 and MoCl4 14 led us to consider the pentahalide. MoCl5 adopts crystal structure with Mo2 Cl10 molecules with Mo centered octahedra dimerized by edge sharing, and these neu-

†

Notice: This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan)

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Chemistry of Materials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

tral molecules are bound to one another via van der Waals interactions. Although there does not appear to be a strong chemical interaction between the metal centers in these particular units, it is interesting to note that transition metal dimers have been proposed as a route to ultrasmall nanomagnets with strong anisotropy. 15 Dimerized units of fused metal centered octahedra (M2 X10 , M = metal cation, X = halide anion) are relatively common among early and heavy transition metal pentahalides. 16 Among chlorides, crystal structures are reported for M = V, Nb, Mo, Ta, W, Re, and Os (as well as Sb and U). These structures are stabilized less frequently with the less electronegative halogens, and are limited to M = Nb, Ta, W (and U) with Br, and only Nb with I. With oxidiation state +5 the group V metals are not expected to be magnetic, but partially filled d-levels should impart magnetism to the compounds with group VI and later metals Mo, W, Re, and Os (keeping in mind that there is no indication of metal-metal bonding in these M2 X10 units that could quench the magnetic moments). Indeed, previous studies have reported paramagnetic behavior consistent with local magnetic moments in several of these materials. 17–19 In particular, temperature dependent magnetization measurement on MoCl5 reported in the literature have shown paramagnetic effective moments smaller than expected for S = 1/2, along with ferromagnetic interactions. 17,18 Based on the magnetic data available at the time, Knox and Coffey 17 suggested low temperature magnetization measurement would be of interest, and subsequently a ferromagnetic transition near 22 K was indeed observed in MoCl5 . 20 As noted above, the structure of MoCl5 comprises molecular Mo2 Cl10 units made of two edge sharing octahedra. The original structure was reported by Sands and Zalkin, and is now known as α−MoCl5 . 21 Subsequently the structures of three additional polymorphs of have been reported, all formed by various packing of the same Mo2 Cl10 dioctahedra, and the paramagnetic behavior of one of these, β-MoCl5 , was found to be similar to the earlier reports. 22 Here we revisit the crystal structure and

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magnetism of MoCl5 , motivated by previous magnetic observations and the expectation of strong spin-orbit coupling that may lead to significant magnetic anisotropy. The structure determined for as received commercial MoCl5 powder is in agreement with that reported for the α form. 21 Temperature dependent magnetization measurements confirm the previously reported ferromagnetic order below about 22.3 K and reduced paramagnetic effective moment. At 2 K, a saturation moment of 0.67 µB /Mo is determined. This is suppressed by about 30% from the expected value for S = 1/2, and consistent with the reduced effective moment in the paramagnetic state. Recrystallization of the as received powder in vacuum produced a fifth polymorph referred to here as -MoCl5 . We find ferromagnetism in MoCl5 below a Curie temperature of 14 K with a saturation moment of 0.7−0.8 µB per Mo. We use first-principles calculations and classical Monte Carlo simulations to further investigate the magnetism in α-MoCl5 and find a ferromagnetic ground state with a significant unquenched orbital moment, consistent with the magnetic data. Most significantly we predict strong magnetocrystalline anisotropy due to spin-orbit coupling. We find experimental evidence of this in both α-MoCl5 and -MoCl5 , with anisotropy fields at 2 K of ≥ 120 kOe for both compounds. Importantly, our calculations on isolated Mo2 Cl10 molecules predict strongly anisotropic magnetism as well, indicating true molecular magnetism. Similar calculations on isostructural and isoelectronic α-WCl5 predict this compound to also be ferromagnetic, with a higher transition temperature than α-MoCl5 and much stronger anisotropy. Our preliminary experimental study of this compound revealed a first order crystallographic transition to an unknown structure upon cooling below about 150 K, which appears to be antiferromagnetic, and motivates further study of the crystallography and strongly anisotropic molecular magnetism in the Mo1−x Wx Cl5 system.


