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

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.

Graphical abstract

Keywords

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

References

[1] D.Wagner, Introduction to the Theory of Magnetism: International Series of Monographs in Natural Philosophy, Vol. 48, Elsevier, 2013

[2] J.Kübler, Theory of Itinerant Electron Magnetism, Vol. 106, Oxford University Press, 2017

[3] J. Zak. Dynamics of electrons in solids in external fields. Phys. Rev., 1968, 168(3): 686

[4] F. Bloch. Bemerkung zur Elektronentheorie des Ferromagnetismus und der elektrischen Leitfähigkeit. Eur. Phys. J. A, 1929, 57(7–8): 545

[5] S. Misawa. Ferromagnetism of an electron gas. Phys. Rev., 1965, 140(5A): A1645

[6] E. C. Stoner. Collective electron ferronmagnetism. Proc. R. Soc. Lond. A, 1938, 165(922): 372

[7] E. C. Stoner. LXXX. Atomic moments in ferromagnetic metals and alloys with non-ferromagnetic elements. Lond. Edinb. Dublin Philos. Mag. J. Sci., 1933, 15(101): 1018

[8] R. A. Duine, A. H. MacDonald. Itinerant ferromagnetism in an ultracold atom Fermi gas. Phys. Rev. Lett., 2005, 95(23): 230403

[9] S. Pilati, G. Bertaina, S. Giorgini, M. Troyer. Itinerant ferromagnetism of a repulsive atomic Fermi gas: A quantum Monte Carlo study. Phys. Rev. Lett., 2010, 105(3): 030405

[10] L. He, X. G. Huang. Nonperturbative effects on the ferromagnetic transition in repulsive Fermi gases. Phys. Rev. A, 2012, 85(4): 043624

[11] L. He, X. J. Liu, X. G. Huang, H. Hu. Stoner ferromagnetism of a strongly interacting Fermi gas in the quasirepulsive regime. Phys. Rev. A, 2016, 93(6): 063629

[12] L. He. Finite range and upper branch effects on itinerant ferromagnetism in repulsive Fermi gases: Bethe–Goldstone ladder resummation approach. Ann. Phys., 2014, 351: 477

[13] P. Massignan, Z. Yu, G. M. Bruun. Itinerant ferromagnetism in a polarized two-component Fermi gas. Phys. Rev. Lett., 2013, 110(23): 230401

[14] I. Zintchenko, L. Wang, M. Troyer. Ferromagnetism of the repulsive atomic Fermi gas: Three-body recombination and domain formation. Eur. Phys. J. B, 2016, 89(8): 180

[15] H. Tajima, K. Iida. Non-Hermitian ferromagnetism in an ultracold Fermi gas. J. Phys. Soc. Jpn., 2021, 90(2): 024004

[16] G. B. Jo, Y. R. Lee, J. H. Choi, C. A. Christensen, T. H. Kim, J. H. Thywissen, D. E. Pritchard, W. Ketterle. Itinerant ferromagnetism in a Fermi gas of ultracold atoms. Science, 2009, 325(5947): 1521

[17] G. Valtolina, F. Scazza, A. Amico, A. Burchianti, A. Re-cati, T. Enss, M. Inguscio, M. Zaccanti, G. Roati. Exploring the ferromagnetic behaviour of a repulsive Fermi gas through spin dynamics. Nat. Phys., 2017, 13(7): 704

[18] F. Arias de Saavedra, F. Mazzanti, J. Boronat, A. Polls. Ferromagnetic transition of a two-component Fermi gas of hard spheres. Phys. Rev. A, 2012, 85(3): 033615

[19] C. W. von Keyserlingk, G. J. Conduit. Itinerant ferromagnetism with finite-ranged interactions. Phys. Rev. B, 2013, 87(18): 184424

[20] Z. Sun, Q. Gu. Ferromagnetic transition in harmonically trapped Fermi gas with higher partial-wave interactions. J. Phys. At. Mol. Opt. Phys., 2017, 50(1): 015302

[21] E. Vermeyen, C. A. R. Sá de Melo, J. Tempere. Exchange interactions and itinerant ferromagnetism in ultracold Fermi gases. Phys. Rev. A, 2018, 98(2): 023635

[22] Y. Hu, Y. Fei, X. L. Chen, Y. Zhang. Collisional dynamics of symmetric two-dimensional quantum droplets. Front. Phys., 2022, 17(6): 61505

