In the present paper, we consider the following magnetic nonlinear Choquard equation {(−i∇+A(x))2u+μg(x)u=λu+(|x|−α⁎|u|2⁎ α)|u|2α ⁎−2uinRn,u∈H1(Rn,C) where n≥4, 2α ⁎=[Formula presented], α∈(0,n), μ>0, λ>0 is a parameter, A(x):Rn→Rn is a magnetic vector potential and g(x) is a real valued potential function on Rn. Using variational methods, we establish the existence of least energy solution under some suitable conditions. Moreover, the concentration behavior of solutions is also studied as μ→+∞. © 2018 Elsevier Inc.}, author_keywords={Choquard equation; Hardy–Littlewood–Sobolev critical exponent; Magnetic potential; Nonlinear Schrödinger equations}, references={Alves, C.O., Figueiredo, G.M., Multiple solutions for a semilinear elliptic equation with critical growth and magnetic field (2014) Milan J. Math., 82 (2), pp. 389-405; Alves, C.O., Figueiredo, G., Yang, M., Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity (2016) Adv. Nonlinear Anal., 5 (4), pp. 331-345; Alves, C.O., Figueiredo, G.M., Yang, M., Multiple semiclassical solutions for a nonlinear Choquard equation with magnetic field (2016) Asymptot. Anal., 96 (2), pp. 135-159; Alves, C.O., Gao, F., Squassina, M., Yang, M., Singularly perturbed critical Choquard equations (2017) J. Differential Equations, 263 (7), pp. 3943-3988; Alves, C.O., Yang, M., Existence of semiclassical ground state solutions for a generalized Choquard equation (2014) J. Differential Equations, 257 (11), pp. 4133-4164; Ambrosetti, A., Badiale, M., Cingolani, S., Semiclassical states of nonlinear Schrödinger equations (1997) Arch. Ration. Mech. Anal., 140 (3), pp. 285-300; Ambrosetti, A., Malchiodi, A., Secchi, S., Multiplicity results for some nonlinear Schrödinger equations with potentials (2001) Arch. Ration. Mech. Anal., 159 (3), pp. 253-271; Arioli, G., Szulkin, A., A semilinear Schrödinger equation in the presence of a magnetic field (2003) Arch. Ration. Mech. Anal., 170 (4), pp. 277-295; Ba, N., Deng, Y., Peng, S., Multi-peak bound states for Schrödinger equations with compactly supported or unbounded potentials (2010) Ann. Inst. H. Poincaré Anal. Non Linéaire, 27 (5), pp. 1205-1226; Bartsch, T., Wang, Z.-Q., Multiple positive solutions for a nonlinear Schrödinger equation (2000) Z. Angew. Math. Phys., 51, pp. 366-384; Bartsch, T., Pankov, A., Wang, Z.Q., Nonlinear Schrödinger equations with steep potential well (2001) Commun. Contemp. Math., 3, pp. 549-569; Cao, D., Tang, Z., Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields (2006) J. Differential Equations, 222 (2), pp. 381-424; Chabrowski, J., Szulkin, A., On the Schrödinger equation involving a critical Sobolev exponent and magnetic field (2005) Topol. Methods Nonlinear Anal., 25, pp. 3-21; Cingolani, S., Clapp, M., Secchi, S., Multiple solutions to a magnetic nonlinear Choquard equation (2012) Z. Angew. Math. Phys., 63 (2), pp. 233-248; Cingolani, S., Clapp, M., Secchi, S., Intertwining semiclassical solutions to a Schrödinger–Newton system (2013) Discrete Contin. Dyn. Syst. Ser. S, 6 (4), pp. 891-908; Cingolani, S., Lazzo, M., Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions (2000) J. Differential Equations, 160 (1), pp. 118-138; Cingolani, S., Secchi, S., Semiclassical limit for nonlinear Schrödinger equation with electromagnetic fields (2002) J. Math. Anal. Appl., 275 (1), pp. 108-130; Cingolani, S., Secchi, S., Squassina, M., Semi-classical limit for Schrödinger equations with magnetic field and Hartree-type nonlinearities (2010) Proc. Roy. Soc. Edinburgh Sect. A, 140 (5), pp. 973-1009; Clapp, M., Ding, Y., Positive solutions of a Schrödinger equation with critical nonlinearity (2004) Z. Angew. Math. Phys., 55 (4), pp. 592-605; Clapp, M., Salazar, D., Positive and sign changing solutions to a nonlinear Choquard equation (2013) J. Math. Anal. Appl., 407 (1), pp. 1-15; d'Avenia, P., Squassina, M., Ground