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Results and Discussion

with the twin law being a 2-fold rotation about the a-axis. The refinement results are summarized in Table 1, and a list of atomic positions and anisotropic atomic displacement parameters are located in the Supporting Information. Powder x-ray diffraction data indicate the α polymorph is the main phase present in the as received powder (Supporting Information). Fitting powder x-ray diffraction data collected at 300 K gives a = 17.990(1) ˚ A, b = 17.680(1) ˚ A, ˚ c = 5.760(3) A, and β = 90.277(3) degrees. Temperature dependent powder diffraction measurements show the α-MoCl5 structure is maintained down to at least 16 K (Supporting Information). The α-MoCl5 structure is shown in Figure 1a. Isolated Mo2 Cl10 units are loosely packed together via van der Waals forces. Within each unit the coordination around Mo is distorted so the Mo atoms are moved away from one another, indicating the absence of Mo−Mo bonding interactions. The intramolecular Mo-Mo distance is 3.82 ˚ A, and the closest intermolecular Mo-Mo distance is 5.71 ˚ A. Considering these two shortest contacts, the Mo1 and Mo2 sublattices separately form isolated ladder like structures running along the c axis. The next shortest distance, 5.81 ˚ A, connects between Mo1 ladders. The Mo−Cl bond distances range from 2.25 to 2.53 ˚ A, with the longer distances corresponding to the bridging Cl atoms bonded to both Mo atoms in a unit. Single crystal diffraction data from several rectangular prismatic crystals of MoCl5 produced by recrystallized in vacuum indicted primitive monoclinic symmetry but with a unit cell volume about half of that reported for the known primitive monoclinc structure δ-MoCl5 . 22 Analysis of the diffraction data showed that these crystals represent a fifth structure-type for MoCl5 , denoted here by . The results of the structure refinement are summarized in Table 1, and a list of atomic positions and anisotropic atomic displacement parameters are reported in the Supporting Information. The -MoCl5 structure is shown in Figure 1b. The structure is made up of the same Mo2 Cl10 units found in the other four poly-

Crystal Structures (a)

a-MoCl5

a b

c

a

Mo2

b

Mo1

(b)

Mo2

c

Mo1

e-MoCl5

a b

a

c

b c

c b

Figure 1: The crystal structure of α-MoCl5 (a) and -MoCl5 (b), with Mo sites at the centers of the octahedra that share edges to form isolated Mo2 Cl10 molecules. The green spheres are the coordinating Cl ions. Coordination around the unique Mo sites are shown for each structure. A view along the a-axis is also shown for -MoCl5 , highlighting the non-colinear arrangement of the Mo2 Cl10 units in this polymorph. Indexing single crystal diffraction data from as received MoCl5 indicated C-centered monoclinic symmetry with a unit cell similar to the structure originally reported by Sands and Zalkin. 21 Similar unit cells were observed in several crystals. Refinement of the structure confirmed that the crystal represented the α polymorph. The crystal was identified as a twin,


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Table 1: Crystal data and structural refinement results for α-MoCl5 and -MoCl5 . Atom positions and atomic displacement parameters are listed in the Supporting Information Temperature Wavelength Crystal system Space group, Z a b c β Volume Density (calculated) Crystal size Refl. collected / independent Rint Data / restraints / parameters Goodness-of-fit on F2 R indices [I > 2σ(I)] R indices (all data) Largest diff. peak and hole

α−MoCl5 175 K 0.71073 ˚ A Monoclinic C2/m, 12 17.9067(14) ˚ A 17.6050(14) ˚ A 5.7065(5) ˚ A 90.212(2) deg. 1798.9(3) ˚ A3 3.026 g/cm3 0.130 x 0.065 x 0.020 mm3 10552 / 2065 0.0416 2065 / 0 / 89 0.995 R1 = 0.0402, wR2 = 0.0907 R1 = 0.0511, wR2 = 0.0965 5.838 and -1.118 e/˚ A3

morphs with similar distortions. It is apparent in the figure that the dimeric units are packed in a staggered fashion. This is unique among the known MoCl5 structures; all previously reported polymorphs have collinear Mo−Mo dimers. The shortest Mo−Mo distance, within the Mo2 Cl10 units, is 3.97 ˚ A. The closest interdimer distances are 5.53 and 6.03 ˚ A. In -MoCl5 the Mo−Cl bond distances range from 2.07 to 2.66 ˚ A. The larger distortion of the octahedral environment in -MoCl5 compared to α-MoCl5 is apparent from the larger range of Mo−Cl distances and the larger separation of the Mo atoms.

