Magatsu-Izanagi is the Persona of Tohru Adachi, the one responsible for the murders in Inaba. It follows the form of Izanagi, as it is actually bestowed upon Adachi without Adachi's knowledge by Izanami when he first arrived in the rural town. Magatsu-Izanagi takes the form of a bloody Izanagi, and its stats and skills form Adachi's battle stats. Magatsu-Izanagi also has a hidden resistance to Physical attacks, and as a result Adachi will only take half damage from them.
"The world is about to change... Your existence won't belong there!"
—Tohru Adachi, Persona 4
Although Adachi doesn't seem to represent any Arcana in the original release of Persona 4 and Persona 4 The Animation, he actually encompasses the reversed Fool Arcana: impulsiveness, poor judgement, obsession and frivolity. Adachi acted on impulse when he murdered Mayumi Yamano and Saki Konishi because they both weren't interested in him. He shows poor judgement when he underestimated the protagonist and his group during their confrontation. Additionally, he was obsessed with keeping his "cat-and-mouse" game alive, doing whatever it takes to ensure the murders continue, such as tossing Mitsuo Kubo into the TV. Lastly, Adachi lacked tact, holding no degree of seriousness during his interactions with the Investigation Team and the protagonist's family--often going into topics in such a way that it usually drags down the mood or gets him beaten around by Dojima himself.
Magatsu-Izanagi also represents "Emptiness"; Adachi himself represents "Emptiness", distaste for the world at large, in Izanami's experiment to determine the value of humanity, which further shows Magatsu-Izanagi's connection to the Fool Arcana.
As Adachi appears in this game (as DLC), by proxy, Magatsu-Izanagi also appears as well as his Persona. In P4's story mode he merges with Izanagi to become a giant sword, which strikes down the Malevolent Entity.
A majority of Magatsu-Izanagi's moves are shown to be much more feral and brutal than its noble twin, and Adachi can also use minor alternate versions of Yu's Ziodyne and Cross Slash, respectively as his 5D and 2D (both ground and midair). Magatsu-Izanagi's lightning also is shown to have a shade of blood red, as opposed to Yu's blue lightning, Kanji's yellow lightning and Akihiko's violet lightning.
Magtsu-Izanagi's only SMT series skills in this game are Ziodyne (presumably for his 5D as it only resembles the Ziodyne used by Yu Narukami), Evil Smile, Megidola, Heat Riser, Atom Smasher, and Ghastly Wail.
Though in the original games, Megidola cannot be learned and it is only in Persona 4 Golden Magatsu-Izanagi has an Almighty-element spell (which is ironically Megidolaon), and Ziodyne can only be used by Adachi himself in the original Persona 4. Heat Riser also functions as not only a status buff, but also as a fire-based attack used by Magatsu-Izanagi.
Using cheat codes in Persona 4, it is possible to have the protagonist equip Magatsu-Izanagi as a Persona, categorized as a Persona of the Fool Arcana. He has his own stats, a portrait, but no moves, so one must hack in skills for him to use. It is possible that Atlus intended for Magatsu-Izanagi to be available to the player normally, but did not finish implementing him. Alternatively, this may have simply been to test Magatsu-Izanagi without having to fight Adachi repeatedly.
In Persona 4,if a player uses a hacked-in physical skill with Magatsu-Izanagi,he will make a move similar to his Ghastly Wail SP move in Ultimax,lunging at his enemies and stabbing them repeatedly instead of swinging his spear in Golden.It can be seen in this video:https://www.youtube.com/watch?v=7b7ZjpRq3go Interestingly,this is unavailable when fighting Adachi and Ameno-sagiri.
Thanks to this,Magatsu-Izanagi is the only Persona in Persona 4 that has more than two animations.
As the negative form of Izanagi, he has different animations when attacking or casting spells. Izanagi looks more dignified, while Magatsu-Izanagi makes more arrogant and threatening movements. Also, unlike Izanagi, Magatsu-Izanagi wields his spear in an under-hand fashion.
Also in Ultimax, Magatsu-Izanagi also acts very feral in its actions almost like a berserker, such as using claw rips during Adachi's 5C moves, tackling his opponent during his 2C attacks, and also using a vicious claw slash for Ghasty Wail (and impaling its opponent to death if they are inflicted with fear).