Ferromagnetic van der Waals Crystal VI3 - Journal of the American

Subscriber access provided by UNIV OF TEXAS DALLAS

Article 3

Ferromagnetic van der Waals crystal VI

Shangjie Tian, Jian-Feng Zhang, Chenghe Li, Tianping Ying, Shiyan Li, Xiao Zhang, Kai Liu, and Hechang LEI J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 11 Mar 2019 Downloaded from http://pubs.acs.org on March 11, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28

(a)

(c)

(b)

(d)

(006)

(005)

(004)

(003)

(001)

(002)

(e)

Intensity (a.u.)

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

Journal of the American Chemical Society

10 20 30 40 50 60 70 80 90 ACS Paragon Plus Environment

2

(deg.)

3.0

H ab Hc

Sample 1

T T

s

= 79 K

c

= 50 K

30 40 50 60 70 80 90

T

(K)

0.0 100

150

T

200

250

(K)

Sample 1

0

(d)

H

=5T

B

/V) (

8

100

150

T

200

250

300

H

=0.1T,

H ab //

FC

4

' FC

2

(f)

'

Sample 2

0 40

T

3

T

70

=2K

75

60 (K)

80

T

80

100 ACS Paragon Plus Environment

//

85

90

95 100

(K)

H ab Hc // //

1 0 -1

Sample 1

0

0

ZFC

20

65

(K)

6

0

2 60

2

3

4

5

(T)

T

6

4

H

1

Sample 2

H ab H

=28K

//

0

=1mT

ac

1Hz

24

2

26

28

T

30

32

0.1Hz

(K)

ac

50

//

4

-3 -5 -4 -3 -2 -1

(emu/mol-Oe)

( -

0

//

6

-2

//

0

(emu/mol-Oe)

M

//

0

)

H ab Hc

50

8

2

100

0 (e)

300

150

-1

(mol Oe/emu)

(c) 200

50

5T,

/dT

0

10

ac

0.5

//

0.1T,

d

1.0

x 50

Hc Hc H ab H ab

0.1T, 5T,

'

5T

Sample 1

12

( 10

B

//

0.5T

1.5

(

emu/mol-Oe)

0.1T

2.0

M

//

dM/dT

/V)

2.5

(b)

Page 2 of 28

14

-2

(a)

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


10Hz 100Hz

0 10

15

20

25

T

(K)

30

35

40

(b)

-2

120

0.3

K )

-1

0.0 0

p

/

0.1

-1

2

(K )

H

5T

80

(K)

0

=

-1

1T

T

0.20

0.15

0

55

60

(K)

65 1.5

H

1.2

=0T

0.9 0.10 0.6

mag

/

T

3T 5T

50

0.05

0.3

C

p

(J mol

0.5T

70

45

-1

0T

(J mol

C

(d)

H

80

-1

100

K )

T

60

40 40

-2

90

40

K )

(c)

20

3T

=0T

0 0

1T

45

60 70

0.0

0.00 75

T

80

85

90

30

ACS Paragon Plus Environment

(K)

K )

0

0.5T

(J mol

20

0T

C

C

p

40

50

=

mag

2

80 100

H

S

T

60

0

-1

40

(J mol

60

20

55

-1

(J mol

0.2

p

(J mol

-1

80

C T

K )

100

-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

60

-1

1(a)


K )

Page 3 of 28

35

40

45

T

(K)

50

55

60

65

2

Journal of the American Chemical Society (a)

(b)

Bulk

Monolayer

1 spin up spin dn

F

E-E (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Page 4 of 28

0

-1

ACS Paragon Plus Environment -2 M

K

A

L

H

A

M

K

(d) 0.3

(J/m )

(c)

(b)

0.2

B

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

E

(a)


2

Page 5 of 28

0.1

0.0 0

2

4

6


Interlayer separation

8

d (Å)

10

Journal of the American Chemical Society 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

Ferromagnetic van der Waals crystal VI3 Shangjie Tian,1,† Jian-Feng Zhang,1,† Chenghe Li,1 Tianping Ying,2 Shiyan Li,2,3 Xiao Zhang,4,∗ Kai Liu,1,∗ and Hechang Lei1,∗ 1

Department of Physics and Beijing Key Laboratory of Opto-electronic Functional

Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China 2

State Key Laboratory of Surface Physics, Department of Physics, and Laboratory of Advanced Materials, Fudan University, Shanghai 200438, China

3 4

Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China

State Key Laboratory of Information Photonics and Optical Communications & School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China E-mail: [email protected],[email protected],[email protected]

Abstract We report structural, physical properties and electronic structure of van der Waals (vdW) crystal VI3 . Detailed analysis reveals that VI3 exhibits a structural transition from monoclinic C2/m to rhombohedral R¯3 at Ts ∼ 79 K, similar to CrX3 (X = Cl, Br, I). Below Ts , a long-range ferromagnetic (FM) transition emerges at Tc ∼ 50 K. The local moment of V in VI3 is close to the high-spin state V3+ ion (S = 1). Theoretical calculation suggests that VI3 may be a Mott insulator with a band gap of about 0.90 eV. In addition, VI3 has a relative small interlayer binding energy and can be exfoliated easily down to few layers experimentally. Therefore, VI3 is a candidate of two-dimensional FM semiconductor. It also provides a novel platform to explore 2D magnetism and vdW heterostructures in S = 1 system.

