Universal behaviors of magnon-mediated spin transport in disordered nonmagnetic metal-ferromagnetic insulator heterostructures

doi:10.1007/s11467-023-1275-5

Front. Phys.

2023, Vol. 18

Issue (3) : 33310 https://doi.org/10.1007/s11467-023-1275-5

RESEARCH ARTICLE

Universal behaviors of magnon-mediated spin transport in disordered nonmagnetic metal-ferromagnetic insulator heterostructures

Gaoyang Li¹, Fuming Xu¹, Jian Wang^1,²(

)

¹. College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
². Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China

Download: PDF(5630 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We numerically investigate magnon-mediated spin transport through nonmagnetic metal/ferromagnetic insulator (NM/FI) heterostructures in the presence of Anderson disorder, and discover universal behaviors of the spin conductance in both one-dimensional (1D) and 2D systems. In the localized regime, the variance of logarithmic spin conductance σ²(lnG_T) shows a universal linear scaling with its average ⟨lnG_T⟩, independent of Fermi energy, temperature, and system size in both 1D and 2D cases. In 2D, the competition between disorder-enhanced density of states at the NM/FI interface and disorder-suppressed spin transport leads to a non-monotonic dependence of average spin conductance on the disorder strength. As a result, in the metallic regime, average spin conductance is enhanced by disorder, and a new linear scaling between spin conductance fluctuation rms(G_T) and average spin conductance G_T is revealed which is universal at large system width. These universal scaling behaviors suggest that spin transport mediated by magnon in disordered 2D NM/FI systems belongs to a new universality class, different from that of charge conductance in 2D normal metal systems.

Keywords universal statistical behaviors magnon-mediated spin transport disorder-enhanced spin conductance

Corresponding Author(s): Jian Wang

Issue Date: 24 March 2023

Cite this article:

Gaoyang Li,Fuming Xu,Jian Wang. Universal behaviors of magnon-mediated spin transport in disordered nonmagnetic metal-ferromagnetic insulator heterostructures[J]. Front. Phys. , 2023, 18(3): 33310.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1275-5
https://academic.hep.com.cn/fop/EN/Y2023/V18/I3/33310

Fig.1 Schematic view of the 2D NM/FI system. The left NM lead and the right FI lead are connected to the central NM scattering region, which is of width

L 1

and length

L 2

. Magnon-mediated transport is along the

x

direction. A typical experimental setup for this model is the bilayer structure of Pt/YIG.

Fig.2 (a) Average spin conductance

? G T ?

and its fluctuation

r m s (G T)

as a function of the disorder strength

W

. (b) The variance of

l n G T

dependence on

? l n G T ?

for different Fermi energies and temperatures. (c–e) Spin conductance distribution

P (G T)

and

P (l n G T)

for different

W

. 40000 disorder samples are collected. Parameters:

μ L = 40

meV and

T = 50

K. The gray dashed line separates the diffusive (ii) and localized (iii) regimes.

Fig.3 (a) Average

? G T ?

and its fluctuation

r m s (G T)

as a function of

W

in the first and second subbands of the 2D NM/FI system. Parameters for the first and second subbands:

μ L = {0.9, 3}

meV,

ω c = {0.24, 0.2}

meV, and

T = 5

K. (b) Local DOS in the scattering region without disorder. (c–e) LDOS for three typical configurations at disorder strength

W = 1.84

. The spin conductances for these configurations are

G T = {4.107, 4.7, 0.0786}

, respectively. Here iDOS is the total interfacial DOS at the NM/FI interface and we set parameters in the first subband.

Fig.4 Spin conductance distribution

P (l n G T)

of the 2D system for different

W

in the first subband (a) and the second subband (b). Parameters are the same as Fig.3.

Fig.5 Statistics of spin conductance for Fermi energies

μ L = {0.9, 1.0, 1.1, 1.2, 1.3}

meV and temperatures

T = {2, 3, 5}

K. All Fermi energies are in the first subband. Figure legends are shown in (d). The gray dashed lines separate (ii) the diffusive regime and (iii) the localized regime. (a) Average spin conductance as a function of the disorder strength

W

. (b)

? l n G T ?

