Itinerant ferromagnetism entrenched by the anisotropy of spin−orbit coupling in a dipolar Fermi gas

doi:10.1007/s11467-023-1283-5

Front. Phys.

2023, Vol. 18

Issue (5) : 52303 https://doi.org/10.1007/s11467-023-1283-5

RESEARCH ARTICLE

Itinerant ferromagnetism entrenched by the anisotropy of spin−orbit coupling in a dipolar Fermi gas

Xue-Jing Feng¹, Jin-Xin Li¹, Lu Qin¹, Ying-Ying Zhang¹, ShiQiang Xia¹, Lu Zhou², ChunJie Yang¹(

), ZunLue Zhu¹(

), Wu-Ming Liu³, Xing-Dong Zhao¹(

)

¹. School of Physics, Henan Normal University, Xinxiang 453000, China
². Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China
³. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

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Abstract

We investigate the itinerant ferromagnetism in a dipolar Fermi atomic system with the anisotropic spin−orbit coupling (SOC), which is traditionally explored with isotropic contact interaction. We first study the ferromagnetism transition boundaries and the properties of the ground states through the density and spin-flip distribution in momentum space, and we find that both the anisotropy and the magnitude of the SOC play an important role in this process. We propose a helpful scheme and a quantum control method which can be applied to conquering the difficulties of previous experimental observation of itinerant ferromagnetism. Our further study reveals that exotic Fermi surfaces and an abnormal phase region can exist in this system by controlling the anisotropy of SOC, which can provide constructive suggestions for the research and the application of a dipolar Fermi gas. Furthermore, we also calculate the ferromagnetism transition temperature and novel distributions in momentum space at finite temperature beyond the ground states from the perspective of experiment.

Keywords itinerant ferromagnetism spin−orbit coupling cold atom quantum simulation dipolar Fermi gas dipole−dipole interaction

Corresponding Author(s): ChunJie Yang,ZunLue Zhu,Xing-Dong Zhao

Issue Date: 26 April 2023

Cite this article:

Xue-Jing Feng,Jin-Xin Li,Lu Qin, et al. Itinerant ferromagnetism entrenched by the anisotropy of spin−orbit coupling in a dipolar Fermi gas[J]. Front. Phys. , 2023, 18(5): 52303.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1283-5
https://academic.hep.com.cn/fop/EN/Y2023/V18/I5/52303

Fig.1 (a) Schematic diagram of the experimental realization of the anisotropic 3D spin−orbit coupling [44]. Three pairs of Raman lasers propagating in three directions are polarized in the directions displayed above. The

x

-direction and the

z

-direction Raman laser, along with the

y

-direction and the

z

-direction Raman laser, comprise a double-

Λ

configuration leading to a 3D SOC. The atoms interact with each other through a long-range anisotropic dipole−dipole interaction (DDI). (b) Density of states (DOS) of the lower-branch of single-atom excitation energy with different anisotropy parameters

γ

. The unit energy

? λ = ℏ 2 λ 2 / (2 m)

with

λ = α 0 m / ℏ 2

. The unit of DOS

D m i n = V λ 3 / ? λ

. When

γ = 0

(Rashba SOC) or

γ = 1

(Weyl SOC), energy unit is

E m i n = ? λ

. When

γ = 2

and

γ = 5

which correspond to two anisotropic circumstances, the energy unit

E m i n = 4 ? λ

and

E m i n = 25 ? λ

, respectively. The singularities of DOS with anisotropic SOC occur at

E = − ? λ .