1


Page 6 of 28

Page 7 of 28 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


Introduction Two-dimensional (2D) materials have induced great interest since the discovery of graphene. 1 They exhibit various exotic physical properties, such as enhanced direct-gap semiconductor in monolayer MoS2 , 2 Ising superconductivity in ion-gated MoS2 and atomic layer NbSe2 , 3,4 robust in-plane ferroelectricity in atomic-thick SnTe, 5 and so on. In theory, the long-range 2D magnetic order is strongly suppressed above zero temperature for isotropic Heisenberg model because the fluctuation is so strong that will destroy the spontaneous symmetry breaking (Merin-Wagner theorem). 6 But when magnetic anisotropy is included, the 2D ferromagnetism can be stabilized and it has been realized in monolayer Cr2 Ge2 Te6 and CrI3 just in recent. 7,8 These 2D ferromagnets provide unique opportunities for understanding, exploring and utilizing novel low-dimensional magnetism. Because of its thickness of one or few unit cells, it may be able to control the 2D magnetic properties by applying electric field, light or strain. Such magneto-electrical, magneto-optical, or spin-lattice coupling effects are usually difficult to realize in bulk crystals. For instance, recent studies show that the electrostatic doping can control the magnetism in atomically-thin CrI3 and Fe3-x GeTe2 flakes, leads to the dramatic enhancement of Tc from about 100 K to room temperature for the latter. 9,10 Moreover, the weak van der Waals (vdW) interlayer coupling allows to design heterostructures between these 2D magnets and other vdW materials without considering lattice mismatch. For example, in the vdW heterostructures formed by an ultrathin CrI3 and a monolayer WSe2 , the WSe2 photoluminescence intensity strongly depends on the relative alignment between photoexcited spins in WSe2 and the CrI3 magnetization. 11 Besides Cr2 Ge2 Te6 and CrI3 , CrSiTe3 and CrX3 (X = Cl and Br) vdW crystals are also easy to be exfoliated and predicted to be a 2D ferromagnetic (FM) semiconductors for monolayers. 12–14 Until now, however, such magnetic vdW materials are still scarce and they are mainly chromium compounds with high spin Cr3+ (S = 3/2). In recent, the 2D ferromagnetism has been predicted in VX3 (X = Cl and Br) with S = 1. 15 It is found that VX3 is cleavable and the calculated Curie temperature Tc is 80 and 98 K for VCl3 and VI3 2



monolayers, respectively, higher than those in CrX3 . In this work, we grow VI3 single crystals successfully and carry out a comprehensive study on their structure, physical properties and electronic structure. VI3 exhibits a structural transition from monoclinic to rhombohedral at Ts ∼ 79 K and then a long-range FM ordering appears at Tc ∼ 50 K. Moreover, VI3 should be a Mott insulator and can be exfoliated easily to few layers.

Experimental Single Crystal Growth. Single crystals of VI3 were grown by chemical vapor transport method. Vanadium powder (99.99%) and iodine flake (99.999%) in 1 : 3 molar ratio were put into a silica tube with the length of 200 mm and the inner diameter of 14 mm. The tube was evacuated down to 10−2 Pa and sealed under vacuum. The tubes were placed in two-zone horizontal tube furnace and the source and growth zones were raised to 923 K and 823 K for 3 days, and then held there for 7 days. The shiny black plate-like crystals with lateral dimensions up to several millimeters can be obtained. Because the VI3 is hygroscopic, the samples were stored in glovebox in order to avoid degradation of crystals.

X-ray Crystallography. Single crystal X-ray diffraction (XRD) patterns at 40 K, 60 K and 100 K were collected using a Bruker D8 VENTURE PHOTO II diffractometer with multilayer mirror monochromatized Mo Kα (λ = 0.71073 ˚ A) radiation. Unit cell refinement and data merging were done with the SAINT program, and an absorption correction was applied using Multi-Scans. At T = 100 K, an inspection of the systematic absences immediately showed the structure to be C centered. In XPrep, the suggested possible space group is C2, C2/m and Cm with the value of combined figure of merit (CFOM) 11.86, 2.01 and 14.71, respectively. The mean value 3


Page 8 of 28

Page 9 of 28 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


of | E 2 − 1 | (1.067) is more close to the value for a centrosymmetric space group (0.968) than that for a non-centrosymmetric one (0.736), suggesting the centrosymmetric structure of VI3 . Finally the space group C2/m with the smallest CFOM value is selected. When T = 40 K, an inspection of the systematic absences immediately showed the structure to be R lattice. The possible space group is R¯3, R3, R3m, R32 and R¯3m with the vaule of CFOM 7.68, 25.36, 47.09, 47.09 and 31.27, respectively. The mean value of | E 2 − 1 | (1.213) also suggested that the space group is centrosymmetric, thus the space group R¯3 with the smallest CFOM value is selected. A structural solutions with the C2/m and R¯3 space group were obtained for VI3 by intrinsic phasing methods using the program APEX3, 16 and the final refinement was completed with the SHELXL suite of programs. 17

Measurements of Physical Properties. The magnetic properties were measured using a Quantum Design magnetic property measurement system (MPMS-3). A piece of VI3 single crystal was mounted in the plastic straw with different orientations in order to measure the anisotropy of magnetization. Heat capacity measurements were performed using a Quantum Design physical property measurement system (PPMS-14T). Exfoliation of bulk VI3 was achieved using mechanical exfoliation with scotch tape and transferred onto a 90 nm SiO2 covered Si substrate. Atomic force microscopy was carried out using a Bruker Edge Dimension atomic force microscope.