versus the disorder strength. (c) Scaling of the variance

σ 2 (l n G T)

on average

l n G T

in the localized regime. Inset: data for different Fermi energies at

T = 5

K. (d) Scaling of spin conductance fluctuation on average spin conductance in the metallic regime.

Fig.6 (a–d) Skewness

γ 1

, kurtosis

γ 2

, third and fourth cumulants

κ 3, κ 4

l n G T

for the 2D NM/FI system in the first subband. Parameters are the same as in Fig.5 [65]. Legends are shown in (d). The gray dashed lines separate the localized regime and diffusive regime. The inset of (c) shows

κ 3

versus

? − ln ? G T ? 3 / 2

. (e)

P (ln ? G T)

at a fixed value

? l n G T ? = − 12.80

for different Fermi energies and temperatures in the localized regime with

W = 13.78

. The red curve is the fitted Gaussian distribution

Fig.7

? G T ?

(a, b) and

? l n G T ?

(c) versus the 1D system length

L

for different

W

. (d) Localization length

ξ

extracted from the slopes in (c). (e) Universal scaling of

σ 2 (l n G T)

? l n G T ?

in the localized regime (iii) for different system lengths. The red line is the same as in Fig.2(c). (f) The scaling of

? G T ?

as a function of the ratio

L / ξ

for different disorder strengths. 30000 disorder samples are collected to smooth the curve. The gray dashed line corresponds to the localization length

ξ ≈ 10

, which is much smaller than the system size.

Fig.8 The average of

G T

(a),

l n G T

(b) and the scaling in the localized regime (c) for different 2D system widths

L 1 = {20, 30, 40}

and lengths

L 2 = {20, 30, 40}

. The legends for (a)–(c) is shown in (c). (d) The scaling of

r m s (G T)

? G T ?

in the metallic regime for different

L 1

and

L 2

. (e) The localization length

ξ

of system width

L 1 = 20

as a function of

W

. The black points are numerically extracted and the red curve is the fitted exponential function. Parameters are chosen in the first subband,

μ L = {0.9, 0.5, 0.3}

meV,

T = {5, 2, 1.1}

K, and

ω c = {0.24, 0.05, 0.03}

meV for width

L 1 = {20, 30, 40}

, respectively.