−MoCl5 175 K 0.71073 ˚ A Monoclinic P 21 /c, 4 6.0628(7) ˚ A 16.667(2) ˚ A 6.4569(8) ˚ A 115.502(2) deg. 588.88(12) ˚ A3 3.081 g/cm3 0.200 x 0.120 x 0.050 mm3 7927 / 1464 0.0201 1464 / 0 / 55 1.129 R1 = 0.0498, wR2 = 0.1215 R1 = 0.0507, wR2 = 0.1220 2.452 and -2.513 e/˚ A3

described by the Curie Weiss model, and the fitting parameters are shown on the plot for data between 120 and 300 K. The Weiss temperature of 30 K is positive, indicating ferromagnetic interactions, and is close to the Curie temperature. The low temperature magnetic susceptibility reveals the ferromagnetic transition near 20 K (Figure 2b). These observations are in agreement with those previously published. 17,18,20 Isothermal magnetization curves at temperatures above, near, and well below the ferromagnetic transition are given Figure 2c. At 2 K the magnetization saturates quickly to a value near 0.71 µB /Mo in the highest measurement field. This is significantly smaller than expected for the 4d1 configuration (S = 1/2, g = 2), but consistent with the reduced p paramagnetic effective moment (µef f = g S(S + 1)µB ) from the Curie Weiss fits. The fits give µef f = 1.4−1.5 µB /Mo, and 1.73 µB would be expected for S = 1/2. The reduction of both the paramagnetic effective moment and the ferromagnetic saturation moment could arise from Mo−Mo cova-

Experimental Magnetic Behavior The magnetic properties of samples from two different batches of as received MoCl5 powder (α-MoCl5 ) are summarized in Figure 2. These are “free” powders in the sense that the grains were individually free to rotate in the applied field, so the measurements are effectively along the magnetic easy axis. The behaviors of the two samples are very similar. The temperature dependence in the paramagnetic state is well


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from the temperature dependence shown in Figure 2b. The Curie temperature is surprisingly high considering that the intermolecular Mo−Mo distances are all longer than 5.6 ˚ A with no simple superexchange paths. This is explored further in the theoretical results presented below. Of particular interest to the present work is the anisotropy in the ordered state. As discussed in detail below, our first-principles calculations predict a large magnetocrystalline anisotropy due to spin-orbit coupling and an anisotropic orbital moment in α-MoCl5 . Measurements on free powders approximate measurements along the ferromagnetic easy axis, since the particles are allowed to rotate to minimize their potential energy in the applied magnetic field. Indeed the 2 K data in Figure 2c approach saturation at very low applied fields. To observe the effects of magnetocrystalline anisotropy, non-oriented powders were “fixed” in epoxy at room temperature, so that measurements approximate the isotropic average behavior. Comparison of the magnetic behavior of free and fixed powders are shown in Figure 3a and 3b. Two fixed-powder samples were examined and found to be consistent with one another, and have Curie temperatures consistent with the free powders. However, the isothermal magnetization curves differ strongly between the free and fixed powders. The magnetization curves for the fixed powders at 2 K (Figure 3b) show evidence of strong magnetocrystalline anisotropy. We find that saturation is not quite reached even at an applied field of 120 kOe. Lower field magnetization loops are shown in Figure 3c. Some coercivity is seen well below the Curie temperature, indicating some magnetic domain wall pinning within the grains. Since -MoCl5 grew as well formed and sizable single crystals, anisotropic measurements were possible. A crystal encapsulated in epoxy for measurements is shown in Figure 4 and the three directions along which the measurements were performed are illustrated. Due to the plate-like morphology, the “out of plane” direction is well defined and expected to be the same in all crystals. An x-ray diffraction pat-

(a) -MoCl

1000

H/M (mol cm

H = 1 kOe 5

free powder 1

-3

)

1200

C = 0.25 cm

800

3

K mol

-1

= 30 K

600

400

free powder 2 C = 0.27 cm

200

3

K mol

-1

= 30 K

0 0

50

100

150

200

250

300

T (K) (b)