Theoretical Calculation. The fully spin-polarized electronic structure calculations were carried out with the projector augmented wave (PAW) method 18,19 as implemented in the VASP package. 20–23 The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) type 24 was chosen for the exchange-correlation functional. The kinetic energy cutoff of the plane-wave basis was set to be 400 eV. The low-temperature (40 K) R¯3 crystal structure with the experimental lattice constants (Table 1) was adopted. Four typical intralayer magnetic configurations, 15 4



i.e., the ferromagnetic (FM) state, the checkerboard antiferromagnetic (AFM) Néel state, the AFM stripy state, and the AFM zigzag state, were investigated. These magnetic config√ urations were studied with a 3 × 1 × 1 orthorhombic supercell, which contains four V atoms in each layer, and a 4 × 8 × 4 k-point mesh. The Fermi level was broadened by the Gaussian smearing method with a width of 0.05 eV. The vdW interactions between the VI3 layers were considered by adopting the optB86b-vdW functional. 26 The internal atomic positions were allowed to relax until all forces on atoms were smaller than 0.01 eV/˚ A. The binding energy EB was calculated by increasing the interlayer distance d of a R¯3 conventional cell. 27 For monolayer VI3 , atomic positions were relaxed with the in-plane lattice constants fixed at bulk values. Once the equilibrium structures of bulk and monolayer VI3 were obtained, the electronic correlation effect among V 3d electrons was incorporated to study the band structure. The GGA + U formalism of Dudarev et al. 25 was used with an effective Hubbard U of 3.68 eV, which was determined for VI3 by a linear response approach. 15

Results and Discussion As shown in Table 1 and 2, the crystal structure of VI3 at high temperature is not rhombohedral BiI3 type reported in previous study on the VI3 polycrystal, 28 but monoclinic AlCl3 type (space group C2/m, No. 12), similar to high-temperature structure of CrX3 . 14,29,30 For this structure (Fig. 1(a)), the V3+ cations are surrounded by six I− anions with an octahedral coordination. These edge-shared distorted octahedra form honeycomb layers in the ab plane. The slabs of VI3 are stacked along the c axis and there are vdW gaps between them. On the other hand, when decreasing temperature, there is a structural transition from monoclinic phase to rhombohedral one with space group R¯3 (Tables 1 and 2, Fig. 1(b)), same as CrX3 (X = Cl, Br, I). 14,29,30 The key difference between these two structures is the stacking patterns of V-I slabs along the c axis. For the monoclinic structure, the V-I slab shifts layer-by-layer along the a axis. Because the β is about 108.558◦ and the a and c axial

5


Page 10 of 28

Page 11 of 28

(a)

(c)

(b)

(d)

(006)

(005)

(004)

(003)

(001)

(002)

(e)

Intensity (a.u.)

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


10 20 30 40 50 60 70 80 90 2

(deg.)

Figure 1: (a) and (b) High- and low-temperature crystal structures of VI3 , respectively. (c) and (d) Stacking pattern of the V layers in the high- and low-temperature structures of VI3 , respectively. The labels of A, B and C denote the different layers of V atoms. (e) XRD pattern of a VI3 single crystal. Inset: photo of typical VI3 single crystals on a 1 mm grid paper.

6



Page 12 of 28

Table 1: Crystallographic Data for VI3 at Different Temperatures. T (K) space group crystal system a (˚ A) b (˚ A) c (˚ A) ˚ V (A3 ) Z dimens min/mid/max(mm3 ) calcd density (g cm−3 ) abs coeff (mm−1 ) h k l reflns collected/unique/R(int) data/params/restraints GOF on F 2 R indices (all data) (R1/wR2)a

40 60 100 R¯3 R¯3 C2/m trigonal trigonal monoclinic 6.8351(7) 6.8325(6) 6.8416(3) 6.8351(7) 6.8325(6) 11.8387(6) 19.696(2) 19.6776(2) 6.9502(4) 796.90(19) 795.54(16) 533.66(36) 6 6 4 0.03/0.28/0.37 0.03/0.28/0.37 0.03/0.28/0.37 5.399(1) 5.408(1) 5.375(4) 19.117 19.149 19.031 -9 ≤ h ≤ 9 -8 ≤ h ≤ 8 -9 ≤ h ≤ 9 -8 ≤ k ≤ 7 -9 ≤ k ≤ 9 -15 ≤ k ≤ 15 -26 ≤ l ≤ 26 -26 x≤ l ≤ 26 -9 ≤ l ≤ 9 3799/442/0.0409 4793/442/0.0471 4901/681/0.0417 442/15/0 442/15/0 681/22/0 1.228 1.287 1.025 0.0636/0.1691 0.0502/0.1549 0.0724/0.1828

Table 2: Atomic Positions and Equivalent Isotropic Displacement Parameters Ueq for VI3 at Different Temperatures. atom 40 K V I 60 K V I 100 K V I1 I2

x/a

y/b

6c 18f

1/3 0.00134(7)

2/3 0.6509(2)

0.50035(11) 0.0056(7) 0.42086(3) 0.0074(5)

6c 18f

1/3 0.00143(8)

2/3 0.6507(2)

0.50035(11) 0.0052(7) 0.42086(3) 0.0069(5)

4g 4i 8j

0 0.16658(18) 0 0.0136(7) 0.2255(2) 0 0.23895(15) 0.0167(5) 0.25103(10) 0.32498(8) 0.23547(13) 0.0163(5)