1	P. Umbach C., Washburn S., B. Laibowitz R., A. Webb R.. Magnetoresistance of small, quasi-one-dimensional, normal-metal rings and lines. Phys. Rev. B, 1984, 30(7): 4048 https://doi.org/10.1103/PhysRevB.30.4048
2	A. Lee P., D. Stone A.. Universal Conductance Fluctuations in Metals. Phys. Rev. Lett., 1985, 55(15): 1622 https://doi.org/10.1103/PhysRevLett.55.1622
3	L. Altshuler B.. Fluctuations in the extrinsic conductivity of disordered conductors. JETP Lett., 1985, 41: 648
4	A. Lee P., D. Stone A., Fukuyama H.. Universal conductance fluctuations in metals: Effects of finite temperature, interactions, and magnetic field. Phys. Rev. B, 1987, 35(3): 1039 https://doi.org/10.1103/PhysRevB.35.1039
5	Qiao Z., Xing Y., Wang J.. Universal conductance fluctuation of mesoscopic systems in the metal-insulator crossover regime. Phys. Rev. B, 2010, 81(8): 085114 https://doi.org/10.1103/PhysRevB.81.085114
6	Zhang L., Zhuang J., Xing Y., Li J., Wang J., Guo H.. Universal transport properties of three-dimensional topological insulator nanowires. Phys. Rev. B, 2014, 89(24): 245107 https://doi.org/10.1103/PhysRevB.89.245107
7	L. Han Y., H. Qiao Z.. Universal conductance fluctuations in Sierpinski carpets. Front. Phys., 2019, 14(6): 63603 https://doi.org/10.1007/s11467-019-0919-y
8	W. Anderson P.. Absence of diffusion in certain random lattices. Phys. Rev., 1958, 109(5): 1492 https://doi.org/10.1103/PhysRev.109.1492
9	Kramer B., MacKinnon A.. Localization: Theory and experiment. Rep. Prog. Phys., 1993, 56(12): 1469 https://doi.org/10.1088/0034-4885/56/12/001
10	Abrahams E., 50 Years of Anderson Localization, World Scientific, Singapore, 2010
11	F. Mott N.. Conduction in glasses containing transition metal ions. J. Non-Cryst. Solids, 1968, 1(1): 1 https://doi.org/10.1016/0022-3093(68)90002-1
12	T. Edwards J., J. Thouless D.. Numerical studies of localization in disordered systems. J. Phys. C, 1972, 5: 807 https://doi.org/10.1088/0022-3719/5/8/007
13	Abrahams E., W. Anderson P., C. Licciardello D., V. Ramakrishnan T.. Scaling theory of localization: Absence of quantum diffusion in two dimensions. Phys. Rev. Lett., 1979, 42(10): 673 https://doi.org/10.1103/PhysRevLett.42.673
14	W. Anderson P., J. Thouless D., Abrahams E., S. Fisher D.. New method for a scaling theory of localization. Phys. Rev. B, 1980, 22(8): 3519 https://doi.org/10.1103/PhysRevB.22.3519
15	A. Müller C.Delande D., Disorder and interference: Localization phenomena, arXiv: 1005.0915 (2010)
16	Shapiro B., in: Percolation Structures and Processes, edited by G. Deutscher, R. Zallen, and J. Adler, Ann. Isr. Phys. Soc. 5, 367 (1983)
17	Shapiro B.. Scaling properties of probability distributions in disordered systems. Philos. Mag. B, 1987, 56: 1031
18	MacKinnon A., Kramer B.. One-parameter scaling of localization length and conductance in disordered systems. Phys. Rev. Lett., 1981, 47(21): 1546 https://doi.org/10.1103/PhysRevLett.47.1546
19	MacKinnon A., Kramer B.. The scaling theory of electrons in disordered solids: Additional numerical results. Z. Phys. B, 1983, 53(1): 1 https://doi.org/10.1007/BF01578242
20	Prior J., M. Somoza A., Ortuno M.. Conductance fluctuations and single-parameter scaling in two-dimensional disordered systems. Phys. Rev. B, 2005, 72(2): 024206 https://doi.org/10.1103/PhysRevB.72.024206
21	La Magna A., Deretzis I., Forte G., Pucci R.. Violation of the single-parameter scaling hypothesis in disordered graphene nanoribbons. Phys. Rev. B, 2008, 78(15): 153405 https://doi.org/10.1103/PhysRevB.78.153405
22	La Magna A., Deretzis I., Forte G., Pucci R.. Conductance distribution in doped and defected graphene nanoribbons. Phys. Rev. B, 2009, 80(19): 195413 https://doi.org/10.1103/PhysRevB.80.195413
23	N. Dorokhov O.. Transmission coefficient and the localization length of an electron in N bond disorder chains. JETP Lett., 1982, 36: 318
24	A. Mello P., Pereyra P., Kumar N.. Macroscopic approach to multichannel disordered conductors. Ann. Phys., 1988, 181(2): 290 https://doi.org/10.1016/0003-4916(88)90169-8
25	Plerou V., Q. Wang Z.. Conductances, conductance fluctuations, and level statistics on the surface of multilayer quantum Hall states. Phys. Rev. B, 1998, 58(4): 1967 https://doi.org/10.1103/PhysRevB.58.1967