(c)

H = 1 kOe

0.6 -1

)

Mo

0.4

B

0.2

m (

-1

0.4

B

Mo

2 K

)

0.6

m (

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


25 K 0.2

T C = 22.3 K 0.0

40 K

0.0 0

10

20

T (K)

30

40

0

10

20

30

40

H (kOe)

Figure 2: Magnetic behavior of α-MoCl5 powder, with powder grains free to rotate in the applied magnetic field. Results of temperature dependent measurements on two samples in a 1 kOe applied field is shown in (a) and (b). Solid lines in (a) are results of Curie-Weiss fits for data between 60 and 300 K. The isothermal magnetization curves in (c) show a saturation moment near 0.67 µB per Mo at 2 K, and paramagnetic behavior well above the Curie temperature. Data for both powder samples at 2 K are shown in (c).

lent interactions, but this is unlikely because the Mo−Mo distance in the Mo2 Cl10 units is large (3.82 ˚ A), and the Mo ions in fact show an apparent repulsion within the molecules (Figure 1). The effective moment determined here is similar to those reported for Mo5+ double perovskite compounds. For example, 1.4 µB was found for La2 LiMoO6 , 23 Ba2 YMoO6 , 24 and Ba2 LuMoO6 , 25 where quantum fluctuations are often cited as the origin of the moment reduction. One of these reports find a value closer to the spin-only value for Ba2 YMoO6 , 23 and an effective moment of 1.69 µB is reported for MoOPO4 . 26 A Curie temperature of 22.3 K is estimated


5


(a)

free powder

-MoCl

beled “in plane 1” and “in plane 2” are chosen along the longest and intermediate dimensions, respectively, as shown in Figure 4. The magnetization data presented below suggest that these two in-plane directions may not correspond to the same crystallographic directions in different crystals. Measurements were performed on two crystals of -MoCl5 . Results are shown in Figure 4. The temperature dependence up to 300 K is shown in Figure 4a and 4b. Ferromagnetic ordering is apparent at low temperature. Little anisotropy is seen in the paramagnetic state of -MoCl5 , which suggests that the data shown for the paramagnetic state of the free powders of α-MoCl5 (Figure 2) may closely approximate the true powder average. Curie Weiss fits (Figure 4b) for -MoCl5 give Curie constants slightly higher than and Weiss temperatures slightly lower than those determined above for α-MoCl5 . Low temperature data for the two crystals are reported in panels c-f of Figure 4. Low field measurements indicate a Curie temperature of 14 K for both crystals, and show strong dependence on crystallographic orientation below this temperature. Isothermal magnetization curves show isotropic behavior above TC and indicate strong magnetocrystalline anisotropy in the ordered state. The out of plane direction [100] is the magnetically hardest direction measured in both crystals. The magnetically easiest of the directions measured is in the plane, along the longer in-plane dimension in crystal 1, and along the shorter in-plane dimension in crystal 2. This is consistent with the calculations described below which find the preferred moment direction to be along the Mo-Mo dimer in the Mo2 Cl10 molecules, which is in the bcplane for -MoCl5 (Figure 1b). The data indicate a maximum anisotropy field near 120 kOe in -MoCl5 , and a saturation moment at 2 K of 0.71−0.76 µB per Mo. In both polymorphs of MoCl5 examined here, the paramagnetic effective moment and the saturation moment in the ferromagnetic state are suppressed relative to the expected values for spin 1/2. This suggests the spins may be coupled to an unquenched orbital moment and

5

0.4

M (

B

Mo

-1

)

0.6

0.2

fixed powder

H = 1 kOe 0.0 0

5

10

15

20

25

30

T (K) (b) 0.8

0.6 fixed powder, 2 K

M (

B

Mo

-1

)

free powder, 2 K

0.4

0.2 fixed powder, 40 K

0.0 0

20

40

60

80

100

120

H (kOe) (c)

0.4

0.2

B

Mo

-1

)

fixed powder

M (

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.0

2 K -0.2

16 K 25 K

-0.4 -10

-5

0

5

Page 6 of 14

10

H (kOe)