7

z/c

Ueq (A2 )

site


Page 13 of 28 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


lattice parameters are 6.8416 and 6.9502 ˚ A, the a/[c cos(180◦ − β)] is 3.09, i.e., the stacking is nearly the ABC fashion (Fig. 1(c)). For the rhombohedral structure (Fig. 1(b)), the stacking of V-I slabs along the c axis is exactly the ABC fashion, i.e., each V-I layer shifts the distance of V-V bond (∼ 3.95 ˚ A) along one edge of V honeycomb (the [¯110] direction) (Fig. 1(d)). This shift direction is distinctly different from that perpendicular to one edge of V honeycomb in the monoclinic structure. In contrast to the drastic change of stacking order, the intralayer structure is almost intact, except a slight decreased distortion of V honeycomb and V-I octahedron in rhombohedral structure. The bond lengths of V-I are spread between 2.7122 and 2.7195 ˚ A in monoclinic structure and narrow down to 2.7173 and 2.7179 ˚ A for the low-temperature phase (Table 3). Moreover, in high-temperature structure, the V honeycomb is distorted with two bond lengths of V-V (3.9442 and 3.9501 ˚ A). It becomes undistorted in low-temperature structure and the single bond length of V-V is about 3.9463 ˚ A. In the XRD pattern of a VI3 single crystal (Fig. 1(e)), only the (00l) reflections of monoclinic structure can be observed, indicating that the surface of crystal is parallel to the ab plane. The single crystals of VI3 show plate-like shapes (inset of Fig. 1(e)), consistent with the single crystal XRD pattern and the layered structure of VI3 . The actual atomic ratio of V : I determined from the EDX analysis is 1.00 : 2.90(1) when setting the content of V as 1, in agreement with the nominal formula of VI3 . Table 3: Selected Bond Lengths (in ˚ A) for VI3 at Different Temperatures. 40 K V-I V-I 60 K V-I V-I 100 K V-I2 V-I2 V-I1

3× 3×

2.7143(14) 2.7179(14)

3× 3×

2.7118(15) 2.7161(14)

2× 2× 2×

2.7122(17) 2.7138(8) 2.7195(18)

Figure 2(a) shows the temperature dependence of magnetic moment M (T ) of the VI3 8



3.0

H ab Hc

Sample 1

T T

s

= 79 K

c

= 50 K

30 40 50 60 70 80 90

T

(K)

0.0 100

150

T

200

250

(K)

Sample 1

0

(d)

H

=5T

/V) B

(

0

8

100

150

T

200

250

H

=0.1T,

H ab

(f)

//

ZFC

FC

4

' FC

2

'

Sample 2

0 40

T

3

T

70

=2K

75

80

T

60

80

85

100

90

95 100

(K)

H ab Hc // //

1 0 -1

Sample 1

0

0

6

20

65

(K)

0

0

2 60

-3 -5 -4 -3 -2 -1

300

(emu/mol-Oe)

50

4

-2

//

//

//

6

2

3

4

5

(T)

T

6

4

H

1

Sample 2

H ab H

=28K

//

0

=1mT

ac

1Hz

24

2

26

28

T

30

32

0.1Hz

(K)

ac

( -

M

//

0

)

H ab Hc

50

8

2

100

0 (e)

300

150

-1

(mol Oe/emu)

(c) 200

50

5T,

/dT

0

//

//

0.1T,

10

ac

0.5

Hc Hc H ab H ab

0.1T, 5T,

'

1.0

x 50

Sample 1

12

d

5T

14

-2

B

(

//

0.5T

1.5

M

emu/mol-Oe)

0.1T

2.0

dM/dT

/V)

2.5

(b)

//

( 10

(a)

(emu/mol-Oe)

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

Page 14 of 28

10Hz 100Hz

0 10

15

(K)

20

25

T

30

35

40

(K)

Figure 2: (a) Temperature dependence of magnetic moment M (T ) of VI3 single crystal (sample 1) with zero-field-cooling (ZFC) mode at µ0 H = 0.1, 0.5, and 5 T for Hkab and Hkc. Inset: dM (T )/dT vs. T at µ0 H = 0.1 T for Hkc. (b) enlarged magnetic susceptibility χ(T ) of sample 1 between 60 - 100 K at µ0 H = 0.1 and 5 T for both field directions. (c) Inverse magnetic susceptibility of sample 1 (points) and Curie-Weiss fits (solid lines) as a function of temperature at µ0 H = 5 T for Hkab and Hkc. Fitted temperature-independent terms χ0 are subtracted. (d) Isothermal M (H) curves of sample 1 at 2 K for both field directions. (e) Temperature dependence of χZFC (T ) (ZFC mode) and χFC (T ) (field-cooling 0 (FC) mode) along with the calculated χFC (T ) for sample 2 when µ0 H = 0.1 T and Hkab. 0 (f) ac magnetic susceptibility χac (T ) of sample 2 as a function of temperatures at various 0 frequencies when µ0 Hac = 1 mT and Hkab. Inset: temperature dependence of dχac (T )/dT .