26	A. Muttalib K., Wolfle P.. “One-sided” log-normal distribution of conductances for a disordered quantum wire. Phys. Rev. Lett., 1999, 83(15): 3013 https://doi.org/10.1103/PhysRevLett.83.3013
27	J. Roberts P.. Joint probability distributions for disordered 1D wires. J. Phys.: Condens. Matter, 1992, 4(38): 7795 https://doi.org/10.1088/0953-8984/4/38/011
28	I. Deych L., A. Lisyansky A., L. Altshuler B.. Single parameter scaling in one-dimensional localization revisited. Phys. Rev. Lett., 2000, 84(12): 2678 https://doi.org/10.1103/PhysRevLett.84.2678
29	García-Martín A., J. Saenz J.. Universal conductance distributions in the crossover between diffusive and localization regimes. Phys. Rev. Lett., 2001, 87(11): 116603 https://doi.org/10.1103/PhysRevLett.87.116603
30	Schreiber M., Ottomeier M.. Localization of electronic states in 2D disordered systems. J. Phys.: Condens. Matter, 1992, 4(8): 1959 https://doi.org/10.1088/0953-8984/4/8/011
31	M. Somoza A., Ortuno M., Prior J.. Universal distribution functions in two-dimensional localized systems. Phys. Rev. Lett., 2007, 99(11): 116602 https://doi.org/10.1103/PhysRevLett.99.116602
32	M. Somoza A., Prior J., Ortuno M., V. Lerner I.. Crossover from diffusive to strongly localized regime in two-dimensional systems. Phys. Rev. B, 2009, 80(21): 212201 https://doi.org/10.1103/PhysRevB.80.212201
33	W. Kantelhardt J., Bunde A.. Sublocalization, superlocalization, and violation of standard single-parameter scaling in the Anderson model. Phys. Rev. B, 2002, 66(3): 035118 https://doi.org/10.1103/PhysRevB.66.035118
34	L. A. Queiroz S.. Failure of single-parameter scaling of wave functions in Anderson localization. Phys. Rev. B, 2002, 66(19): 195113 https://doi.org/10.1103/PhysRevB.66.195113
35	In Ref. [20], lnR is used instead of lnG. Note the resistence R is the inverse of conductance G, then we have ⟨ln G ⟩ = −⟨ln R⟩ thus the same result is obtained
36	Brataas A., van Wees B., Klein O., de Loubens G., Viret M.. Spin insulatronics. Phys. Rep., 2020, 885: 1 https://doi.org/10.1016/j.physrep.2020.08.006
37	Tserkovnyak Y., Brataas A., E. W. Bauer G.. Spin pumping and magnetization dynamics in metallic multilayers. Phys. Rev. B, 2002, 66(22): 224403 https://doi.org/10.1103/PhysRevB.66.224403
38	Tserkovnyak Y., Brataas A., E. W. Bauer G., I. Halperin B.. Nonlocal magnetization dynamics in ferromagnetic heterostructures. Rev. Mod. Phys., 2005, 77(4): 1375 https://doi.org/10.1103/RevModPhys.77.1375
39	Azevedo A., H. V. Leão L., L. Rodriguez-Suarez R., B. Oliveira A., M. Rezende S.. dc effect in ferromagnetic resonance: Evidence of the spin-pumping effect?. J. Appl. Phys., 2005, 97: 10C715 https://doi.org/10.1063/1.1855251
40	Saitoh E., Ueda M., Miyajima H., Tatara G.. Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect. Appl. Phys. Lett., 2006, 88(18): 182509 https://doi.org/10.1063/1.2199473
41	Uchida K., Takahashi S., Harii K., Ieda J., Koshibae W., Ando K., Maekawa S., Saitoh E.. Observation of the spin Seebeck effect. Nature, 2008, 455(7214): 778 https://doi.org/10.1038/nature07321
42	Uchida K., Xiao J., Adachi H., Ohe J., Takahashi S., Ieda J., Ota T., Kajiwara Y., Umezawa H., Kawai H., E. W. Bauer G., Maekawa S., Saitoh E.. Spin Seebeck insulator. Nat. Mater., 2010, 9(11): 894 https://doi.org/10.1038/nmat2856
43	E. W. Bauer G., Saitoh E., J. vanWees B.. Spin caloritronics. Nat. Mater., 2012, 11(5): 391 https://doi.org/10.1038/nmat3301
44	Adachi H., Uchida K., Saitoh E., Maekawa S.. Theory of the spin Seebeck effect. Rep. Prog. Phys., 2013, 76(3): 036501 https://doi.org/10.1088/0034-4885/76/3/036501
45	M. Tang G., B. Chen X., Ren J., Wang J.. Rectifying full-counting statistics in a spin Seebeck engine. Phys. Rev. B, 2018, 97(8): 081407 https://doi.org/10.1103/PhysRevB.97.081407
46	Wu H., Huang L., Fang C., S. Yang B., H. Wan C., Q. Yu G., F. Feng J., X. Wei H., F. Han X.. Magnon valve effect between two magnetic insulators. Phys. Rev. Lett., 2018, 120(9): 097205 https://doi.org/10.1103/PhysRevLett.120.097205
47	F. Miao B., Y. Huang S., Qu D., L. Chien C.. Inverse spin Hall effect in a ferromagnetic metal. Phys. Rev. Lett., 2013, 111(6): 066602 https://doi.org/10.1103/PhysRevLett.111.066602