[23] H. Guo, Y. Ji, Q. Liu, T. Yang, S. Hou, J. Yin. A driven three-dimensional electric lattice for polar molecules. Front. Phys., 2022, 17(5): 52505

[24] T. S. Zeng, L. Yin. Supersolidity of a dipolar Fermi gas in a cubic optical lattice. Phys. Rev. B, 2014, 89(17): 174511

[25] Z. Wu, J. K. Block, G. M. Bruun. Coexistence of density wave and superfluid order in a dipolar Fermi gas. Phys. Rev. B, 2015, 91(22): 224504

[26] S. G. Bhongale, L. Mathey, S. W. Tsai, C. W. Clark, E. Zhao. Unconventional spin-density waves in dipolar Fermi gases. Phys. Rev. A, 2013, 87(4): 043604

[27] K. K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’Er, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S. Jin, J. Ye. A high phase-space-density gas of polar molecules. Science, 2008, 322(5899): 231

[28] B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, J. Ye. Observation of dipolar spin-exchange interactions with lattice-confined polar molecules. Nature, 2013, 501(7468): 521

[29] A. Chotia, B. Neyenhuis, S. A. Moses, B. Yan, J. P. Covey, M. Foss-Feig, A. M. Rey, D. S. Jin, J. Ye. Long-lived dipolar molecules and Feshbach molecules in a 3D optical lattice. Phys. Rev. Lett., 2012, 108(8): 080405

[30] K. K. Ni, S. Ospelkaus, D. Wang, G. Quéméner, B. Neyenhuis, M. H. G. de Miranda, J. L. Bohn, J. Ye, D. S. Jin. Dipolar collisions of polar molecules in the quantum regime. Nature, 2010, 464(7293): 1324

[31] C. H. Wu, J. W. Park, P. Ahmadi, S. Will, M. W. Zwierlein. Ultracold fermionic Feshbach molecules of ²³Na ⁴⁰K. Phys. Rev. Lett., 2012, 109(8): 085301

[32] M. Lu, N. Q. Burdick, B. L. Lev. Quantum degenerate dipolar Fermi gas. Phys. Rev. Lett., 2012, 108(21): 215301

[33] N. Q. Burdick, Y. Tang, B. L. Lev. Long-lived spin–orbit-coupled degenerate dipolar Fermi gas. Phys. Rev. X, 2016, 6(3): 031022

[34] X. J. Feng, L. Yin. Phase diagram of a spin–orbit coupled dipolar Fermi gas at T = 0 K. Chin. Phys. Lett., 2020, 37(2): 020301

[35] X. J. Feng, X. D. Zhao, L. Qin, Y. Y. Zhang, Z. Zhu, H. J. Tian, L. Zhuang, W. M. Liu. Itinerant ferromagnetism of a dipolar Fermi gas with Raman-induced spin–orbit coupling. Phys. Rev. A, 2022, 105(5): 053312

[36] B. M. Fregoso, E. Fradkin. Ferronematic ground state of the dilute dipolar Fermi gas. Phys. Rev. Lett., 2009, 103(20): 205301

[37] T. Miyakawa, T. Sogo, H. Pu. Phase-space deformation of a trapped dipolar Fermi gas. Phys. Rev. A, 2008, 77(6): 061603

[38] S. Ronen, J. L. Bohn. Zero sound in dipolar Fermi gases. Phys. Rev. A, 2010, 81(3): 033601

[39] Y. J. Lin, K. Jiménez-García, I. B. Spielman. Spin–orbit-coupled Bose–Einstein condensates. Nature, 2011, 471(7336): 83

[40] P. Wang, Z. Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, J. Zhang. Spin–orbit coupled degenerate Fermi gases. Phys. Rev. Lett., 2012, 109(9): 095301

[41] Z. Wu, L. Zhang, W. Sun, X. T. Xu, B. Z. Wang, S. C. Ji, Y. Deng, S. Chen, X. J. Liu, J. W. Pan. Realization of two-dimensional spin–orbit coupling for Bose– Einstein condensates. Science, 2016, 354(6308): 83

[42] Z. Meng, L. Huang, P. Peng, D. Li, L. Chen, Y. Xu, C. Zhang, P. Wang, J. Zhang. 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