9


Page 15 of 28 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


single crystal (sample 1) at various fields in the ab plane and along the c axis with zero-field cooling (ZFC) mode. It can be clearly seen that VI3 exhibits a ferromagnetic transition at low temperature for both field directions. The Curie temperature Tc determined from the peak of dM /dT at µ0 H = 0.1 T for Hkc is 50 K (inset of Fig. 2(a)), consistent with previous result. 31 Another important feature is a kink appearing on the χc (T ) curve at Ts ∼ 80 K (> Tc ) and it can be seen more clearly from the small peak of dM /dT at 79 K (inset of Fig. 2(a)). This kink does not shift with the variation of field (Fig. 2(b)). This temperature is in the temperature region of structural transition, thus the anomaly of χc (T ) curve should originate from the change of crystal structure. In contrast, the χab (T ) curves do not show this behavior. It suggests that there is a more stronger coupling of the crystal structure to the magnetism along the stacking direction in VI3 . Moreover, from the structure data shown in Table 1, there is also remarkable change of the interlay spacing from 6.5888 ˚ A[= c sin(180◦ − β)] at 100 K to 6.5592 ˚ A[= c/3] at 60 K. There is about 0.45 % change when compared to the variation of 0.13 % for the intralayer a-axial lattice parameters. Such huge changes of interlayer spacing could not be solely explained by the effect of conventional thermal contraction and the structural transition should take significant effect on it. It is worthy to mention that such subtle change accompanying by the sudden drop interlayer distance when crossing structural phase transition has also been observed in CrX3 , 14,30 indicating the spin-lattice coupling might be a common feature in layered magnetic halide compounds. For both field directions, the M (T ) curves between 100 K and 300 K can be fitted very well using the modified Curie-Weiss law χ(T ) = χ0 + C/(T − θ), where χ0 is a temperatureindependent term including core diamagnetism, van Vleck paramagnetism as well as background signal of sample holder, C is the Curie constant and θ is the Weiss temperature (Fig. 2(c)). The fitted C and θ are 1.684(4) [1.281(8)] emu mol−1 Oe−1 K and 40.5(1) [58.1(3)] K for Hkab [Hkc]. The fitted positive values of θ for both field direction are close to the Tc , confirming the ferromagnetic interaction in VI3 . The obtained values of C correspond to an

10



effective moment of µeff = 3.67(1) and 3.20(2) µB /V for Hkab and Hkc, respectively. These values are somewhat larger than that of spin-only V3+ ions (2.83 µB /V). This suggests that the orbital moment of V3+ ions in VI3 might have some contribution on effective moment. Fig. 2(d) shows the magnetization loops of sample 1 for both field directions at 2 K. The hysteresis loops for both field directions support the FM behavior when T < Tc . There is an obvious magnetic anisotropy at low field region. The initial magnetization curve becomes more quickly saturated for Hkc than Hkab, suggesting the easy axis is the c axis. The coercive field Hc for Hkc is much larger than that for Hkab and it also indicates that the easy axis is along the c axis. For Hkab, the M at 5 T is about 2.02 µB /V, which is close to the expected saturated moment of gS = 2 µB /V for high-spin state V3+ ion. But the M (5T) for Hkc is about 2.47 µB /V, slightly larger than the expected value. The anisotropy of saturation magnetization is still unclear at present. It may be due to the anisotropy g factor with unquenched orbital angular moment. Future experiments such as neutron scattering or electron spin resonance would help to clarify this difference. Moreover, there are sudden jumps at µ0 H ∼ ± 1 T when the field is along the c axis. It can be ascribed to the magnetic domain creeping behavior, i.e., the magnetic domain walls jump from one pinning site to another. This phenomenon has been observed in other ferromagnetic materials, such as yttrium-iron garnet film. 32 It has to be noted that when T < Tc there is a kink locating at about 30 K, and then a decrease of M (T ) at low temperature, which become invisible at high field (Fig. 2(a)). In order to further illustrate this behavior, the χ(T ) curves of sample 2 with ZFC and field-cooling (FC) modes at µ0 H = 0.1 T for Hkab are measured (Fig. 2e). It can be clearly seen that there is a bifurcation behavior between ZFC and FC χ(T ) curves when T < 30 K approximately. At first glance, this behavior might be due to the spin glass state appearing at low temperature and low field region. But the hump position of ac susceptibility χac (T ) for Hkab at T = 28 K (Fig. 2(f)) does not depend on the frequency of the ac field (inset of Fig. 2(f)), in contrast to the typical behavior for spin glass state. Actually, beside the spin glass state, the long-range FM state with magnetic anisotropy (hard ferromagnet and

11


Page 16 of 28

Page 17 of 28 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


sizable coercive field) and/or multi-domain structure can also lead to this kind of irreversible behavior, 33,34 which has also been observed in other long-range FM single crystals, such as U2 RhSi3 . 35 According to the approach proposed by Joy et al., 33 the maximum of the ZFC χ(T ) curve and the irreversibility are related to the variation of the coercive field, which 0

is a measure of the magnetic anisotropy. It has χFC = MFC /(H + Hc ) ≈ MZFC /H. The 0

calculated χFC at various temperatures at which M − H loops are measured (Fig. S1) is 0

shown in Fig. 2(e). The χFC (T ) curve is very similar to that of χZFC (T ) and once the Hc becomes very small at T > 30 K (Fig. S1), the ZFC and FC χ(T ) curves will be overlapped. This analysis suggests that the irreversibility and the drop of ZFC χ(T ) at low temperature can be well ascribed to the significant magnetocrystalline anisotropy of VI3 . Figure 3 shows the temperature dependence of heat capacity Cp (T ) for VI3 single crystals measured between T = 2.2 and 100 K at zero field. Clearly, there are two anomalies shown at T ∼ 50 K and 79 K, in agreement with those temperatures in magnetization curve for Hkc. When increasing magnetic field, the λ-type peak at 49.5 K becomes broaden towards higher temperatures (Fig. 3(b)). This is the typical behavior of FM transition under field, and similar behaviors have been observed in CrX3 . 14,30 Thus, it confirms the bulk nature of the long-range FM order below Tc observed in the magnetization measurement. In contrast, the sharp peak at higher temperature (∼ 79 K) is insensitive to external field and there is almost no shift when the field is up to 5 T (Fig. 3(c)). It undoubtedly indicates that this anomaly of heat capacity is corresponding to the structural transition, consistent with the structural characterization. After subtraction of the phonon contribution Cph (T ) fitted using a polynomial from the total heat capacity (red line in the main panel of Fig. 3(a)), we obtain magnetic specific heat Cmag (T ) and calculate the magnetic entropy Smag (T ) using RT the formula Smag (T ) = 0 Cmag (T )/T dT (Fig. 3(d)). The derived Smag is about 1.37 J mol1 K−1 at 65 K, which is much smaller than the expected value (∼ 15% Rln(2S + 1) = Rln 3) for V3+ ions with high spin state (S = 1). One of possibilities leading to this difference is the overestimation of Cph (T ), reducing the Smag (T ). Another possibility is that there is