Figure 3: Magnetization data for α-MoCl5 comparing free powder to randomly oriented powder fixed in epoxy so the grains cannot rotate in the field. Low field magnetization and low temperature isothermal magnetization are compared in (a) and (b), respectively, with data from measurements on two different fixed powder samples. Magnetization loops measured at the indicated temperature for one fixed powder sample is shown in (c).

tern collected from the largest facet of a crystal suggested that the out-of-plane direction is likely along [100]. The other two directions, la-


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(a)

-1

5

mol-Mo

)

in plane 2

-1

crystal 2

cm

3

0.3

in plane 1

-3

0.2

0.1

M/H (10

mol-Mo 3

M/H (cm

-MoCl

)

(b) H = 10 kOe

0.4

out of plane

0.0 0

50

100

150

200

250

0.6

-MoCl

5

4 C = 0.28 - 0.31 cm

5

)

)

out of plane

1

-1 B

in plane 1 in plane 2

0.3

100

150

-MoCl

0.2

250

T = 2 K

0.6

in plane 1 in plane 2 out of plane

0.4 T = 40 K in plane 1 in plane 2

0.2 0.1

0.0 0

5

10

15

20

0

T (K)

(e)

0.4

5

crystal 2

30

40

-MoCl

5

B

in plane 2

60

T = 2 K

0.6

in plane 1 in plane 2 out of plane

0.4

M (

out of plane

50

crystal 2

) -1

Mo

-1

in plane 1

B

20

H (kOe)

0.8

H = 100 Oe

0.3

10

(f)

-MoCl

0.5

)

out of plane

TC = 13.9 K

0.0

Mo

300

crystal 1

5

M (

out of plane

200

T (K)

Mo

-1

Mo B

M (

0.4

-1

in plane 2

0.5 H = 100 Oe

K mol

in plane 1

2

0.8

crystal 1

3

= 19 - 24 K

3

(d)

-MoCl

5

crystal 2

0 50

300

T (K)

(c)

M (

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.2

T = 40 K

0.2

0.1

in plane 1 in plane 2

TC = 14.3 K

out of plane

0.0

0.0 0

5

10

15

20

0

20

T (K)

40

60

80

100

120

140

H (kOe)

Figure 4: (a) Temperature dependence of the magnetization of an -MoCl5 crystal measured in a 10 kOe field showing paramagnetic behavior at high temperature and a ferromagnetic transition at low temperature. Data are shown for three different orthogonal axes as defined in the inset. (b) Curie Weiss fits to the high temperature data. (c,d) Temperature and field dependence of the magnetization of crystal 1. (e,f) Temperature and field dependence of the magnetization of crystal 2.

that the spin and orbital moments are antialigned. This can be expected for singly occupied t2g orbitals. Our first-principles calculations described below find this to be true, and also find the orbital contribution to be

highly anisotropic, leading to a large magnetic anisotropy, quantitatively described by the theory of Bruno. 27


7


Calculated Magnetic Properties

Next, we discuss the magnetic anisotropy energy (MAE) of α-MoCl5 . For the calculation of MAE we perform total energy calculations for the magnetic moments along the three principal axes. Then the MAE is defined as the difference between the hard direction (highest energy) and easy direction (lowest energy). In this case the hard direction is the c-axis and the easy direction is the b-axis; the moments prefer to lie along the direction defined by the Mo-Mo dimers, as illustrated in Figure 5. On a volumetric basis for α-MoCl5 , the total anisotropy is 2.19 MJ/m3 . For MoCl5 this yields an extremely large anisotropy field, the field required to polarize the magnetism along the hard direction, of 820 kOe. This can be compared to an anisotropy field of about 170 kOe for the rareearth permanent magnet material Nd2 Fe14 B. 28 To gain further insights into the magnetic interactions in α-MoCl5 , we calculated the isotropic Heisenberg exchange parameters (J) by mapping total energies of eleven different spin configurations — including ferromagnetic, antiferromagnetic and random collinear spin arrangements to a Heisenberg model, as described in the Supporting Information. The exchange couplings are identified in Figure 5. Note that there are two crystallographic inequivalent Mo sites in α-MoCl5 due to the nature of the packing of the Mo2 Cl10 units. J1 is the intra-dimer exchange coupling (Mo1-Mo1 and Mo2-Mo2), while the second shortest coupling J2 connects neighboring dimers along the c-axis (Mo1-Mo1 and Mo2-Mo2). J3 and J4 corresponds to the next shortest inter-dimer coupling between Mo1 atoms. The interdimer coupling between Mo1 and Mo2 sites is denoted by J5 . The distance between these Mo sites varies from 6.44 ˚ A to ˚ 6.67 A, and in our fitting we treat these as equivalent. The resulting sets of equations were then solved by a least-squares procedure. The calculated exchange parameters are listed in Table 3. All the calculated exchange constants are ferromagnetic, which explains the observed ferromagnetic ordering in α-MoCl5 . Interestingly, the intradimer interaction (J1 = 2.52 meV) is weaker than the shortest interdimer interaction (J2 = 4.05 meV). This observation suggests there are competing ferro-