Fig.2 (a) Zero-temperature ferromagnetism transition boundaries as functions of

γ

and

λ d

with

λ s = 0

. (b) The same as (a), but as functions of

γ

and

λ s

with

λ d = 0

. In panels (a) and (b), the red dashed line, blue dash-dotted line, and black dash-dot-dotted line are for

λ s o c = 0.6, 0.4, 0.2

, respectively. The green solid line in (a) is the unstable boundary above which the dipolar system undergoes a dynamical instability [36]. (c) The same as (a), but as functions of

λ s o c

and

λ d

. In panel (c), the red dashed line, blue dash-dotted line, and black dash-dot-dotted line are for

γ = 2.5, 2, 1.5

, respectively. (d) Zero-temperature ferromagnetism transition boundaries as functions of

γ

and

λ s o c

. In panel (d), the red dashed line and blue dash-dotted line are for

λ d = 0.3, 0.2

, respectively. Above the boundary curves, this system undergoes a ferromagnetic transition with the magnetization

M > 0

from a normal state with

M = 0

Fig.3 Magnetization (M) and chemical potential (

μ

) as functions of

γ

with

λ d = 0.2

and

λ s o c = 0.4

(a); as functions of

λ s o c

with

λ d = 0.2

and

γ = 2

(b). Both figures indicate a transition from a normal state (M = 0) to a ferromagnetic state (

M > 0

Fig.4 Zero-temperature density distribution

n k, ↑

[panels (a1−a3)],

n k, ↓

[panels (b1−b3)], and spin-flip distribution

| t k |

[panels (c1−c3)] with

λ s o c

= 0.4,

λ d

= 0.2. Panels (a1−c1) are for

γ

= 5.7; panels (a2−c2) are for

γ

= 5.5; panels (a3−c3) are for

γ

= 4.9. These figures from the left column to the right column show a transition from a ferromagnetic state to a normal state.

Fig.5 Density distributions of spin-up [panels (a1−d1)] and spin-down component [panels (a2−d2)] in momentum space. Panels (a1, a2) are for

λ d = 0.1

; panels (b1, b2) are for

λ d = 0.13

; panels (c1, c2) are for

λ d = 0.4

; panels (d1, d2) are for

λ d = 0.5

, and all for

λ s o c = 1.9

γ = 1.2

Fig.6 (a) Ferromagnetic transition temperature as functions of

γ

with

λ d = 0.2

. The red dashed line and blue dash-dotted line are for

λ s o c = 0.4, 0.6

, respectively. (b) Entropy as functions of temperature

λ T

with

λ d

= 0.20,

λ s o c

= 0.4. The red dashed line, blue dash-dotted line, and black dash-dot-dotted line are for

γ = 8, 6.5, 5

, respectively. (c) Ferromagnetic transition temperature as functions of

λ s o c

with

λ d = 0.2

. The red dashed line and blue dash-dotted line are for

γ = 5, 6

, respectively. (d) Ferromagnetic transition temperature as functions of

λ d

with

γ = 5

. The red dashed line and blue dash-dotted line are for

λ s o c = 0.4, 0.5

, respectively.

Fig.7 Density distributions of spin-up [panels (a1, b1)], spin-down [panels (a2, b2)] and spin-flip distribution [panels (a3, b3)]. Panels (a1−a3) are for