12


60

(b)

-2

120

0.3

Page 18 of 28

0.2 -1

(K )

0

H

3T 5T

80

0

(d)

H

-1

=

(J mol

0.5T 1T

5T

50

T

0.20

0.15

0

55

60

(K)

65 1.5

H

1.2

=0T

0.9 0.10 0.6 0.05

0.3

C

mag

/

T

3T

70

45

-1

0T

(J mol

-1

100

(K)

80

p

40 40

-2

T

60

1T

=0T

K )

90

40

K )

(c)

20

0T 0.5T

0 0

=

C

C

20

H

45

p

40

0

50

-1

80 100

K )

60 2

-1

T

2

(J mol

40

mag

20

S

0.0 0

(J mol

60

55

-1

p

/

0.1

p

(J mol

-1

80

C T

-1

K )

100

K )

(J mol

-1

(a)

C

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

K )


60 70

0.0

0.00 75

T

80

85

90

30

35

(K)

40

45

T

50

55

60

65

(K)

Figure 3: (a) Temperature dependence of heat capacity Cp (T ) for VI3 single crystal at zero field. The red solid curve represents the lattice contribution, fitted by a polynomial. Inset: enlarged part at low temperature region. The red solid line represents the fit using the formula Cp (T )/T = βT 2 . (b) The Cp (T ) as a function of T near magnetic transition region at various fields. (c) Enlarged part of Cp (T ) near structural transition region at different fields. (d) Temperature dependence of magnetic specific heat Cmag (T ) after subtracting the lattice contribution fitted by a polynomial. The right axis and its associated solid curve denote the magnetic entropy Smag (T ) associated with the FM transition.

13


Page 19 of 28

2 (a)

(b)

Bulk

Monolayer

1 spin up spin dn

F

E-E (eV)

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

-1

-2 M

K

A

L

H

A

M

K

Figure 4: Calculated electronic band structures of (a) bulk and (b) monolayer VI3 in the ferromagnetic state along the high-symmetry paths of corresponding Brillouin zones. substantial fraction of magnetic entropy released above Tc because of possible short-range or 2D magnetic correlations before long-range order forms. But it has to be mentioned that the Weiss temperature θ determined from the Curie-Weiss law is close to Tc , implying the magnetic correlations/fluctuation should not so strong when T > Tc . Similar behaviors are also observed in CrX3 ., 14,30 suggesting certain universal features in these vdW magnetic materials. Further theoretical and experimental studies are needed in order to understand these phenomena and the relationship between magnetism and low-dimensional structure. At the low temperature, the Cp (T ) curve can be fitted solely by a cubic term βT 3 (inset of Fig. 3(a)) because of the insulating feature of VI3 (the resistance is about 1 MΩ measured using ohmmeter at room temperature). The fitted value of β = 2.63(3) mJ mol−1 K−4 , the Debye temperature is estimated to be ΘD = 144(1) K using the formula ΘD = (12π 4 N R/5β)1/3 . This is slightly larger than that of CrI3 (ΘD = 134 K), 30 possibly ascribed to the smaller atomic mass of V than Cr. To further investigate the magnetic and electronic properties of bulk VI3 in the R¯3 structure at low temperature, we have carried out the spin-polarized first-principles calculations with the experimental lattice constants (Table 1) and the relaxed internal atomic positions. By comparing the relative energies among four typical intralayer magnetic configurations (the FM order, the checkerboard AFM Néel order, the AFM stripy order, and the AFM 14



zigzag order), 15 we find that the magnetic ground state of bulk VI3 is the FM order, being consistent with above measurement. Moreover, our calculations demonstrate that bulk VI3 prefers a weak FM interlayer coupling. As to the electronic structure, without including the Hubbard U , our calculation predicts that VI3 should be metallic, different from the insulating behavior observed in experiment. When considering the effect of Hubbard U (3.68 eV), 15 the calculated band structure of bulk VI3 in the FM ground state shows a direct band gap of ∼ 0.90 eV (Fig. 4(a)). This calculation result suggests that bulk VI3 is a FM Mott insulator. Further calculations on monolayer VI3 indicate that VI3 is still magnetic down to monolayer, similar to Cr2 Ge2 Te6 and CrX3 . 7,8 The band structure of monolayer VI3 in FM state shows a direct band gap of ∼ 0.97 eV (Fig. 4(b)), which is slightly larger than the bulk value. Figure 5(a) displays an atomic force microscopy image of a cleaved thin flake of a VI3 crystal and there are several step edges observed on the flake. As shown in Fig. 5(b), the total thickness of this flake is about tens of nanometers and the area along the ab plane is rather large (∼ 40×40 µm2 ). The hight profile across an edge measured along the white arrow in Fig. 5(b) consists of three steps with heights of 20, 10 and 7 nm (Fig. 5(c)). The minimal step height (∼ 7 nm) is about 10 unit cells of monoclinic structure of VI3 (h = c sin(180◦ − β) = 6.5888 ˚ A). It suggests that VI3 is easy to be exfoliated down to few layers. The binding energy EB was calculated by increasing the interlayer distance d of V3 in a R¯3 conventional cell. 27 The calculated EB as a function of interlayer separation d is shown in Fig. 5(d). The EB increases quickly with increasing d and then converges to the saturation value 0.29 J/m2 (18 meV/˚ A2 ) when d is lager than 6 ˚ A. This value is in good agreement with previous studies on most vdW crystals (EB = 13 - 21 meV/˚ A2 ). 27 Thus it confirms the weak interlayer interaction in VI3 , i.e., its easy exfoliation.