To understand the magnetic properties of MoCl5 we have conducted first-principles calculations (calculation details are presented in the methods section and the Supporting Information) to investigate the three principal quantities of a ferromagnetic material − the magnetization, the Curie point, and the magnetic anisotropy. As the crystal structure and measured magnetic properties of α- and -MoCl5 are somewhat similar, we only study α-MoCl5 theoretically here. The calculated magnetic properties of αMoCl5 are listed in Table 2. As described in the Supporting Information, energies calculated for many magnetic configurations indicate the ground state to be ferromagnetic, in agreement with experiment. We find average spin moments of 0.99 µB for the Mo sites, which is in good agreement with the expectation for Mo5+ . We also find a substantial orbital moment of −0.13 µB at Mo site in the ground state. The magnetic moments prefer to lie along the axis of the Mo-Mo dimers, the b-axis in the C-centered cell shown in Figure 1a. The negative sign indicates that the spin and orbital moments are anti-parallel, resulting in a reduced total moment of 0.86 µB /Mo, which can be compared to the experimental moment at the highest measured field of near 0.71 µB /Mo. In addition, as shown in Table 2 orbital moments exhibit notable anisotropy. Table 2: The calculated spin (µspin Mo ), orbital orb (µMo ), total (mtot ) magnetic moments, and magnetocrystalline anisotropy energy for αMoCl5 . The anisotropy of orbital moments (∆LM o ) calculated as difference between average orbital moment along easy and hard axis is also shown. The presented spin and orbital moments are averaged over all Mo sites. Compound µspin Mo (µB ) µorb Mo (µB ) mtot (µB /f.u.) MAE (MJ/m3 ) ∆LM o (µB )

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MoCl5 0.99 −0.13 0.86 2.19 − 0.06


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Table 3: Exchange interactions (J) for αMoCl5 . The corresponding neighbor distances and multiplicities in the relaxed cell are also listed. J (meV/Mo atom)

Multiplicity

J1 = 2.52

3

3.79

J2 = 4.05

6

5.70

J3 = 3.17

2

5.83

J4 = 0.72

2

5.97

J5 = 0.53

16

6.44 - 6.67

J3 J5

Distance (˚ A)

J1

J2

J4

Mo2

Mo1

a b

c

Figure 5: The ferromagnetic ground state of α-MoCl5 identified by first-principles calculations with red arrows denoting magnetic moments and the exchange interactions described in the text labeled.

magnetic and antiferromagnetic intradimer exchanges that result in a relatively weak net interaction. For edge sharing geometries, there are direct exchange interactions that are usually antiferromagnetic and superexchange interactions that can be ferromagnetic or antiferromagnetic, depending on which oxygen of the p orbitals are involved. 29 The J3 to J5 exchange interactions decrease monotonically with distance. Despite its smaller value, due to a higher coordination number J5 plays an important role in determining the ordering point of MoCl5 . Based on the calculated exchange parameters, classical Monte Carlo simulations were performed to estimate the ordering temperature. For α-MoCl5 we obtained a Curie point of about 36 K which is in reasonable agreement with our measured value of 22.3 K. To further examine the origin of MAE in MoCl5 , we calculated MAE for a single isolated Mo2 Cl10 dimer. We find a MAE of 4.75 meV, which agrees well with the MAE of 4.1 meV for bulk material on a per dimer basis. Also the calculated spin moment (0.98 µB ) and orbital moment (-0.10 µB ) of Mo atoms in an isolated Mo2 Cl10 dimer is comparable with that in bulk MoCl5 . Therefore the magnetic properties of MoCl5 can be attributed to single Mo2 Cl10 dimer unit, and the compound can be effectively described as a molecular magnet. Because the spin-orbit coupling strength that dictates magnetocrystalline anisotropy increases strongly with atomic number, we also examined the 5d analogue WCl5 . This com-