λ T = 0.3

and panels (b1−b3) are for

λ T = 1

. All panels are for

γ = 8

λ s o c = 0.4

and

λ d = 0.2

1	Wagner D., Introduction to the Theory of Magnetism: International Series of Monographs in Natural Philosophy, Vol. 48, Elsevier, 2013
2	Kübler J., Theory of Itinerant Electron Magnetism, Vol. 106, Oxford University Press, 2017
3	Zak J.. Dynamics of electrons in solids in external fields. Phys. Rev., 1968, 168(3): 686 https://doi.org/10.1103/PhysRev.168.686
4	Bloch F.. Bemerkung zur Elektronentheorie des Ferromagnetismus und der elektrischen Leitfähigkeit. Eur. Phys. J. A, 1929, 57(7–8): 545 https://doi.org/10.1007/BF01340281
5	Misawa S.. Ferromagnetism of an electron gas. Phys. Rev., 1965, 140(5A): A1645 https://doi.org/10.1103/PhysRev.140.A1645
6	C. Stoner E.. Collective electron ferronmagnetism. Proc. R. Soc. Lond. A, 1938, 165(922): 372 https://doi.org/10.1098/rspa.1938.0066
7	C. Stoner E.. LXXX. Atomic moments in ferromagnetic metals and alloys with non-ferromagnetic elements. Lond. Edinb. Dublin Philos. Mag. J. Sci., 1933, 15(101): 1018 https://doi.org/10.1080/14786443309462241
8	A. Duine R., H. MacDonald A.. Itinerant ferromagnetism in an ultracold atom Fermi gas. Phys. Rev. Lett., 2005, 95(23): 230403 https://doi.org/10.1103/PhysRevLett.95.230403
9	Pilati S., Bertaina G., Giorgini S., Troyer M.. Itinerant ferromagnetism of a repulsive atomic Fermi gas: A quantum Monte Carlo study. Phys. Rev. Lett., 2010, 105(3): 030405 https://doi.org/10.1103/PhysRevLett.105.030405
10	He L., G. Huang X.. Nonperturbative effects on the ferromagnetic transition in repulsive Fermi gases. Phys. Rev. A, 2012, 85(4): 043624 https://doi.org/10.1103/PhysRevA.85.043624
11	He L., J. Liu X., G. Huang X., Hu H.. Stoner ferromagnetism of a strongly interacting Fermi gas in the quasirepulsive regime. Phys. Rev. A, 2016, 93(6): 063629 https://doi.org/10.1103/PhysRevA.93.063629
12	He L.. Finite range and upper branch effects on itinerant ferromagnetism in repulsive Fermi gases: Bethe–Goldstone ladder resummation approach. Ann. Phys., 2014, 351: 477 https://doi.org/10.1016/j.aop.2014.09.009
13	Massignan P., Yu Z., M. Bruun G.. Itinerant ferromagnetism in a polarized two-component Fermi gas. Phys. Rev. Lett., 2013, 110(23): 230401 https://doi.org/10.1103/PhysRevLett.110.230401
14	Zintchenko I., Wang L., Troyer M.. Ferromagnetism of the repulsive atomic Fermi gas: Three-body recombination and domain formation. Eur. Phys. J. B, 2016, 89(8): 180 https://doi.org/10.1140/epjb/e2016-70302-5
15	Tajima H., Iida K.. Non-Hermitian ferromagnetism in an ultracold Fermi gas. J. Phys. Soc. Jpn., 2021, 90(2): 024004 https://doi.org/10.7566/JPSJ.90.024004
16	B. Jo G., R. Lee Y., H. Choi J., A. Christensen C., H. Kim T., H. Thywissen J., E. Pritchard D., Ketterle W.. Itinerant ferromagnetism in a Fermi gas of ultracold atoms. Science, 2009, 325(5947): 1521 https://doi.org/10.1126/science.1177112
17	Valtolina G., Scazza F., Amico A., Burchianti A., Re-cati A., Enss T., Inguscio M., Zaccanti M., Roati G.. Exploring the ferromagnetic behaviour of a repulsive Fermi gas through spin dynamics. Nat. Phys., 2017, 13(7): 704 https://doi.org/10.1038/nphys4108