15


Page 20 of 28

Page 21 of 28

(a)

(c)

(b)

(d)

0.2

B

2

(J/m )

0.3

E

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


0.1

0.0 0

2

4

6

8

10

Interlayer separation d (Å) Figure 5: (a) AFM image of a cleaved thin flake of VI3 crystal. (b) Height profile of whole flake. The different colors represent the various heights of surface. (c) Height profile across several step edges along the direction shown by the arrow in (b). (d) Calculated binding energy EB as a function of the interlayer separation d.

16



Page 22 of 28

Conclusion In summary, we synthesized VI3 single crystals successfully and studied the structural and physical properties of novel vdW magnetic compound VI3 in detail. The structure of VI3 at high temperature is monoclinic and changes to rhombohedral at Ts = 79 K. The long-range FM order appears at Tc = 50 K with the saturate moment close to 2 µB /V. It suggests that the V3+ ion in VI3 is at high-spin state with S = 1. Theoretical calculation implies that VI3 might be a FM Mott insulator. Moreover, it is easy to be cleaved down to few layers, thus it is a promising candidate of 2D ferromagnet with S = 1. Exploration of magnetic vdW materials with different magnetic moments will not only expand the family of 2D magnets but also deepen the understanding of the relationship between dimensionality and degrees of freedom for spin space.

Associated Content Supporting Information M − H loops at various temperatures for Hkab

Notes The authors declare no competing financial interest.

Acknowledgement This work is supported by the National Key R&D Program of China (Grants No. 2015CB921400, 2016YFA0300504 and 2017YFA0302903), the National Natural Science Foundation of China (Grants No. 11574394, 11774423, 11774424 and 11822412), the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (Grants

17


Page 23 of 28 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


No. 15XNLF07, 18XNLG14 and 19XNLG17). Computational resources were provided by the Physical Laboratory of High Performance Computing at Renmin University of China. †

These authors contributed equally to this work.

References (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A., Electric field effect in atomically thin carbon films. Science 2004, 306, 666-669. (2) Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F., Atomically Thin MoS2 : A New Direct-Gap Semiconductor. Physical Review Letters 2010, 105, 136805. (3) Lu, J. M.; Zheliuk, O.; Leermakers, I.; Yuan, N. F. Q.; Zeitler, U.; Law, K. T.; Ye, J. T.,Evidence for two-dimensional Ising superconductivity in gated MoS2 . Science 2015, 350, 1353-1357. (4) Xi, X.; Wang, Z.; Zhao, W.; Park, J.-H.; Law, K. T.; Berger, H.; Forro, L.; Shan, J.; Mak, K. F., Ising pairing in superconducting NbSe2 atomic layers. Nature Physics 2016, 12, 139-143. (5) Chang, K.; Liu, J.; Lin, H.; Wang, N.; Zhao, K.; Zhang, A.; Jin, F.; Zhong, Y.; Hu, X.; Duan, W.; Zhang, Q.; Fu, L.; Xue, Q.-K.; Chen, X.; Ji, S.-H., Discovery of robust in-plane ferroelectricity in atomic-thick SnTe. Science 2016, 353, 274-278. (6) Mermin, N. D.; Wagner, H., Absence of Ferromagnetism or Antiferromagnetism in Oneor Two-Dimensional Isotropic Heisenberg Models. Physical Review Letters 1966, 17, 1133-1136. (7) Gong, C.; Li, L.; Li, Z.; Ji, H.; Stern, A.; Xia, Y.; Cao, T.; Bao, W.; Wang, C.; Wang, Y.; Qiu, Z. Q.; Cava, R. J.; Louie, S. G.; Xia, J.; Zhang, X., Discovery of 18



Intrinsic Ferromagnetism in Two-Dimensional van der Waals Crystals. Nature 2017, 546, 265-269. (8) Huang, B.; Clark, G.; Navarro-Moratalla, E.; Klein, D. R.; Cheng, R.; Seyler, K. L.; Zhong, D.; Schmidgall, E.; McGuire, M. A.; Cobden, D. H.; Yao, W.; Xiao, D.; JarilloHerrero, P.; Xu, X., Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 2017, 546, 270-273. (9) Jiang, S.; Li, L.; Wang, Z.; Mak, K. F.; Shan, J., Controlling magnetism in 2D CrI3 by electrostatic doping. Nature Nanotechnology 2018, 13, 549-553. (10) Deng, Y.; Yu, Y.; Song, Y.; Zhang, J.; Wang, N. Z.; Sun, Z.; Yi, Y.; Wu, Y. Z.; Wu, S.; Zhu, J.; Wang, J.; Chen, X. H.; Zhang, Y., Gate-tunable room-temperature ferromagnetism in two-dimensional Fe3 GeTe2 . Nature 2018, 563, 94-99. (11) Zhong, D.; Seyler, K. L.; Linpeng, X.; Cheng, R.; Sivadas, N.; Huang, B.; Schmidgall, E.; Taniguchi, T.; Watanabe, K.; McGuire, M. A.; Yao, W.; Xiao, D.; Fu, K.-M. C.; Xu, X., Van der Waals engineering of ferromagnetic semiconductor heterostructures for spin and valleytronics. Science Advances 2017, 3, e1603113. (12) Lin, M.-W.; Zhuang, H. L.; Yan, J.; Ward, T. Z.; Puretzky, A. A.; Rouleau, C. M.; Gai, Z.; Liang, L.; Meunier, V.; Sumpter, B. G.; Ganesh, P.; Kent, P. R. C.; Geohegan, D. B.; Mandrus, D. G.; Xiao, K., Ultrathin nanosheets of CrSiTe3 : a semiconducting two-dimensional ferromagnetic material. Journal of Materials Chemistry C 2016, 4, 315-322. (13) Zhang, W.-B.; Qu, Q.; Zhua, P.; Lam, C.-H., Robust intrinsic ferromagnetism and half semiconductivity in stable two-dimensional single-layer chromium trihalides. Journal of Materials Chemistry C 2015, 3, 12457-12468. (14) McGuire, M. A.; Clark, G.; Santosh, K. C.; Chance, W. M.; Jellison, G. E., Jr.; Cooper,