pound is reported to adopt the structure of α-MoCl5 , 30 but no reports of magnetic ordering in WCl5 were found in the literature. A full list of our theoretical results for WCl5 are included in the Supporting Information. Our calculations indicate a ferromagnetic ground state, with a total moment of 0.69 µB /W, which is smaller than MoCl5 . This is due to the fact that W sites carry a larger orbital moment (−0.25 µB ), where the negative sign again indicates antialignment with the spin moment. Notably, the large spin orbit coupling of W atoms gives rise to a large MAE (20 meV per dimer), which is about 5 times greater than the MAE for MoCl5 (4.1 meV per dimer). In addition, we find the ferromagnetic state of WCl5 to have slightly extended exchange interactions compared to α-MoCl5 , resulting in a higher calculated Curie point of about 48 K. Inspired by these theoretical findings we synthesized WCl5 . We briefly summarize our initial experimental results here, with details and data in the Supporting Information. Powder x-ray diffraction indicated that the majority of the product had the α-MoCl5 structure (C2/m). After cooling to low temperature for


9


magnetization measurements the crystals were observed to have been pulverized into fine powder, suggesting a violent first order structural transition below room temperature. Subsequently we observed by diffraction a transition near 150 K to a yet unknown structure. As a result, the magnetic ground state of α-MoCl5 type WCl5 cannot be accessed for comparison with the calculations or with α-MoCl5 . Magnetometry suggests the unknown low temperature structure of WCl5 is in fact antiferromagnetic. However, the C2/m ferromagnetic structure will likely persist for Mo-rich compositions of Mo1−x Wx Cl5 alloys.

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can be realized within the non-magnetic matrix of isostructural NbCl5 . As noted in the Introduction, there are at least nine different metal cations known to form similar dimerized structures with the halogens Cl, Br, and I. We therefore expect these findings will encourage future exploration of magnetic properties of MoCl5 , WCl5 , and the related compounds.

Experimental and Computational Methods MoCl5 is extremely air sensitive and must be kept under vacuum or inert gas. Commercial powder was obtained from Alfa Aesar with stated purity of 99.6% (metals basis). This material was studied both as-received, and after recrystallization. Recrystallizations were performed in silica tubes (16 mm inner diameter, 1.5 mm wall thickness) flame sealed under vacuum. The as-received powder was opened and loaded into the tubes in a glovebox. The tubes were placed horizontally on the floor of a small box furnace, heated to the desired temperature measured by thermocouples attached to the silica tubes and left for approximately an hour, and then cooled to room temperature by turning off the furnace power. MoCl5 is reported to melt at 194◦ C and boil at 268◦ C. 31 The largest crystals were obtained with a maximum temperature of 250−265◦ C, using 400−800 mg of MoCl5 in tubes approximately 15 cm long (30 cm3 in volume). Crystals formed as platelike rectangular prisms with dimensions up to several millimeters. WCl5 was also prepared as a part of this study, as described in the Supporting Information. Single crystal x-ray diffraction measurements were performed by covering crystals in Paratone oil before removal from the glovebox and then mounting them on a Bruker APEX diffractometer (Mo Kα radiation). Full hemispheres of data were collected and reduced using SAINTPlus, with empirical absorption corrections applied using SADABS and space group identification and further data preparation carried out using XPREP. The structures were solved using Sir92 and refined using ShelXL within WinGX.