[43] L. Huang, Z. Meng, P. Wang, P. Peng, S. L. Zhang, L. Chen, D. Li, Q. Zhou, J. Zhang. Experimental realization of two-dimensional synthetic spin–orbit coupling in ultracold Fermi gases. Nat. Phys., 2016, 12(6): 540

[44] Z. Y. Wang, X. C. Cheng, B. Z. Wang, J. Y. Zhang, Y. H. Lu, C. R. Yi, S. Niu, Y. Deng, X. J. Liu, S. Chen, J.W. Pan. Realization of an ideal Weyl semimetal band in a quantum gas with 3D spin–orbit coupling. Science, 2021, 372(6539): 271

[45] Y. Zhang, M. E. Mossman, T. Busch, P. Engels, C. Zhang. Properties of spin–orbit-coupled Bose–Einstein condensates. Front. Phys., 2016, 11(3): 118103

[46] P. H. Lu, X. F. Zhang, C. Q. Dai. 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

[47] C. Jiao, J. C. Liang, Z. F. Yu, Y. Chen, A. X. Zhang, J. K. Xue. 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

[48] H. Yang, Q. Zhang, Z. Jian. 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):

[49] S. S. Zhang, J. Ye, W. M. Liu. 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

[50] W. E. Liu, S. Chesi, D. Webb, U. Zülicke, R. Winkler, R. Joynt, D. Culcer. Generalized Stoner criterion and versatile spin ordering in two-dimensional spin–orbit coupled electron systems. Phys. Rev. B, 2017, 96(23): 235425

[51] H. Vivas C. Magnetic stability for the Hartree–Fock ground state in two dimensional Rashba–Gauge electronic systems. J. Magn. Magn. Mater., 2020, 498(166113):

[52] Q. Gu, L. Yin. Spin–orbit-coupling-induced resonance in an ultracold Bose gas. Phys. Rev. A, 2018, 98(1): 013617

[53] T. D. Stanescu, B. Anderson, V. Galitski. Spin–orbit coupled Bose–Einstein condensates. Phys. Rev. A, 2008, 78(2): 023616

[54] C. F. Liu, Y. M. Yu, S. C. Gou, W. M. Liu. Vortex chain in anisotropic spin–orbit-coupled spin-1 Bose– Einstein condensates. Phys. Rev. A, 2013, 87(6): 063630

[55] B. Liao, Y. Ye, J. Zhuang, C. Huang, H. Deng, W. Pang, B. Liu, Y. Li. Anisotropic solitary semivortices in dipolar spinor condensates controlled by the two-dimensional anisotropic spin–orbit coupling. Chaos Solitons Fractals, 2018, 116: 424

[56] D. W. Zhang, J. P. Chen, C. J. Shan, Z. D. Wang, S. L. Zhu. 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

[57] X. J. Liu, H. Hu, H. Pu. 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

[58] J.R. Li, W. G. Tobias, K. Matsuda, C. Miller, G. Valtolina, L. De Marco, R. R. Wang, L. Lassablière, G. Quéméner, J. L. Bohn, J. Ye. Tuning of dipolar interactions and evaporative cooling in a three-dimensional molecular quantum gas. Nat. Phys., 2021, 17(10): 1144

[59] J. Stuhler, A. Griesmaier, T. Koch, M. Fattori, T. Pfau, S. Giovanazzi, P. Pedri, L. Santos. Observation of dipole–dipole interaction in a degenerate quantum gas. Phys. Rev. Lett., 2005, 95(15): 150406

[60] K. Aikawa, S. Baier, A. Frisch, M. Mark, C. Ravensbergen, F. Ferlaino. Observation of Fermi surface deformation in a dipolar quantum gas. Science, 2014, 345(6203): 1484

Acknowledgements

Thank Xi-Bo Zhang for helpful dicussions about the experimental realization. This work was supported by the National Key R&D Program of China (Grant Nos. 2021YFA1400900, 2021YFA0718300, and 2021YFA1400243), the Key Scientific Research Project of colleges and Universities in Henan Province (Nos. 20A140018 and 23A140001), the National Natural Science Foundatiion of China (Grant Nos. 12074105, 12074106, 12074120, 12247146, 12104135, and 61835013), and the Natural Science Foundation of Shanghai (Grant No. 20ZR1418500).

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