19


Page 24 of 28

Page 25 of 28 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


V. R.; Xu, X.; Sales, B. C., Magnetic behavior and spin-lattice coupling in cleavable van der Waals layered CrCl3 crystals. Physical Review Materials 2017, 1, 014001. (15) He, J.; Ma, S.; Lyu, P.; Nachtigall, P., Unusual Dirac half-metallicity with intrinsic ferromagnetism in vanadium trihalide monolayers. Journal of Materials Chemistry C 2016, 4, 2518-2526. (16) APEX3 Ver. 2015, 2015, Bruker AXS, Inc., Madison, WI. (17) Sheldrick, G. M., A short history of SHELX. Acta Crystallographica Section A 2008, 64, 112-122. (18) Blöchl, P. E., Projector augmented-wave method. Physical Review B 1994, 50, 1795317979. (19) Kresse, G.; Joubert, D., From ultrasoft pseudopotentials to the projector augmentedwave method. Physical Review B 1999, 59, 1758-1775. (20) Kresse, G.; Hafner, J., Ab initio molecular dynamics for liquid metals. Physical Review B 1993, 47, 558-561. (21) Kresse, G.; Hafner, J., Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition-Elements. Journal of Physics-Condensed Matter 1994, 6, 8245-8257. (22) Kresse, G.; Furthm¨ uller, J., Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. x, 15-50. (23) Kresse, G.; Furthm¨ uller, J., Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Physical Review B 1996, 54, 11169-11186. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple. Physical Review Letters 1996, 77, 3865-3868.

20



(25) Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P., Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Physical Review B 1998, 57, 1505-1509. (26) Klimes, J.; Bowler, D. R.; Michaelides, A., Chemical accuracy for the van der Waals density functional. Journal of Physics-Condensed Matter 2010, 22, 022201. (27) Björkman, T.; Gulans, A.; Krasheninnikov, A. V.; Nieminen, R. M., van der Waals Bonding in Layered Compounds from Advanced Density-Functional First-Principles Calculations. Physical Review Letters 2012, 108, 235502. (28) Berry, K. O.; Smardzewski, R. R.; McCarley, R. E., Vaporization reactions of vanadium iodides and evidence for gaseous vanadium(IV) iodide. Inorganic Chemistry 1969, 8, 1994-1997. (29) Morosin, B.; Narath, A., X-ray Diffraction and Nuclear Quadrupole Resonance Studies of Chromium Trichloride. The Journal of Chemical Physics 1964, 40, 1958-1967. (30) McGuire, M. A.; Dixit, H.; Cooper, V. R.; Sales, B. C., Coupling of Crystal Structure and Magnetism in the Layered, Ferromagnetic Insulator CrI3 . Chemistry of Materials 2015, 27, 612-620. (31) Wilson, J. A.; Maule, C.; Strange, P.; Tothill, J. N., Anomalous Behavior in the Layer Halides and Oxyhalides of Titanium and Vanadium - a Study of Materials Close to Delocalization. Journal of Physics C-Solid State Physics 1987, 20, 4159-4167. (32) Novoselov, K. S.; Morozov, S. V.; Dubonos, S. V.; Missous, M.; Volkov, A. O.; Christian, D. A.; Geim, A. K., Submicron probes for Hall magnetometry over the extended temperature range from helium to room temperature. Journal of Applied Physics 2003, 93, 10053-10057.

21


Page 26 of 28

Page 27 of 28 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


(33) Joy, P. A.; Anil Kumarz, P. S.; Date S. K., Physical and The relationship between fieldcooled and zero-field-cooled susceptibilities of some ordered magnetic systems. Journal of Physics-Condensed Matter 1998, 10, 11049-11054. (34) Senchuk, A.; Kunkel, H. P.; Roshkoa, R. M.; Viddal, C.; Wei, Li; Williams, G.; Zhou, X. Z., La0.5 Sr0.5 CoO3 : A ferromagnet with strong irreversibility. European Physical Journal B 2004, 37, 285-292. (35) Szlawska, M.; Majewicz, M.; Kaczorowski, D., Ferromagnetic ordering in singlecrystalline U2 RhSi3 with fully ordered crystal structure. Journal of Alloys Compounds 2016, 662, 208-212.

22



TOC

23


Page 28 of 28

Ferromagnetic van der Waals Crystal VI3 - Journal of the American

Recommend Documents