48	F. Jakobsen M., Qaiumzadeh A., Brataas A.. Scattering theory of transport through disordered magnets. Phys. Rev. B, 2019, 100(13): 134431 https://doi.org/10.1103/PhysRevB.100.134431
49	Yang L., Gu Y., Chen L., Zhou K., Fu Q., Wang W., Li L., Yan C., Li H., Liang L., Li Z., Pu Y., Du Y., Liu R.. Absence of spin transport in amorphous YIG evidenced by nonlocal spin transport experiments. Phys. Rev. B, 2021, 104(14): 144415 https://doi.org/10.1103/PhysRevB.104.144415
50	Li G., Jin H., Wei Y., Wang J.. Giant effective electron−magnon coupling in a nonmagnetic metal–ferromagnetic insulator heterostructure. Phys. Rev. B, 2022, 106(20): 205303 https://doi.org/10.1103/PhysRevB.106.205303
51	S. Wang J., K. Agarwalla B., Li H., Thingna J.. Nonequilibrium Green’s function method for quantum thermal transport. Front. Phys., 2014, 9(6): 673 https://doi.org/10.1007/s11467-013-0340-x
52	Zhang C., Xu F., Wang J.. Full counting statistics of phonon transport in disordered systems. Front. Phys., 2021, 16(3): 33502 https://doi.org/10.1007/s11467-020-1027-8
53	Z. Yu Z.H. Xiong G.F. Zhang L., A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach, Front. Phys. 16(4), 43201 (2021)
54	S. Wang J., Peng J., Q. Zhang Z., M. Zhang Y., Zhu T.. Transport in electron–photon systems. Front. Phys., 2023, 18(4): 43602 https://doi.org/10.1007/s11467-023-1260-z
55	Holstein T., Primakoff H.. Field dependence of the intrinsic domain magnetization of a ferromagnet. Phys. Rev., 1940, 58(12): 1098 https://doi.org/10.1103/PhysRev.58.1098
56	S. Zheng J., Bender S., Armaitis J., E. Troncoso R., A. Duine R.. Green’s function formalism for spin transport in metal−insulator−metal heterostructures. Phys. Rev. B, 2017, 96(17): 174422 https://doi.org/10.1103/PhysRevB.96.174422
57	Ren J.. Predicted rectification and negative differential spin Seebeck effect at magnetic interfaces. Phys. Rev. B, 2013, 88(22): 220406 https://doi.org/10.1103/PhysRevB.88.220406
58	Christen T., Buttiker M.. Low frequency admittance of a quantum point contact. Phys. Rev. Lett., 1996, 77(1): 143 https://doi.org/10.1103/PhysRevLett.77.143
59	Datta S., Electronic Transport in Mesoscopic Systems, Cambridge University Press, New York, 1995, Chapter 3
60	I. Melnikov V., Fluctuations in the resistivity of a finite disordered system, Fiz. Tverd. Tela (Leningrad) 23, 782 (1981) [Sov. Phys. Solid State 23, 444 (1981)]
61	A. Abrikosov A.. The paradox with the static conductivity of a one-dimensional metal. Solid State Commun., 1981, 37(12): 997 https://doi.org/10.1016/0038-1098(81)91203-5
62	Janssen M.. Statistics and scaling in disordered mesoscopic electron systems. Phys. Rep., 1998, 295(1−2): 1 https://doi.org/10.1016/S0370-1573(97)00050-1
63	Ren W., Wang J., S. Ma Z.. Conductance fluctuations and higher order moments of a disordered carbon nanotube. Phys. Rev. B, 2005, 72(19): 195407 https://doi.org/10.1103/PhysRevB.72.195407
64	When calculating spin conductance for one specific disorder sample, one has to perform a double integration [see Eq. (13)]. In the calculation, we have chosen grid points 100 × 100 which amounts to an increase of computational cost by the factor of 10000 comparing with the charge conductance calculation in normal metal systems
65	The Fermi energies used in scaling analysis (Fig.5 and Fig.6) are near the center of the first subband. This is the region where SPS works in normal metal system [20]. Although the ranges of Fermi energies and temperatures are not very wide, the spin conductance in Fig.5(a) varies large enough in magnitude to support our scaling analysis.
66	Mohanty P., A. Webb R.. Anomalous conductance distribution in quasi-one-dimensional gold wires: Possible violation of the one-parameter scaling hypothesis. Phys. Rev. Lett., 2002, 88: 146601 https://doi.org/10.1103/PhysRevLett.88.146601
67	M. Somoza A., Prior J., Ortuño M.. Conductance fluctuations in the localized regime: Numerical study in disordered noninteracting systems. Phys. Rev. B, 2006, 73: 184201 https://doi.org/10.1103/PhysRevB.73.184201

Viewed

Full text

Abstract

Cited

Shared

Discussed