18	Arias de Saavedra F., Mazzanti F., Boronat J., Polls A.. Ferromagnetic transition of a two-component Fermi gas of hard spheres. Phys. Rev. A, 2012, 85(3): 033615 https://doi.org/10.1103/PhysRevA.85.033615
19	W. von Keyserlingk C., J. Conduit G.. Itinerant ferromagnetism with finite-ranged interactions. Phys. Rev. B, 2013, 87(18): 184424 https://doi.org/10.1103/PhysRevB.87.184424
20	Sun Z., Gu Q.. Ferromagnetic transition in harmonically trapped Fermi gas with higher partial-wave interactions. J. Phys. At. Mol. Opt. Phys., 2017, 50(1): 015302 https://doi.org/10.1088/1361-6455/50/1/015302
21	Vermeyen E., A. R. Sá de Melo C., Tempere J.. Exchange interactions and itinerant ferromagnetism in ultracold Fermi gases. Phys. Rev. A, 2018, 98(2): 023635 https://doi.org/10.1103/PhysRevA.98.023635
22	Hu Y., Fei Y., L. Chen X., Zhang Y.. Collisional dynamics of symmetric two-dimensional quantum droplets. Front. Phys., 2022, 17(6): 61505 https://doi.org/10.1007/s11467-022-1192-z
23	Guo H., Ji Y., Liu Q., Yang T., Hou S., Yin J.. A driven three-dimensional electric lattice for polar molecules. Front. Phys., 2022, 17(5): 52505 https://doi.org/10.1007/s11467-022-1174-1
24	S. Zeng T., Yin L.. Supersolidity of a dipolar Fermi gas in a cubic optical lattice. Phys. Rev. B, 2014, 89(17): 174511 https://doi.org/10.1103/PhysRevB.89.174511
25	Wu Z., K. Block J., M. Bruun G.. Coexistence of density wave and superfluid order in a dipolar Fermi gas. Phys. Rev. B, 2015, 91(22): 224504 https://doi.org/10.1103/PhysRevB.91.224504
26	G. Bhongale S., Mathey L., W. Tsai S., W. Clark C., Zhao E.. Unconventional spin-density waves in dipolar Fermi gases. Phys. Rev. A, 2013, 87(4): 043604 https://doi.org/10.1103/PhysRevA.87.043604
27	K. Ni K., Ospelkaus S., H. G. de Miranda M., Pe’Er A., Neyenhuis B., J. Zirbel J., Kotochigova S., S. Julienne P., S. Jin D., Ye J.. A high phase-space-density gas of polar molecules. Science, 2008, 322(5899): 231 https://doi.org/10.1126/science.1163861
28	Yan B., A. Moses S., Gadway B., P. Covey J., R. A. Hazzard K., M. Rey A., S. Jin D., Ye J.. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature, 2013, 501(7468): 521 https://doi.org/10.1038/nature12483
29	Chotia A., Neyenhuis B., A. Moses S., Yan B., P. Covey J., Foss-Feig M., M. Rey A., S. Jin D., Ye J.. Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice. Phys. Rev. Lett., 2012, 108(8): 080405 https://doi.org/10.1103/PhysRevLett.108.080405
30	K. Ni K., Ospelkaus S., Wang D., Quéméner G., Neyenhuis B., H. G. de Miranda M., L. Bohn J., Ye J., S. Jin D.. Dipolar collisions of polar molecules in the quantum regime. Nature, 2010, 464(7293): 1324 https://doi.org/10.1038/nature08953
31	H. Wu C., W. Park J., Ahmadi P., Will S., W. Zwierlein M.. Ultracold fermionic Feshbach molecules of 23Na 40K. Phys. Rev. Lett., 2012, 109(8): 085301 https://doi.org/10.1103/PhysRevLett.109.085301
32	Lu M., Q. Burdick N., L. Lev B.. Quantum degenerate dipolar Fermi gas. Phys. Rev. Lett., 2012, 108(21): 215301 https://doi.org/10.1103/PhysRevLett.108.215301