states for fractional magnetic operators (2018) ESAIM Control Optim. Calc. Var., 24, pp. 1-24; Ding, Y., Liu, X., Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities (2013) Manuscripta Math., 140, pp. 51-82; Ekeland, I., On the variational principle (1974) J. Math. Anal. Appl., 47, pp. 324-353; Fiscella, A., Pinamonti, A., Vecchi, E., Multiplicity results for magnetic fractional problems (2017) J. Differential Equations, 263 (8), pp. 4617-4633; Gao, F., Yang, M., Brezis–Nirenberg type critical problem for nonlinear Choquard equation (2018) Sci. China Math.; Gao, F., Yang, M., On nonlocal Choquard equations with Hardy–Littlewood–Sobolev critical exponents (2017) J. Math. Anal. Appl., 448, pp. 1006-1041; Ghimenti, M., Schaftingen, J.V., Nodal solutions for the Choquard equation (2016) J. Funct. Anal., 271 (1), pp. 107-135; Goubet, O., Hamraoui, E., Blow-up of solutions to a cubic nonlinear Schrödinger equations with defect: the radial case (2017) Adv. Nonlinear Anal., 6 (2), pp. 183-197; Li, G., Peng, S., Wang, C., Infinitely many solutions for nonlinear Schrödinger equations with electromagnetic fields (2011) J. Differential Equations, 251 (12), pp. 3500-3521; Holzleitner, M., Kostenko, A., Teschl, G., Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions (2016) Opuscula Math., 36 (6), pp. 769-786; Lieb, E.H., Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation (1977) Stud. Appl. Math., 57 (2), pp. 93-105; Lieb, E.H., Loss, M., Analysis (2001), 2nd edition AMS; Lü, D., Existence and concentration behavior of ground state solutions for magnetic nonlinear Choquard equations (2016) Commun. Pure Appl. Anal., 15 (5), pp. 1781-1795; Oh, Y.G., Existence of semiclassical bound states of nonlinear Schrödinger equations with potentials of the class (V)a (1988) Comm. Partial Differential Equations, 13, pp. 1499-1519; Mingqi, X., Pucci, P., Squassina, M., Zhang, B., Nonlocal Schrödinger–Kirchhoff equations with external magnetic field (2017) Discrete Contin. Dyn. Syst., 37 (3), pp. 1631-1649; Mingqi, X., Rădulescu, V., Zhang, B., A critical fractional Choquard–Kirchhoff problem with magnetic field (2018) Commun. Contemp. Math.; Molica Bisci, G., Rădulescu, V., Ground state solutions of scalar field fractional Schrödinger equations (2015) Calc. Var. Partial Differential Equations, 54 (3), pp. 2985-3008; Mukherjee, T., Sreenadh, K., Fractional Choquard equation with critical nonlinearities (2017) NoDEA Nonlinear Differential Equations Appl., 24, p. 63; Mukherjee, T., Sreenadh, K., Positive solutions for nonlinear Choquard equation with singular nonlinearity (2017) Complex Var. Elliptic Equ., 62, pp. 1044-1071; Salazar, D., Vortex-type solutions to a magnetic nonlinear Choquard equation (2015) Z. Angew. Math. Phys., 66 (3), pp. 663-675; Secchi, S., Squassina, M., On the location of spikes for the Schrödinger equation with electromagnetic field (2005) Commun. Contemp. Math., 7 (2), pp. 251-268; Squassina, M., Soliton dynamics for the nonlinear Schrödinger equation with magnetic field (2009) Manuscripta Math., 130 (4), pp. 461-494; Szulkin, A., The method of Nehari manifold revisited (2011) RIMS Kokyuroku, no. 1740, pp. 89-102. , Research Institute for Mathematical Sciences, Kyoto University Kyoto; Yang, M., Wei, Y., Existence and multiplicity of solutions for nonlinear Schrödinger equations with magnetic field and Hartree type nonlinearities (2013) J. Math. Anal. Appl., 403 (2), pp. 680-694; Wang, X., On concentration of positive bound states of nonlinear Schrödinger equations (1993) Comm. Math. Phys., 153 (2), pp. 229-244}, correspondence_address1={Sreenadh, K.; Department of Mathematics, Hauz Khaz, India; email: sreenadh@maths.iitd.ernet.in}, publisher={Academic Press Inc.}, issn={0022247X}, language={English}, abbrev_source_title={J. Math. Anal. Appl.}, document_type={Article}, source={Scopus},