Summary and Conclusions With crystallographic and magnetic measurements and first-principles calculations we have highlighted several novel and unusual aspects of structure and magnetism in MoCl5 , a system comprising molecular transition metal dimers. In the α-polymorph we confirm ferromagnetic order below about 23 K, and report a new polymorph, -MoCl5 , that is ferromagnetic below 14 K. Most compellingly, first-principles calculations predict strong magnetic anisotropy in αMoCl5 arising from spin-orbit coupling in the 4d transition metal Mo. Corresponding large anisotropy fields were confirmed experimentally in both polymorphs. The experimental and theoretical results are consistent with spin-1/2 with antialigned orbital moments on Mo. The calculations predict similar magnetic behavior in single Mo2 Cl10 molecules, pointing to the true molecular nature of the magnetism in these materials. Even larger magnetic anisotropy is predicted for WCl5 , with much stronger spin-orbit coupling. Experimental evidence for a first order crystallographic phase transition in the tungsten analogue motivates the study of Mo1−x Wx Cl5 alloys for hard ferromagnetic molecular structures with enhanced Curie temperatures and molecular magnets with enhanced anisotropy. We suggest here that a path to further study molecular magnetism in these materials may be found in Nb1−x (Mo/W)x Cl5 alloys, if well separated (Mo/W)2 Cl10 molecules


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Powder x-ray diffraction data from the as received powder was collected using a PANalytical X’Pert Pro MPD with a dome-style air sensitive sample holder made by Anton Paar. Magnetization measurements were performed on loose powders and on powders fixed so that the grains could not rotate in the applied field. Samples were prepared inside a helium filled glove box. The loose powder samples were placed inside gelcaps sealed with Apeiezon Ngrease. The fixed powders were prepared by mixing with epoxy (Hardman Double/Bubble Extra Fast Set). Single crystals were prepared for magnetization measurements by coating them in epoxy and placing them on weighing paper to cure, and then trimming excess epoxy away. Density functional theory calculations employed the generalized gradient approximation 32 of Perdew, Burke, and Ernzerhof. These calculations were performed within the all-electron linearized augmented planewave (LAPW) method as implemented in WIEN2K code 33 at the experimental lattice parameters. The atomic positions were relaxed until the residual forces on all the atoms were less than 2 mRyd/Bohr. For structural relaxation 500 k-points were used in the full Brillouin zone. Sphere radii of 2.15 Bohr for Mo, 2.17 Bohr for W, 1.94 Bohr for Cl in MoCl5 (1.87 Bohr for Cl in WCl5 ) were used. For good basis-set convergence, a RKmax: product of plane-wave expansion wave vector and the smallest muffintin radius value of 7.0 is used. For the calculation of magnetic-anisotropy energy (MAE) the total energy of the system was calculated including spin-orbit coupling and the magnetization direction was considered along various crystallographic directions. The convergence of MAE with respect to k-points was carefully checked, and the MAE results presented here correspond to 1000 k-points. To understand the observed ferromagnetic behavior and Curie point of MoCl5 , the Heisenberg exchange parameters Jij were calculated. For this purpose first, the total energy of eleven different collinear spin configurations were computed. These calculations were performed within the VASP code. 34,35 The exchange-

correlation effects were included by the PerdewBurke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA). 32 Twelve (4p 6 5s 1 4d 5 ) and seven (3s 2 3p 5 ) valence electron were used for Mo and Cl in the PAW potential. The computed energies were mapped onto a Heisenberg Hamiltonian and the resulting sets of equations were then solved by least-squares fit procedure. The calculated exchange parameters were used in the classical Monte Carlo simulations using the METROPOLIS algorithm for estimating Curie temperature as implemented in the UppASD code. 36 To eliminate the finite size effects, supercell sizes of 10×10×10, and 15×15×15 with periodic boundary conditions were used. Acknowledgement Research supported by the U. S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. This research used resources of the Compute and Data Environment for Science (CADES) at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22725.

Supporting Information Available Atomic coordinates and anisotropic displacement parameters for α-MoCl5 and -MoCl5 . Powder diffraction from as received MoCl5 and temperature dependent lattice parameters. χT plots for MoCl5 . Further details of theoretical calculations, including results for WCl5 . Preliminary experimental results for WCl5 .

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2 Dimers with Strong Anisotropy in MoCl5

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