33	Q. Burdick N., Tang Y., L. Lev B.. Long-lived spin–orbit-coupled degenerate dipolar Fermi gas. Phys. Rev. X, 2016, 6(3): 031022 https://doi.org/10.1103/PhysRevX.6.031022
34	J. Feng X., Yin L.. Phase diagram of a spin–orbit coupled dipolar Fermi gas at T = 0 K. Chin. Phys. Lett., 2020, 37(2): 020301 https://doi.org/10.1088/0256-307X/37/2/020301
35	J. Feng X., D. Zhao X., Qin L., Y. Zhang Y., Zhu Z., J. Tian H., Zhuang L., M. Liu W.. Itinerant ferromagnetism of a dipolar Fermi gas with Raman-induced spin–orbit coupling. Phys. Rev. A, 2022, 105(5): 053312 https://doi.org/10.1103/PhysRevA.105.053312
36	M. Fregoso B., Fradkin E.. Ferronematic ground state of the dilute dipolar Fermi gas. Phys. Rev. Lett., 2009, 103(20): 205301 https://doi.org/10.1103/PhysRevLett.103.205301
37	Miyakawa T., Sogo T., Pu H.. Phase-space deformation of a trapped dipolar Fermi gas. Phys. Rev. A, 2008, 77(6): 061603 https://doi.org/10.1103/PhysRevA.77.061603
38	Ronen S., L. Bohn J.. Zero sound in dipolar Fermi gases. Phys. Rev. A, 2010, 81(3): 033601 https://doi.org/10.1103/PhysRevA.81.033601
39	J. Lin Y., Jiménez-García K., B. Spielman I.. Spin–orbit-coupled Bose–Einstein condensates. Nature, 2011, 471(7336): 83 https://doi.org/10.1038/nature09887
40	Wang P., Q. Yu Z., Fu Z., Miao J., Huang L., Chai S., Zhai H., Zhang J.. Spin–orbit coupled degenerate Fermi gases. Phys. Rev. Lett., 2012, 109(9): 095301 https://doi.org/10.1103/PhysRevLett.109.095301
41	Wu Z., Zhang L., Sun W., T. Xu X., Z. Wang B., C. Ji S., Deng Y., Chen S., J. Liu X., W. Pan J.. Realization of two-dimensional spin–orbit coupling for Bose– Einstein condensates. Science, 2016, 354(6308): 83 https://doi.org/10.1126/science.aaf6689
42	Meng Z., Huang L., Peng P., Li D., Chen L., Xu Y., Zhang C., Wang P., Zhang J.. Experimental observation of a topological band gap opening in ultracold Fermi gases with two-dimensional spin–orbit coupling. Phys. Rev. Lett., 2016, 117(23): 235304 https://doi.org/10.1103/PhysRevLett.117.235304
43	Huang L., Meng Z., Wang P., Peng P., L. Zhang S., Chen L., Li D., Zhou Q., Zhang J.. Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases. Nat. Phys., 2016, 12(6): 540 https://doi.org/10.1038/nphys3672
44	Y. Wang Z., C. Cheng X., Z. Wang B., Y. Zhang J., H. Lu Y., R. Yi C., Niu S., Deng Y., J. Liu X., Chen S., Pan J.W.. Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin–orbit coupling. Science, 2021, 372(6539): 271 https://doi.org/10.1126/science.abc0105
45	Zhang Y., E. Mossman M., Busch T., Engels P., Zhang C.. Properties of spin–orbit-coupled Bose–Einstein condensates. Front. Phys., 2016, 11(3): 118103 https://doi.org/10.1007/s11467-016-0560-y
46	H. Lu P., F. Zhang X., Q. Dai C.. Dynamics and formation of vortices collapsed from ring dark solitons in a two-dimensional spin−orbit coupled Bose–Einstein condensate. Front. Phys., 2022, 17(4): 42501 https://doi.org/10.1007/s11467-021-1134-1
47	Jiao C., C. Liang J., F. Yu Z., Chen Y., X. Zhang A., K. Xue J.. Bose–Einstein condensates with tunable spin–orbit coupling in the two-dimensional harmonic potential: The ground-state phases. stability phase diagram and collapse dynamics, Front. Phys., 2022, 17(6): 61503 https://doi.org/10.1007/s11467-022-1180-3
48	Yang H., Zhang Q., Jian Z.. Dynamics of rotating spin−orbit-coupled spin-1 Bose–Einstein condensates with in-plane gradient magnetic field in an anharmonic trap. Front. Phys., 2022, 10(910818): https://doi.org/10.3389/fphy.2022.910818
49	S. Zhang S., Ye J., M. Liu W.. Itinerant magnetic phases and quantum Lifshitz transitions in a three-dimensional repulsively interacting Fermi gas with spin–orbit coupling. Phys. Rev. B, 2016, 94(11): 115121 https://doi.org/10.1103/PhysRevB.94.115121
50	E. Liu W., Chesi S., Webb D., Zülicke U., Winkler R., Joynt R., Culcer D.. Generalized Stoner criterion and versatile spin ordering in two-dimensional spin–orbit coupled electron systems. Phys. Rev. B, 2017, 96(23): 235425 https://doi.org/10.1103/PhysRevB.96.235425
51	Vivas C H.. Magnetic stability for the Hartree–Fock ground state in two dimensional Rashba–Gauge electronic systems. J. Magn. Magn. Mater., 2020, 498(166113): https://doi.org/10.1016/j.jmmm.2019.166113
52	Gu Q., Yin L.. Spin–orbit-coupling-induced resonance in an ultracold Bose gas. Phys. Rev. A, 2018, 98(1): 013617 https://doi.org/10.1103/PhysRevA.98.013617
53	D. Stanescu T., Anderson B., Galitski V.. Spin–orbit coupled Bose–Einstein condensates. Phys. Rev. A, 2008, 78(2): 023616 https://doi.org/10.1103/PhysRevA.78.023616
54	F. Liu C., M. Yu Y., C. Gou S., M. Liu W.. Vortex chain in anisotropic spin–orbit-coupled spin-1 Bose– Einstein condensates. Phys. Rev. A, 2013, 87(6): 063630 https://doi.org/10.1103/PhysRevA.87.063630
55	Liao B., Ye Y., Zhuang J., Huang C., Deng H., Pang W., Liu B., Li Y.. Anisotropic solitary semivortices in dipolar spinor condensates controlled by the two-dimensional anisotropic spin–orbit coupling. Chaos Solitons Fractals, 2018, 116: 424 https://doi.org/10.1016/j.chaos.2018.10.001
56	W. Zhang D., P. Chen J., J. Shan C., D. Wang Z., L. Zhu S.. Superfluid and magnetic states of an ultracold Bose gas with synthetic three-dimensional spin–orbit coupling in an optical lattice. Phys. Rev. A, 2013, 88(1): 013612 https://doi.org/10.1103/PhysRevA.88.013612
57	J. Liu X., Hu H., Pu H.. Three-dimensional spin–orbit coupled Fermi gases: Fulde–Ferrell pairing. Majorana fermions, Weyl fermions.and gapless topological superfluidity. Chin. Phys. B, 2015, 24(5): 050502 https://doi.org/10.1088/1674-1056/24/5/050502
58	Li J.R., G. Tobias W., Matsuda K., Miller C., Valtolina G., De Marco L., R. Wang R., Lassablière L., Quéméner G., L. Bohn J., Ye J.. Tuning of dipolar interactions and evaporative cooling in a three-dimensional molecular quantum gas. Nat. Phys., 2021, 17(10): 1144 https://doi.org/10.1038/s41567-021-01329-6
59	Stuhler J., Griesmaier A., Koch T., Fattori M., Pfau T., Giovanazzi S., Pedri P., Santos L.. Observation of dipole–dipole interaction in a degenerate quantum gas. Phys. Rev. Lett., 2005, 95(15): 150406 https://doi.org/10.1103/PhysRevLett.95.150406
60	Aikawa K., Baier S., Frisch A., Mark M., Ravensbergen C., Ferlaino F.. Observation of Fermi surface deformation in a dipolar quantum gas. Science, 2014, 345(6203): 1484 https://doi.org/10.1126/science.1255259

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